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Scale 631: "Zygian"

Scale 631: Zygian, 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

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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

Zeitler
Zygian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,5,6,9}
Forte Number7-Z17
Rotational Symmetrynone
Reflection Axes3
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?yes
Deep Scaleno
Interval Vector434541
Interval Spectrump4m5n4s3d4t
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,6}
<3> = {4,5,7}
<4> = {5,7,8}
<5> = {6,8,9,10}
<6> = {9,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.433
Myhill Propertyno
Balancedno
Ridge Tones[6]
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}242
F{5,9,0}331.5
A{9,1,4}231.75
Minor Triadsdm{2,5,9}231.75
f♯m{6,9,1}331.5
am{9,0,4}242
Augmented TriadsC♯+{1,5,9}421.25
Diminished Triadsf♯°{6,9,0}231.75
Parsimonious Voice Leading Between Common Triads of Scale 631. Created by Ian Ring ©2019 C#+ C#+ dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m A A C#+->A D D dm->D D->f#m f#° f#° F->f#° am am F->am f#°->f#m am->A

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.

Diameter4
Radius2
Self-Centeredno
Central VerticesC♯+
Peripheral VerticesD, am

Modes

Modes are the rotational transformation of this scale. Scale 631 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2363
Scale 2363: Kataptian, Ian Ring Music TheoryKataptian
3rd mode:
Scale 3229
Scale 3229: Aeolaptian, Ian Ring Music TheoryAeolaptian
4th mode:
Scale 1831
Scale 1831: Pothian, Ian Ring Music TheoryPothian
5th mode:
Scale 2963
Scale 2963: Bygian, Ian Ring Music TheoryBygian
6th mode:
Scale 3529
Scale 3529: Stalian, Ian Ring Music TheoryStalian
7th mode:
Scale 953
Scale 953: Mela Yagapriya, Ian Ring Music TheoryMela Yagapriya

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [631, 2363, 3229, 1831, 2963, 3529, 953] (Forte: 7-Z17) is the complement of the pentatonic modal family [283, 433, 1571, 2189, 2833] (Forte: 5-Z17)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 631 is 3529

Scale 3529Scale 3529: Stalian, Ian Ring Music TheoryStalian

Transformations:

T0 631  T0I 3529
T1 1262  T1I 2963
T2 2524  T2I 1831
T3 953  T3I 3662
T4 1906  T4I 3229
T5 3812  T5I 2363
T6 3529  T6I 631
T7 2963  T7I 1262
T8 1831  T8I 2524
T9 3662  T9I 953
T10 3229  T10I 1906
T11 2363  T11I 3812

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 629Scale 629: Aeronimic, Ian Ring Music TheoryAeronimic
Scale 627Scale 627: Mogimic, Ian Ring Music TheoryMogimic
Scale 635Scale 635: Epolian, Ian Ring Music TheoryEpolian
Scale 639Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllic
Scale 615Scale 615: Phrothimic, Ian Ring Music TheoryPhrothimic
Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian
Scale 599Scale 599: Thyrimic, Ian Ring Music TheoryThyrimic
Scale 567Scale 567: Aeoladimic, Ian Ring Music TheoryAeoladimic
Scale 695Scale 695: Sarian, Ian Ring Music TheorySarian
Scale 759Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllic
Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic
Scale 119Scale 119, Ian Ring Music Theory
Scale 375Scale 375: Sodian, Ian Ring Music TheorySodian
Scale 1143Scale 1143: Styrian, Ian Ring Music TheoryStyrian
Scale 1655Scale 1655: Katygyllic, Ian Ring Music TheoryKatygyllic
Scale 2679Scale 2679: Rathyllic, Ian Ring Music TheoryRathyllic

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.