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usually octave shifted to place them all within the same octave, which has no effect on interval relations and the consonance of the triads. The possibility of an octave being a solution is not outside of Wilson's conception and is used in cases of placing larger combination product sets upon
Generalized Keyboards.
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To make this into a conventional harmonic construct with 1/1 as the first note, all the notes are first reduced to the octave. Since the harmonic construct as Erv called it as he did not consider it a scale and it does not have a 1/1 yet, any note chosen can be used to divide every note up to octave
247:
Simply, the hexany is the 2 out of 4 set. It is constructed by taking any four factors and a set of two at a time, then multiplying them in pairs. For instance, the harmonic factors 1, 3, 5 and 7 are combined in pairs of 1*3, 1*5, 1*7, 3*5, 3*7, 5*7, resulting in 1, 3, 5, 7 Hexanies. The notes are
259:
an interval and each face a triad. It thus has eight just intonation triads where each triad has two notes in common with three of the other chords. Each triad occurs just once with its inversion represented by the opposing 3 tones. The edges of the octahedron show musical intervals between the
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vertices, usually chosen to be consonant intervals from the harmonic series. The points represent musical notes, and the three notes that make each of the triangular faces represent musical triads. Wilson also pointed out and explored the idea of melodic
Hexanies.
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It is referred to as an uncentered structure, meaning that it implies no tonic. It achieves this by using consonant relations as opposed to the dissonance methods normally employed by atonality. While it is often and confusingly overlapped with the
244:. In this construction, the hexany is the third cross-section of the four-factor set and the first uncentered one. hexany is the name that Erv Wilson gave to the six notes in the 2-out-of-4 combination product set, abbreviated as 2*4 CPS.
324:
184:
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236:, the subsequent stellation of Wilson's combination product sets (CPS) are outside of that Genus. The Euler Fokker Genus fails to see 1 as a possible member of a set except as a starting point. The numbers of
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reduction. The ratios' notation here shows the ratios of the frequencies of the notes. If the 1/1 is 500 hertz, then 6/5 is 600 hertz, and so forth.
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In this 2D construction the interval relationships are the same. See also figure two of Kraig Grady's paper.
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610:. Original hexany papers showing different facets and configurations, not assembled by Erv Wilson (1967 on)
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The hexany is the figure containing both the triangles shown as well as the connecting lines between them.
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629:. With a hexany you can turn around and click on any of its vertices, edges, or faces to hear the chords.
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380:(minor type) chord since it can be written as 3Ă—5Ă—7Ă—(1/3, 1/5, 1/7), using low-numbered
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Proceedings of the 7th
International Conference on Music Perception and Cognition, Sydney, 2002
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372:(major type) chord since it can be written as 5Ă—(1, 3, 7), using low numbered
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669:. Dave Keenan's Dekany tumbling in 4 dimensions — as a musical Excel spreadsheet
560:"Tempered Dekanies: Chorus effect using microtonal intervals based on just intonation"
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Divisions of the
Tetrachord: a Prolegomenon to the Construction of Musical Scales
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255:. The notes are arranged so that each point represents a pitch, each
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For example, the face with vertices 3Ă—5, 1Ă—5, 5Ă—7 is an
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This shows the three dimensional version of the hexany.
602:"Some hexany and hexany Diamond Lattices (and Blanks)"
60:. Unsourced material may be challenged and removed.
502:Microtonality and the tuning systems of Erv Wilson
251:The hexany can be thought of as analogous to the
1186:
408:have used pitch structures based on hexanies.
240:of his combination sets follow the numbers in
688:
763:List of intervals in 5-limit just intonation
695:
681:
533:: CS1 maint: location missing publisher (
498:
120:Learn how and when to remove this message
553:, vol. 7, no. 1, pp. 8–11
131:
14:
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469:
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58:adding citations to reliable sources
29:
702:
376:. The 5Ă—7, 3Ă—7, 3Ă—5 is a
24:
633:"Combination-Product Set Patterns"
574:
492:
304:
203:Problems playing these files? See
142:
25:
1221:
595:
838:Ptolemy's intense diatonic scale
577:"D'Alessandro, Like a Hurricane"
348:
339:Problems playing this file? See
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280:
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34:
45:needs additional citations for
463:
450:
429:
13:
1:
659:. Intro. to musical geometry.
