v .... K. . Kt. ‘ . . . . 9...... ... «facafizm. a..a...a.¢v...rt. .. a ..A .............:. I. ...w.»......... 11.3.... .... ... ................. 2:73.... ...... . . .... .. . .. ......Lr 1.. ..........._...../...._..r...r..,....H. .....v....:..o. ”Til/4. T... ...............:.....I... .21 . ...... . ......5......_.......4........:......v ...... . .. ...... n... 1...... ......v. ...: . .. rm....................a.u.......}... ...... ... ........_..._ _ ...................... 1.3....” n... ......r . .. 5.....::.. $32... -.....—..4..4J~. .......: ...... ...... . . ............ .r..._.. ....Z.. .. 1:11.... 3.2.... 2......1... .... 1...! . w a...;.....:..v. ¢.05 for the initial test and F=.40, df 7/187, p>.05 for the retention test). Test results re- vealed no logical pattern of correlation between achieve— ment levels and program sequence, thus the hypothesis was rejected. There was, however, a higher error incidence among scrambled forms than with their ordered counterparts. The authors suggest that the students possibly bridged the gaps between items in a scrambled program, thus indicating a discovery and inductive development of learning. The study did not indicate whether the material presented was classified according to a stratified model of learning. Perhaps that information could provide the reason for rejection of the hypothesis. Teaching machines were used by Evans, Glaser and Homme (1960) in an investigation of verbal learning se- quences. In one experiment of a series of five, they were interested in whether or not it would be possible to pro- duce the same level of learning performance with varying amounts of programed material. The editing out of some repetitive material would create larger "steps" since fewer statements and responses were required. The four final programs contained 30, 40, 51, and 68 steps respectively. Four groups of five subjects each, all graduate students taking psychology courses, were given the sequences. After 28 completing the sequences, the students were given an im- mediate post test and sometime later a retention test. Results indicated that: 1. small-step sequences produced significantly better performance (p<.05) on both immediate and reten- tion tests than did the shorter large-step sequences, 2. small-step sequences produced significantly fewer response errors (p<.05) during the learning se- quence despite increased opportunities for error, and 3. small-step sequences in general took more time than large-step sequences. The authors conclude that smaller steps in a program are associated with better immediate test performance, better retention, and fewer response errors in the course of learning. One phase of a self-instructional program by Moore (1968) studied the effects of gaps in sequences. The gaps principle asserts that criterion performance is increased by the absence of gaps and decreased by the presence of gaps. Two types of frames appear to fill gaps in a program. Type 1 are frames logically related to the task, which a content analysis indicates are intermediate steps to learn- ing the criterion task. Type 2 are frames identical or similar to questions on the criterion test. In the experi- ment only frames of the second type were excluded. 29 A total of 184 eighth grade students participated in the investigation. _Four general information tests of 30 questions each were constructed and the degree of dif- ficulty was varied. Condition and instrument administra- tion were carefully controlled. Two days after the pro- gramed exposure the subjects were tested. Moore offered two tentative conclusions that are of interest. Where a gap exists that simulates the criterion task, learning is more effective than when the simulation is absent. Secondly, if gaps are introduced into the pro- gram, mastery of the remaining material does not appear to benefit instruction. Levin and Baker (1963) did a thorough study on the topic of item scrambling in a self-instructional program. It was conducted to determine the importance of presenting items in a standard, logical sequence which had been arrived at on the basis of prior planning and experimenta- tion. A matched—group experiment was planned which would make it possible to examine the effects of scrambling item sequence in one unit of a program on (a) error rate during acquisition, (b) performance on a subsequent unit of the program, and (0) performance on an achievement test which measured retention and transfer. The 36 second-grade participants were placed in two equal groups. The research instruments included two forms of a specially developed self—instructional program, 30 teaching machines for presenting the programs, and two tests. The devised program, informal geometry, had under- gone a validation study and was found to produce a statisti- cally significant amount of learning. The program consisted of 180 items grouped in five units, the first being an in— structional unit on teaching machine operation. The other four units comprised a linear sequence in which concepts and notation taught in one unit were used and built upon in subsequent units. The only portion of the experimental program which differed from the standard form was the unit on angles, chosen because of its difficulty and place in the program. The content of the units for both control and experimental groups was identical. The material was scrambled for the latter. The subjects were told and their material indicated that there were differences in the two units. Two achievement tests had been developed. Test S was designed for screening purposes and Test 1 developed to assess learning incurred during the program. Spearman- Brown corrected split-half reliabilities for Test S and Test 1 were .68 and .87 respectively. . The experiment began with the screening test and con- cluded 17 days later. All work was in the home classroom and instruction was about 15 minutes per day. The students were matched and assigned randomly to treatment groups. After finishing the angles unit (treatment period), all 31 subjects were taken through the remaining section. Final testing was the next class day. Analysis of group comparisons of acquisition, re- tention, and transfer data indicated that the experimental treatment had no statistically significant effects. The authors suggest that while the findings failed to support the assumption that item sequence is important, it seems neither appropriate nor even tempting to abandon the hypothesis that the order of presentation matters under some conditions. Roe, Case and Roe (1962) conducted an experiment investigating the effect of scrambling and ordered sequence in auto-instructional programs. Stated as a hypothesis: The mean performance in a criterion test of students who have studied a proper sequential ordering of related sub— ject items will be significantly different from the mean perfbrmance on the same criterion test by students who have :atudied a random ordering of the subject items. The mate- Jflial sequence was based on the premise that each item de- Peflnfled on a preceding item and on the student's terminal bekuavior. The authors expected to gain some knowledge of 13KB effects by (a) eliminating the repetition of missed itenus, (b) eliminating the leveling effect of time on long- ternl retention by administering the criterion test imme- diatnely after the learning session, and (c) scrambling larger blocks of items. 32 A group of 36 freshman psychology students were classified into upper, middle, and lower thirds according to their prior mathematical ability as indicated by scores on CEEB examinations. Within each third students were randomly assigned to each sequencing group. Prior exper- ience showed that lower division students had little know- ledge of the material content. Learning items on elementary probability developed over a two year period consisted of 71 frames registered on 4 x 6 inch cards. Half the students received cards with an ordered sequence and the other half received cards in a scrambled order. On completing the program each student was given a criterion test and his completed program was examined for response errors. Analyses of variance were performed on time for learning, error score for learning, time for criterion test, and.test scores. The two variables in each of these analy- Ses.of variance were the method of sequencing items and tine students mathematical aptitude. It was found that item sexquence had no significant effect on the dependent vari— Efllles, nor was there any significant effect on the inter- afifi:ions between sequencing and aptitude. The authors believe the experiment indicates that Collxage level students may not require the careful sequencing 0f Euato-instructional items as had previously been supposed. 33 Research Model In recent years psychologists have presented a num- ber of theoretical models of learning. The specific proto- type for this study is a hierarchical model suggested by Robert Gagné. Gagné states his rationale for a model of hierarchi- cal learning sets in a recent publication (Gagné and Gephart, 1968). According to Gagné: Knowledge consists of a set of subordinate capa- bilities called learning sets which are arranged in a hierarchy. Each learning set may have several other learning sets subordinate to it. Together the subordinate learning sets mediate positive transfer to the learning set of the next higher order in the hierarchy. If one or more of the subordinate learning sets is not present or cannot be recalled,transfer to the next higher order of learning set is predicted to be zero. The learn- ing sets at the bottom of the hierarchy are basic human abilities relevant to the superordinate learning sets. The learning sets higher in the hierarchy are the sets of behavior particularly related to the problems and tasks to be learned in a sequence of instruction. Learning sets, along with instructions, comprise the two fundamental variables of the theory. To- gether these two variables are used to predict transfer as it operated in instruction. To define the hierarchy of learning sets relevant to any given learning task, Gagné suggests the re- searcher begin with the following question: "What would the individual have to know how to do in order to be able to achieve this (new) task, when given only instructions?" By answering this ques- tion, the experimenter begins the first cycle of the analysis of the final task. Each of the subordinate learning sets obtained by answering the above question is in turn investigated with the same question which leads to a definition of the next level of subordinate learning sets. This procedure is reiterated until the entire hierarchy is defined. 34 An earlier article (Gagné, 1962) emphasizes the transfer aSpect embodied in the model. A human learner begins the acquisition of the capability of performing a particular class of tasks with an individual array of relevant learning sets, previously acquired. He then acquires new learning sets at progressively higher levels of the know- ledge hierarchy until the final class of tasks is achieved. Attaining each new learning set depends upon a process of positive transfer, which is depen- dent upon (a) the recall of relevant subordinate learning sets, and upon (b) the effects of instruc— tions (p. 358). Many thinkers in the field of educational instruc- tion agree that the sequence of material effects learn- ing. Jerome Bruner stresses the necessity of sequence in the educational process while leaving room for indi- viduality (Bruner, 1966). Instruction consists of leading the learner through a sequence of statements and restatements of a problem or body of knowledge that increase the learner's ability to grasp, transform, and transfer what he is learning. In short, the se- quence in which a learner encounters materials within a domain of knowledge affects the diffi- culty he will have in achieving mastery. There are usually a variety of sequences that are equivalent in their ease and difficulty for learners. There is no unique sequence for all learners, and the optimum in any particular case will depend upon a variety of factors, including past learning, state of development, nature of the material, and individual differences (p. 313). In addition to a strong belief in classification of learning tasks, Gagné concurs with Bruner on the matter of preparing instruction for individuality. Gagné (1962) comments regarding personalized attention in learning: 35 If one wants to investigate the effects of an experimental treatment on the behavior of indi- viduals or groups who start from the same point, he would be well advised to measure and map out for each individual the learning sets relevant to the eXperimental task (p. 365). A lucid account in a Russian education periodical illustrates the international interest in learning sequen— tially (Talyzina, 1968). In the first place, operations (activity) on the part of the pupil adequate to the knowledge to be mastered should be identified as necessary means of assimilation. In the second place, these actions should be initially modeled in external, material (or materialized) form, which makes it possible not only to make their content clear to the pupil but to assure that they will be mastered. In the third place, a program should be drawn up for step-by-step changes in these acts, and they should be modified at each stage in accordance with independent characteristics. In the fourth place, at each of the steps in the modification of the operations, control over their performance should be provided, operation by operation. In the final stages of assimilation, this becomes self-monitoring. All this taken together permits planned direction of the shaping of mental actions and, through them, of the shaping of knowledge as their products. It becomes possible to shape in all pupils know— ledge and abilities with prOperties determined beforehand, to reduce considerably the time re- quired to assimilate this knowledge, to diminish considerably the scattering of grades received, and to cause the successes scored to approximate the upper possible limits. Moreover, the diversity of the intermediate stages disappears, as do the errors characteristic of each stage. It becomes possible to shape various types of intellectual activity at an earlier age than is generally regarded as possible (p. 39). 