The Exciting Universe Of Music Theory

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Scale 3099

Scale 3099, 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).


Cardinality6 (hexatonic)
Pitch Class Set{0,1,3,4,10,11}
Forte Number6-Z3
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 2823
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
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
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
Diminished Triadsa♯°{10,1,4}000

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


Modes are the rotational transformation of this scale. Scale 3099 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3597
Scale 3597, Ian Ring Music Theory
3rd mode:
Scale 1923
Scale 1923, Ian Ring Music Theory
4th mode:
Scale 3009
Scale 3009, Ian Ring Music Theory
5th mode:
Scale 111
Scale 111, Ian Ring Music TheoryThis is the prime mode
6th mode:
Scale 2103
Scale 2103, Ian Ring Music Theory


The prime form of this scale is Scale 111

Scale 111Scale 111, Ian Ring Music Theory


The hexatonic modal family [3099, 3597, 1923, 3009, 111, 2103] (Forte: 6-Z3) is the complement of the hexatonic modal family [159, 993, 2127, 3111, 3603, 3849] (Forte: 6-Z36)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3099 is 2823

Scale 2823Scale 2823, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3099 is chiral, and its enantiomorph is scale 2823

Scale 2823Scale 2823, Ian Ring Music Theory


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

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 3097Scale 3097, Ian Ring Music Theory
Scale 3101Scale 3101, Ian Ring Music Theory
Scale 3103Scale 3103, Ian Ring Music Theory
Scale 3091Scale 3091, Ian Ring Music Theory
Scale 3095Scale 3095, Ian Ring Music Theory
Scale 3083Scale 3083, Ian Ring Music Theory
Scale 3115Scale 3115, Ian Ring Music Theory
Scale 3131Scale 3131, Ian Ring Music Theory
Scale 3163Scale 3163: Rogian, Ian Ring Music TheoryRogian
Scale 3227Scale 3227: Aeolocrian, Ian Ring Music TheoryAeolocrian
Scale 3355Scale 3355: Bagian, Ian Ring Music TheoryBagian
Scale 3611Scale 3611, Ian Ring Music Theory
Scale 2075Scale 2075, Ian Ring Music Theory
Scale 2587Scale 2587, Ian Ring Music Theory
Scale 1051Scale 1051, 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.