423:
801:Harry Partch's 43-tone scale
665:, "Unusual musical scales",
571:(see the Background section)
7:
411:
391:
27:Class of musical pitch sets
10:
1226:
1195:Multi-dimensional geometry
768:List of meantone intervals
499:Narushima, Terumi (2018).
439:, p.116. Frog Peak Music.
435:Chalmers, John H. (1993).
1200:Just tuning and intervals
1135:
1052:
1015:
968:
875:
866:
781:
758:List of musical intervals
753:Consonance and dissonance
710:
657:Music and Virtual Flowers
263:
458:Musicworks, Issues 55–60
274:Orthographic projection.
18:Combination-product sets
667:Dave Keenan's Home Page
544:"Ervin Wilson's Hexany"
472:"Ervin Wilson's Hexany"
639:(1986) by Kraig Grady.
460:, p.43. Music Gallery.
309:
214:musical tuning systems
195:hexany scale without 7
147:
137:
1025:Temperament ordinaire
663:"The Tumbling Dekany"
614:"The Wilson Archives"
542:Grady, Kraig (1991),
470:Grady, Kraig (1991).
308:
146:
135:
828:List of compositions
396:Composers including
331:9-limit dekany scale
169:7-limit hexany scale
54:improve this article
607:The Wilson Archives
1062:Chinese musicology
848:Scale of harmonics
843:Pythagorean tuning
791:Euler–Fokker genus
653:"Musical Geometry"
627:RobertInventor.com
569:, pp. 300–302
418:Euler–Fokker genus
310:
234:Euler–Fokker genus
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138:
136:Regular octahedron
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643:"Eikosany Papers"
512:978-1-315-71858-3
445:978-0-945996-04-0
402:Daniel James Wolf
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242:Pascal's triangle
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16:(Redirected from
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1205:Hexatonic scales
1021:Well temperament
1007:Regular diatonic
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551:Just Intonation
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647:Anaphoria.com
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584:Xenharmonikon
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575:Wilson, Erv.
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71: –
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65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
1173:Lambda scale
1080:Arabic maqam
1037:Werckmeister
868:Temperaments
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382:subharmonics
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211:
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116:
107:
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83:
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64:
52:Please help
47:verification
44:
1168:Delta scale
1163:Gamma scale
1153:Alpha scale
1055:non-Western
1053:Traditional
748:Pitch class
728:Millioctave
711:Measurement
398:Kraig Grady
110:August 2018
1210:Hexachords
1189:Categories
1158:Beta scale
1136:Non-octave
1127:Tetrachord
1029:Kirnberger
992:Schismatic
521:1019658301
505:. London.
485:(1): 8–11.
424:References
341:media help
253:octahedron
222:Erv Wilson
205:media help
80:newspapers
1148:A12 scale
1102:Octoechos
1067:ShĂ-èr-lÇś
1016:Irregular
833:Otonality
773:Microtone
590:: 10, 21.
529:cite book
374:harmonics
1033:Vallotti
986:septimal
978:Meantone
738:Interval
623:"hexany"
456:(1993).
412:See also
392:In music
238:vertices
69:"Hexany"
1122:Slendro
1072:Dastgah
997:Miracle
960:96-tone
955:72-tone
950:58-tone
945:53-tone
940:41-tone
935:34-tone
930:31-tone
920:24-tone
915:23-tone
910:22-tone
905:19-tone
900:17-tone
895:15-tone
890:12-tone
821:7-limit
816:5-limit
94:scholar
1090:Mugham
1076:Maqam
970:Linear
924:pieces
885:6-tone
806:Hexany
733:Savart
519:
509:
443:
404:, and
378:utonal
370:otonal
264:Tuning
218:hexany
216:, the
96:
89:
82:
75:
67:
1107:Pelog
1095:Muqam
1041:Young
1002:Magic
877:Equal
811:Limit
718:Pitch
580:(PDF)
563:(PDF)
547:(PDF)
475:(PDF)
193:limit
101:JSTOR
87:books
1112:Raga
723:Cent
535:link
517:OCLC
507:ISBN
441:ISBN
257:edge
226:sets
73:news
212:In
56:by
1191::
1039:,
1035:,
1031:,
984:,
655:,
645:,
635:,
625:,
616:,
604:,
588:12
586:.
582:.
565:,
549:,
531:}}
527:{{
515:.
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477:.
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228:.
191:9-
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696:e
689:t
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483:7
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117:(
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108:(
98:·
91:·
84:·
77:·
50:.
20:)
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