36 For a more thorough understanding of the theoretical model of this study it is necessary to examine Gagné's hierarchical system (Hilgard, 1966). Gagné accepts eight types or categories of learn— ing, each with its own rules, but arranges them in a hierarchy from simple to complex, on the assump- tion that each higher order learning depends upon the mastery of the one below it. Hence the theory is not strictly an eclectic theory (which chooses good principles from here and there without any order among them), but is the beginning of a uni- fied theory on the assumption that appropriate transformation equations could be found for moving from one level to the next. The proposal of eight kinds of learning is sufficiently elaborated to be deserving of review. Gagné's own summary of the eight types are as follows: Type 1. Signal learning. The individual learns to make a general diffuse response to a signal. This is the classical conditioned response of Pavlov. The reSponses are a type of learning that has a truly "involuntary" character, and applies to responses that are not typically under voluntary control. Type 2. Stimulus-response learning. The learner acquires a precise response to a discriminated stimulus. What is learned is a connection or a discriminated Operant, sometimes called an instru- mental response. Regarding a dog which a master is attempting to teach to "shake hands": after several repetitions of raising the dog's paw, shaking it, and rewarding the animal, the dog raises his own paw when his master says, "shake hands." Eventually, the dog comes to perform this act promptly and more or less precisely whenever the proper signal is given. It can then be said that the dog has learned what may be called a stimulus—response capability. Obviously, this kind of learning is distin— guishable from signal learning in terms of its outcome. The response acquired by this means is a fairly precise, circumscribed, skeletal muscu- lar act, far different from the generalized emo- tional responding that characterizes the Pav- lovian kind of signal—responding. This differ- entiation is shown by using an arrow rather than the line between the S and the R, as S+R, to 37 emphasize that a process of discrimination is an integral part of this kind of learning. A degree of precision has been established in the response, which can easily be distinguished from similar although "wrong" responses. Still another characteristic of stimulus— response learning must be noted before the de- scription is complete. Every uncomplicated example of S+R learning indicates that it is motor learning. The implication of this state- ment is not simply to the effect that muscular movements are involved in the outcome, because this may be true of other varieties, including signal learning (as when an animal learns to struggle or run at a signal originally paired with shock). In S+R learning, though, an impor- tant component of the stimulus itself is gener- ated by muscular movements. While the act is being established, the external stimulus "shake hands" is accompanied by proprioceptive stimula— tion from the muscles that raise the dog's paw. Even when the act is fully learned, some parts of this stimulation are still present. For example, the dog often raises his paw "as if voluntarily," even when no one has said "shake hands." He may now "invite" his master to shake hands. Presumably, this portion of the total stimulation plays an important role in the learning process. Type 3. Chaining. What is acquired is a chain of two or more stimulus—response connections. The conditions for such learning have been de— scribed by Skinner (1938) and others, notably by Gilbert. Type 4. Verbal Association. Verbal association is the learning of chains that are verbal. Basic— ally the conditions resemble those for other (motor) chains. However, the presence of lan- guage in the human being makes this a special type because internal links may be selected from the individual's previously learned repertoire of language. Type 5. Multiple Discrimination. The individual learns to make different identifying responses to as many different stimuli, which may resemble each other in physical appearance to a greater or lesser degree. Although the learning of each stimulus—response connection is a simple Type 2 occurrence, the connections tend to interfere with each other's retention. 38 Type 6. Concept Learning. The learner acquires a capability of making a common response to a class of stimuli that may differ from each other widely in physical appearance. He is able to make a reSponse that identifies an entire class of objects or events. Type 7. Principle Learning. In simplest terms, a principle is a chain of two or more concepts. It functions to control behavior in the manner suggested by a verbalized rule of the form "If A, then B," where A and B are concepts. However, it must be carefully distinguished from the mere verbal sequence "If A, then B," which, of course, may be learned as Type 4. Type 8. Problem Solving. Problem solving is a kind of learning that requires the internal events usually called thinking. Two or more previously acquired principles are somehow com- bined to produce a new capability that can be shown to depend on a 'higher-order' principle. The notion that each of the higher stages requires the next lower as a prerequisite is limited for Gagné only by some uncertainty with respect to Types 1 and 2; he is not convinced that Type 2 has Type 1 as its essential background. Gagné rejects the inter" pretation that learning is basically the same for all types; their differences are said to be more impor- tant than their similarities. A strong emphasis within Gagné's analysis is upon the structure of knowledge, an important supplement to principles of learning whenever a practical instructional task is under consideration (pp. 569-570). Application to Music Learning The model which Gagné has constructed is potentially very flexible. A beginning student of the violin may ex- perience the Problem Solving level (Type 8) in performing a major scale while the seasoned violinist, on the same scale, would function at a Type 7 or Type 6 level. Given a learning task, three students could conceivably operate on as many different levels of the hierarchy at the same 39 time. The sliding nature of Gagné's system makes it highly adaptable to individualized learning. When a student labors with a learning assignment he uses one or more of his four Operational faculties. The cognitive, affective, psychomotor, and perceptual domains may be functioning simultaneously on any given task. Gagné does not identify these Operations in relation to the con— ditions of learning he has established. For certain types of research it would seem necessary to specify the kind of operations(s) involved. Integrating the operational domains with Gagné's model would enable the teacher or researcher to more precisely define the functions of a student in— volved in a learning task. Effective problem—solving entails a clear View of the problem itself and subsequent gathering of all facts, materials, and responses necessary to arrive at a solution. The person who structures a learning situation can best assist the student by clearly delineating the problem and then supplying the means to solve it. If a problem—solving situation is structured from the simplest level upward, there is a danger that extraneous subtasks may be included; whereas, if the problem is clearly understood, the lower level components will be an outgrowth of the problem and other subtasks may be added as needed. Although music is considered a nonverbal medium, there are learning tasks in music that correSpond to the 40 categories of Gagné's model. The specific musical elements chosen to relate to Gagné's hierarchy and serve as vehicles for this research are the major and minor triads. These triads and their constituent parts relate to Gagné's model as presented in the following flow chart: Problem Solving (Type 8) is the ability to (a) employ major and minor triads with other musical elements (rhythm, dynamics, etc.) in performance with proficiency and, (b) transfer this technique ,tg unfamiliar music literature. Principle Learning (Type 7) is the ability to trans- fer major and minor triad qualities from notation and verbal cues to performance in a music medium. Concept Learning (Type 6) is the ability to think of major and minor triads (a) as belonging to the same class, (b) as functioning in a similar manner in music literature, and (c) in abstract terms, men- tally recreating either triad when given a visual or aural stimulus representing them. Multiple Discrimination Learning(Type 5) is the ability to (a) identify major and minor triads from aural and visual stimuli, (b) recognize these triad qualities as a means of classification, and (c) re— tain the knowledge and identification skills relating to major and minor triads. 41 I Verbal Association (Type 4) is the ability to (a) apply musical terminlogy to the aural and visual symbols of major and minor triads and their consti- tuent parts and, (b) notate major and minor triads and their components. Chaining (Type 3) is the ability to recognize, notate, and perform major and minor triads and their separate intervals given proper cues. Stimulus-Response (Type 2) is the ability to perform, vocally and at the keyboard, the minor third, major third, perfect fifth, and major and minor triads. This performance would be by imitation. l Signal Learnipg (Type 1) is an involuntary diffuse re- sponse to sound and is considered an entering be— havior for adults. In View of the subjects available for this experiment and the course content restrictions, it was advisable to limit model. the present study to Types 3, 4, and 5 of Gagné's The other levels are vital to the model but are beyond the scope of this research. three Review of Colwell Music Achievement Test (MAT) 1 s 2 As part of a pre-treatment evaluation in this study, tests were administered. One criterion measure was 42 a composite score from Colwell Music Achievement Tests 1 and 2 (Colwell, 1968). The Music Achievement Tests are designed to provide an accurate measurement of achievement for some of the most important objectives of the music education program. They are divided into independent tests covering the areas of pitch discrimination, interval discrimination, meter discrimination, major-minor mode discrimination, feeling for tonal center, and auditory— visual discrimination. The MATS do not purport to measure total "musicianship" but provide (a) a measure of the ex- tent to which a pupil has profited from past musical in- struction, (b) a measure of the quality of his musical instruction, and (c) an indication of the extent to which the pupil is likely to profit from further musical instruc- tion. Validity, standardization, and reliability of the Music Achievement Tests were established in accordance with practices acceptable to the research community. The reli— ability of MATS l and 2 was computed in two of the most common ways: (a) split—half reliability and (b) Kuder— Richardson formula 21. The reliability of Test 1 estimated by K-R 21 is .88, standard deviation 10.41, with a sample size of 7,710 students, while the split-half method yielded an estimated reliability of .94, mean standard deviation 5.3 with a sample size of 7,725 subjects. Other detailed information on the MATS is contained in the Interpretive 43 Manual (Colwell, 1969), including item analysis, test ques- tion descriptions, scoring instruction, tables or norms, etc. For the present study, only Parts 1 and 2 of MAT 1 and Parts 1 and 3 of MAT 2 were used, for only these parts related directly to the musical elements of concern in the experiment. Since statistics on college-level subjects are not included in Colwell's Interpretive Manual, it was not possible to compare the students in the present study with these of his population sample. The purpose of using the MAT series was to (a) employ the data as a means of correlating and validating the instruments devised for the present study, and (b) use it as a covariate in an analysis of post treatment criterion measures. Summary A review of the literature germane to the present study reveals an implied sense of stratification of content material. There are numerous semantical parallels to Gagné's terminology. Whereas one researcher would employ the terms concepts and subconcepts, another would use macro-order and micro-order, and still a third, learning sets and subsets; these all allude to the idea of different levels of cognitive endeavor. The substance of the literature review indicates that scrambling items within a program will not inhibit learning as long as the overall sequence of learning material is 44 not disrupted. Hamilton (1964) seems to summarize the literature review quite adequately when she states: Randomizing the sequence of frames probably does not impede the learner and may well provide him with a useful form of active organizing response, if all the information is available to the learner, if the concepts to be gained from the randomized se- quence are few and simple or if the randomizing is done so that the concepts to be learned remain se- quenced according to the order in which it is neces— sary that they be acquired (randomizing within sub- units of a task) (p. 264). CHAPTER III DESIGN OF THE STUDY Sample Forty-one college students participated in this study during the winter term of 1970. They were all elementary education majors on the bachelor degree level at Michigan State University and ranged in age from 18 to 32 years. By class level there were 10 freshmen, l4 SOpomores, 11 juniors, and 5 seniors. Only two of the subjects were male. All students completed the programed material and atten- dance during the study was slightly under 90 per cent. Musical background, as determined by the Colwell Musig Achievement Tests, indicates no significant difference among groups. The 40 students were randomly assigned to four ex- perimental groups: A, B, C, and D. The students were not informed that they were involved in a study and did not realize this even at the time of the delayed retention test. They were in two different classes that met at 10:20 A.M. and 1:30 P.M. There were 21 students in the earlier section and 19 in the later section. The final test of the seven was given 13 weeks after the treatment 45 46 period. Participation was on a purely voluntary basis and data was collected on 21 of the original 40 students. Criterion Measures Prior to the treatment period the students were given a battery of three tests. The Music Achievement Tests 1 and 2, described in Chapter II, were two of the measures. Since the study involved harmonic elements, only certain parts of the MAT series were applicable; these were Parts l'and 2 of MAT 1 and Parts 1 and 3 of MAT 2. Using the Kuder-Richardson 20 formula, the two tests yielded a mean reliability factor of .93 for the students in this study. For the purpose of this study three testable areas were identified that relate to harmonic elements. A thorough survey of available standardized tests revealed a necessity to construct measuring devices peculiar to the needs of this study. The following scheme defines the three major areas and their subtests (the complete forms of the self-constructed measures may be found in the appendix section): Section I-eAural and Visual Discrimination of Intervals and Triads Subtest A-—Aural The purpose of this phase of the test was to determine the ability of the subject to identify, by comparison, the similarity in interval or 47 triad quality among three sound units. Three sound units were played from a pre—recorded tape and the student was asked to determine which, if any, of the sound units were alike in interval or triad quality. This task correSponds to Type 5 (Multiple Discrimination) on Gagné's model. Subtest B--Visua1 This portion of the test purposed to determine the ability of the student to relate physical distance to interval distance. The student was asked to match a two- or three—note sound unit with the corresponding keyboard diagram. There were three keyboard diagrams and a "none of the above" Option for each item. Chaining (Type 3) is the learning level used in this subtest, al— though Multiple Discrimination is an option, depending on the cognitive function Of the student. Section II--Aura1 to Keyboard Transfer Subtest A--Matching Aural with Notation The subject was to match an aural stimulus with the corresponding musical notation. A two- or three—note sound unit was played. The student was to choose which staff notation, if any, sym- bolized the given unit. Multiple Discrimination is the type Of learning involved in this subtest. 