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Scale 1661: "Gonyllic"

Scale 1661: Gonyllic, 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
Gonyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,4,5,6,9,10}
Forte Number8-Z15
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1997
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

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 TriadsD{2,6,9}441.82
F{5,9,0}342
A♯{10,2,5}242.18
Minor Triadsdm{2,5,9}341.91
d♯m{3,6,10}342
am{9,0,4}242.27
Augmented TriadsD+{2,6,10}341.91
Diminished Triads{0,3,6}242.27
d♯°{3,6,9}242.09
f♯°{6,9,0}242.09
{9,0,3}242.36
Parsimonious Voice Leading Between Common Triads of Scale 1661. Created by Ian Ring ©2019 d#m d#m c°->d#m c°->a° dm dm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° D+->d#m D+->A# d#°->d#m F->f#° am am F->am a°->am

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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1661 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1439
Scale 1439: Rolyllic, Ian Ring Music TheoryRolyllic
3rd mode:
Scale 2767
Scale 2767: Katydyllic, Ian Ring Music TheoryKatydyllic
4th mode:
Scale 3431
Scale 3431: Zyptyllic, Ian Ring Music TheoryZyptyllic
5th mode:
Scale 3763
Scale 3763: Modyllic, Ian Ring Music TheoryModyllic
6th mode:
Scale 3929
Scale 3929: Aeolothyllic, Ian Ring Music TheoryAeolothyllic
7th mode:
Scale 1003
Scale 1003: Ionyryllic, Ian Ring Music TheoryIonyryllic
8th mode:
Scale 2549
Scale 2549: Rydyllic, Ian Ring Music TheoryRydyllic

Prime

The prime form of this scale is Scale 863

Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic

Complement

The octatonic modal family [1661, 1439, 2767, 3431, 3763, 3929, 1003, 2549] (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 1661 is 1997

Scale 1997Scale 1997: Raga Cintamani, Ian Ring Music TheoryRaga Cintamani

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1661 is chiral, and its enantiomorph is scale 1997

Scale 1997Scale 1997: Raga Cintamani, Ian Ring Music TheoryRaga Cintamani

Transformations:

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

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 1663Scale 1663: Lydygic, Ian Ring Music TheoryLydygic
Scale 1657Scale 1657: Ionothian, Ian Ring Music TheoryIonothian
Scale 1659Scale 1659: Maqam Shadd'araban, Ian Ring Music TheoryMaqam Shadd'araban
Scale 1653Scale 1653: Minor Romani Inverse, Ian Ring Music TheoryMinor Romani Inverse
Scale 1645Scale 1645: Dorian Flat 5, Ian Ring Music TheoryDorian Flat 5
Scale 1629Scale 1629: Synian, Ian Ring Music TheorySynian
Scale 1597Scale 1597: Aeolodian, Ian Ring Music TheoryAeolodian
Scale 1725Scale 1725: Minor Bebop, Ian Ring Music TheoryMinor Bebop
Scale 1789Scale 1789: Blues Enneatonic II, Ian Ring Music TheoryBlues Enneatonic II
Scale 1917Scale 1917: Sacrygic, Ian Ring Music TheorySacrygic
Scale 1149Scale 1149: Bydian, Ian Ring Music TheoryBydian
Scale 1405Scale 1405: Goryllic, Ian Ring Music TheoryGoryllic
Scale 637Scale 637: Debussy's Heptatonic, Ian Ring Music TheoryDebussy's Heptatonic
Scale 2685Scale 2685: Ionoryllic, Ian Ring Music TheoryIonoryllic
Scale 3709Scale 3709: Katynygic, Ian Ring Music TheoryKatynygic

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.