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Scale 637: "Debussy's Heptatonic"

Scale 637: Debussy's Heptatonic, Ian Ring Music Theory

Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

41161837294116105072918310504116183
Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

Common Names

Named After Composers
Debussy's Heptatonic
Zeitler
Katodian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,3,4,5,6,9}
Forte Number7-10
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1993
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes6
Prime?no
prime: 607
Deep Scaleno
Interval Vector445332
Interval Spectrump3m3n5s4d4t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5,6}
<3> = {3,4,5,6,7,8}
<4> = {4,5,6,7,8,9}
<5> = {6,7,8,9,10}
<6> = {9,10,11}
Spectra Variation3.143
Maximally Evenno
Maximal Area Setno
Interior Area2.433
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsD{2,6,9}331.63
F{5,9,0}331.63
Minor Triadsdm{2,5,9}231.75
am{9,0,4}231.75
Diminished Triads{0,3,6}231.88
d♯°{3,6,9}231.75
f♯°{6,9,0}231.75
{9,0,3}231.88
Parsimonious Voice Leading Between Common Triads of Scale 637. Created by Ian Ring ©2019 d#° d#° c°->d#° c°->a° dm dm D D dm->D F F dm->F D->d#° f#° f#° D->f#° F->f#° am am F->am a°->am

view full size

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 637 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1183
Scale 1183: Sadian, Ian Ring Music TheorySadian
3rd mode:
Scale 2639
Scale 2639: Dothian, Ian Ring Music TheoryDothian
4th mode:
Scale 3367
Scale 3367: Moptian, Ian Ring Music TheoryMoptian
5th mode:
Scale 3731
Scale 3731: Aeryrian, Ian Ring Music TheoryAeryrian
6th mode:
Scale 3913
Scale 3913: Bonian, Ian Ring Music TheoryBonian
7th mode:
Scale 1001
Scale 1001: Badian, Ian Ring Music TheoryBadian

Prime

The prime form of this scale is Scale 607

Scale 607Scale 607: Kadian, Ian Ring Music TheoryKadian

Complement

The heptatonic modal family [637, 1183, 2639, 3367, 3731, 3913, 1001] (Forte: 7-10) is the complement of the pentatonic modal family [91, 1547, 1729, 2093, 2821] (Forte: 5-10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 637 is 1993

Scale 1993Scale 1993: Katoptian, Ian Ring Music TheoryKatoptian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 637 is chiral, and its enantiomorph is scale 1993

Scale 1993Scale 1993: Katoptian, Ian Ring Music TheoryKatoptian

Transformations:

T0 637  T0I 1993
T1 1274  T1I 3986
T2 2548  T2I 3877
T3 1001  T3I 3659
T4 2002  T4I 3223
T5 4004  T5I 2351
T6 3913  T6I 607
T7 3731  T7I 1214
T8 3367  T8I 2428
T9 2639  T9I 761
T10 1183  T10I 1522
T11 2366  T11I 3044

Nearby Scales:

These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.

Scale 639Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllic
Scale 633Scale 633: Kydimic, Ian Ring Music TheoryKydimic
Scale 635Scale 635: Epolian, Ian Ring Music TheoryEpolian
Scale 629Scale 629: Aeronimic, Ian Ring Music TheoryAeronimic
Scale 621Scale 621: Pyramid Hexatonic, Ian Ring Music TheoryPyramid Hexatonic
Scale 605Scale 605: Dycrimic, Ian Ring Music TheoryDycrimic
Scale 573Scale 573: Saptimic, Ian Ring Music TheorySaptimic
Scale 701Scale 701: Mixonyphian, Ian Ring Music TheoryMixonyphian
Scale 765Scale 765, Ian Ring Music Theory
Scale 893Scale 893: Dadyllic, Ian Ring Music TheoryDadyllic
Scale 125Scale 125, Ian Ring Music Theory
Scale 381Scale 381: Kogian, Ian Ring Music TheoryKogian
Scale 1149Scale 1149: Bydian, Ian Ring Music TheoryBydian
Scale 1661Scale 1661: Gonyllic, Ian Ring Music TheoryGonyllic
Scale 2685Scale 2685: Ionoryllic, Ian Ring Music TheoryIonoryllic

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.