48 Subtest B--Interval and Triad Construction Given a two— or three-note sound unit with the lowest tone notated, the student was to complete the upper note(s) of the unit. This subtest is considered a function on the Multiple Discrimina- tion level. Section III--Simulated Keyboard Application Subtest A--Keyboard to Notation Transfer The student, for all but the retention test, was at an electronic keyboard instrument for this section and was permitted to play the identified sound units. An interval or triad was identi— fied by X's on a keyboard diagram. The student was to match the diagram with one of three staff notations. A fourth, "none of the above," was an Option. The learning task level of this sub- test is considered tO be Type 3 (Chaining). Subtest B-—Notation From a given letter/number symbol the student was to construct that interval or triad. The low note of the sound unit was placed on the staff and the student was to complete the upper note(s). As in the preceding subtest, each student had an electronic keyboard instrument and was permitted to play the sound unit represented by the letter/ number symbol. Verbal Association (Type 4) is the learning level involved in this subtest. 49 All sections of each test which required an aural stimulus were pre-recorded on tape at 7-1/2 ips. This included narrated instructions plus at least one example item for every subtest. The low pitch limit was f (second f below 'middle c') with a high pitch limit of f (second f above 'middle c'). The four devised instruments, as described above, were used to collect data. Prior to the study it was de- termined that certain subtests could be used in the later stages of the experiment that could not be used at the beginning. This was possible because students acquired terminology and functional skills as the study progressed, which permitted them to Operate in broadened musical experiences. The following matrix identifies the subtests used in each Of the four devised instruments (Table 3.1). In all four tests, items within a subtest were iden- tical or extremely similar; similar, in that an interval or triad was transferred from G to F clef or the converse. From test to test, items within a particular subtest were Often reordered to vary the pattern but were otherwise identical. Reliability coefficients for the four constructed tests were determined during the study on the participating subjects. These reliability estimates (see Table 3.2) were derived from the Kuder-Richardson 20 formula. The Evalua- tion Services at Michigan State University processed the data, which had been recorded on mark sense scoring sheets. 50 TABLE 3.l.--Subtest Matrix. u 4J u u a : :4J c G 0 m4) mun «no m-a gun a m saw 8-» m m m.p m:» o c r-l-lJm c-l-IJV' c—ICU In r-ld) l\ thale wine: mra a m-u B H O m m t)mr~ ()maa ocaur~ c)m ,. "-4 a «4 B "-1 we «4 z c >. c:»ua £3>1mlh c:» B (301m 0 can Om E>UJ E>4Jm E>4JUJ :4m nxam Lama: Laucnm morn: «05:1: csom «321mm mcn~’ mcn~r mcnnwv :naaa~v Section I-Aural and Visual Discrimination Subtest A-Aural X* X X X Subtest B-Visual x X X X Section II-Aural to Keyboard Transfer Subtest A-Matching Aural with Notation X X X X Subtest B-Interval and Triad Construction X X X Section III-Simulated Keyboard Application Subtest A-Keyboard to Notation Transfer x X Subtest B-Notation from Letter/Number Symbol X X X *An "X" identifies the subtests used in each Of the four self-constructed tests. 51 TABLE 3.2.--Reliability Coefficients Of Constructed Tests. Harmonic Element Survey Pretest (HESPRE) T3 40 students; 20 items .61 Harmonic Element Survey Posttest (HESPST) T4 .80 40 students; 25 items Harmonic Element Survey Retention Test (HESRTN) T5 .81 40 students; 25 items Harmonic Element Survey Delayed Retention Test (HESDRT) T7 21 students; 30 items .90 Two other test titles, identified for computer usage as PERPRE (T1) and PERPST (T6) may appear occasionally in this thesis. These tests were part of standard measure- ment for the course in which the subjects were enrolled. They relate only indirectly to this study and are mentioned so their presence may not cause undue confusion. Programed Material A pilot study had been attempted in the term preceding the one in which the experiment was actually realized. The problem of control Of material content became a very Ob- vious concern so it was decided to program the necessary information. The programed material was then given to an instructor who taught 76 students enrolled in other sec- tions of the same course as the experimental subjects. The 52 76 students were asked to write comments and questions in the margins of the programed material in the event that clarity or continuity were lacking. Following a thorough review of errors, comments and questions, the material was revised and prepared for the treatment period of this study. Several authoritative works on programing were studied and served as guidelines to the develOpment Of the resultant linear program (Lunsdaine and Glaser, 1960; Galanter, 1959; Smith and Moore, 1962). The final revised material appears in the Appendix. Design The 40 subjects were randomly assigned to four ex— perimental groups Of equal size. All students were given two tests (T2 and T3) prior to the treatment period and two tests (T4 and T5) following the experimental treatment. In response to a letter Of request, 21 students (52-1/2 per cent) returned 13 weeks after the treatment period to participate in the Delayed Retention Test (T7). Table 3.3 indicates the time schedule of the study. During the seven class hours of the treatment period the students came to the regularly assigned room and each student was given a programed booklet according to the predetermined pattern for his assigned group. The student took his booklet to a piano practice room and proceeded to reSpond to each item. If the student finished with the booklet before the class hour ended, he 53 TABLE 3.3.--Experiment Time Schedule. January 9 Perception Pretest (PERPRE) T1 (27 items) January 12 Colwell MAT 1 (Parts 1 & 2) Colwell MAT 2 (Parts 1 & 3) (COLWEL) T2 (111 items) January 21 Harmonic Element Survey Pretest (HESPRE) T3 (20 items) January 23, 26, Treatment Period 28, 30 and (seven 50 minute class periods) February 2, 4, 6 February 9 Harmonic Element Survey Posttest (HESPST) T4 (30 items) March 11 Harmonic Element Survey Retention Test (HESRTN) T5 (25 items) March 13 Perception Posttest (PERPST) T6 (34 ‘ itemS) May 11-15 Harmonic Element Survey Delayed Retention Test (HESDRT) T7 (30 items) returned it to the instructor and began the next booklet in his treatment sequence. If he did not complete the booklet that class hour, he returned it to the instructor and resumed from that juncture the next class period. Students were aware that the order of material was differ- ent among class members but were told that their sequence had been determined by the achievement level of a test administered the first day of class. 54 The devised program material was organized into three (3) sections. One section included Series A (Terminology, Scales, and Notation-—82 frames) and Series M (Intervals-- 33 frames) and was denoted as treatment XMa. Another sec- tion was Series R (Major and Minor Triad Construction-- 14 frames) and was labeled treatment XMb. A third section was Series B (Major and Minor Triad Terminology--ll frames) and was labeled treatment XMc' The sequence in which these three sections were pre- sented comprised the treatment. Each Of the four groups of subjects received a different order Of programed mate- rial. In addition to varying the sequence of material, one section (XMb) was entirely omitted for two Of the groups (Groups B and D). Table 3.4 indicates the order in which the four groups were presented sections Of programed material. Testable Hypotheses Some of the hypotheses are stated as negatives (null) and the remainder are in positive form. The computer pro- gram was established before the researcher was totally aware of the mixed positive and negative directions Of the hypotheses. Rather than revising the computer program the hypotheses were allowed to remain in the original form. The study was designed to test six hypotheses. These are: 55 TABLE 3.4.--Test and Treatment Design. m m m m 4J 4J 4J +3 4:: nor: 0:: QC 0) (D (D (D at mp me me :35 3:3 :35 D D O4J O4J 04J 0.9 H0) 340‘) Hm H0) (9 U (D 0 o c> o o mr4 mra m.4 m a: Perception Pretest (PERPRE) Tl N=10 N=10 N=10 N=10 Colwell MATS 1 & 2 (COLWEL) T2 N=10 N=10 N=10 N=10 Harmonic Element Survey Pretest (HESPRE) T3 N=10 N=10 N=10 N=10 Treatment Period XMa* XMC XM XM, a c ** XMb XMa XM XM c a **‘k XMC XMb Harmonic Element Survey Posttest (HESPST) T4 N=10 N=10 N=10 N=10 Harmonic Element Survey Retention Test (HESRTN) T5 N=10 N=10 N=10 N=10 Perception Posttest (PERPST) T6 N=10 N=10 N=10 N=10 Harmonic Element Survey Delayed Retention Test (HESDRT) T7 N=7 N 5 N=5 =4 *XMa: Programed Series A (Terminology, Scales, & Nota- tion-~82 frames) & Programed Series M (Intervals-— 33 frames). **XMb: PrOgramed Series R (Major and Minor Triad Construction-~14 frames). ***XMC: Programed Series B (Major and Minor Triad Terminoloqv--ll frames). 56 Hypothesis I: The students receiving the full, ordered sequence of material (Group A) will attain greater achievement than the other groups as measured by the Posttest. Hypothesis II: There will be no difference between students exposed to the full, ordered sequence of material (Group A) and those experiencing the full, scrambled sequence (Group C) measured by the Retention Test. Alternate: Groups A and C will have equal achieve- ment on the Retention Test. Hypothesis III: The students experiencing incomplete se- quences (Groups B and D) will Show no difference on the Retention Test. Alternate: Groups B and D will differ on the Retention Test. Hypothesis IV: Students exposed to the full sequence of material (Groups A and C), whether scrambled or ordered, will have a higher achievement on the Posttest than the other two groups. Hypothesis V: Students experiencing the scrambled, incom- plete program sequence (Group D) will have a lower Posttest score than the other groups. Hypothesis VI: There will be no difference in retention levels among all four groups as evaluated by the post- treatment tests. Alternate: A difference will exist among groupS' on the retention tests. 57 Analysis Raw data from the individual tests were transferred to mark sense scoring sheets and processed by Evaluation Services at Michigan State University. This process fur- nished the mean, variance, standard deviation, standard error of measurement, mean item difficulty, mean item dis- crimination, and mean point biserial correlation for each of the five tests. Computer cards were punched for all 40 students and included the standard score Of each of the tests. A pro- gram, written by Jeremy Finn (1968), State University of New York at Buffalo, for analysis of covariance was used to test the six hypotheses. In addition to the coeffici- ents Of confidence for each test, cell means and a corre- lation matrix were derived. Those figures appear in Chapter V. CHAPTER IV PRESENTATION OF THE DATA Review Of Procedure The purpose of this study was to investigate how scrambling and/or omitting portions of sequenced material would affect the learning and retention of harmonic ele— ments when employing Gagné's hierarchical system as a theoretical framework. Forty college students participated in the experi- ment in the winter term Of 1970 at Michigan State Univer- sity. During the Spring term, 21 of the 40 responded to take a delayed retention test. Table 4.1 shows the fre- quency of participation. The data collected from the tests were recorded on computer cards and prepared for processing through an IBM 3600 at the Computer Center, Michigan State University. An analysis of covariance was the means of determining acceptance or rejection Of each hypothesis. The specific treatment is a sub-prOgram of a multivariate analysis of variance developed by Jeremy Finn, State University Of New York at Buffalo. 58 59 TABLE 4.l.--Analysis of Participation. 4 m U o m m m m H 5 s 5 5 m o o o o u H H H H o w o 0 o E Pre-treatment test battery: 10 10 10 10 N=40 (PERPRE) T1 (COLWEL) T2 (HESPRE) T3 Treatment Period 10 10 10 10 N=40 Post-treatment tests: 10 10 10 10 N=40 (HESPST) T4 (HESRTN) T5 (PERPST) T6 Post—treatment test: 7 5 5 4 N=21 (HESDRT) T7 In Table 4.2 the means of the criterion measures are shown in terms of standard scores. Table 4.3 contains an estimation of the correlations among the seven instru- ments. 60 HNHZ ovuz ovuz ovnz ovnz ovnz ovuz Ase m.om o.ss o.ma m.me o.am «.me m.om .a gnome Ame m.em m.om m.mm m.ma m.om m.om «.ms o ozone Ame «.ma m.sa H.ss m.ms a.om H.0m e.Hm m asono Ase H.0m S.ma s.Hm a.mm G.Hm N.Hm H.Hm a moose emommm ammmmm zemmmm amammm madman . umzqoo mmmmmm .m#C®§H#wfiH OGHHSmMTE SO mHHQU MO mQMQZII.N.v maHmHNH. 61 oooo.H Ahmm.o ommm.o mmmm.o omem.o Naom.o mmmh.o Emammm ooo.H vuwn.o mmmh.o doom.o vmvh.o hhm5.0 Emmmmm oooo.H hmvn.o wmvm.o vomm.o vmwm.o 29mmmm oooo.H mvvv.o mmmn.o mmwm.o Emmmmm oooo.H momm.o omno.o mmmmmm oooo.H HNHS.0 QMBQOU oooo.H mmmmmm emammm Emmmmm 29mmmm Bmmmmm mmmmmm QMBQOU mmmmmm .mucmESHDmcH mcflHSmmmz mo xflnumz coflumamunoonu.m.v momma 62 Hypotheses Hypothesis I The group exposed to the full, ordered sequence of material (Group A) will have a greater increment of learn- ing than the (ther groups as measured by the Posttest (HESPST). . The obtained F value indicates a rejection Of the hypothesis. The probability of this occurring by change was less than .94 for 40 subjects. Results are shown in Table 4.4. TABLE 4.4.--Analysis of Covariance Summary between the Pre— test (T3) and the Posttest (T4). Source SS df MS F Between groups 0.5 l 0.5 0.06 Within groups 3010.0 35 86.0 Totals 3010.5 36 Hypothesis II There will be no difference in achievement between the students (Group A) exposed to the full, ordered sequence of material and the students (Group C) experiencing the full, scrambled sequence as measured by the Retention Test (HESRTN). Alternate: The students (Group A) exposed to the full, ordered sequence of material will have a higher achievement, as measured by the Retention Test (HESRTN) than the students (Group C) experiencing the full but scrambled sequence of material. The F value indicates acceptance of the null hypothesis that no statistically significant difference exists between 63 Groups A and C (see Table 4.5). The probability of this occurring by chance was less than .29 for the 40 students. TABLE 4.5.