The Exciting Universe Of Music Theory

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Scale 2951

Scale 2951, 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{0,1,2,7,8,9,11}
Forte Number7-5
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 3131
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
prime: 239
Deep Scaleno
Interval Vector543342
Interval Spectrump4m3n3s4d5t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6}
<3> = {3,4,7}
<4> = {5,8,9}
<5> = {6,9,10}
<6> = {7,10,11}
Spectra Variation3.429
Maximally Evenno
Maximal Area Setno
Interior Area1.933
Myhill Propertyno
Ridge Tonesnone

Harmonic Chords

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 TriadsG{7,11,2}110.5
Diminished Triadsg♯°{8,11,2}110.5
Parsimonious Voice Leading Between Common Triads of Scale 2951. Created by Ian Ring ©2019 Parsimonious Voice Leading Between Common Triads of Scale 2951. Created by Ian Ring ©2019 G g#° g#° G->g#°

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.



Modes are the rotational transformation of this scale. Scale 2951 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3523
Scale 3523, Ian Ring Music Theory
3rd mode:
Scale 3809
Scale 3809, Ian Ring Music Theory
4th mode:
Scale 247
Scale 247, Ian Ring Music Theory
5th mode:
Scale 2171
Scale 2171, Ian Ring Music Theory
6th mode:
Scale 3133
Scale 3133, Ian Ring Music Theory
7th mode:
Scale 1807
Scale 1807, Ian Ring Music Theory


The prime form of this scale is Scale 239

Scale 239Scale 239, Ian Ring Music Theory


The heptatonic modal family [2951, 3523, 3809, 247, 2171, 3133, 1807] (Forte: 7-5) is the complement of the pentatonic modal family [143, 481, 2119, 3107, 3601] (Forte: 5-5)


The inverse of a scale is a reflection using the root as its axis. The inverse of 2951 is 3131

Scale 3131Scale 3131, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 2951 is chiral, and its enantiomorph is scale 3131

Scale 3131Scale 3131, Ian Ring Music Theory


T0 2951  T0I 3131
T1 1807  T1I 2167
T2 3614  T2I 239
T3 3133  T3I 478
T4 2171  T4I 956
T5 247  T5I 1912
T6 494  T6I 3824
T7 988  T7I 3553
T8 1976  T8I 3011
T9 3952  T9I 1927
T10 3809  T10I 3854
T11 3523  T11I 3613

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 2949Scale 2949, Ian Ring Music Theory
Scale 2947Scale 2947, Ian Ring Music Theory
Scale 2955Scale 2955: Thorian, Ian Ring Music TheoryThorian
Scale 2959Scale 2959: Dygyllic, Ian Ring Music TheoryDygyllic
Scale 2967Scale 2967: Madyllic, Ian Ring Music TheoryMadyllic
Scale 2983Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic
Scale 3015Scale 3015: Laptyllic, Ian Ring Music TheoryLaptyllic
Scale 2823Scale 2823, Ian Ring Music Theory
Scale 2887Scale 2887: Gaptian, Ian Ring Music TheoryGaptian
Scale 2695Scale 2695, Ian Ring Music Theory
Scale 2439Scale 2439, Ian Ring Music Theory
Scale 3463Scale 3463, Ian Ring Music Theory
Scale 3975Scale 3975, Ian Ring Music Theory
Scale 903Scale 903, Ian Ring Music Theory
Scale 1927Scale 1927, 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 ( 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.