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Scale 3699: "Galyllic"

Scale 3699: Galyllic, 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
Galyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,4,5,6,9,10,11}
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

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 TriadsF{5,9,0}331.67
F♯{6,10,1}242
A{9,1,4}331.67
Minor Triadsf♯m{6,9,1}331.67
am{9,0,4}242
a♯m{10,1,5}331.67
Augmented TriadsC♯+{1,5,9}421.33
Diminished Triadsf♯°{6,9,0}242
a♯°{10,1,4}242
Parsimonious Voice Leading Between Common Triads of Scale 3699. Created by Ian Ring ©2019 C#+ C#+ F F C#+->F f#m f#m C#+->f#m A A C#+->A a#m a#m C#+->a#m f#° f#° F->f#° am am F->am f#°->f#m F# F# f#m->F# F#->a#m am->A a#° a#° A->a#° a#°->a#m

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
Radius2
Self-Centeredno
Central VerticesC♯+
Peripheral Verticesf♯°, F♯, am, a♯°

Modes

Modes are the rotational transformation of this scale. Scale 3699 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3897
Scale 3897: Kalyllic, Ian Ring Music TheoryKalyllic
3rd mode:
Scale 999
Scale 999: Ionodyllic, Ian Ring Music TheoryIonodyllic
4th mode:
Scale 2547
Scale 2547: Raga Ramkali, Ian Ring Music TheoryRaga Ramkali
5th mode:
Scale 3321
Scale 3321: Epagyllic, Ian Ring Music TheoryEpagyllic
6th mode:
Scale 927
Scale 927: Gaptyllic, Ian Ring Music TheoryGaptyllicThis is the prime mode
7th mode:
Scale 2511
Scale 2511: Aeroptyllic, Ian Ring Music TheoryAeroptyllic
8th mode:
Scale 3303
Scale 3303: Mylyllic, Ian Ring Music TheoryMylyllic

Prime

The prime form of this scale is Scale 927

Scale 927Scale 927: Gaptyllic, Ian Ring Music TheoryGaptyllic

Complement

The octatonic modal family [3699, 3897, 999, 2547, 3321, 927, 2511, 3303] (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 3699 is 2511

Scale 2511Scale 2511: Aeroptyllic, Ian Ring Music TheoryAeroptyllic

Transformations:

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

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 3697Scale 3697: Ionarian, Ian Ring Music TheoryIonarian
Scale 3701Scale 3701: Bagyllic, Ian Ring Music TheoryBagyllic
Scale 3703Scale 3703: Katalygic, Ian Ring Music TheoryKatalygic
Scale 3707Scale 3707: Rynygic, Ian Ring Music TheoryRynygic
Scale 3683Scale 3683: Dycrian, Ian Ring Music TheoryDycrian
Scale 3691Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic
Scale 3667Scale 3667: Kaptian, Ian Ring Music TheoryKaptian
Scale 3635Scale 3635: Katygian, Ian Ring Music TheoryKatygian
Scale 3763Scale 3763: Modyllic, Ian Ring Music TheoryModyllic
Scale 3827Scale 3827: Bodygic, Ian Ring Music TheoryBodygic
Scale 3955Scale 3955: Pothygic, Ian Ring Music TheoryPothygic
Scale 3187Scale 3187: Koptian, Ian Ring Music TheoryKoptian
Scale 3443Scale 3443: Verdi's Scala Enigmatica, Ian Ring Music TheoryVerdi's Scala Enigmatica
Scale 2675Scale 2675: Chromatic Lydian, Ian Ring Music TheoryChromatic Lydian
Scale 1651Scale 1651: Asian, Ian Ring Music TheoryAsian

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.