-—Ana1ysis of Covariance Summary between the Pre- test (T3) and the Retention Test (T5). Source SS df MS F Between groups 101.5 1 101.5 1.17 Within groups 3208.4 35 91.7 Totals 3309.9 36 Hypothesis III The students (Groups B and D) exposed to anincomplete sequence of materials, whether ordered or scrambled, will not differ in achievement on the Retention Test (HESRTN). Alternate: The students of Groups B and D will differ in achievement as measured by the Retention Test (HESRTN). The null hypothesis that there is no difference in achievement between student groups exposed to an imcomplete sequence was accepted at the .16 level of probability (see Table 4.6). TABLE 4.6.--Analysis of Covariance Summary between the Pre- test (T3) and the Retention Test (T5). ‘ Source SS df MS F Between Groups 151.4 1 151.4 2.0 Within groups 2649.5 35 75.7 Totals 2800.9 36 —_ 64 Hypgthesis IV The students (Groups A and C) that are exPosed to the full sequence of material, whether ordered or scrambled, will show a higher achievement on the Posttest (HESPST) than the students (Groups B and D) eXperiencing an incom- plete sequence. The hypothesis that groups exposed to the full se- quence of material will realize a higher achievement than groups having an incomplete sequence was rejected. The results are shown in Table 4.7. The probability Of this occurring by chance was less than 0.42 for the 40 partici- pants. TABLE 4.7.--Analysis of Covariance Summary between the Post- test (T4) and Pretest (T3). Source SS df MS F Between groups 58.4 1 58.4 0.68 Within groups 3022.3 .35 86.4 Totals 3080.7 36 Hypothesis V The students undergoing a scrambled, incomplete pro- gram series (Group D) will have a lower achievement than the other groups, as measured by the Posttest (HESPST). The Obtained F factor indicated that there is not a significant difference between the students (Group D) having a scrambled, incomplete program and the others (see Table 4.8). The probability of this occurring by chance was less than .51 for the 40 subjects. 65 TABLE 4.8.--Analysis of Covariance Summary between the Pre- test (T3) and the Posttest (T4). Source SS df MS F Between groups 37.8 1 37.8 0.44 Within groups 3021.9 35. 86.3 Totals 3059.7 36 Hypothesis VI There will be no difference in retention levels among the four groups as measured by the post-treatment tests. Alternate: The groups undergoing the full program series (Groups A and C), whether ordered or scrambled, will have a higher retention score than the other two groups. As seen in Table 4.9, on the basis of 40 students, the F ratio indicates acceptance of the null hypothesis. The probability of this occurring by chance is less than .60 for the 40 students. TABLE 4.9.--Analysis of Covariance Summary between the Post- test (T4) and the Pretest (T3). Source SS df MS F Between groups 164.4 3 54.8 0.63 Within groups 3022.3 35 86.4 Totals 3186.7 38 66 A comparison of a different set of tests for the same hypothesis shows similar results (see Table 4.10). The four groups showed no difference in retention levels. The probability of this occurring by chance is less than .50 for the 40 participants. TABLE 4.10.--Analysis of Covariance Summary between the Retention Test (T5) and the Pretest (T3). Source SS df MS F Between groups 180.0 3 I 60.0 0.80 Within groups 2640.4 35 75.4 Totals 2820.4 38 Twenty-one students were used to test the null hypo- thesis that there is no difference in retention levels among the four groups. The F value as shown in Table 4.11 signi- fies acceptance of the hypothesis. The probability of this occurring by chance was less than .55. TABLE 4.ll.--Analysis of Covariance Summary between the Pre- test (T3) and Delayed Retention Test (T7) for 21 Students. Source SS df MS F Between groups 144.6 3 48.2 0.72 Within grOUps 1072.9 16 67.1 Totals 1217.5 19 The complexity of hypotheses and the tests with Table 4.12. tests specified. 67 which each is identified may be simplified by referring to For each hypothesis, data are analyzed for significance on group achievement comparisons for the two TABLE 4.12.--Hypothesis Matrix, Qualifying Tests, and Results of Data Analysis. H N m V‘ Ln KO l‘ B E B a B B B a E E? E ’z‘ E? E? m m B m m m E m m m m o m a m m m m m m o m m m m m N 9: 8 E 5 E 91 5 Results 40 X X rejected (H0) 40 X X accepted (H0) 40 X X accepted 40 X X rejected 40 X X rejected (H0) 40 X X accepted (H0) 40 X X accepted (H ) 21 X X accepted CHAPTER V SUMMARY AND CONCLUSIONS Review and Summagy This chapter has four sections: a review of purpose, pOpulation sample, procedures of the study and a summary of the findings; conclusions drawn from obtained data; a discussion; and suggestions for future research. The purpose of this study was to investigate a num- ber Of questions related to scrambling and/or omitting sequenced instructional material and the effect this has on the learning and retention Of harmonic elements when using Gagné's hierarchical model as a theoretical frame- work. The 40 elementary education majors that participated in this experiment at Michigan State University in the winter term of 1970 were enrolled in a required music funda— mentals course. These undergraduates from two of the 15 sections were randomly assigned to four experimental groups for the ten weeks of testing and treatment. Twenty-one students voluntarily returned nine weeks later (the fol- lowing term) to write the Delayed Retention Test. The actual treatment took place in seven class periods of 50 68 69 minutes each encompassing 15 days. A battery of three tests preceded the treatment. These were: Perception Pretest (PERPRE) Tl: a nonstandardized test already being uSed in the course for mea— suring aural discrimination. Colwell Music Achievement Test 1 and 2 (COLWEL) T2: standardized tests designed to measure pitch, meter, and mode discrimination. Harmonic Element Survey Pretest (HESPRE) T3: a self- developed instrument devised for this study to measure aural and visual discrimination of major and minor chords and their constituent parts. Four tests followed the treatment; one test was given immediately, one test given five weeks later, and another was given after a thirteen week delay. The fourth test (Perception Posttest) was used in relationship to the course in which the students were enrolled, but has no direct bearing on this study. This is a terse description of each of the posttests: Harmonic Element Survey Posttest (HESPST) T4: but ex- a self- developed measure similar in kind to T3 panded to include construction Of triads and inter- vals. Harmonic Element Survey Retention Test (HESRTN) T5: T but reordered; also a self- the same items as 4 developed measure. 7O Perception Posttest (PERPST) T6: similar in type to T1 but including additional items. Harmonic Element Survey Delayed Retention Test 7(HESDRT) T7: a self-developed aural and visual discriminating instrument using notation and simulated keyboard to measure intervals and triads. The treatment consisted Of auto-instructional mate- rial specially written for this study and distributed to the subjects in original, scrambled or omitted order, or a combination Of the last two. Six hypotheses were tested for statistical signifi- cance. Each hypothesis and the research results are found on pages 71 and 72. Conclusions What has been found true of the 40 students who took part in this study cannot be assumed to be true for other similar student groups due to the peculiar background and' conditions of this research. The conclusions drawn from this study relate only to the sample from which data were Obtained. Based on the results of this investigation, the following conclusions can be admitted: 1. When nonmusicians undergo a series Of programed learning material, a reordering of the blocks within the program has no statistically signifi- cant effect On the overall learning. 71 .maoauouos mo oocosvom ouonEoocH no on Oomomxo ouoB pony mesoum cooBuon usoao>oflnom CH oocouommac on mos oHone .Uoumoooo mos mflmonuommn Has: one .coumoooo mos pnoEo>oHnoo ca oonouom IMHO on o>on UHDOB .pouopuo no poanfionom Honuons .oocosvom anew onu mcflocofluom Ixo mesoum onn nonn mHmonuommn Hans one .Uouoomou moz unofiouonfl Monmoum o o>on OH503 mamanouofi mo oonosqom couocuo .HHSM onu mcfi>on msoum on» pony mflmonuoehn one muasmom .Azemmmmv umoe coaucouom onn no nnoEo>oHnoo SH Homwac non HHHB .Ooanfiouom Ho couocno Honnonx .maoau IopoE mo oocoswom opoHQEoonH no on comom Ixo no pno m mesouov mucopoum one .HHH .Azemmmmv umoe coflucmuom onu en poMSmooE mo oocoswom UoHnEoHom .HHSM onn mnflocofluomxo AU msouwv mnnopsnm onn can Hoanonofi mo oososqom conopmo .HHSm onn on pomomxo Am msonwv munocsum onu noosnon ncoE Io>oflnom nfl oononoMMHc on on HHH3 ouone .HH .Aemmmmmv nmonumom on» en coHSmooE mo mmsoum Monno onn nmnu mcflcuooa mo unoEouocH Houmoum o o>on HHHB A4 moonov Hoflnonofi mo oonosqom couocuo .Hasm onn on comomxo msoum one .H mamonuommm .wflmonnomen Haas onu mcflumoooo can mcHEuHmcoo enouonu .mmsoum macaw mao>oa noflucouou so moocoquMHc unconnecmflm on ouos ouone .Uouooflou mos memonuomen onu .ouomonone .muonuo on» nonn oonoHoMMHc nnoEo>oanom 2 7 unconmacmflm on non mofinom Eonmonm ononEoo Ina .UoHnEouom o mnHOmHoccs mpnocsum one .couoomou mos muonuo onu conu ucoao>oflnoo nonman c mcfi3onm Hmwnoumfi mo oocosqom Hasm o mca>mn mesonm non“ mamonuommn one .mumop nnofiuoonulpmom onu an OoHSmooE mo mmsoum HSOM onu mnoso mao>oa coannon now an oocoquMHp on on Haas ouone .MN . Temmmmmv umoupmom onu en nonemoofi mo .mmsoum nonuo onp conu ucoeo>oanoo HoBOH o o>on HHHB AD QSOHDV mofluom Eoumoum ouonEOOCH .UoHnEmuom m manomuoccs mucocsum one .N .oocosvom ouonEOocfl no mcwoso Iflnomxo AD can m mesonov munocsum on» non» Aewmmmmv “monumom onu no ucoEo>ownoo nonman m sonm Haas .coanaouom Ho couocuo Honuon3 .HMHHouoE mo oocosqom HHSM on» on comomxo oum nonu no can d mesouov mucocsum one .>H 73 2. Providing all facts necessary for mastering a specific task are present, the omission of addi- tional information does not impair students' achievement level. An abridged auto-instructional program does not necessarily inhibit learning. 3. A combination of scrambling and abridging a pro- gramed sequence Of learning has no statistically detrimental effect on terminal achievement. This assumes, of course, that scrambling does not take place within blocks nor that abridgment removes vital information. 4. Retention level is not adversely effected at a statistically significant level by scrambling segments of a programed series. The implication is that items within segments remain in order. 5. Students can more likely overcome the effect Of omitted material in an auto-instructional pro- gram, even though the task is compounded by scrambling segments of instruction. The reten- tion level is equal for students whether the program is scrambled or abridged. Discussion Every effort was made to construct the programed Inaterial in accordance with Gagné's theory specifically as it related to the three types of learning tasks used .in the experiment (Types 3, 4, and 5). An analysis Of the 74 data reveals little difference as a result of the various treatments and that students in the four groups were able to overcome deficiencies imposed by the experimental design. It is quite probable that the imposed treatment deficien- cies were overcome due to (a) the musical background brought to the learning situation, (b) formal or informal learning outside of class during and after the treatment period, and (c) contact with, and application Of, the know- ledge and skills of the programed material through the lec- ture and taped series in which all subjects participated as part Of a course requirement. Observation indicated that there was a much higher incident of queStions and evident frustration on the part Of the students who received a scrambled and/or an abridged series than among those who were assigned the complete, ordered sequence. Questions were answered by the instructor by repeating material that had been presented in lecture, lab, tapes, and pro- gramed material. According to the findings, this question— ing did not preclude eventual recovery and subsequent mas- tery of the learning tasks. The narrowed variance on the Delayed Retention mea- sure (T7) implies a homogeneity among the 21 students that voluntarily returned to take an additional test. This might suggest something about the nonacademic nature of the students who returns to cooperate in a non-required activity, although test scores indicate the 21 students as being representative of the original 40 participants. 75 The findings of this research are generally in accord with studies of similar nature. Studies reviewed in Chapter II have two basic agreements: (a) that the learner can "fill in the gap" when material is missing if the task is generally within the SOOpe of his capabilities and (b) that a person can mentally assimilate and reorganize mate- rials presented in a scrambled order. The present study has not disproved these findings but rather is in harmony with them. This is not to say that this experiment can be compared on a direct basis with all of those reviewed be- cause a fundamental difference does exist. Many of the studies reviewed do not clarify or identify levels of learning for the task involved. When structuring a learn- ing sequence for students, it would seem desirable to iden- tify a multiple-level model of learning to assist in for— mulating the sequence of instruction, for evaluation pur- poses or whatever other phase of the teaching/learning procedure is involved. This was not clear in some of the studies which makes it impossible to draw a direct com- parison with the present inquiry. Suggestions for Future Research l. A replication of this study, using a larger and more diversified academic population, would be of interest. 76 2. Use Of a similar study on the elementary school level might provide some valuable information concerning musical learning. 3. A study designed to limit the possibilities of "filling the gap" through external means might enhance the likelihood of significant differ- ences. 4. Extending the length of the experiment and broadening the learning content would furnish some valuable information. 