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Scale 2431: "Gythygic"

Scale 2431: Gythygic, 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

Zeitler
Gythygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,4,5,6,8,11}
Forte Number9-2
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 4051
Hemitonia7 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 767
Deep Scaleno
Interval Vector777663
Interval Spectrump6m6n7s7d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {6,7,8,9}
<7> = {7,8,9,10}
<8> = {9,10,11}
Spectra Variation2.444
Maximally Evenno
Maximal Area Setno
Interior Area2.683
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 TriadsC♯{1,5,8}342.43
E{4,8,11}342.14
G♯{8,0,3}342.14
B{11,3,6}342.29
Minor Triadsc♯m{1,4,8}242.43
fm{5,8,0}342.29
g♯m{8,11,3}442.07
bm{11,2,6}342.43
Augmented TriadsC+{0,4,8}442.07
Diminished Triads{0,3,6}242.5
{2,5,8}242.57
{5,8,11}242.5
g♯°{8,11,2}242.43
{11,2,5}242.57
Parsimonious Voice Leading Between Common Triads of Scale 2431. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm C+->G# C# C# c#m->C# C#->d° C#->fm d°->b° E->f° g#m g#m E->g#m f°->fm g#° g#° g#°->g#m bm bm g#°->bm g#m->G# g#m->B b°->bm bm->B

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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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2431 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3263
Scale 3263: Pyrygic, Ian Ring Music TheoryPyrygic
3rd mode:
Scale 3679
Scale 3679: Rycrygic, Ian Ring Music TheoryRycrygic
4th mode:
Scale 3887
Scale 3887: Phrathygic, Ian Ring Music TheoryPhrathygic
5th mode:
Scale 3991
Scale 3991: Badygic, Ian Ring Music TheoryBadygic
6th mode:
Scale 4043
Scale 4043: Phrocrygic, Ian Ring Music TheoryPhrocrygic
7th mode:
Scale 4069
Scale 4069: Starygic, Ian Ring Music TheoryStarygic
8th mode:
Scale 2041
Scale 2041: Aeolacrygic, Ian Ring Music TheoryAeolacrygic
9th mode:
Scale 767
Scale 767: Raptygic, Ian Ring Music TheoryRaptygicThis is the prime mode

Prime

The prime form of this scale is Scale 767

Scale 767Scale 767: Raptygic, Ian Ring Music TheoryRaptygic

Complement

The nonatonic modal family [2431, 3263, 3679, 3887, 3991, 4043, 4069, 2041, 767] (Forte: 9-2) is the complement of the tritonic modal family [11, 1537, 2053] (Forte: 3-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2431 is 4051

Scale 4051Scale 4051: Ionilygic, Ian Ring Music TheoryIonilygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2431 is chiral, and its enantiomorph is scale 4051

Scale 4051Scale 4051: Ionilygic, Ian Ring Music TheoryIonilygic

Transformations:

T0 2431  T0I 4051
T1 767  T1I 4007
T2 1534  T2I 3919
T3 3068  T3I 3743
T4 2041  T4I 3391
T5 4082  T5I 2687
T6 4069  T6I 1279
T7 4043  T7I 2558
T8 3991  T8I 1021
T9 3887  T9I 2042
T10 3679  T10I 4084
T11 3263  T11I 4073

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 2429Scale 2429: Kadyllic, Ian Ring Music TheoryKadyllic
Scale 2427Scale 2427: Katoryllic, Ian Ring Music TheoryKatoryllic
Scale 2423Scale 2423, Ian Ring Music Theory
Scale 2415Scale 2415: Lothyllic, Ian Ring Music TheoryLothyllic
Scale 2399Scale 2399: Zanyllic, Ian Ring Music TheoryZanyllic
Scale 2367Scale 2367: Laryllic, Ian Ring Music TheoryLaryllic
Scale 2495Scale 2495: Aeolocrygic, Ian Ring Music TheoryAeolocrygic
Scale 2559Scale 2559: Zogyllian, Ian Ring Music TheoryZogyllian
Scale 2175Scale 2175, Ian Ring Music Theory
Scale 2303Scale 2303: Stanygic, Ian Ring Music TheoryStanygic
Scale 2687Scale 2687: Thacrygic, Ian Ring Music TheoryThacrygic
Scale 2943Scale 2943: Dathyllian, Ian Ring Music TheoryDathyllian
Scale 3455Scale 3455: Ryptyllian, Ian Ring Music TheoryRyptyllian
Scale 383Scale 383: Logyllic, Ian Ring Music TheoryLogyllic
Scale 1407Scale 1407: Tharygic, Ian Ring Music TheoryTharygic

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.