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Scale 3691: "Badyllic"

Scale 3691: Badyllic, 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
Badyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,5,6,9,10,11}
Forte Number8-Z15
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2767
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 863
Deep Scaleno
Interval Vector555553
Interval Spectrump5m5n5s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3691 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3893
Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic
3rd mode:
Scale 1997
Scale 1997: Raga Cintamani, Ian Ring Music TheoryRaga Cintamani
4th mode:
Scale 1523
Scale 1523: Zothyllic, Ian Ring Music TheoryZothyllic
5th mode:
Scale 2809
Scale 2809: Gythyllic, Ian Ring Music TheoryGythyllic
6th mode:
Scale 863
Scale 863: Pyryllic, Ian Ring Music TheoryPyryllicThis is the prime mode
7th mode:
Scale 2479
Scale 2479: Harmonic and Neapolitan Minor Mixed, Ian Ring Music TheoryHarmonic and Neapolitan Minor Mixed
8th mode:
Scale 3287
Scale 3287: Phrathyllic, Ian Ring Music TheoryPhrathyllic

Prime

The prime form of this scale is Scale 863

Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic

Complement

The octatonic modal family [3691, 3893, 1997, 1523, 2809, 863, 2479, 3287] (Forte: 8-Z15) is the complement of the tetratonic modal family [83, 773, 1217, 2089] (Forte: 4-Z15)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3691 is 2767

Scale 2767Scale 2767: Katydyllic, Ian Ring Music TheoryKatydyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3691 is chiral, and its enantiomorph is scale 2767

Scale 2767Scale 2767: Katydyllic, Ian Ring Music TheoryKatydyllic

Transformations:

T0 3691  T0I 2767
T1 3287  T1I 1439
T2 2479  T2I 2878
T3 863  T3I 1661
T4 1726  T4I 3322
T5 3452  T5I 2549
T6 2809  T6I 1003
T7 1523  T7I 2006
T8 3046  T8I 4012
T9 1997  T9I 3929
T10 3994  T10I 3763
T11 3893  T11I 3431

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 3689Scale 3689: Katocrian, Ian Ring Music TheoryKatocrian
Scale 3693Scale 3693: Stadyllic, Ian Ring Music TheoryStadyllic
Scale 3695Scale 3695: Kodygic, Ian Ring Music TheoryKodygic
Scale 3683Scale 3683: Dycrian, Ian Ring Music TheoryDycrian
Scale 3687Scale 3687: Zonyllic, Ian Ring Music TheoryZonyllic
Scale 3699Scale 3699: Galyllic, Ian Ring Music TheoryGalyllic
Scale 3707Scale 3707: Rynygic, Ian Ring Music TheoryRynygic
Scale 3659Scale 3659: Polian, Ian Ring Music TheoryPolian
Scale 3675Scale 3675: Monyllic, Ian Ring Music TheoryMonyllic
Scale 3627Scale 3627: Kalian, Ian Ring Music TheoryKalian
Scale 3755Scale 3755: Phryryllic, Ian Ring Music TheoryPhryryllic
Scale 3819Scale 3819: Aeolanygic, Ian Ring Music TheoryAeolanygic
Scale 3947Scale 3947: Ryptygic, Ian Ring Music TheoryRyptygic
Scale 3179Scale 3179: Daptian, Ian Ring Music TheoryDaptian
Scale 3435Scale 3435: Prokofiev, Ian Ring Music TheoryProkofiev
Scale 2667Scale 2667: Byrian, Ian Ring Music TheoryByrian
Scale 1643Scale 1643: Locrian Natural 6, Ian Ring Music TheoryLocrian Natural 6

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.