5. A study based on a greater number of levels in Gagné's model and in musical aspects other than the element of harmony could be helpful. The music profession has had difficulty in defending some teaching/learning practices and in providing a ration— ale for the existence of music in the school curriculum. Certainly it is to the profession's advantage to obtain data to support its case. TO this end an increase in re— search is recommended. A replication Of the present study employing a larger and more academically diversified col— 1ege population would provide music teachers with greater information on music learning. This in turn could lead to innovation and upgrading music teaching. Use Of a Similar study on elementary school levels may furnish drastically different information, in which case the teaching approach should be adapted to take 77 advantage of research findings. Tighter controls on a similar study would increase the possibility of significant statistical differences and would assist in determining how students compensate for acquired or imposed handicaps. A closer look at the musical background and entering musi- cal behavior Of the subjects should be considered and in- cluded. Extending the length of time Of the experiment would increase the opportunity for retention and learning rate observations. An extended study would also enable the researcher to use more complex learning constructs and concurrently provide more detailed evaluation. The full use of Gagné's model on studies involving a number of problem-solving tasks representing the study Of music would furnish data on the whole of music learning and not merely a small facet. This is needful that music learning may be observed in its total perspective and not out of context. BIBLIOGRAPHY 78 BIBLIOGRAPHY Periodicals Gagné, Robert M. "The Acquisition of Knowledge," Psycho- logical Review, Vol. 69, No. 4 (1962), 355-65. Hamilton, Nancy Russell. "Effects of Logical versus Random Sequencing of Items in an Autoinstructional Program under Two Conditions of Covert Response." Journal of Educational Psychology, Vol. 55, No. 5 (1964), 258-66. Jeffries, Thomas B. "The Effects of Order of Presenta- tion and Knowledge of Results on the Aural Recogni- tion of Melodic Intervals." Journal of Research in Music Education, Vol. XV, No. 3 (Fall, 1967), 179-90. Levin, Gerald R., and Baker, Bruce L. "Item Scrambling in a Self-instructional Program." Journal of Educa- tional ngchology, Vol. 54, NO. 37(1963), 138-43. Mager, Robert F. "On the Sequencing of Instructional Content." Psycholqgical Reports, Vol. 9 (1961), Merrill, M. David. "Correction and Review on Successive Parts in Learning a Hierarchical Task." Journal Of Educational Psychology, Vol. 56, NO. 5 (1965), 225-34. Milak, John. "An Application of Certain Learning Theories to the Teaching Of Musical Rhythm." Missouri Journal of Research in Music Education, Vol. II, No. 3 TAutumn, 1969), 49-67. Miller, Herbert R. "Sequencing and Prior Information in Linear Programed Instruction." AV Communication 'Review, Vol. 17, NO. 1 (Spring, 1969), 63-76. Moore, James C. "Manipulating the Effectiveness Of a Self- Instructional Program." Journal of Educational Psychology, Vol. 59, NO. 5 (1968), 315-19. 79 80 Newton, John M.; and Hickey, Albert E. "Sequential Effects in Programed Learning of a Verbal Concept." Journal of Educational Psychology, Vol. 56, No. 3 (19657, 140-47. Payne, David A.; Krathwohl, David R.; and Gordon, John. "The Effect of Sequence on Programed Instruction." American Education Research Journal, Vol. 4, No. 2 (March, I967), 125—32. Roe, K. Vlachouli; Case, H. W.; and Roe, A. "Scrambled versus Ordered Sequence in Autoinstructional Pro- grams." Journal of Educational Psychology, Vol. 53, No. 2 (1962), 101-104. Talyzina, N. F. "The Stage Theory of Formation of Mental Operations and the Problem of the Development of Thought." Soviet Education, Vol. X, No. 4 (February, 1968)] 38-42. Books Bruner, Jerome S. Toward a Theory of Instruction. Cambridge, Mass.: The Belknap Press of Harvard University Press, 1966. Colwell, Richard. Interpretive Manual: Music Achievement Tests 1 and 2. Chicago: Follett Educational Corp.T 1969. " Evans, J. F.; Glaser, Robert; and Homme, Lloyd E. "A Pre- liminary Investigation of Variation in the Properties of Verbal Learning Sequences of the Teaching Machine Type." Teaching Machines and Programmed Learning: A Source Book. Edited by A. A. Lumsdaine and Robert Glaser. Washington, D. C.: National Education Association Department of AV Instruction, 1960. Gagné, Robert. Conditions of Learning. New York: Holt, Rinehart and Winston, Inc., 1965. Gagné, Robert M., and Gephart, William J., eds. Eighth Annual Phi Delta Kappa Symposium on Educational Research. Itasca, Ill.: F. E. Peacock Publishers, Inc., 1968. Galanter, Eugene, ed. Automatic Teaching: The State of the Art. New York: John Wiley & Sons, Inc., 1959. 81 Hilgard, Ernest R., and Bower, Gordon H. 'Theories of ‘Learning. 3rd Edition. New York: Appleton-Century- Crofts, 1966. Lumsdaine, A. A., and Glaser, Robert, eds. Teachin Machines and Programed Learning: A Source Book. Washington, D. C.: National Education Association, 1960. Smith,Wende11, and Moore, J. William. Programed Learning. Princeton, N. J.: D. Van Nostrand Company, Inc., 1962. Miscellaneous Colwell, Richard. Music Achievement Tests 1 and 2. Chicago: Follett Educational Corporation, 1968. Finn, Jeremy. "Multivariance." Version 4. Department of Educational Psychology, State University of New York at Buffalo, 1968. (Mimeographed.) APPENDICES 82 APPENDIX A PROGRAMED MATERIAL 83 Name Section MUSIC 135 PROGRAMED MATERIAL--SERIES A TERMINOLOGY, SCALES, AND NOTATION Instructions: (a) (b) (e) (d) (6) this programed study has been structured to progress systematically and will offer maximum benefit if followed sequentially use a 4 X 6 card or something similar to cover the printed answer while you write in your response you may want to refer to previous frames to reinforce your learning: some frames will direct you to earlier material for review if a frame appears vague or ambiguous to you, please write a few words stating the source of confusion and how it may be eliminated it is important that you use a keyboard instrument as you study this material 84 85 1. Music, in the traditional sense, is based on sound. Any study of music eventually necessitates a consider- ation of _, . 222m. XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 2. One of the characteristics of sound is pitch, which we describe as being relatively high or low. The ”highness” or "lowness" of sound is defined as . pitch XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 3. We perceive musical sounds and are able to hear differ- ences in pitch which we discriminate as relative "highness" or "lowness". A piccolo, for example, is capable of playing a higher than the bassoon: and a bass in a quartet is able to sing a lower than the soprano. pitch pitch XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX h. The pitches used in making music are arranged in tonal ladders. The steps of the ladder may be numbered, lettered, have representative syllables, etc. Pitches can be into a tonal ladder. arranged XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 86 5. The numerical sequence below represents a tonal ladder. Supply the missing numbers to this organized series. 1 2 3 ____ 5 6 ___' 8 34.2 XXXXXXXXXOO O O 00 O 6. West civilization has historically employed a tonal ladder (scale) of seven (7) tones in creating music. The progressive arrangement of seven pitches used as the foundation of traditional music is known as a . seals XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 7. You may have noticed that a seven-tone scale actually has eight members. The sound represented by the eighth step is similar to the first step; this similarity is known as the octave. The pitch difference between the low and high notes of an eight-tone scale is labeled the octave XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 8. The octave is one of a number of intervals that you will use in music study. An interval is defined as the differ- ence of pitch between two tones. Two different pitches form an . interval )QO(O O O O O XXXXXXXXXXXXXXXXXX 87 9. The smallest interval in our tonal system is the half- step. A half-step is heard when the following tones are played. Play and sing these intervals. -- and -- (keyboard and vocal response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 10. The distance defined as a half-step is heard as the difference between any one key and the nearest key to the left or right, black or white. Play and sing the interval of a half-step from the keys marked by Xs. Identify the nearest half-step with another X. 2 X \1 or (keyboard and vocal response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 11. The smallest difference in pitch on the keyboard is the half-stgp XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 88 12. The whole-step, as its name implies, is made up of two half-steps. The keys of a whole-step will always have one key between them. Play and sing these keyboard examples. ['1'] mm (keyboard and vocal response) 0 o o o o o o 13. The distance known as the whole-step is heard as the difference between any one key and a key two half—steps away. This may be higher (right) or lower (left) in pitch. Play and sing these whole-step intervals from the notes marked by Xs. \,,I (keyboard and vocal response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 14. The distance from one note to a tone two half-steps higher (right) or lower (left) in pitch is termed a whole-stgp XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 89 15. In your study of music you will be using the keyboard extensively. As a point of reference use the white note at the center of the keyboard and immediately to the left of a group of two black notes. This note is labeled by the letter '0'. Mark this 'middle 0' with an X on the keyboard diagram. 16. On a keyboard instrument, play and sing* the notes identified by Xs on the diagram below and you will have performed the eight-tone scale. III; III; L'l'l mu : it: 4 5 6 7 8 (keyboard and vocal response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX *note;-when requested to sing, it may be easiest to use the neutral syllable 'la': if the example is out of your voice range, you will need to sing an octave higher or lower. 9O 17. On the keyboard instrument, and by singing, begin in a different location than in frame 16 and perform another eight-tone scale (the first step of this scale is immediately to the left of the group of three black notes) as indicated on this diagram. l'l'l L'I'I'J III! III: (keyboard and vocal response) XXXXXXXXXXXXXO O O 0 000 O OO 18. Using the same starting location as in frame 17, play and sing the eight-tone scale using only the white keys as in this diagram. ”1999159939”! (keyboard and vocal responses) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 19. The scale played and sang in frame 17 (did) (did not) have the same 'sound' as that in frame 18. did not XXXXXXXXXXXXXXXX o o o o 91 20. The reason the two scales did not 'sound' the same is due to the differing arrangement of whole- and half- steps within the octave. The difference in the 'sound' of the scales heard in frames 17 and 18 can be accounted for by the differing arrangement of - and -steps. whole half 0 oo o ' o o o o o o oo o 21. We now return for closer inspection to the scale begin- ning on 'c'. The distance from the lowest (left) note to the highest (right) note is an . (Refer to frame 5) 5'6 7‘8 L—fl_deJLJLJ\J Label as whole- or half-steps, the seven intervals between members of the scale. Intervals between 1-2, 3-4, and 5-6 have been labeled for you. (Hint: is there a key between?) 1 whole 2 3 half a 5 whole 6 7 8 m g 4L JV' _JL 4: JV octave (eighth) 1 whole 2 whole 3 half A whole 5 whole 6 whole 7 half 8 l "““ZJI"“‘ I\\__,/’L'T‘TLQuJL__:___JL______J‘\~_.»’ .XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 92 22. Half-steps occur between members - , and . Whole-steps account for the remaining five (5) intervals. 3-4, and 7-8 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 23. Now consider a scale beginning, not on 'c', but with a note two-and—a-half steps higher (note letter name 'f'). Label the intervals between members of the scale as either whole- or half-steps. LII: Mm 1 whole 2 whole 3 half a whole 5 whole 6 whole 7 half 8 1 4L 1v L_,,,, _. ._._. _IL_____.I L____._J\_/ xxxxxx 0 o o IOXXXXXXXXXXXX 24. This sequence of whole- and half-steps, employing eight pitches within the octave, is termed the major scale. The major scale can be defined as a series of (numBer) notes whose extreme interval is an octave. — steps are located between keys 3-4 and 7-8. All the other intervals are -steps. eight (8) Half whole XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 93 25. There are scales having the same, fewer, or a greater number of members, but the sound unit symbolized by this keyboard diagram is known as a III; m; L'l'l mun LzLLL5JJV5 major scale xx 0’ o o o o o o 909 o o o o o o o 26. In an earlier frame it was determined necessary, when using 'f' as the beginning note of a major scale, to use a black key as step A. IIIIIMIIJI m This was necessary to maintain the proper order of whole- and half-steps of the Play and sing the constructed scale. major scalp (keyboard and vocal response) XXXXXXXXXXXXXXXXXXX a». o o o o 9h 27. Had we begun at 'f', and played only white keys, the nth step would have distorted the major scale sequence. It was necessary to flatten (lower a half-step) the white key between the 3rd and 5th steps of the scale. A note is flatted when it is ___ a half-step. lowered XXXXXXXXXXXXXXX O 000 O 000 00 O O O O O O 28. The 'b flat' (b’) became the hth step of the major scale whose lowest (keynote) tone is '__'. If. 0 o o o o 90 o o o o oo o 29. The note a half-step lower than '0' can be called '0 '. The note a half-step lower than 'a' is '__ '; than 'e' is '__ '3 etc. flat (b) a flat e flat XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 95 30. If a major scale began on the note 'g', the whole- and half-steps being observed as in frames 21-25, the result would be as seen in the diagram below. Play and sing this major scale whose keynote is '3'. WI 1111‘I1III1I1I1I1IJ l 2.3 4.5'6 7GB L.JL.JVL_II_JL.JU (keyboard and vocal response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 31. You have no doubt noticed the one note (7th scale degree) played on a black key. This was necessary to maintain the proper sequence of - and -steps of the . whole- and half- major scale XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 96 32. Given 'g' as the keynote and having been asked to play a major scale, you might have played only white notes up through the octave. Play and sing the eight white. notes from 'g' up through the octave as in the diagram below. You have heard a scale quite different from the major. It was necessary to raise (sharp) the 'f' a half-step in pitch to realize the major scale. 6 def g a. be J of -1. h 11111111111 (keyboard and vocal response) XXXXXXXXXXXXXXXXXXX O 33. The 'f' sharp (r45 became the 7th degree of the major scale whose lowest (keynote) pitch is '__'. .5 O 00 O O 0 O O O IOXXXXXXXXXXXX 3h. A tone a half-step higher than 'f' is called 'f . The note a half-step higher than 'c' is than 'b' is '__ '3 etc. sharp (#1 'c shagpf 'b sharp' XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 97 35. The half—steps in the major scale occur between steps _"'__ and '__-'__. 