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Scale 4051: "Ionilygic"

Scale 4051: Ionilygic, 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
Ionilygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,4,6,7,8,9,10,11}
Forte Number9-2
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2431
Hemitonia7 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 767
Deep Scaleno
Interval Vector777663
Interval Spectrump6m6n7s7d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {6,7,8,9}
<7> = {7,8,9,10}
<8> = {9,10,11}
Spectra Variation2.444
Maximally Evenno
Maximal Area Setno
Interior Area2.683
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{0,4,7}342.29
E{4,8,11}242.43
F♯{6,10,1}342.43
A{9,1,4}442.07
Minor Triadsc♯m{1,4,8}342.14
em{4,7,11}342.43
f♯m{6,9,1}342.29
am{9,0,4}342.14
Augmented TriadsC+{0,4,8}442.07
Diminished Triadsc♯°{1,4,7}242.5
e°{4,7,10}242.57
f♯°{6,9,0}242.5
g°{7,10,1}242.57
a♯°{10,1,4}242.43
Parsimonious Voice Leading Between Common Triads of Scale 4051. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E am am C+->am c#°->c#m A A c#m->A e° e° e°->em g° g° e°->g° em->E f#° f#° f#m f#m f#°->f#m f#°->am F# F# f#m->F# f#m->A F#->g° a#° a#° F#->a#° am->A A->a#°

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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 4051 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 4073		Scale 4073: Sathygic, Ian Ring Music TheorySathygic
3rd mode:
Scale 1021		Scale 1021: Ladygic, Ian Ring Music TheoryLadygic
4th mode:
Scale 1279		Scale 1279: Sarygic, Ian Ring Music TheorySarygic
5th mode:
Scale 2687		Scale 2687: Thacrygic, Ian Ring Music TheoryThacrygic
6th mode:
Scale 3391		Scale 3391: Aeolynygic, Ian Ring Music TheoryAeolynygic
7th mode:
Scale 3743		Scale 3743: Thadygic, Ian Ring Music TheoryThadygic
8th mode:
Scale 3919		Scale 3919: Lynygic, Ian Ring Music TheoryLynygic
9th mode:
Scale 4007		Scale 4007: Doptygic, Ian Ring Music TheoryDoptygic

Prime

The prime form of this scale is Scale 767

Scale 767Scale 767: Raptygic, Ian Ring Music TheoryRaptygic

Complement

The nonatonic modal family [4051, 4073, 1021, 1279, 2687, 3391, 3743, 3919, 4007] (Forte: 9-2) is the complement of the tritonic modal family [11, 1537, 2053] (Forte: 3-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 4051 is 2431

Scale 2431Scale 2431: Gythygic, Ian Ring Music TheoryGythygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 4051 is chiral, and its enantiomorph is scale 2431

Scale 2431Scale 2431: Gythygic, Ian Ring Music TheoryGythygic

Transformations:

T0 4051  T0I 2431
T1 4007  T1I 767
T2 3919  T2I 1534
T3 3743  T3I 3068
T4 3391  T4I 2041
T5 2687  T5I 4082
T6 1279  T6I 4069
T7 2558  T7I 4043
T8 1021  T8I 3991
T9 2042  T9I 3887
T10 4084  T10I 3679
T11 4073  T11I 3263

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 4049Scale 4049: Stycryllic, Ian Ring Music TheoryStycryllic
Scale 4053Scale 4053: Kyrygic, Ian Ring Music TheoryKyrygic
Scale 4055Scale 4055: Dagyllian, Ian Ring Music TheoryDagyllian
Scale 4059Scale 4059: Zolyllian, Ian Ring Music TheoryZolyllian
Scale 4035Scale 4035, Ian Ring Music Theory
Scale 4043Scale 4043: Phrocrygic, Ian Ring Music TheoryPhrocrygic
Scale 4067Scale 4067: Aeolarygic, Ian Ring Music TheoryAeolarygic
Scale 4083Scale 4083: Bathyllian, Ian Ring Music TheoryBathyllian
Scale 3987Scale 3987: Loryllic, Ian Ring Music TheoryLoryllic
Scale 4019Scale 4019: Lonygic, Ian Ring Music TheoryLonygic
Scale 3923Scale 3923: Stoptyllic, Ian Ring Music TheoryStoptyllic
Scale 3795Scale 3795: Epothyllic, Ian Ring Music TheoryEpothyllic
Scale 3539Scale 3539: Aeoryllic, Ian Ring Music TheoryAeoryllic
Scale 3027Scale 3027: Rythyllic, Ian Ring Music TheoryRythyllic
Scale 2003Scale 2003: Podyllic, Ian Ring Music TheoryPodyllic

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.