The Exciting Universe Of Music Theory

more than you ever wanted to know about...

Scale 3011

Scale 3011, 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{0,1,6,7,8,9,11}
Forte Number7-5
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 2171
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
Minor Triadsf♯m{6,9,1}110.5
Diminished Triadsf♯°{6,9,0}110.5
Parsimonious Voice Leading Between Common Triads of Scale 3011. Created by Ian Ring ©2019 f#° f#° f#m f#m f#°->f#m

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 3011 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3553
Scale 3553, Ian Ring Music Theory
3rd mode:
Scale 239
Scale 239, Ian Ring Music TheoryThis is the prime mode
4th mode:
Scale 2167
Scale 2167, Ian Ring Music Theory
5th mode:
Scale 3131
Scale 3131, Ian Ring Music Theory
6th mode:
Scale 3613
Scale 3613, Ian Ring Music Theory
7th mode:
Scale 1927
Scale 1927, Ian Ring Music Theory


The prime form of this scale is Scale 239

Scale 239Scale 239, Ian Ring Music Theory


The heptatonic modal family [3011, 3553, 239, 2167, 3131, 3613, 1927] (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 3011 is 2171

Scale 2171Scale 2171, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3011 is chiral, and its enantiomorph is scale 2171

Scale 2171Scale 2171, Ian Ring Music Theory


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

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 3009Scale 3009, Ian Ring Music Theory
Scale 3013Scale 3013: Thynian, Ian Ring Music TheoryThynian
Scale 3015Scale 3015: Laptyllic, Ian Ring Music TheoryLaptyllic
Scale 3019Scale 3019, Ian Ring Music Theory
Scale 3027Scale 3027: Rythyllic, Ian Ring Music TheoryRythyllic
Scale 3043Scale 3043: Ionayllic, Ian Ring Music TheoryIonayllic
Scale 2947Scale 2947, Ian Ring Music Theory
Scale 2979Scale 2979: Gyptian, Ian Ring Music TheoryGyptian
Scale 2883Scale 2883, Ian Ring Music Theory
Scale 2755Scale 2755, Ian Ring Music Theory
Scale 2499Scale 2499, Ian Ring Music Theory
Scale 3523Scale 3523, Ian Ring Music Theory
Scale 4035Scale 4035, Ian Ring Music Theory
Scale 963Scale 963, Ian Ring Music Theory
Scale 1987Scale 1987, 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.