2:1». 7_-_§ XXXXXXXXXXXXXXXXX O O 0 O 0 0 O 36. Given the keynote 'd', use Xs to indicate the remaining seven notes of the major scale. Play and sing the scale. LJRARJLijLJLES cdef'abcdefgb (keyboard and vocal response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 98 37. With 'b' flat (bb) as the keynote locate, by Xs, the other members of the major scale on the keyboard diagram. Play and sing the resulting scale. 12346678- M'II'I'I'I'I 1 (keyboard and vocal response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 38. What is the keynote of the B flat (Bb) major scale?_____ 53 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 39. What is the keynote of D* major scale? D XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX #0. The keynote is synonomous with the degree (step) of the scale. first XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX *note--it is customary to use an upper case (capital) charac- ter when referring to a major scale by its letter name 99 #1. Regardless of the starting keyboard pitch, if - steps are observed between 3-4 and 7-8 and the remaining intervals are -steps, the resulting sound unit will be a . gag; 111212 major scale )OOOOOOOOOOO( O O O O 0 )00000000( #2. As suggested in frame 25, there are other ways of arranging the eight notes within the octave. One such arrangement is diagramed below. Play and sing (by numbers) this new arrangement. 1'1'11'11'11'1'11'1'1'1 1:13 4 6'6 WLJLJ (keyboard and vocal response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX #3. Identify the whole step intervals used in this scale by labeling with the whole number one (1). 1'111'1'11'1'1'1 1 l 2 3 1 L1 1 5 6 7 8 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx 100 44. We saw five (5) whole steps in the major scale, but only in this arrangement.> The whole-steps occur between degrees - , - , and - . three (3) 1-2, 3-b, and h-5 009 o oo o o o o o co oo o 0999 000 00 o 990 #5. Now identify the locations of half-steps in this scale by labeling them with the fraction one-half («1). e bdf 111111 1 2 3 h 5 6 7 8 1 2‘33 L1 5%6 7%8 O O O O O O O O O O O. O O 00 O. O O O. 0 0000000000 46. Whereas only two (2) half-step intervals exist in the major scale, three (3) are found in this harmonic minor scale. The three occur between degrees - , , and "' o a 2-3, 5-6, and 7-8 o o o 000 o o 0000 o o o o o o co 0 o 9099 o 09 0099 #7. You have now identified six of the seven intervals of the harmonic minor scale, whose keynote is 'c'. There are whole-steps and half-steps. 3.whole-steps and 3_half-steps. O. O .000 OO O O O OO O. O. O. 000 00000 O... 000 O. 101 #8. Referring to the previous frames, note by whole number (1) or fraction (fi) the location of whole- and half-steps in the harmonic minor scale. L.__.I\./L__| [_Jv 1 2 3 u 5 6 7 8 L__+JF_/ _———— fl .1. .i..1. .1. .i.’ " .i XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX #9. The interval between degrees and has not yet been analyzed. It is different from either the whole- or half-step because it has a pitch _ (wider1(harrower) compass. g and Z wider XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 50. The step-and-a-half (ab to b) that exists between the sixth and degrees of the harmonic ___scale give it a uniquely different sound than the major scale. seventh minor .00 00000000 OOOOOOOOOOOOXXXXXXXXX , . .1 ~ 41 4.. .O¥l__.\.o 1. ‘0. . .. a»... :3 102 51. Give the entire intervallic sequence of the 'c'* harmonic minor scale using the numerical symbols 1, 1, and 11'. League, 1__.2._.3.__‘L_.5..6__7._ 6 _Li.L.L.i._1%_fi XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 52. Just as a major scale can use any keyboard pitch as the keynote, so may a harmonic scale begin at any tone. minor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 53. Use 'd' as the keynote for the harmonic minor scale and identify the other seven members by Xs. Play and sing 1'1'11'1'1'1 1"11'1'1'1 5W‘ 1 the scale. 111111111 (keyboard and vocal response) IXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX ‘*note--it is customary to use a lower case character when referring to a minor scale by letter name 103 5h. This 'd' harmonic minor scale could be symbolized by using letter names for the eight members. When spelled the scale would appear as follows (fill-in the missing letters). d __ __ __ __ by c*# __ (d) e r £1113») (01‘) _d_ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 55. Use Xs to denote the members of the 'a' harmonic minor scale and complete its spelling. 1111111 111111111l (a) be c d e f (S#§.2; 990 one 000 o 000"" OXXXXXXXHX 10“ 56. Do the same with the 'e' harmonic minor scale. 1111111111111 (e) (M i 0000 O 00 O o o o o o o 000 57. Summarize the study of major and harmonic minor scales by showing a comparison of their interval sequences. Place the numerical symbols for the scale in the spaces provided. major scale: 1 2 113‘}le 6I L8 harmonic minor scale: 1 2 3 1 5 6 8 WWW major scale: 1 2 3"? 5 6 ix)? _l..1_il 1 1.1 harmonic minor scale: 1 2 3 h 5 6 7 8 L.__Jv1___.11__1vn__._1v __1__%._1__l__2‘z_li_%. XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 105 58. The information covered in the previous frames increases in usefulness when recorded for purposes of visual- interpretation. Musical notation has become a finely developed art, although new symbols and altered forms of traditional characters are being introduced regularly. (no written response required) «u on «coon o u o 0000" o o n o u o onxxxxxx 59. The five-line staff is the frame upon which musical symbols are placed. These horizontal lines * num er form the musical . The staff looks like this: five {51 staff XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 60. At the left margin of the staff is located a clef, a symbol that acts as a point of reference in pitch relationship. A symbol placed on a staff to determine pitch reference is termed a clef O 00000 00. O 0.000 O O O O. O. 00 O O O O GO GO. 106 61. In this study you will be most concerned with only two of the clefs. One of these is associated with instruments generally performing at or above middle 'c' (e.g., flute, violin, s0prano, etc.) and is known as the treble or G clef (¢ ). The or G is normally used with instruments playing in the upper half of the keyboard range. treble clef XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 62. The treble clef would be seen as in the example below. Construct five or six treble clefs on the staff space. ‘ é 0.0000000000000000...coco.OIOOOOOOOIOOOOOoooeooooooooOOOOOOOr (construction of treble clefs on the staff) 0 o o oo o o o o o o o o o oo o o oo 63. The G or treble clef encircles the second staff line which symbolizes the 'g' above 'middle c'. Lines and spaces of the staff are always numbered from the bottom. The letters used in music are limited to the seven (7) initial members of the alphabet (i.e., ’a' through '3'). Each line and space has its own alphabetical indicant. (no written response required) XXXXXXOO 0000 0 000 O O. O. O O O 000 0 000 O. O O 107 6h. The alphabetical sequence is terminated by ‘g' on the line and resumes with 'a' on the second space. second XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 65. Working up and down from 'g', fill in the missing letters that represent pitches on the staff. W :3: E? :1 er’ ‘3 O __ __ J; __ __ __ __ __ __ 108 66. The letters you have placed have their representative counterparts on the white notes of the keyboard. Complete the letter/note combinations as begun in the diagram below and play the series. £l5fl9¥;§ v4yfizi 171 *F1 1e 1111111. 11 III II III (e)fgabcdef XXXXXXXXXXXXXXXXXXXXXXXXXXX 67. Supply the letters for the following notes: e g_ a b b a c 00 o co co co oo o o oo o o o o o o 0000 000 o o o o o 68. The bass or F clef ( 9: ) is generally used with instruments or voices that perform below 'middle c' (e.g., bassoon, string bass, tuba, bass, etc.). The sign used in musical notation for pitches in the lower half of the keyboard range is the or F . bass clef XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 109 69. The fourth line of the staff lies between the two dots of the or bass clef. The letter name assigned to this line is 'f' and it is the first 'f' below 'middle 0'. F XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 70. An F or clef has been placed on the staff: construct five or six clefs similar to it on the remaining space. no 'lo I bass (construction of bass clefs) 00 0000000000.. 000000000 XXXXX 71. Moving up and down from the 'f' on the fourth line, supply the missing letters that represent pitches. (g) a b c d e f‘_g (a) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 110 72. As with the treble clef, the bass clef letters represent pitches located on the keyboard. Complete the letter/ note links in the diagram and play them. 4n 5???— }' €0??1l 11 I111|1 11 1 111"” 111111] 'middle c' g a b c d e Ajf) 8 %_ (keyboard response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 73. Supply the letters for the following notes: g a b d c e f XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 111 7h. Although many notes exist above the treble clef and below the bass staff there are only three (3) white keys between the two staffs. Locate these notes on the keyboard and fill-in the missing letters. Play them. 11 111 11111 1 / '1'":- 1 bass staff range treble staff range 'middle ' 2L__21_.g (keyboard response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 112 75. It is often desirable to place the G and F clefs together as when a pianist or choral group performs. The combined symbol is termed the great staff. The three notes between the staffs are lettered __H, ___. and ___. Play the entire series on the keyboard. awn 932—9—— 43 Ei—e 0&3 a9 \ ’ 1 * 1 1 The range of the _ is nearly three (3) octaves. bI cI d (keyboard response) great staff XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 113 .76. The leger line supplied through 'middle c' is a partial staff line that extends the downward range of the treble clef (or upward range of the bass clef). Give the letter names of the notes located beyond the staff range on the following diagrams. Play these on the keyboard. (a 49-12.12: 110 a v :11? c’-£> 15"}. a g e f (a) (g) f e d c (e) (f) g a b c (keyboard response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 77. In relating the great staff to the keyboard, we have studied only the white notes. In frames Zh-Bh you saw that each white tone could be sharped (7?) by it a half-step or flatted (b) by it a half-step. raising lowering XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 11h 78. Placing a sharp in front of note (#0) raises the pitch; thus this 'a' E with a sharp Ebecomes an '1 p '. A flat placed similarly E the tone and it becomes an ' 'a sharp' lowers 'a flat' XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 79. Locate 'd#' (third line of the F clef) and 'eP' (third space F clef) on the keyboard. Are they the same note? 28$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 80. A black note, then, can have letter names: it behaves as a to the white note on its left and as a to the one on the right. ......OCOOOOIOOOOOI00.00.00000I0....00.0.0.0..000‘000000000.. two (2} sharp flat XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 115 81. In the spaces provided, label each selected black note with its two letter names. IIHI II III II III __/\_ _/\__ g#orab; a#orbb; c‘or d”; d#or eb XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 82. Although there are notes higher and lower than those on the staff below, this four-octave range will easily serve our study purposes. For each note marked by an X, draw a connecting line to its keyboard location. Play the entire series and sing as much of it as is ossible. p fléygpilfit -Glcrg yea ‘2‘. 'l. a€9ifl駧£f€B '9' (MIDDLE C' great (keyboard and vocal response) IXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Name Section MUSIC 135 PROGRAMED MATERIAL--SERIES M INTERVALS Instructions: (81) (b) (c) (d) (e) this programed study has been structured to progress systematically and will offer maximum benefit if followed sequentially Use a n X 6 card or something similar to cover the printed answer while you write- in your response you may wish to refer to previous frames to reinforce your learning; some frames will direct you to earlier material for reference and review if a frame appears vague or ambiguous, please write a few words stating the source of confusion and how it may be eliminated it is important that you use a keyboard instrument as you study 116 117 l. The distance between two pitches is called an interval. An interval can be expressed in sound or symbolized by notation. An, is the distance be- tween any two musical tones. interval XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 2. A note that is repeated, that is, played again without changing pitch, is said to comprise a unison or prime. Check the letter of two-note groups that are unison. A repeated note is called a or iiEE At_e_;339‘ - C? a! A___ B___ C___ D___ E___ F___ AI DI F unison prime XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 118 3. Intervals may occur by step or leap. .An interval by step would be from one letter name degree to the next, either up or down. The notes 'g' to 'a' and 'f' to 'e' would be examples of a , even though the latter is only a half-step. Check the intervals of a step in the examplesbelow. XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX b. An interval by leap would occur when nonadjacent letters of the staff are used. The notes 'g' to 'b' and {f' to 'c' are examples of a . Check the intervals of a leap from these examples. A B C D E leap AI BI E XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 119 5. A commonly accepted way of labeling intervals is by the letter-number system. A capital M (major), the lower case m (minor), and a P (perfect) are the letters used in this system. The numbers two through eight are used to identify the interval. The intervals studied are as follows: unison or prime P5 - 3% steps (repeated note) M6 - h% steps M2 - 1 step M7 - 5% steps (% step m3 - 1% steps less than an octave) M3 - 2 steps P8 - 6 steps Ph - 2% steps (no written response necessary) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 6. Please consider the major\scale whose keynote is 'c'. From the first degree ('c') to 'd' is a Whole step or major second (M2). A step is the name of the distance between the first and second steps of a major scale. SiEEEEE Examples: ......OOOOOOIIOI......OOOOOOO......COCCOOQUIIOOIOOI.00...... whole XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 120 7. Play and sing the five intervals below. Place an X below those intervals that are a M2. 1¢‘l_. Pffifl A;___ B___. C___ D E A, C, D, E (keyboard and vocal response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 8. From the given note, write in another note higher to create the interval of a M2. Play and sing each 1:11 ‘1! 