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Scale 123

Scale 123, 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).

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,3,4,5,6}
Forte Number6-Z3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3009
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes5
Prime?no
prime: 111
Deep Scaleno
Interval Vector433221
Interval Spectrump2m2n3s3d4t
Distribution Spectra<1> = {1,2,6}
<2> = {2,3,7}
<3> = {3,4,8,9}
<4> = {5,9,10}
<5> = {6,10,11}
Spectra Variation4.333
Maximally Evenno
Maximal Area Setno
Interior Area1.433
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
Diminished Triads{0,3,6}000

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.

Modes

Modes are the rotational transformation of this scale. Scale 123 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2109
Scale 2109, Ian Ring Music Theory
3rd mode:
Scale 1551
Scale 1551, Ian Ring Music Theory
4th mode:
Scale 2823
Scale 2823, Ian Ring Music Theory
5th mode:
Scale 3459
Scale 3459, Ian Ring Music Theory
6th mode:
Scale 3777
Scale 3777, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 111

Scale 111Scale 111, Ian Ring Music Theory

Complement

The hexatonic modal family [123, 2109, 1551, 2823, 3459, 3777] (Forte: 6-Z3) is the complement of the hexatonic modal family [159, 993, 2127, 3111, 3603, 3849] (Forte: 6-Z36)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 123 is 3009

Scale 3009Scale 3009, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 123 is chiral, and its enantiomorph is scale 3009

Scale 3009Scale 3009, Ian Ring Music Theory

Transformations:

T0 123  T0I 3009
T1 246  T1I 1923
T2 492  T2I 3846
T3 984  T3I 3597
T4 1968  T4I 3099
T5 3936  T5I 2103
T6 3777  T6I 111
T7 3459  T7I 222
T8 2823  T8I 444
T9 1551  T9I 888
T10 3102  T10I 1776
T11 2109  T11I 3552

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 121Scale 121, Ian Ring Music Theory
Scale 125Scale 125, Ian Ring Music Theory
Scale 127Scale 127, Ian Ring Music Theory
Scale 115Scale 115, Ian Ring Music Theory
Scale 119Scale 119, Ian Ring Music Theory
Scale 107Scale 107, Ian Ring Music Theory
Scale 91Scale 91, Ian Ring Music Theory
Scale 59Scale 59, Ian Ring Music Theory
Scale 187Scale 187, Ian Ring Music Theory
Scale 251Scale 251, Ian Ring Music Theory
Scale 379Scale 379: Aeragian, Ian Ring Music TheoryAeragian
Scale 635Scale 635: Epolian, Ian Ring Music TheoryEpolian
Scale 1147Scale 1147: Epynian, Ian Ring Music TheoryEpynian
Scale 2171Scale 2171, 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, 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.