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Scale 1147: "Epynian"

Scale 1147: Epynian, 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
Epynian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,4,5,6,10}
Forte Number7-Z36
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3013
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 367
Deep Scaleno
Interval Vector444342
Interval Spectrump4m3n4s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation3.143
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 TriadsF♯{6,10,1}221.2
Minor Triadsd♯m{3,6,10}231.4
a♯m{10,1,5}231.4
Diminished Triads{0,3,6}142
a♯°{10,1,4}142
Parsimonious Voice Leading Between Common Triads of Scale 1147. Created by Ian Ring ©2019 d#m d#m c°->d#m F# F# d#m->F# a#m a#m F#->a#m a#° a#° a#°->a#m

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 VerticesF♯
Peripheral Verticesc°, a♯°

Modes

Modes are the rotational transformation of this scale. Scale 1147 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2621
Scale 2621: Ionogian, Ian Ring Music TheoryIonogian
3rd mode:
Scale 1679
Scale 1679: Kydian, Ian Ring Music TheoryKydian
4th mode:
Scale 2887
Scale 2887: Gaptian, Ian Ring Music TheoryGaptian
5th mode:
Scale 3491
Scale 3491: Tharian, Ian Ring Music TheoryTharian
6th mode:
Scale 3793
Scale 3793: Aeopian, Ian Ring Music TheoryAeopian
7th mode:
Scale 493
Scale 493: Rygian, Ian Ring Music TheoryRygian

Prime

The prime form of this scale is Scale 367

Scale 367Scale 367: Aerodian, Ian Ring Music TheoryAerodian

Complement

The heptatonic modal family [1147, 2621, 1679, 2887, 3491, 3793, 493] (Forte: 7-Z36) is the complement of the pentatonic modal family [151, 737, 1801, 2123, 3109] (Forte: 5-Z36)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1147 is 3013

Scale 3013Scale 3013: Thynian, Ian Ring Music TheoryThynian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1147 is chiral, and its enantiomorph is scale 3013

Scale 3013Scale 3013: Thynian, Ian Ring Music TheoryThynian

Transformations:

T0 1147  T0I 3013
T1 2294  T1I 1931
T2 493  T2I 3862
T3 986  T3I 3629
T4 1972  T4I 3163
T5 3944  T5I 2231
T6 3793  T6I 367
T7 3491  T7I 734
T8 2887  T8I 1468
T9 1679  T9I 2936
T10 3358  T10I 1777
T11 2621  T11I 3554

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 1145Scale 1145: Zygimic, Ian Ring Music TheoryZygimic
Scale 1149Scale 1149: Bydian, Ian Ring Music TheoryBydian
Scale 1151Scale 1151: Mythyllic, Ian Ring Music TheoryMythyllic
Scale 1139Scale 1139: Aerygimic, Ian Ring Music TheoryAerygimic
Scale 1143Scale 1143: Styrian, Ian Ring Music TheoryStyrian
Scale 1131Scale 1131: Honchoshi Plagal Form, Ian Ring Music TheoryHonchoshi Plagal Form
Scale 1115Scale 1115: Superlocrian Hexamirror, Ian Ring Music TheorySuperlocrian Hexamirror
Scale 1083Scale 1083, Ian Ring Music Theory
Scale 1211Scale 1211: Zadian, Ian Ring Music TheoryZadian
Scale 1275Scale 1275: Stagyllic, Ian Ring Music TheoryStagyllic
Scale 1403Scale 1403: Espla's Scale, Ian Ring Music TheoryEspla's Scale
Scale 1659Scale 1659: Maqam Shadd'araban, Ian Ring Music TheoryMaqam Shadd'araban
Scale 123Scale 123, Ian Ring Music Theory
Scale 635Scale 635: Epolian, Ian Ring Music TheoryEpolian
Scale 2171Scale 2171, Ian Ring Music Theory
Scale 3195Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic

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.