4' 1" interval. 1D j a"- I.00.0.00.........OOOOOOOOOOOOOOOUCO......OOIOOOQCOO00.0.30. # ae— (keyboard and vocal response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 9. In the C major scale the interval from 'c' to 'e' is a major third (M3). Two whole-steps constitute the interval of a . Examples: r-—- M3 (major third) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 121 10. Play and sing the five intervals below. Check the _intervals that are M3s. A___I B___ C___ D___ ‘E___ (keyboard and vocal response) AI CI E XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 11. From each of the given notes, place a note above that creates a M3. Play and sing each interval as a check against error. P113153 9 ,— (keyboard and vocal response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 122 12. Although the minor third (m3) interval can not be notated as the distance from the first to the third degrees of the major scale, its continual use in melody and harmony dictates its inclusion in our study. A step and a half (i.e., 'c' to 'eb') is the distance of a m3 (minor third). By this we see its distance is a half- step greater than the but a smaller than the M3. pg half-step XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 13. This interval (m3) between the M2 and M3 is generally considered a decreased . In terms of distance it would consist of steps. £2 it. XXXXXXXXXXXXXXXXX XXXXXXXXX 1h. Play and sing these intervals and check those that are m3s. Si; is E;A bEEEEEEEEEE IA B C D E (keyboard and vocal response) A1 C, D, E Km. 00 0 .00 000000000 0 0.9 O CO. 00 0 0000 O 00.00 123 15. Above the notes on this staff, place another that will form the m3. Confirm your notation by singing and playing each interval. 4‘ 9*— 2: ; £_g¥£: (keyboard and vocal response) XXXXXXXXXXXX 16. The perfect fourth (Pb) is the interval illustrated by the first and fourth degrees of the major scale. In the key of C the 'c' to would comprise the two-and-a-half step sound. A M3 plus a _____¢step constitute the P#. Of! half .00... O. O O O .0. 0000000 0.090000 0.000 O O 00 0000000 17. Check any of the following intervals that are Phs. I Play and sing each. «a- A B C D E AI CI D (keyboard and vocal response) o 9990 00 o o 0 9900900 9 o o o 00 09090 oo .90 o co 124 18. Above the given notes place another that will construct a series of P4 intervals. Test each by playing and Lap—rt: singing. £2...- I! (keyboard and vocal response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 19. The P“ (2% steps) plus a whole-step yields the interval of a perfect fifth (P5). Arange of ‘ steps produces a P5. .An example would be the distance from '0' to '8'- 22 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 20. Play and sing the five intervals below, checking those that qualify as P58. A B C D E (keyboard and vocal response) A, B, D O... O. O O. O. 00 O O 0000 0.000 COO. 0000 0000.090 0 125 21. The tones on this staff are the lower ones of the P5 intervals you are to construct. Confirm each one by playing and singing the notes. 5 9— :2"— .:_____E! a, I, - 119' 1 1 .:.__._.£_1 fig 1. (keyboard and vocal response) 9 o 0900 o oo o o 990 o o o o oo oo o o 00 or coo 22. Four-and-a-half steps or one step greater than the P5 produces the major sixth (M6). This interval is realized from 'f' to 'd' or 'c' to . ......COOCOC0.0.00.00...OOCCOOOOOOOOOOIOOOOIOOOO0.0.00.0!... 'a' XXXX XXXXXXXXXXXXXXXXXXXXXXXX 23. Some of these intervals exhibit the sound of the M6. Analyze which ones are M6s and place an X below them. Play and sing all M6 intervals (4% steps). a . f v v iEEEEEf: ‘19- 19b Ap___ E___, C DL___ E___ C (keyboard and vocal response) XXXXX XXXX 126 24. Add a note above each of these tones that will constitute a M6 interval. Confirm your choice by playing and singing each interval. A t he 0 -e-" . a " e 0 6'9— (keyboard and vocal response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 25. One half-step short of an octave or five—and-a-half steps bring us to the major seventh (M7). The is a half-step less than the octave. The notes 'c' to 'b' or 'g' to illustrate the M7. IIICOOOOOOI....IIOOOIOOCICOOCIICOOIQUCCOO....ll...........'. 122 If I XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 26. Analyze the intervals on this staff and mark with an X the one or ones qualifying as the M7. Sing and play each. E 4. A 71: a e V :2 .Li _ c) 0 J9 '7 A B C D E A, B, E (keyboard and vocal response) XX3CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 127 27. Above each given note on this staff place another to construct a M? interval. Test each interval by play- ing and singing. EL 11:1 AF; 2:: " C? a A #9 4‘, v V A_ ‘e‘“ V a (keyboard and vocal response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 28. Six whole steps ('0' to 'c', 'f' to 'f', etc.) constitute the octave (8va) interval. The distance between the first and eighth degree of the major scale is the octave XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 29. Which of these intervals are octaves? Play and sing each one. L A 0 1L. 1’ " ‘1? £1 a I 5 0 ~0- A B c D E OoooclolIOIOO-oooonnocloonocOIIIIIOIOoCOIOOOOOO B, C, D, E (keyboard and vocal response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 128 30. These notes are the lower ones to the interval of an octave. Add the higher pitch and confirm your choice at the keyboard and vocally. 31 HF & 713—”: El: fer—1’“ (keyboard and vocal response) XXXXXXXXXXXXXXXXXXXXXXXXXXXX 31. Label the intervals on these staffs by letter (M, m, or P) and number (2, 3, 4, etc.). Confirm each by playing and singing. [3 HA A 3 O H B 3 ‘ v a .1 a 9— A. A__ B__ c__ D____ E__ F_____ G___ H-___ 35:27.1“? 1" 4.; M '__“—"" if“ ”£3 119‘ ‘2’ Diff 13. A B__ C___ D____ E___ F____ G____ E___ A. A322 13.1.4.2. 0.141 13.2.11 E422 B. F_M_6_ G__M2 HP8 All}. 3.1.41 6.14.; 0.25 E35. F_mz G_Iié H.242 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 129 32. After singing and playing this series, analyze and label the intervals between the notes. The first ones have been done to illustrate the technique. :47 i: {a a ”see ‘19'95' "“31‘3q319- A f a c [I £¥F l, 1112 E? 0 -e- CIO‘CIIIIOIIIOIICOOIOCCIICII.0...00".I'll-IUOCCOIIOIOIOCCI. (keyboard and vocal response) (P5): (1113). (M3): M7! m3! M21 PL": M21 M2 m3, M2, M6, m3, M2, P5, P4 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 130 33. From these letter/number symbols, write the staff notation for each interval directly above the given notes. Play and sing them to verify your choices. W v P8 M3 M6 m3 P4 M7 M2 P5 A ( i0 56 -e— 3 M3 M6 m3 P8 P5 M2 M7 P4 1d I) A . -9- M3 M6 m3 P8 P5 M2 M7 P4 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Name Section MUSIC 135 PROGRAMED MATERIAL--SERIES R MAJOR AND MINOR TRIAD CONSTRUCTION Instructions: (a) this programed study has been structured to progress systematically and will offer maximum benefit if followed sequentially (b) use a 4 X 6 card or something similar to cover the printed answer while you write- in your response (0) you may wish to refer to previous frames to reinforce your learning: some frames will direct you to earlier material for review and reference (d) if a frame appears vague or ambiguous to you, please write a few words stating the source of confusion and how it may be eliminated (e) it is important that you use a keyboard instrument as you study this material 131 132 1. In the musical sense of the term, a triad ia a sound unit of three tones. Our particular interest is with two types: the major triad and the minor triad. A major or minor triad has members with intervals of two thirds (M3 and m3) encompassed by a fifth (P5). three XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 2. Play these two triads: Do they have different sound qualities? (1) Analyze the intervals. In triad A: 'c' to 'e' is a (2) 3 'e' to 'g' is a (3) g 'c' to 'g' is a (4) __. In triad B: 'c' to 'ev' is a (5) ; 'eb' to 'g' is a (6) g 'c' to 'g' is a (2) . (keyboard reSponse) (1) 133(2) M3 (3) m3 (1.) P5 (5)1111 161142. (7115.. XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 133 .3. From earlier instruction you will recall the letter/ number system of labeling intervals. A capital M signifies a major interval, a lower case m stands for , and a capital P symbolizes a perfect interval. The numbers two (2) through eight (8) are used to identify the interval distance. The intervals studied are as follows: unison or prime P5 - 3% steps (repeated note) M6 - 4% steps M2 - 1 step M7 - 5% steps (% step m3 - 1% steps less than an octave) M3 - 2 steps P8 - 6 steps (octave) P4 - 2% steps minor XJCXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX “w Which interval remains constant for both triads in frame 2? the outer (P5) )CX3(XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX .5- From the root or generating tone of a triad, we can follow this scheme in constructing a major quality triad. major triad: n P5 (no written response required) X)Q(IiCXXX)CXXXX1CX)CJCXXXXXXXXDQCKXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXJOC 134 6. Analyze, label, play and sing the intervals of these triads. Is the quality major? A B 0 4D E r-L 7r -1 ;ME r II V 1 I ., ' .' . .' | .I : ‘__-2. :__" I ': ' ’I I [I ' I I 1 A. 22,25 B. Q3 25. C. 23 22 D. ml 22 E. Q3 11: m 1.12 M: 112 (keyboard and vocal response) ygg XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 7. You have observed that the notes of a triad are located on consecutive spaces or lines of the staff. This placement corresponds to using every other letter in the alphabetical system of labeling notes. In frame 6, triad B is spelled 'f'-'a'-'c'. Triad D is spelled 'bb'-'d'-'___', not 'a#-'d'-'f'. From the root note a triad is always spelled using alternate letters of the staff. If! XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 135 8. Through cognitive and aural analysis, determine which of these triads are major in quality. Circle those that are major. (keyboard and vocal response) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 9. Add a note above each of the two-note groups that will complete a major (M) triad. W 5' “3 J . ¥ 11C) ——8 I!" a XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 136 13. Place a third note above these two-note groups that will complete a minor triad (m3). 153— fi+——————8— $213 5: 4 18—“ a: mg: 00 o co 0 o o o o o o o o o o o o O)OGOOOOOO( 14. Only the roots of M and m triads are notated on the staffs below. Complete the triad construction. major triads : W 1 A. minor triads: .%%! 53 £9.— iEEZEi‘“'€*——‘—‘—' I: _. c7 major triads: minor triads: .0000 0 .00 00000000000000 137 10. From the generating tone of B triad in frame 2, we may deduce the construction scheme of a minor quality triad (m). -..- 1 # .1 minor triad: H J (no written response required) XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 11. Analyze, label, play, and sing the intervals of these triads. Are they major or minor? A B C D -- L I f I 5+ 1 1 1 1 1 ' 1 44' 1 . 1 ‘__. II—.| ' ...—... ' ‘__. | _— ' , ___. 1 ___.! : ...! 1 __.' : ___1 __I ___.. ._...l _J —1 A. M; B. M2 0. 24.3. D. £2 E. M3. P 22 22 22 .122 ..‘i 1112 22 £12 1112 1112 (keyboard and vocal response) minor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 12. Through aural and mental analysis, ascertain which of the following chords are minor in quality. Circle them. 51 5 0.0.0.00. .00.000....000030000000......OOOOOOOOOOOOOOO0.000 A A A. I ‘lo 4 T 0 {D 0 4' 000' 0 0’ 0 (D 0 CD 0 0 {D 0 '1 N — .11 O (“NH NNHJ 00 4D 0 Name Section MUSIC 135 PROGRAMED MATERIAL--SERIES B MAJOR AND MINOR TRIAD TERMINOLOGY Instructions: (a) this programed study has been structured to progress systematically and will offer maximum benefit if followed sequentially (b) use a 4 X 6 card or something similar to cover the printed answer while you write- in your response (0) you may wish to refer to previous frames to reinforce your learning; some frames will direct you to earlier material for reference and review (d) if a frame appears vague or ambiguous, please write a few words stating the source of confusion and how it may be eliminated (e) it is important that you use a keyboard instrument as you study 138 139 1. In musical context, a triad is a chord of three tones consisting of superimposed thirds (2) and an outside 1 range of a fifth. A triad has members with intervals of two (M3 and m3) and an outer compass of a fifth (P5). three thirds XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 2. From previous instruction you will remember the letter/ number system of labeling intervals. A capital M signifies a major interval, a lower case m stands for , and a capital P symbolizes a perfect interval. The numbers two (2) through eight (8) are used to identify the interval distance. The intervals studied are these: unison or prime P5 - 3% steps (repeated note) M6 - 4% steps M2 - 1 step , M7 - 5% steps (% step m3 - 1% steps less than an octave) M3 - 2 steps P8 - 6 steps (octave) P4 - 2% steps minor 0 0 0000 00 0 0 0 000 0 0 140 3. Analyze, label, play, and sing the intervals of the following triads. Circle the ones that are major in quality. A. (keyboard and vocal response) )00000000{ 0 o to o o o o o o o oo o o 4. You have no doubt noticed that the notes of a triad are located on consecutive spaces or lines of the staff. This placement on the staff corresponds to using every other letter in the alphabetical system of notation. In frame 3, triad A is Spelled 'g'-'b'—'d'. Triad C is spelled 'a'-'d#S-'___': not 'a'-'db'-'e'. From the root note a triad is always spelled using alternate letters of the staff. 0e. 0 0 0000 0 000000000 0 00 00000 0000 00000000 00000000 141 50 When two or more notes are played on a keyboard instrument they may be performed either separately (melodically) or simultaneously (harmonically) This é—Ta— is an example of triad members being played separately or : and this is an example of triad members being sounded simultaneously or melodically harmonically o o o o 000 o 00 o o o o o o o o o oxx 6. Play and sing these notes of the major triad: ~—" Are they notated melodically or harmonically? (keyboard and vocal response) melodically o o o o 00 oo o o o o oo o o 7. After having played and sung these triads, identify those that are major in quality by printing a capital M in the space provided. A. :1:— :.,_§;:aiF c.__: (keyboard and vocal response) A.M B. c.1413.M E.MF. XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 142 8. From the keyboard diagrams, transfer the M triads to melodic staff notation. (Remember that notes of a triad are located on consecutive lines or spaces of the staff.) A. Ln 1*: B. III H I" fi {1’ C. 22' A: D- -.-.l—_ 1 :1 a .1 ° E‘— a [v B. ig; E; —T .52 A- U 0 >either :1. _ _55 C. ..L e 19 E. D. 'J' 96 3+ 143 9. Play and sing the notes of this minor (m) triad. w (keyboard and vocal response) )O(9 0 o 0 909099000090 0 o oo 00 090909090 9 coo o 000 90 10. Play and sing the following triads. Identify those that are minor by placing a small m in the space provided. 1. 332F1UEWP¢ _ErzL $1; “+72: (keyboard and vocal response) A. E- B.