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Scale 3031: "Epithygic"

Scale 3031: Epithygic, 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
Epithygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,4,6,7,8,9,11}
Forte Number9-9
Rotational Symmetrynone
Reflection Axes4
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections1
Modes8
Prime?no
prime: 1519
Deep Scaleno
Interval Vector676683
Interval Spectrump8m6n6s7d6t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {5,6}
<5> = {6,7}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {10,11}
Spectra Variation1.333
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedno
Ridge Tones[8]
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{0,4,7}342.21
D{2,6,9}242.57
E{4,8,11}342.21
G{7,11,2}342.43
A{9,1,4}342.29
Minor Triadsc♯m{1,4,8}342.21
em{4,7,11}342.29
f♯m{6,9,1}342.43
am{9,0,4}342.21
bm{11,2,6}242.57
Augmented TriadsC+{0,4,8}442
Diminished Triadsc♯°{1,4,7}242.57
f♯°{6,9,0}242.57
g♯°{8,11,2}242.57
Parsimonious Voice Leading Between Common Triads of Scale 3031. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E am am C+->am c#°->c#m A A c#m->A D D f#m f#m D->f#m bm bm D->bm em->E Parsimonious Voice Leading Between Common Triads of Scale 3031. Created by Ian Ring ©2019 G em->G g#° g#° E->g#° f#° f#° f#°->f#m f#°->am f#m->A G->g#° G->bm am->A

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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 3031 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3563
Scale 3563: Ionoptygic, Ian Ring Music TheoryIonoptygic
3rd mode:
Scale 3829
Scale 3829: Taishikicho, Ian Ring Music TheoryTaishikicho
4th mode:
Scale 1981
Scale 1981: Houseini, Ian Ring Music TheoryHouseini
5th mode:
Scale 1519
Scale 1519: Locrian/Aeolian Mixed, Ian Ring Music TheoryLocrian/Aeolian MixedThis is the prime mode
6th mode:
Scale 2807
Scale 2807: Zylygic, Ian Ring Music TheoryZylygic
7th mode:
Scale 3451
Scale 3451: Garygic, Ian Ring Music TheoryGarygic
8th mode:
Scale 3773
Scale 3773: Raga Malgunji, Ian Ring Music TheoryRaga Malgunji
9th mode:
Scale 1967
Scale 1967: Diatonic Dorian Mixed, Ian Ring Music TheoryDiatonic Dorian Mixed

Prime

The prime form of this scale is Scale 1519

Scale 1519Scale 1519: Locrian/Aeolian Mixed, Ian Ring Music TheoryLocrian/Aeolian Mixed

Complement

The nonatonic modal family [3031, 3563, 3829, 1981, 1519, 2807, 3451, 3773, 1967] (Forte: 9-9) is the complement of the tritonic modal family [133, 161, 1057] (Forte: 3-9)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3031 is 3451

Scale 3451Scale 3451: Garygic, Ian Ring Music TheoryGarygic

Transformations:

T0 3031  T0I 3451
T1 1967  T1I 2807
T2 3934  T2I 1519
T3 3773  T3I 3038
T4 3451  T4I 1981
T5 2807  T5I 3962
T6 1519  T6I 3829
T7 3038  T7I 3563
T8 1981  T8I 3031
T9 3962  T9I 1967
T10 3829  T10I 3934
T11 3563  T11I 3773

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 3029Scale 3029: Ionocryllic, Ian Ring Music TheoryIonocryllic
Scale 3027Scale 3027: Rythyllic, Ian Ring Music TheoryRythyllic
Scale 3035Scale 3035: Gocrygic, Ian Ring Music TheoryGocrygic
Scale 3039Scale 3039: Godyllian, Ian Ring Music TheoryGodyllian
Scale 3015Scale 3015: Laptyllic, Ian Ring Music TheoryLaptyllic
Scale 3023Scale 3023: Mothygic, Ian Ring Music TheoryMothygic
Scale 3047Scale 3047: Panygic, Ian Ring Music TheoryPanygic
Scale 3063Scale 3063: Solyllian, Ian Ring Music TheorySolyllian
Scale 2967Scale 2967: Madyllic, Ian Ring Music TheoryMadyllic
Scale 2999Scale 2999: Chromatic and Permuted Diatonic Dorian Mixed, Ian Ring Music TheoryChromatic and Permuted Diatonic Dorian Mixed
Scale 2903Scale 2903: Gothyllic, Ian Ring Music TheoryGothyllic
Scale 2775Scale 2775: Godyllic, Ian Ring Music TheoryGodyllic
Scale 2519Scale 2519: Dathyllic, Ian Ring Music TheoryDathyllic
Scale 3543Scale 3543: Aeolonygic, Ian Ring Music TheoryAeolonygic
Scale 4055Scale 4055: Dagyllian, Ian Ring Music TheoryDagyllian
Scale 983Scale 983: Thocryllic, Ian Ring Music TheoryThocryllic
Scale 2007Scale 2007: Stonygic, Ian Ring Music TheoryStonygic

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.