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Scale 23

Scale 23, 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.

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).

Analysis

Cardinality4 (tetratonic)
Pitch Class Set{0,1,2,4}
Forte Number4-2
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3329
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes3
Prime?yes
Deep Scaleno
Interval Vector221100
Interval Spectrummns2d2
Distribution Spectra<1> = {1,2,8}
<2> = {2,3,9,10}
<3> = {4,10,11}
Spectra Variation5.5
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
Coherenceno
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 23 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 2059
Scale 2059, Ian Ring Music Theory
3rd mode:
Scale 3077
Scale 3077, Ian Ring Music Theory
4th mode:
Scale 1793
Scale 1793, Ian Ring Music Theory

Prime

This is the prime form of this scale.

Complement

The tetratonic modal family [23, 2059, 3077, 1793] (Forte: 4-2) is the complement of the octatonic modal family [383, 2033, 2239, 3167, 3631, 3863, 3979, 4037] (Forte: 8-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 23 is 3329

Scale 3329Scale 3329, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 23 is chiral, and its enantiomorph is scale 3329

Scale 3329Scale 3329, Ian Ring Music Theory

Transformations:

T0 23  T0I 3329
T1 46  T1I 2563
T2 92  T2I 1031
T3 184  T3I 2062
T4 368  T4I 29
T5 736  T5I 58
T6 1472  T6I 116
T7 2944  T7I 232
T8 1793  T8I 464
T9 3586  T9I 928
T10 3077  T10I 1856
T11 2059  T11I 3712

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 21Scale 21, Ian Ring Music Theory
Scale 19Scale 19, Ian Ring Music Theory
Scale 27Scale 27, Ian Ring Music Theory
Scale 31Scale 31, Ian Ring Music Theory
Scale 7Scale 7, Ian Ring Music Theory
Scale 15Scale 15, Ian Ring Music Theory
Scale 39Scale 39, Ian Ring Music Theory
Scale 55Scale 55, Ian Ring Music Theory
Scale 87Scale 87, Ian Ring Music Theory
Scale 151Scale 151, Ian Ring Music Theory
Scale 279Scale 279: Poditonic, Ian Ring Music TheoryPoditonic
Scale 535Scale 535, Ian Ring Music Theory
Scale 1047Scale 1047, Ian Ring Music Theory
Scale 2071Scale 2071, Ian Ring Music Theory

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, and MIDI playback by MIDI.js. Bibliography