-——-m._ COW... DOL E.“ FOL X00 0 0 0 000 0 0000 00 0 0 00 0 0 0 0000 00 144 11. From the keyboard diagrams, transfer these minor triads to harmonic staff notation. 1 A 3' . $— A! B. 3;! c. .5 - _ 5 III >¢ lll’ Ell _III III 3' ' either APPENDIX B SELF-CONSTRUCTED TESTS 145 Name Section Harmonic Element Survey Pretest (HESPRE) on I btest A--Sound Unit Comparison Instructions. You will hear three units of sounds. Some of these will have only two tones(interval) while others will have three(triads). Two of these three units may or may not sound alike. You are to decide which, if any, of the two units sound alike and place an X to the left of the statement that 4 corresponds with what you have heard. Each item will be heard twice: in one the tones are sounded separately and in the other, simultaneously. Two examples are recorded. Here is example A: EXAMPLE A ___a. units 1 and 2 sounded alike ___b. units 1 and 3 sounded alike 0. units 2 and 3 sounded alike d. none of the units sounded alike EXAMPLE B ___a. units 1 and 2 sounded alike b. units 1 and 3 sounded alike c. units 2 and 3 sounded alike d. none of the units sounded alike a. units 1 and 2 sounded alike b. units 1 and 3 sounded alike 0. units 2 and 3 sounded alike d. none of the units sounded alike 146 d. Item 4: Item 5: 81. units 1 units 1 units 2 none of units 1 units 1 units 2 none of units 1 units 1 units 2 none of units 1 units 1 units 2 none of and and and the and and and the and and and the and and and the 14? 2 sounded alike 3 sounded alike 3 sounded alike units sounded alike 2 sounded alike 3 sounded alike 3 sounded alike units sounded alike 2 sounded alike 3 sounded alike 3 sounded alike units sounded alike 2 sounded alike 3 sounded alike 3 sounded alike units sounded alike .Ih 1.. 148 Subtest B--Aural transfer to Keyboard Instructions. In this section, as in Subtest A, you will hear a two-or three-tone unit. You are to match the sound unit with one of the three keyboard diagrams, if any matches. Record your choice by placing an X to the left of the correct diagram. Each sound unit will be heard four times: once with the tones sounded separately, once simultaneously, and then a repeat of each. There are two practice examples. Here is Example A. EXAMPLE A __a- W UUU .UU UUU 1.1. [W .UUU UU UUU —°- UU UUU UU UUU d. none of the above __1. TUU UUU UU UUU _1. .UUU UU UU —°' UU UW UU UUU d. none of the above UU UUU UU UUU LLII :3 o 1 :3 (D 1 O H) IL L I. L UU U UU UUU. UU UUU ..UUU UU UUU 1 1.UUU UU UUU UUU 1 UUULUU UU UUU UU UUU W UUU L1 UUU none of UUU UU UUU L 10 L 1 UUU UU UUU 9; IO '13" U x ”U UU UUU UUU 23 gag—t: o —: "b E; UU UUU UU UU- UUU UUU UU x UUU L L LI 5 8 (DE «—= o l; H: x d :3 UUU UU 151 on II btest A-—Aural Transfer to Staff Notation Instructions. You will hear a two- or three—note sound unit. You are to select the musical staff notation which, if any, agrees with what you have heard. Register your choice by placing an X to the left of the letter representing the correct staff notation. Each item will be heard four times. At first hearing, the notes will be heard separately--the second, simultaneously. This will be repeated. There are two examples. Here is Example A. EXAMPLE A d. none of the above EXAMPLE B I W {m —*" 455ng d. none of the above tem 1: tem 3: 152 none of the above i} none of the above fl H In ‘r I L f *‘ 3 none of the above 153 :em a: d. none of the above d. none of the above 15h on III btest A—-Transfer of Keyboard to Staff Notation Instructions. Two or three pitches are identified by Xs on a keyboard diagram. Play these notes on your keyboard and choose the staff notation that corresponds with what you have played, if any matches. Mark an X in the blank by the answer of your choice. Here are two examples. EXAMPLE A a,% UUU H'W —b- @ ——°' E d. none of the above EXAMPLE B W yum —b- E d. none of the above 3m 1: ___a. % W W _b. % _c- Lébé d. none of the above 155 ;em 5: [1H 156 d. none of the above Name Section Harmonic Element Survey Posttest (HESPST) tion I Subtest A--Sound Unit Comparison Instructions. You will hear three units of sounds. Some of these will have only two tones (interval) while others will have three (triad). units may or may not sound alike. decide which, if any, Two of these You are to of the two units sound alike and place an x to the left of the statement that corresponds with what you have heard. will be heard twice; Each item in one the tones are sounded separately and in the other, simultaneously. Two examples are recorded. Here is example.A: EXAMPLE A r ___a. units 1 and 2 sounded alike _5_b. units 1 and 3 sounded alike ___c. units 2 and 3 sounded alike ___d. none of the units sounded alike EXAMPLE B ___a. units 1 and 2 sounded alike ___b. units 1 and 3 sounded alike ___c. units 2 and 3 sounded alike ___d. none of the units sounded alike Item 1: ___a. units 1 and 2 sounded alike ___b. units 1 and 3 sounded alike ___c. units 2 and 3 sounded alike d. none of the units sounded alike 15? Item 2: Item 3: 8. units 1 units 1 units 2 none of units 1 units 1 units 2 none of units 1 units 1 units 2 none of units 1 units 1 units 2 none of 158 and 2 sounded alike and 3 sounded alike and 3 sounded alike the units sounded alike and 2 sounded alike and 3 sounded alike and 3 sounded alike the units sounded alike and 2 sounded alike and 3 sounded alike and 3 sounded alike the units sounded alike and 2 sounded alike and 3 sounded alike and 3 sounded alike the units sounded alike 159 ubtest B--Aural to Keyboard Transfer Instructions. In this section, as in Subtest A, you will hear a two— or three—tone unit. You are to match the sound unit with one of the three keyboard diagrams, if any matches. Record your choice by placing an X to the left of the correct diagram. Each sound unit will be heard four times: once with the tones sounded separately and once simultaneously and then a repeat. There are two practice examples. Here is Example A. .UELW WU .W. W W --°° W .U UUU d. none of the above EXAMPLE A I; E E EXAMPLE B _— __.. w M w M -b- wxuw uw --°' 1,1 UUU ‘U W d. none of the above (III I III! UUU W. . UUXU UU none of the ab UU , WU W - _ UUU UU W . UUU W % UUU UU none of the abov W ‘ x xUU UUU UU UU I!!! * WIS UUUUU U WU w W 3 3 9., C i 9., L L, L! U UUU UUU UW UU UUU 162 ion II ubtest A--Transfer: Aural to Staff Notation Instructions. You will hear a two- or three-note sound unit. You are to select the musical staff notation which agrees with what you have heard. Register your choice by placing an X to the left (u‘the letter representing the correct answer. If’none agree with what you have heard, the correct answer will be "d” (none of the above). Each item will be heard four times. At first hearing the notes will be heard separately--the second, simultaneously. This will be repeated. There are two examples. Here is example A. EXAMPLE A a. E 95 6 ; ___b. y 3 X o. $ 115‘ d. none of the above EXAMPLE B 9 71;. r . g a. g 3}: l b. i i I. c 4F f d. none of the above Item 1: 163 none of the above . e ' ' er :1»— ; 5 1:? none of the above wU o . 22: E none of the above Item 1h 161+ ? om f a} none of the above __Ll J L OD is; none of the above 165 1btest B--Interva1 and Triad Construction Instructions. This section of the test is designed to measure your ability to notate intervals and triads on the G or F staff from a sound unit. The lowest note of the interval or triad will be given. When you hear the sound unit write in the remaining note(s) above the one given. Each item will be heard four times-- twice melodically and twice harmonically. Here is the first of two examples. EXAMPLE A (1 $er 3 EXAMPLE B 3L: J (3 Item 1: Item 2: Item 3: Item 4: cu m ’ i} Item 5: :IP \A WI?* 11:) Lon III 166 lbtest A--Transfer: Keyboard to Staff Notation Instructions. Two or three pitches are identified by Xs on a keyboard diagram. Play these notes on your keyboard and choose the staff notation that corresponds with what you have played. Mark an X in the blank by the answer of your choice. Here are two examples. EXAMPLE A UU ——b- E EXAMPLE B i“ E d. none of the above UUU d. none of the above 167 Item 1: W1“ W1 l'l'l'l d. none of the above Item 2: ___a. v I - ‘ mull“ Ill .10. _'__,,:_ L _ v - ___c. I __ —wSF—-——- G ___d. none of the above Item 3: 1'1'1'1 [W i d. none of the above Item #3 168 WU W Item 5: UUU none of the above - 9E ZZZIIZZZIIIZZIZI none of the above 169 Subtest B--Staff Notation from Letter/Number Symbols Instructions. In this phase of the test you are to notate a specified interval or triad given the letter/number symbol and the lowest pitch. Here are two examples. EXAMPLE A Complete a major triad "' above the given note EXAMPLE B Complete a M? above the given note Item 1: complete a M3 above the E given note _______________ Item 2: complete a m triad above E the given note ° __—9__.__._ Item 3: complete a P5 above the given note Item A: complete 3 Ph above the given note Item 5: complete a M2 above the given note ‘L_.A Name Section Harmonic Element Survey Retention Test (HESRTN) :ion I Subtest A--Interval and Triad Recognition Instructions. Decide which, if any, of the sound units are alike in interval or, in the case of triads, alike in quality. Each sound unit will be played twice. EXAMPLE ___a. units 1 and 2 sounded alike ___b. units 1 and 3 sounded alike ___c. units 2 and 3 sounded alike ___d. none of the units sounded alike Item 1: ___a. units 1 and 2 sounded alike ___b. units 1 and 3 sounded alike ___c. units 2 and 3 sounded alike ___d. none of the units sounded alike Item 2: ___a. units 1 and 2 sounded alike ___b. units 1 and 3 sounded alike ___c. units 2 and 3 sounded alike d. none of the units sounded alike 170 Item 3: a. b. Item 5: units 1 units 1 units 2 none of units 1 units 1 units 2 none of units 1 units 1 units 2 none of and and and the and and and the and and and the 171 2 sounded alike 3 sounded alike 3 sounded alike units sounded alike 2 sounded alike 3 sounded alike 3 sounded alike units sounded alike 2 sounded alike 3 sounded alike 3 sounded alike units sounded alike 172 Summst B--Sound to Keyboard Instructions. Match the sound unit heard to the corresponding keyboard diagram. Each sound unit will be heard three times. EXAMPLE _3. TW WU W UUU —b' , [INTI xlIJ All!“I UUU -—°' UU WMW d. none of the above _a. ULUW UU UUU —b- .U W UUU —°' TUUxWU UU UUU d. none of the above :UU WU .W- UUU I WU UU W —:' E .. UW UU UUU UUU W UUU .WU UU WU B .9! s) O' 9 M) § \ 1 g o 3 9: 9. c’. :3. d’ UUU UU UUU .. UUUUUUU b- IUEUW W W— °' LW WUUUUUU : U .UWJUU UUU UUU UU .UW 175 on II ubtest A--Matching: Sound to Notation Instructions. Match the sound you hear with the appropriate staff notation. Each sound will be heard three times. EXAMPLE A l! _a. $ A _IL —b- HE C. i d. none of the above Item 1: i _.. a i -—"' a J c. d. none of the above d. none of the above Item 3: Item A: a. b. 0. d. Item 5: Um none of the above 9 1f— «a: *K We! 1, 3? none of the above U UUU none mfi: above 1?? :ubtest B--Notation Instructions. The lowest note of an interval or triad is given. You are to notate the remaining note(s). Each item will be played three times. _5 EXAMPLE 3L Item 1: $}% 7 1 9 Item 2: 53% T 97;“ 4 Item 3: + 4 Item A: A} is e Item 5: T 178 Lon III :ubtest B--Notation Instructions. From the given letter/number symbol, complete the notation above the note on the staff. EXAMPLE Complete a major triad above the given note. Item 1: Complete a M3 above the given note. Item 2: Complete a minor triad above the given note. Item 3: Complete a P5 above the given note. Complete a m3 above the given note. Item 5: , Complete a major triad E above the given note. Name Section Harmonic Element Survey Delayed Retention Test Lon I Instructions. (HESDRT) ;ubtest A--Interva1 and Triad Recognition Decide which, if any, of the sound units are alike in interval or, in the case of triads, alike in quality. Each sound unit series will be played twice. EXAMPLE: ___a. units 1 and 2 sounded alike ___b. units 1 and 3 sounded alike ___c. units 2 and 3 sounded alike ___d. none of the units sounded alike Item 1: ___a. units 1 and 2 sounded alike ___b. units 1 and 3 sounded alike ___c. units 2 and 3 sounded alike ___d. none of the units sounded alike Item 2: ___a. units 1 and 2 sounded alike ___4b. units 1 and 3 sounded alike .___0. units 2 and 3 sounded alike c. none of the units sounded alike 179 Item 3: a. b. d. Item A: an Item 5: units 1 units 1 units 2 none of units 1 units 1 units 2 none of units 1 units 1 units 2 none of and and and the and and and the and and and the 2 sounded alike 3 sounded alike 3 sounded alike units sounded alike 2 sounded alike 3 sounded alike 3 sounded alike units sounded alike 2 sounded alike 3 sounded alike 3 sounded alike units sounded alike 181 &flmest B--Matching Sound to Keyboard Instructions. Match the sound unit heard to the corresponding keyboard diagram, if any matches. Each sound unit will be heard three times. EXAMPLE -—a- mu WUW uuu —‘°' UU UUULWUUUT —°' UWLW UUU d. none of the above _a- W UUU UU UUU —b- EULUUU UU W —°' UU UUU W .UUU d. none of the above .W .W UUU w UUU W WU UU UUU . UUU UU UUU UU UU UUU UUU O 0‘ 9 u o . :3 3 * a 3 o g f i g cf {3‘ CD UW W UUU W UUU UU- UUU ,. W *— . UW UU UUU W WU W .WU b. . none of UUU UU- Section II 18“ Subtest A--Matching Sound to Notation Instructions. Match the sound you hear with the appropriate staff notation. In the event that none match, place an.X in cption 'd'. Each sound will be heard three times. EXAMPLE (7 g a. b. i we ___ ;§¥ ‘7 ___.. $1: d. none of the above Item 1: a. b. i c. d. none of the above 185 Item 2: I!” w ¥ _L T i __b o $ 3 c. d. none of the above Item 3: ha I ' a a. 74 b. d. none of the above Item A: 186 \10 AL '0 LIL _L.¥ none of the above _L E‘s: none of the above 187 Subtest B--Notation ‘ Instructions. The lowest note of an interval or triad is given. You are to notate the remaining note(s). Each item will be played three times. Above the given note construct the interval or triad that you hear. EXAMPLE 3‘. 1 Item 1 I 8 I: Item 2 ' 1W Item 3: it’ _A. Wises Item b: :i: # e 1 Item 5: 188 Section III Subtest A--Keybcard to Staff Notation Transfer Instructions. Two or three pitches are identified by Xs on a keyboard diagram. Choose the staff notation that corresponds with what you have seen on the keyboard diagram. Mark an X in the blank by the answer of your choice. EXAMPLE UU WU -"' E -= a d. none of the above Item 1: W W UU ‘b' —c- a: d. none of the above 189 Item 2: '_- ___.—___a.— V . 1 W .___O J“ 4— ‘l7““' :1. none of the above Item 3: 1'1'1'1 [W l'l'l'l Item u: WW I”! l'l'l'J d. none of the above 190 v Item b. U. W UUU n O b a e h t f O 191 Subtest B--Notation Instructions. From the given letter/number symbol, complete the notation above the note on the staff. EXAMPLE Complete a major triad above the given note. Item 1: Complete a M3 above the given note. Item 2: Complete a minor triad above the given note. Item 3: Complete a P5 above the given note. Item A: Complete a m3 above . the given no... E Item 5: Complete a major triad , above the given note. ”TIWITILHIWWflUIILITHTLEI'IWWU’“