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Scale 581: "Eporic"

Scale 581: Eporic, 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
Eporic

Analysis

Cardinality4 (tetratonic)
Pitch Class Set{0,2,6,9}
Forte Number4-27
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1097
Hemitonia0 (anhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes3
Prime?no
prime: 293
Deep Scaleno
Interval Vector012111
Interval Spectrumpmn2st
Distribution Spectra<1> = {2,3,4}
<2> = {5,6,7}
<3> = {8,9,10}
Spectra Variation1.5
Maximally Evenno
Maximal Area Setno
Interior Area1.866
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyStrictly Proper
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 TriadsD{2,6,9}110.5
Diminished Triadsf♯°{6,9,0}110.5
Parsimonious Voice Leading Between Common Triads of Scale 581. Created by Ian Ring ©2019 D D f#° f#° D->f#°

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 581 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 1169
Scale 1169: Raga Mahathi, Ian Ring Music TheoryRaga Mahathi
3rd mode:
Scale 329
Scale 329: Mynic, Ian Ring Music TheoryMynic
4th mode:
Scale 553
Scale 553: Rothic, Ian Ring Music TheoryRothic

Prime

The prime form of this scale is Scale 293

Scale 293Scale 293: Raga Haripriya, Ian Ring Music TheoryRaga Haripriya

Complement

The tetratonic modal family [581, 1169, 329, 553] (Forte: 4-27) is the complement of the octatonic modal family [1463, 1757, 1771, 1883, 2779, 2933, 2989, 3437] (Forte: 8-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 581 is 1097

Scale 1097Scale 1097: Aeraphic, Ian Ring Music TheoryAeraphic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 581 is chiral, and its enantiomorph is scale 1097

Scale 1097Scale 1097: Aeraphic, Ian Ring Music TheoryAeraphic

Transformations:

T0 581  T0I 1097
T1 1162  T1I 2194
T2 2324  T2I 293
T3 553  T3I 586
T4 1106  T4I 1172
T5 2212  T5I 2344
T6 329  T6I 593
T7 658  T7I 1186
T8 1316  T8I 2372
T9 2632  T9I 649
T10 1169  T10I 1298
T11 2338  T11I 2596

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 583Scale 583: Aeritonic, Ian Ring Music TheoryAeritonic
Scale 577Scale 577, Ian Ring Music Theory
Scale 579Scale 579, Ian Ring Music Theory
Scale 585Scale 585: Diminished Seventh, Ian Ring Music TheoryDiminished Seventh
Scale 589Scale 589: Ionalitonic, Ian Ring Music TheoryIonalitonic
Scale 597Scale 597: Kung, Ian Ring Music TheoryKung
Scale 613Scale 613: Phralitonic, Ian Ring Music TheoryPhralitonic
Scale 517Scale 517, Ian Ring Music Theory
Scale 549Scale 549: Raga Bhavani, Ian Ring Music TheoryRaga Bhavani
Scale 645Scale 645, Ian Ring Music Theory
Scale 709Scale 709: Raga Shri Kalyan, Ian Ring Music TheoryRaga Shri Kalyan
Scale 837Scale 837: Epaditonic, Ian Ring Music TheoryEpaditonic
Scale 69Scale 69, Ian Ring Music Theory
Scale 325Scale 325: Messiaen Truncated Mode 6, Ian Ring Music TheoryMessiaen Truncated Mode 6
Scale 1093Scale 1093: Lydic, Ian Ring Music TheoryLydic
Scale 1605Scale 1605: Zanitonic, Ian Ring Music TheoryZanitonic
Scale 2629Scale 2629: Raga Shubravarni, Ian Ring Music TheoryRaga Shubravarni

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.