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Scale 2875: "Ganyllic"

Scale 2875: Ganyllic, 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
Ganyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,4,5,8,9,11}
Forte Number8-19
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2971
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 887
Deep Scaleno
Interval Vector545752
Interval Spectrump5m7n5s4d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {5,6,7}
<5> = {6,7,8}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation1.75
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 TriadsC♯{1,5,8}342.15
E{4,8,11}342.08
F{5,9,0}342
G♯{8,0,3}342.08
A{9,1,4}342.15
Minor Triadsc♯m{1,4,8}331.92
fm{5,8,0}431.77
g♯m{8,11,3}252.62
am{9,0,4}431.77
Augmented TriadsC+{0,4,8}531.54
C♯+{1,5,9}352.38
Diminished Triads{5,8,11}242.31
{9,0,3}242.31
Parsimonious Voice Leading Between Common Triads of Scale 2875. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm G# G# C+->G# am am C+->am C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->fm F F C#+->F C#+->A E->f° g#m g#m E->g#m f°->fm fm->F F->am g#m->G# G#->a° a°->am am->A

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.

Diameter5
Radius3
Self-Centeredno
Central VerticesC+, c♯m, fm, am
Peripheral VerticesC♯+, g♯m

Modes

Modes are the rotational transformation of this scale. Scale 2875 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3485
Scale 3485: Sabach, Ian Ring Music TheorySabach
3rd mode:
Scale 1895
Scale 1895: Salyllic, Ian Ring Music TheorySalyllic
4th mode:
Scale 2995
Scale 2995: Raga Saurashtra, Ian Ring Music TheoryRaga Saurashtra
5th mode:
Scale 3545
Scale 3545: Thyptyllic, Ian Ring Music TheoryThyptyllic
6th mode:
Scale 955
Scale 955: Ionogyllic, Ian Ring Music TheoryIonogyllic
7th mode:
Scale 2525
Scale 2525: Aeolaryllic, Ian Ring Music TheoryAeolaryllic
8th mode:
Scale 1655
Scale 1655: Katygyllic, Ian Ring Music TheoryKatygyllic

Prime

The prime form of this scale is Scale 887

Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic

Complement

The octatonic modal family [2875, 3485, 1895, 2995, 3545, 955, 2525, 1655] (Forte: 8-19) is the complement of the tetratonic modal family [275, 305, 785, 2185] (Forte: 4-19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2875 is 2971

Scale 2971Scale 2971: Aeolynyllic, Ian Ring Music TheoryAeolynyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2875 is chiral, and its enantiomorph is scale 2971

Scale 2971Scale 2971: Aeolynyllic, Ian Ring Music TheoryAeolynyllic

Transformations:

T0 2875  T0I 2971
T1 1655  T1I 1847
T2 3310  T2I 3694
T3 2525  T3I 3293
T4 955  T4I 2491
T5 1910  T5I 887
T6 3820  T6I 1774
T7 3545  T7I 3548
T8 2995  T8I 3001
T9 1895  T9I 1907
T10 3790  T10I 3814
T11 3485  T11I 3533

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 2873Scale 2873: Ionian Augmented Sharp 2, Ian Ring Music TheoryIonian Augmented Sharp 2
Scale 2877Scale 2877: Phrylyllic, Ian Ring Music TheoryPhrylyllic
Scale 2879Scale 2879: Stadygic, Ian Ring Music TheoryStadygic
Scale 2867Scale 2867: Socrian, Ian Ring Music TheorySocrian
Scale 2871Scale 2871: Stanyllic, Ian Ring Music TheoryStanyllic
Scale 2859Scale 2859: Phrycrian, Ian Ring Music TheoryPhrycrian
Scale 2843Scale 2843: Sorian, Ian Ring Music TheorySorian
Scale 2907Scale 2907: Magen Abot 2, Ian Ring Music TheoryMagen Abot 2
Scale 2939Scale 2939: Goptygic, Ian Ring Music TheoryGoptygic
Scale 3003Scale 3003: Genus Chromaticum, Ian Ring Music TheoryGenus Chromaticum
Scale 2619Scale 2619: Ionyrian, Ian Ring Music TheoryIonyrian
Scale 2747Scale 2747: Stythyllic, Ian Ring Music TheoryStythyllic
Scale 2363Scale 2363: Kataptian, Ian Ring Music TheoryKataptian
Scale 3387Scale 3387: Aeryptyllic, Ian Ring Music TheoryAeryptyllic
Scale 3899Scale 3899: Katorygic, Ian Ring Music TheoryKatorygic
Scale 827Scale 827: Mixolocrian, Ian Ring Music TheoryMixolocrian
Scale 1851Scale 1851: Zacryllic, Ian Ring Music TheoryZacryllic

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.