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Scale 3687: "Zonyllic"

Scale 3687: Zonyllic, 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
Zonyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,5,6,9,10,11}
Forte Number8-7
Rotational Symmetrynone
Reflection Axes5.5
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 831
Deep Scaleno
Interval Vector645652
Interval Spectrump5m6n5s4d6t2
Distribution Spectra<1> = {1,3}
<2> = {2,4}
<3> = {3,5,7}
<4> = {4,6,8}
<5> = {5,7,9}
<6> = {8,10}
<7> = {9,11}
Spectra Variation2.5
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tones[11]
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3687 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3891
Scale 3891: Ryryllic, Ian Ring Music TheoryRyryllic
3rd mode:
Scale 3993
Scale 3993: Ioniptyllic, Ian Ring Music TheoryIoniptyllic
4th mode:
Scale 1011
Scale 1011: Kycryllic, Ian Ring Music TheoryKycryllic
5th mode:
Scale 2553
Scale 2553: Aeolaptyllic, Ian Ring Music TheoryAeolaptyllic
6th mode:
Scale 831
Scale 831: Rodyllic, Ian Ring Music TheoryRodyllicThis is the prime mode
7th mode:
Scale 2463
Scale 2463: Ionathyllic, Ian Ring Music TheoryIonathyllic
8th mode:
Scale 3279
Scale 3279: Pythyllic, Ian Ring Music TheoryPythyllic

Prime

The prime form of this scale is Scale 831

Scale 831Scale 831: Rodyllic, Ian Ring Music TheoryRodyllic

Complement

The octatonic modal family [3687, 3891, 3993, 1011, 2553, 831, 2463, 3279] (Forte: 8-7) is the complement of the tetratonic modal family [51, 771, 2073, 2433] (Forte: 4-7)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3687 is 3279

Scale 3279Scale 3279: Pythyllic, Ian Ring Music TheoryPythyllic

Transformations:

T0 3687  T0I 3279
T1 3279  T1I 2463
T2 2463  T2I 831
T3 831  T3I 1662
T4 1662  T4I 3324
T5 3324  T5I 2553
T6 2553  T6I 1011
T7 1011  T7I 2022
T8 2022  T8I 4044
T9 4044  T9I 3993
T10 3993  T10I 3891
T11 3891  T11I 3687

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 3685Scale 3685: Kodian, Ian Ring Music TheoryKodian
Scale 3683Scale 3683: Dycrian, Ian Ring Music TheoryDycrian
Scale 3691Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic
Scale 3695Scale 3695: Kodygic, Ian Ring Music TheoryKodygic
Scale 3703Scale 3703: Katalygic, Ian Ring Music TheoryKatalygic
Scale 3655Scale 3655: Mathian, Ian Ring Music TheoryMathian
Scale 3671Scale 3671: Aeonyllic, Ian Ring Music TheoryAeonyllic
Scale 3623Scale 3623: Aerocrian, Ian Ring Music TheoryAerocrian
Scale 3751Scale 3751: Aerathyllic, Ian Ring Music TheoryAerathyllic
Scale 3815Scale 3815: Galygic, Ian Ring Music TheoryGalygic
Scale 3943Scale 3943: Zynygic, Ian Ring Music TheoryZynygic
Scale 3175Scale 3175: Eponian, Ian Ring Music TheoryEponian
Scale 3431Scale 3431: Zyptyllic, Ian Ring Music TheoryZyptyllic
Scale 2663Scale 2663: Lalian, Ian Ring Music TheoryLalian
Scale 1639Scale 1639: Aeolothian, Ian Ring Music TheoryAeolothian

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.