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Scale 1003: "Ionyryllic"

Scale 1003: Ionyryllic, 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
Ionyryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,5,6,7,8,9}
Forte Number8-Z15
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2809
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 TriadsC♯{1,5,8}242.18
F{5,9,0}441.82
G♯{8,0,3}342
Minor Triadscm{0,3,7}242.27
fm{5,8,0}341.91
f♯m{6,9,1}342
Augmented TriadsC♯+{1,5,9}341.91
Diminished Triads{0,3,6}242.36
d♯°{3,6,9}242.27
f♯°{6,9,0}242.09
{9,0,3}242.09
Parsimonious Voice Leading Between Common Triads of Scale 1003. Created by Ian Ring ©2019 cm cm c°->cm d#° d#° c°->d#° G# G# cm->G# C# C# C#+ C#+ C#->C#+ fm fm C#->fm F F C#+->F f#m f#m C#+->f#m d#°->f#m fm->F fm->G# f#° f#° F->f#° F->a° f#°->f#m G#->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 1003 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2549
Scale 2549: Rydyllic, Ian Ring Music TheoryRydyllic
3rd mode:
Scale 1661
Scale 1661: Gonyllic, Ian Ring Music TheoryGonyllic
4th mode:
Scale 1439
Scale 1439: Rolyllic, Ian Ring Music TheoryRolyllic
5th mode:
Scale 2767
Scale 2767: Katydyllic, Ian Ring Music TheoryKatydyllic
6th mode:
Scale 3431
Scale 3431: Zyptyllic, Ian Ring Music TheoryZyptyllic
7th mode:
Scale 3763
Scale 3763: Modyllic, Ian Ring Music TheoryModyllic
8th mode:
Scale 3929
Scale 3929: Aeolothyllic, Ian Ring Music TheoryAeolothyllic

Prime

The prime form of this scale is Scale 863

Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic

Complement

The octatonic modal family [1003, 2549, 1661, 1439, 2767, 3431, 3763, 3929] (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 1003 is 2809

Scale 2809Scale 2809: Gythyllic, Ian Ring Music TheoryGythyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1003 is chiral, and its enantiomorph is scale 2809

Scale 2809Scale 2809: Gythyllic, Ian Ring Music TheoryGythyllic

Transformations:

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

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 1001Scale 1001: Badian, Ian Ring Music TheoryBadian
Scale 1005Scale 1005: Radyllic, Ian Ring Music TheoryRadyllic
Scale 1007Scale 1007: Epitygic, Ian Ring Music TheoryEpitygic
Scale 995Scale 995: Phrathian, Ian Ring Music TheoryPhrathian
Scale 999Scale 999: Ionodyllic, Ian Ring Music TheoryIonodyllic
Scale 1011Scale 1011: Kycryllic, Ian Ring Music TheoryKycryllic
Scale 1019Scale 1019: Aeranygic, Ian Ring Music TheoryAeranygic
Scale 971Scale 971: Mela Gavambodhi, Ian Ring Music TheoryMela Gavambodhi
Scale 987Scale 987: Aeraptyllic, Ian Ring Music TheoryAeraptyllic
Scale 939Scale 939: Mela Senavati, Ian Ring Music TheoryMela Senavati
Scale 875Scale 875: Locrian Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 7
Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian
Scale 491Scale 491: Aeolyrian, Ian Ring Music TheoryAeolyrian
Scale 1515Scale 1515: Phrygian/Locrian Mixed, Ian Ring Music TheoryPhrygian/Locrian Mixed
Scale 2027Scale 2027: Boptygic, Ian Ring Music TheoryBoptygic
Scale 3051Scale 3051: Stalygic, Ian Ring Music TheoryStalygic

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.