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Scale 2793: "Eporian"

Scale 2793: Eporian, 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
Eporian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,3,5,6,7,9,11}
Forte Number7-28
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 747
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes6
Prime?no
prime: 747
Deep Scaleno
Interval Vector344433
Interval Spectrump3m4n4s4d3t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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{5,9,0}231.88
B{11,3,6}331.63
Minor Triadscm{0,3,7}331.63
Augmented TriadsD♯+{3,7,11}231.75
Diminished Triads{0,3,6}231.75
d♯°{3,6,9}231.75
f♯°{6,9,0}231.88
{9,0,3}231.75
Parsimonious Voice Leading Between Common Triads of Scale 2793. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ cm->a° d#° d#° f#° f#° d#°->f#° d#°->B D#+->B F F F->f#° F->a°

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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2793 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 861
Scale 861: Rylian, Ian Ring Music TheoryRylian
3rd mode:
Scale 1239
Scale 1239: Epaptian, Ian Ring Music TheoryEpaptian
4th mode:
Scale 2667
Scale 2667: Byrian, Ian Ring Music TheoryByrian
5th mode:
Scale 3381
Scale 3381: Katanian, Ian Ring Music TheoryKatanian
6th mode:
Scale 1869
Scale 1869: Katyrian, Ian Ring Music TheoryKatyrian
7th mode:
Scale 1491
Scale 1491: Mela Namanarayani, Ian Ring Music TheoryMela Namanarayani

Prime

The prime form of this scale is Scale 747

Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian

Complement

The heptatonic modal family [2793, 861, 1239, 2667, 3381, 1869, 1491] (Forte: 7-28) is the complement of the pentatonic modal family [333, 837, 1107, 1233, 2601] (Forte: 5-28)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2793 is 747

Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2793 is chiral, and its enantiomorph is scale 747

Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian

Transformations:

T0 2793  T0I 747
T1 1491  T1I 1494
T2 2982  T2I 2988
T3 1869  T3I 1881
T4 3738  T4I 3762
T5 3381  T5I 3429
T6 2667  T6I 2763
T7 1239  T7I 1431
T8 2478  T8I 2862
T9 861  T9I 1629
T10 1722  T10I 3258
T11 3444  T11I 2421

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 2795Scale 2795: Van der Horst Octatonic, Ian Ring Music TheoryVan der Horst Octatonic
Scale 2797Scale 2797: Stalyllic, Ian Ring Music TheoryStalyllic
Scale 2785Scale 2785, Ian Ring Music Theory
Scale 2789Scale 2789: Zolian, Ian Ring Music TheoryZolian
Scale 2801Scale 2801: Zogian, Ian Ring Music TheoryZogian
Scale 2809Scale 2809: Gythyllic, Ian Ring Music TheoryGythyllic
Scale 2761Scale 2761: Dagimic, Ian Ring Music TheoryDagimic
Scale 2777Scale 2777: Aeolian Harmonic, Ian Ring Music TheoryAeolian Harmonic
Scale 2729Scale 2729: Aeragimic, Ian Ring Music TheoryAeragimic
Scale 2665Scale 2665: Aeradimic, Ian Ring Music TheoryAeradimic
Scale 2921Scale 2921: Pogian, Ian Ring Music TheoryPogian
Scale 3049Scale 3049: Phrydyllic, Ian Ring Music TheoryPhrydyllic
Scale 2281Scale 2281: Rathimic, Ian Ring Music TheoryRathimic
Scale 2537Scale 2537: Laptian, Ian Ring Music TheoryLaptian
Scale 3305Scale 3305: Chromatic Hypophrygian, Ian Ring Music TheoryChromatic Hypophrygian
Scale 3817Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic
Scale 745Scale 745: Kolimic, Ian Ring Music TheoryKolimic
Scale 1769Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic II

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.