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Scale 431: "Epyrian"

Scale 431: Epyrian, 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
Epyrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,5,7,8}
Forte Number7-14
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3761
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes6
Prime?yes
Deep Scaleno
Interval Vector443352
Interval Spectrump5m3n3s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {7,8,9,10}
<6> = {8,10,11}
Spectra Variation2.857
Maximally Evenno
Maximal Area Setno
Interior Area2.299
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}231.4
G♯{8,0,3}231.4
Minor Triadscm{0,3,7}142
fm{5,8,0}221.2
Diminished Triads{2,5,8}142
Parsimonious Voice Leading Between Common Triads of Scale 431. Created by Ian Ring ©2019 cm cm G# G# cm->G# C# C# C#->d° fm fm C#->fm fm->G#

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 Verticesfm
Peripheral Verticescm, d°

Modes

Modes are the rotational transformation of this scale. Scale 431 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2263
Scale 2263: Lycrian, Ian Ring Music TheoryLycrian
3rd mode:
Scale 3179
Scale 3179: Daptian, Ian Ring Music TheoryDaptian
4th mode:
Scale 3637
Scale 3637: Raga Rageshri, Ian Ring Music TheoryRaga Rageshri
5th mode:
Scale 1933
Scale 1933: Mocrian, Ian Ring Music TheoryMocrian
6th mode:
Scale 1507
Scale 1507: Zynian, Ian Ring Music TheoryZynian
7th mode:
Scale 2801
Scale 2801: Zogian, Ian Ring Music TheoryZogian

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [431, 2263, 3179, 3637, 1933, 1507, 2801] (Forte: 7-14) is the complement of the pentatonic modal family [167, 901, 1249, 2131, 3113] (Forte: 5-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 431 is 3761

Scale 3761Scale 3761: Raga Madhuri, Ian Ring Music TheoryRaga Madhuri

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 431 is chiral, and its enantiomorph is scale 3761

Scale 3761Scale 3761: Raga Madhuri, Ian Ring Music TheoryRaga Madhuri

Transformations:

T0 431  T0I 3761
T1 862  T1I 3427
T2 1724  T2I 2759
T3 3448  T3I 1423
T4 2801  T4I 2846
T5 1507  T5I 1597
T6 3014  T6I 3194
T7 1933  T7I 2293
T8 3866  T8I 491
T9 3637  T9I 982
T10 3179  T10I 1964
T11 2263  T11I 3928

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 429Scale 429: Koptimic, Ian Ring Music TheoryKoptimic
Scale 427Scale 427: Raga Suddha Simantini, Ian Ring Music TheoryRaga Suddha Simantini
Scale 423Scale 423: Sogimic, Ian Ring Music TheorySogimic
Scale 439Scale 439: Bythian, Ian Ring Music TheoryBythian
Scale 447Scale 447: Thyphyllic, Ian Ring Music TheoryThyphyllic
Scale 399Scale 399: Zynimic, Ian Ring Music TheoryZynimic
Scale 415Scale 415: Aeoladian, Ian Ring Music TheoryAeoladian
Scale 463Scale 463: Zythian, Ian Ring Music TheoryZythian
Scale 495Scale 495: Bocryllic, Ian Ring Music TheoryBocryllic
Scale 303Scale 303: Golimic, Ian Ring Music TheoryGolimic
Scale 367Scale 367: Aerodian, Ian Ring Music TheoryAerodian
Scale 175Scale 175, Ian Ring Music Theory
Scale 687Scale 687: Aeolythian, Ian Ring Music TheoryAeolythian
Scale 943Scale 943: Aerygyllic, Ian Ring Music TheoryAerygyllic
Scale 1455Scale 1455: Phrygiolian, Ian Ring Music TheoryPhrygiolian
Scale 2479Scale 2479: Harmonic and Neapolitan Minor Mixed, Ian Ring Music TheoryHarmonic and Neapolitan Minor Mixed

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.