The Exciting Universe Of Music Theory

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Scale 3113

Scale 3113, 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).


Cardinality5 (pentatonic)
Pitch Class Set{0,3,5,10,11}
Forte Number5-14
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 647
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
prime: 167
Deep Scaleno
Interval Vector221131
Interval Spectrump3mns2d2t
Distribution Spectra<1> = {1,2,3,5}
<2> = {2,4,5,6,7}
<3> = {5,6,7,8,10}
<4> = {7,9,10,11}
Spectra Variation3.6
Maximally Evenno
Maximal Area Setno
Interior Area1.683
Myhill Propertyno
Ridge Tonesnone

Common Triads

There are no common triads (major, minor, augmented and diminished) that can be formed using notes in this scale.


Modes are the rotational transformation of this scale. Scale 3113 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 901
Scale 901, Ian Ring Music Theory
3rd mode:
Scale 1249
Scale 1249, Ian Ring Music Theory
4th mode:
Scale 167
Scale 167, Ian Ring Music TheoryThis is the prime mode
5th mode:
Scale 2131
Scale 2131, Ian Ring Music Theory


The prime form of this scale is Scale 167

Scale 167Scale 167, Ian Ring Music Theory


The pentatonic modal family [3113, 901, 1249, 167, 2131] (Forte: 5-14) is the complement of the heptatonic modal family [431, 1507, 1933, 2263, 2801, 3179, 3637] (Forte: 7-14)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3113 is 647

Scale 647Scale 647, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3113 is chiral, and its enantiomorph is scale 647

Scale 647Scale 647, Ian Ring Music Theory


T0 3113  T0I 647
T1 2131  T1I 1294
T2 167  T2I 2588
T3 334  T3I 1081
T4 668  T4I 2162
T5 1336  T5I 229
T6 2672  T6I 458
T7 1249  T7I 916
T8 2498  T8I 1832
T9 901  T9I 3664
T10 1802  T10I 3233
T11 3604  T11I 2371

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 3115Scale 3115, Ian Ring Music Theory
Scale 3117Scale 3117, Ian Ring Music Theory
Scale 3105Scale 3105, Ian Ring Music Theory
Scale 3109Scale 3109, Ian Ring Music Theory
Scale 3121Scale 3121, Ian Ring Music Theory
Scale 3129Scale 3129, Ian Ring Music Theory
Scale 3081Scale 3081, Ian Ring Music Theory
Scale 3097Scale 3097, Ian Ring Music Theory
Scale 3145Scale 3145: Stolitonic, Ian Ring Music TheoryStolitonic
Scale 3177Scale 3177: Rothimic, Ian Ring Music TheoryRothimic
Scale 3241Scale 3241: Dalimic, Ian Ring Music TheoryDalimic
Scale 3369Scale 3369: Mixolimic, Ian Ring Music TheoryMixolimic
Scale 3625Scale 3625: Podimic, Ian Ring Music TheoryPodimic
Scale 2089Scale 2089, Ian Ring Music Theory
Scale 2601Scale 2601: Raga Chandrakauns, Ian Ring Music TheoryRaga Chandrakauns
Scale 1065Scale 1065, 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.