The Exciting Universe Of Music Theory

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Scale 2159

Scale 2159, 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{0,1,2,3,5,6,11}
Forte Number7-4
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 3779
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
prime: 223
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 TriadsB{11,3,6}221
Minor Triadsbm{11,2,6}221
Diminished Triads{0,3,6}131.5
Parsimonious Voice Leading Between Common Triads of Scale 2159. Created by Ian Ring ©2019 B B c°->B bm bm b°->bm bm->B

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 Verticesbm, B
Peripheral Verticesc°, b°


Modes are the rotational transformation of this scale. Scale 2159 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3127
Scale 3127, Ian Ring Music Theory
3rd mode:
Scale 3611
Scale 3611, Ian Ring Music Theory
4th mode:
Scale 3853
Scale 3853, Ian Ring Music Theory
5th mode:
Scale 1987
Scale 1987, Ian Ring Music Theory
6th mode:
Scale 3041
Scale 3041, Ian Ring Music Theory
7th mode:
Scale 223
Scale 223, Ian Ring Music TheoryThis is the prime mode


The prime form of this scale is Scale 223

Scale 223Scale 223, Ian Ring Music Theory


The heptatonic modal family [2159, 3127, 3611, 3853, 1987, 3041, 223] (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 2159 is 3779

Scale 3779Scale 3779, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 2159 is chiral, and its enantiomorph is scale 3779

Scale 3779Scale 3779, Ian Ring Music Theory


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

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 2157Scale 2157, Ian Ring Music Theory
Scale 2155Scale 2155, Ian Ring Music Theory
Scale 2151Scale 2151, Ian Ring Music Theory
Scale 2167Scale 2167, Ian Ring Music Theory
Scale 2175Scale 2175, Ian Ring Music Theory
Scale 2127Scale 2127, Ian Ring Music Theory
Scale 2143Scale 2143, Ian Ring Music Theory
Scale 2095Scale 2095, Ian Ring Music Theory
Scale 2223Scale 2223: Konian, Ian Ring Music TheoryKonian
Scale 2287Scale 2287: Lodyllic, Ian Ring Music TheoryLodyllic
Scale 2415Scale 2415: Lothyllic, Ian Ring Music TheoryLothyllic
Scale 2671Scale 2671: Aerolyllic, Ian Ring Music TheoryAerolyllic
Scale 3183Scale 3183: Mixonyllic, Ian Ring Music TheoryMixonyllic
Scale 111Scale 111, Ian Ring Music Theory
Scale 1135Scale 1135: Katolian, Ian Ring Music TheoryKatolian

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.