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178:. In other words, each generic interval can be made from one of two possible different specific intervals. For example, there are major or minor and perfect or augmented/diminished variants of all the diatonic intervals:
39:. For example, for every generic interval of a second there are only two possible specific intervals: 1 semitone (a minor second) or 2 semitones (a major second).
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is one less than the number of "chromatic" pitches. In twelve tone equal temperament the largest specific interval is 11. (Johnson 2003, p. 26)
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or collections with exactly two specific intervals for every generic interval, and thus also have the properties of
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possess Myhill's property. The concept appears to have been first described by John Clough and
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Foundations of
Diatonic Theory: A Mathematically Based Approach to Music Fundamentals
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Clough, Engebretsen, and
Kochavi. "Scales, Sets, and Interval Cycles": 78–84.
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the generic interval is one less than the corresponding diatonic interval:
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is one less than the number of scale members. (Johnson 2003, p. 26)
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The largest generic interval in the diatonic scale being 7 − 1 = 6.
303:and named after their associate the mathematician
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307:. (Johnson 2003, p. 106, 158)
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78:is the clockwise distance between
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176:well formed generated collection
90:), in other words the number of
537:Structure implies multiplicity
521:Generic and specific intervals
172:structure implies multiplicity
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1:
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500:Cardinality equals variety
320:. Key College Publishing.
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168:cardinality equals variety
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316:Johnson, Timothy (2003).
384:All-interval tetrachord
98:. The largest specific
51:is the number of scale
389:All-trichord hexachord
297:pentatonic collections
67:. The largest generic
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18:Myhill's property
507:(Deep scale property)
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532:Rothenberg propriety
516:Generated collection
439:Pitch-interval class
113:Adjacent intervals,
558:Diatonic set theory
523:(Myhill's property)
456:Similarity relation
107:diatonic collection
45:diatonic set theory
373:Musical set theory
162:is the quality of
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563:Intervals (music)
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160:Myhill's property
155:Myhill's property
76:specific interval
16:(Redirected from
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527:Maximal evenness
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84:chromatic circle
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505:Common tone
429:Pitch class
424:Permutation
305:John Myhill
33:major scale
552:Categories
487:set theory
466:Z-relation
394:Complement
285:10 and 11
282:m7 and M7
268:m6 and M6
254:d5 and P5
240:P4 and A4
226:m3 and M3
212:m2 and M2
201:intervals
196:intervals
92:half steps
61:collection
191:interval
186:interval
495:Bisector
485:Diatonic
404:Identity
293:diatonic
271:8 and 9
257:6 and 7
243:5 and 6
229:3 and 4
215:1 and 2
199:Specific
194:Diatonic
184:Diatonic
145:Sevenths
100:interval
94:between
69:interval
55:between
311:Sources
189:Generic
127:Fourths
117:, are 1
115:seconds
105:In the
82:on the
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139:Sixths
133:Fifths
121:Thirds
96:notes
65:scale
59:of a
57:notes
53:steps
449:List
322:ISBN
295:and
291:The
276:7th
262:6th
248:5th
234:4th
220:3rd
206:2nd
31:The
444:Set
147:= 6
141:= 5
135:= 4
129:= 3
123:= 2
63:or
43:In
35:is
554::
279:6
265:5
251:4
237:3
223:2
209:1
170:,
74:A
47:a
365:e
358:t
351:v
328:.
86:(
20:)
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