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Scale 319: "Epodian"

Scale 319: Epodian, 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
Epodian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,4,5,8}
Forte Number7-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3985
Hemitonia5 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections4
Modes6
Prime?yes
Deep Scaleno
Interval Vector544431
Interval Spectrump3m4n4s4d5t
Distribution Spectra<1> = {1,3,4}
<2> = {2,4,5,7}
<3> = {3,5,6,8}
<4> = {4,6,7,9}
<5> = {5,7,8,10}
<6> = {8,9,11}
Spectra Variation3.714
Maximally Evenno
Maximal Area Setno
Interior Area2.183
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}331.33
G♯{8,0,3}142
Minor Triadsc♯m{1,4,8}221.33
fm{5,8,0}221.33
Augmented TriadsC+{0,4,8}331.33
Diminished Triads{2,5,8}142
Parsimonious Voice Leading Between Common Triads of Scale 319. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m fm fm C+->fm G# G# C+->G# C# C# c#m->C# C#->d° C#->fm

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♯m, fm
Peripheral Verticesd°, G♯

Modes

Modes are the rotational transformation of this scale. Scale 319 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2207
Scale 2207: Mygian, Ian Ring Music TheoryMygian
3rd mode:
Scale 3151
Scale 3151: Pacrian, Ian Ring Music TheoryPacrian
4th mode:
Scale 3623
Scale 3623: Aerocrian, Ian Ring Music TheoryAerocrian
5th mode:
Scale 3859
Scale 3859: Aeolarian, Ian Ring Music TheoryAeolarian
6th mode:
Scale 3977
Scale 3977: Kythian, Ian Ring Music TheoryKythian
7th mode:
Scale 1009
Scale 1009: Katyptian, Ian Ring Music TheoryKatyptian

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [319, 2207, 3151, 3623, 3859, 3977, 1009] (Forte: 7-3) is the complement of the pentatonic modal family [55, 1795, 2075, 2945, 3085] (Forte: 5-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 319 is 3985

Scale 3985Scale 3985: Thadian, Ian Ring Music TheoryThadian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 319 is chiral, and its enantiomorph is scale 3985

Scale 3985Scale 3985: Thadian, Ian Ring Music TheoryThadian

Transformations:

T0 319  T0I 3985
T1 638  T1I 3875
T2 1276  T2I 3655
T3 2552  T3I 3215
T4 1009  T4I 2335
T5 2018  T5I 575
T6 4036  T6I 1150
T7 3977  T7I 2300
T8 3859  T8I 505
T9 3623  T9I 1010
T10 3151  T10I 2020
T11 2207  T11I 4040

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 317Scale 317: Korimic, Ian Ring Music TheoryKorimic
Scale 315Scale 315: Stodimic, Ian Ring Music TheoryStodimic
Scale 311Scale 311: Stagimic, Ian Ring Music TheoryStagimic
Scale 303Scale 303: Golimic, Ian Ring Music TheoryGolimic
Scale 287Scale 287: Gynimic, Ian Ring Music TheoryGynimic
Scale 351Scale 351: Epanian, Ian Ring Music TheoryEpanian
Scale 383Scale 383: Logyllic, Ian Ring Music TheoryLogyllic
Scale 447Scale 447: Thyphyllic, Ian Ring Music TheoryThyphyllic
Scale 63Scale 63, Ian Ring Music Theory
Scale 191Scale 191, Ian Ring Music Theory
Scale 575Scale 575: Ionydian, Ian Ring Music TheoryIonydian
Scale 831Scale 831: Rodyllic, Ian Ring Music TheoryRodyllic
Scale 1343Scale 1343: Zalyllic, Ian Ring Music TheoryZalyllic
Scale 2367Scale 2367: Laryllic, Ian Ring Music TheoryLaryllic

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.