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Scale 3321: "Epagyllic"

Scale 3321: Epagyllic, 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
Epagyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,3,4,5,6,7,10,11}
Forte Number8-8
Rotational Symmetrynone
Reflection Axes5
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections2
Modes7
Prime?no
prime: 927
Deep Scaleno
Interval Vector644563
Interval Spectrump6m5n4s4d6t3
Distribution Spectra<1> = {1,3}
<2> = {2,4}
<3> = {3,5}
<4> = {4,6,8}
<5> = {7,9}
<6> = {8,10}
<7> = {9,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.5
Myhill Propertyno
Balancedno
Ridge Tones[10]
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3321 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 927
Scale 927: Gaptyllic, Ian Ring Music TheoryGaptyllicThis is the prime mode
3rd mode:
Scale 2511
Scale 2511: Aeroptyllic, Ian Ring Music TheoryAeroptyllic
4th mode:
Scale 3303
Scale 3303: Mylyllic, Ian Ring Music TheoryMylyllic
5th mode:
Scale 3699
Scale 3699: Galyllic, Ian Ring Music TheoryGalyllic
6th mode:
Scale 3897
Scale 3897: Kalyllic, Ian Ring Music TheoryKalyllic
7th mode:
Scale 999
Scale 999: Ionodyllic, Ian Ring Music TheoryIonodyllic
8th mode:
Scale 2547
Scale 2547: Raga Ramkali, Ian Ring Music TheoryRaga Ramkali

Prime

The prime form of this scale is Scale 927

Scale 927Scale 927: Gaptyllic, Ian Ring Music TheoryGaptyllic

Complement

The octatonic modal family [3321, 927, 2511, 3303, 3699, 3897, 999, 2547] (Forte: 8-8) is the complement of the tetratonic modal family [99, 387, 2097, 2241] (Forte: 4-8)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3321 is 999

Scale 999Scale 999: Ionodyllic, Ian Ring Music TheoryIonodyllic

Transformations:

T0 3321  T0I 999
T1 2547  T1I 1998
T2 999  T2I 3996
T3 1998  T3I 3897
T4 3996  T4I 3699
T5 3897  T5I 3303
T6 3699  T6I 2511
T7 3303  T7I 927
T8 2511  T8I 1854
T9 927  T9I 3708
T10 1854  T10I 3321
T11 3708  T11I 2547

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 3323Scale 3323: Lacrygic, Ian Ring Music TheoryLacrygic
Scale 3325Scale 3325: Mixolygic, Ian Ring Music TheoryMixolygic
Scale 3313Scale 3313: Aeolacrian, Ian Ring Music TheoryAeolacrian
Scale 3317Scale 3317: Katynyllic, Ian Ring Music TheoryKatynyllic
Scale 3305Scale 3305: Chromatic Hypophrygian, Ian Ring Music TheoryChromatic Hypophrygian
Scale 3289Scale 3289: Lydian Sharp 2 Sharp 6, Ian Ring Music TheoryLydian Sharp 2 Sharp 6
Scale 3257Scale 3257: Mela Calanata, Ian Ring Music TheoryMela Calanata
Scale 3193Scale 3193: Zathian, Ian Ring Music TheoryZathian
Scale 3449Scale 3449: Bacryllic, Ian Ring Music TheoryBacryllic
Scale 3577Scale 3577: Loptygic, Ian Ring Music TheoryLoptygic
Scale 3833Scale 3833: Dycrygic, Ian Ring Music TheoryDycrygic
Scale 2297Scale 2297: Thylian, Ian Ring Music TheoryThylian
Scale 2809Scale 2809: Gythyllic, Ian Ring Music TheoryGythyllic
Scale 1273Scale 1273: Ronian, Ian Ring Music TheoryRonian

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.