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Scale 3785: "Epagian"

Scale 3785: Epagian, 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
Epagian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,3,6,7,9,10,11}
Forte Number7-16
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 623
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 623
Deep Scaleno
Interval Vector435432
Interval Spectrump3m4n5s3d4t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,6}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {6,8,9,10}
<6> = {9,10,11}
Spectra Variation2.857
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Modes

Modes are the rotational transformation of this scale. Scale 3785 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 985
Scale 985: Mela Sucaritra, Ian Ring Music TheoryMela Sucaritra
3rd mode:
Scale 635
Scale 635: Epolian, Ian Ring Music TheoryEpolian
4th mode:
Scale 2365
Scale 2365: Sythian, Ian Ring Music TheorySythian
5th mode:
Scale 1615
Scale 1615: Sydian, Ian Ring Music TheorySydian
6th mode:
Scale 2855
Scale 2855: Epocrain, Ian Ring Music TheoryEpocrain
7th mode:
Scale 3475
Scale 3475: Kylian, Ian Ring Music TheoryKylian

Prime

The prime form of this scale is Scale 623

Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian

Complement

The heptatonic modal family [3785, 985, 635, 2365, 1615, 2855, 3475] (Forte: 7-16) is the complement of the pentatonic modal family [155, 865, 1555, 2125, 2825] (Forte: 5-16)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3785 is 623

Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3785 is chiral, and its enantiomorph is scale 623

Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian

Transformations:

T0 3785  T0I 623
T1 3475  T1I 1246
T2 2855  T2I 2492
T3 1615  T3I 889
T4 3230  T4I 1778
T5 2365  T5I 3556
T6 635  T6I 3017
T7 1270  T7I 1939
T8 2540  T8I 3878
T9 985  T9I 3661
T10 1970  T10I 3227
T11 3940  T11I 2359

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 3787Scale 3787: Kagyllic, Ian Ring Music TheoryKagyllic
Scale 3789Scale 3789: Eporyllic, Ian Ring Music TheoryEporyllic
Scale 3777Scale 3777, Ian Ring Music Theory
Scale 3781Scale 3781: Gyphian, Ian Ring Music TheoryGyphian
Scale 3793Scale 3793: Aeopian, Ian Ring Music TheoryAeopian
Scale 3801Scale 3801: Maptyllic, Ian Ring Music TheoryMaptyllic
Scale 3817Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic
Scale 3721Scale 3721: Phragimic, Ian Ring Music TheoryPhragimic
Scale 3753Scale 3753: Phraptian, Ian Ring Music TheoryPhraptian
Scale 3657Scale 3657: Epynimic, Ian Ring Music TheoryEpynimic
Scale 3913Scale 3913: Bonian, Ian Ring Music TheoryBonian
Scale 4041Scale 4041: Zaryllic, Ian Ring Music TheoryZaryllic
Scale 3273Scale 3273: Raga Jivantini, Ian Ring Music TheoryRaga Jivantini
Scale 3529Scale 3529: Stalian, Ian Ring Music TheoryStalian
Scale 2761Scale 2761: Dagimic, Ian Ring Music TheoryDagimic
Scale 1737Scale 1737: Raga Madhukauns, Ian Ring Music TheoryRaga Madhukauns

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, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.