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Scale 891: "Ionilyllic"

Scale 891: Ionilyllic, 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
Ionilyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,4,5,6,8,9}
Forte Number8-17
Rotational Symmetrynone
Reflection Axes4.5
Palindromicno
Chiralityno
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?yes
Deep Scaleno
Interval Vector546652
Interval Spectrump5m6n6s4d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {5,7}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Balancedno
Ridge Tones[9]
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}342.21
F{5,9,0}441.93
G♯{8,0,3}342.21
A{9,1,4}342.07
Minor Triadsc♯m{1,4,8}342.21
fm{5,8,0}342.07
f♯m{6,9,1}342.21
am{9,0,4}441.93
Augmented TriadsC+{0,4,8}441.93
C♯+{1,5,9}441.93
Diminished Triadsc°{0,3,6}242.5
d♯°{3,6,9}242.5
f♯°{6,9,0}242.36
a°{9,0,3}242.36
Parsimonious Voice Leading Between Common Triads of Scale 891. Created by Ian Ring ©2019 c° c° d#° d#° c°->d#° G# G# c°->G# C+ C+ c#m c#m C+->c#m fm fm C+->fm 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 f#m f#m C#+->f#m C#+->A d#°->f#m fm->F f#° f#° F->f#° F->am f#°->f#m a° a° 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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 891 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2493		Scale 2493: Manyllic, Ian Ring Music TheoryManyllic
3rd mode:
Scale 1647		Scale 1647: Polyllic, Ian Ring Music TheoryPolyllic
4th mode:
Scale 2871		Scale 2871: Stanyllic, Ian Ring Music TheoryStanyllic
5th mode:
Scale 3483		Scale 3483: Mixotharyllic, Ian Ring Music TheoryMixotharyllic
6th mode:
Scale 3789		Scale 3789: Eporyllic, Ian Ring Music TheoryEporyllic
7th mode:
Scale 1971		Scale 1971: Aerynyllic, Ian Ring Music TheoryAerynyllic
8th mode:
Scale 3033		Scale 3033: Doptyllic, Ian Ring Music TheoryDoptyllic

Prime

This is the prime form of this scale.

Complement

The octatonic modal family [891, 2493, 1647, 2871, 3483, 3789, 1971, 3033] (Forte: 8-17) is the complement of the tetratonic modal family [153, 531, 801, 2313] (Forte: 4-17)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 891 is 3033

Scale 3033Scale 3033: Doptyllic, Ian Ring Music TheoryDoptyllic

Transformations:

T0 891  T0I 3033
T1 1782  T1I 1971
T2 3564  T2I 3942
T3 3033  T3I 3789
T4 1971  T4I 3483
T5 3942  T5I 2871
T6 3789  T6I 1647
T7 3483  T7I 3294
T8 2871  T8I 2493
T9 1647  T9I 891
T10 3294  T10I 1782
T11 2493  T11I 3564

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 889Scale 889: Borian, Ian Ring Music TheoryBorian
Scale 893Scale 893: Dadyllic, Ian Ring Music TheoryDadyllic
Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic
Scale 883Scale 883: Ralian, Ian Ring Music TheoryRalian
Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic
Scale 875Scale 875: Locrian Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 7
Scale 859Scale 859: Ultralocrian, Ian Ring Music TheoryUltralocrian
Scale 827Scale 827: Mixolocrian, Ian Ring Music TheoryMixolocrian
Scale 955Scale 955: Ionogyllic, Ian Ring Music TheoryIonogyllic
Scale 1019Scale 1019: Aeranygic, Ian Ring Music TheoryAeranygic
Scale 635Scale 635: Epolian, Ian Ring Music TheoryEpolian
Scale 763Scale 763: Doryllic, Ian Ring Music TheoryDoryllic
Scale 379Scale 379: Aeragian, Ian Ring Music TheoryAeragian
Scale 1403Scale 1403: Espla's Scale, Ian Ring Music TheoryEspla's Scale
Scale 1915Scale 1915: Thydygic, Ian Ring Music TheoryThydygic
Scale 2939Scale 2939: Goptygic, Ian Ring Music TheoryGoptygic

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.