The Exciting Universe Of Music Theory

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Scale 223

Scale 223, 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

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).


Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,4,6,7}
Forte Number7-4
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 3937
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Deep Scaleno
Interval Vector544332
Interval Spectrump3m3n4s4d5t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6}
<3> = {3,4,7,8}
<4> = {4,5,8,9}
<5> = {6,9,10}
<6> = {7,10,11}
Spectra Variation3.714
Maximally Evenno
Maximal Area Setno
Interior Area1.933
Myhill Propertyno
Ridge Tonesnone

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}221
Minor Triadscm{0,3,7}221
Diminished Triads{0,3,6}131.5
Parsimonious Voice Leading Between Common Triads of Scale 223. Created by Ian Ring ©2019 cm cm c°->cm C C cm->C c#° c#° C->c#°

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.

Central Verticescm, C
Peripheral Verticesc°, c♯°


Modes are the rotational transformation of this scale. Scale 223 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2159
Scale 2159, Ian Ring Music Theory
3rd mode:
Scale 3127
Scale 3127, Ian Ring Music Theory
4th mode:
Scale 3611
Scale 3611, Ian Ring Music Theory
5th mode:
Scale 3853
Scale 3853, Ian Ring Music Theory
6th mode:
Scale 1987
Scale 1987, Ian Ring Music Theory
7th mode:
Scale 3041
Scale 3041, Ian Ring Music Theory


This is the prime form of this scale.


The heptatonic modal family [223, 2159, 3127, 3611, 3853, 1987, 3041] (Forte: 7-4) is the complement of the pentatonic modal family [79, 961, 2087, 3091, 3593] (Forte: 5-4)


The inverse of a scale is a reflection using the root as its axis. The inverse of 223 is 3937

Scale 3937Scale 3937, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 223 is chiral, and its enantiomorph is scale 3937

Scale 3937Scale 3937, Ian Ring Music Theory


T0 223  T0I 3937
T1 446  T1I 3779
T2 892  T2I 3463
T3 1784  T3I 2831
T4 3568  T4I 1567
T5 3041  T5I 3134
T6 1987  T6I 2173
T7 3974  T7I 251
T8 3853  T8I 502
T9 3611  T9I 1004
T10 3127  T10I 2008
T11 2159  T11I 4016

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 221Scale 221, Ian Ring Music Theory
Scale 219Scale 219: Istrian, Ian Ring Music TheoryIstrian
Scale 215Scale 215, Ian Ring Music Theory
Scale 207Scale 207, Ian Ring Music Theory
Scale 239Scale 239, Ian Ring Music Theory
Scale 255Scale 255, Ian Ring Music Theory
Scale 159Scale 159, Ian Ring Music Theory
Scale 191Scale 191, Ian Ring Music Theory
Scale 95Scale 95, Ian Ring Music Theory
Scale 351Scale 351: Epanian, Ian Ring Music TheoryEpanian
Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic
Scale 735Scale 735: Sylyllic, Ian Ring Music TheorySylyllic
Scale 1247Scale 1247: Aeodyllic, Ian Ring Music TheoryAeodyllic
Scale 2271Scale 2271: Poptyllic, Ian Ring Music TheoryPoptyllic

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 ( 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.