The Exciting Universe Of Music Theory

more than you ever wanted to know about...

Scale 3139

Scale 3139, 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{0,1,6,10,11}
Forte Number5-5
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 2119
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
prime: 143
Deep Scaleno
Interval Vector321121
Interval Spectrump2mns2d3t
Distribution Spectra<1> = {1,4,5}
<2> = {2,5,6,9}
<3> = {3,6,7,10}
<4> = {7,8,11}
Spectra Variation4.4
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
Major TriadsF♯{6,10,1}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 3139 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 3617
Scale 3617, Ian Ring Music Theory
3rd mode:
Scale 241
Scale 241, Ian Ring Music Theory
4th mode:
Scale 271
Scale 271, Ian Ring Music Theory
5th mode:
Scale 2183
Scale 2183, Ian Ring Music Theory


The prime form of this scale is Scale 143

Scale 143Scale 143, Ian Ring Music Theory


The pentatonic modal family [3139, 3617, 241, 271, 2183] (Forte: 5-5) is the complement of the heptatonic modal family [239, 1927, 2167, 3011, 3131, 3553, 3613] (Forte: 7-5)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3139 is 2119

Scale 2119Scale 2119, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3139 is chiral, and its enantiomorph is scale 2119

Scale 2119Scale 2119, Ian Ring Music Theory


T0 3139  T0I 2119
T1 2183  T1I 143
T2 271  T2I 286
T3 542  T3I 572
T4 1084  T4I 1144
T5 2168  T5I 2288
T6 241  T6I 481
T7 482  T7I 962
T8 964  T8I 1924
T9 1928  T9I 3848
T10 3856  T10I 3601
T11 3617  T11I 3107

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 3137Scale 3137, Ian Ring Music Theory
Scale 3141Scale 3141: Kanitonic, Ian Ring Music TheoryKanitonic
Scale 3143Scale 3143: Polimic, Ian Ring Music TheoryPolimic
Scale 3147Scale 3147: Ryrimic, Ian Ring Music TheoryRyrimic
Scale 3155Scale 3155: Ladimic, Ian Ring Music TheoryLadimic
Scale 3171Scale 3171: Zythimic, Ian Ring Music TheoryZythimic
Scale 3075Scale 3075, Ian Ring Music Theory
Scale 3107Scale 3107, Ian Ring Music Theory
Scale 3203Scale 3203, Ian Ring Music Theory
Scale 3267Scale 3267, Ian Ring Music Theory
Scale 3395Scale 3395, Ian Ring Music Theory
Scale 3651Scale 3651, Ian Ring Music Theory
Scale 2115Scale 2115, Ian Ring Music Theory
Scale 2627Scale 2627, Ian Ring Music Theory
Scale 1091Scale 1091, 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.