The Exciting Universe Of Music Theory

more than you ever wanted to know about...

Scale 137: "Ute Tritonic"

Scale 137: Ute Tritonic, 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).

Common Names

Carnatic Raga
Ute Tritonic
Peruvian Tritonic 2


Cardinality3 (tritonic)
Pitch Class Set{0,3,7}
Forte Number3-11
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 545
Hemitonia0 (anhemitonic)
Cohemitonia0 (ancohemitonic)
Deep Scaleno
Interval Vector001110
Interval Spectrumpmn
Distribution Spectra<1> = {3,4,5}
<2> = {7,8,9}
Spectra Variation1.333
Maximally Evenno
Maximal Area Setno
Interior Area1.183
Myhill Propertyno
Ridge Tonesnone
ProprietyStrictly Proper

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 Triadscm{0,3,7}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 137 can be rotated to make 2 other scales. The 1st mode is itself.

2nd mode:
Scale 529
Scale 529: Raga Bilwadala, Ian Ring Music TheoryRaga Bilwadala
3rd mode:
Scale 289
Scale 289, Ian Ring Music Theory


This is the prime form of this scale.


The tritonic modal family [137, 529, 289] (Forte: 3-11) is the complement of the nonatonic modal family [1775, 1915, 1975, 2935, 3005, 3035, 3515, 3565, 3805] (Forte: 9-11)


The inverse of a scale is a reflection using the root as its axis. The inverse of 137 is 545

Scale 545Scale 545, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 137 is chiral, and its enantiomorph is scale 545

Scale 545Scale 545, Ian Ring Music Theory


T0 137  T0I 545
T1 274  T1I 1090
T2 548  T2I 2180
T3 1096  T3I 265
T4 2192  T4I 530
T5 289  T5I 1060
T6 578  T6I 2120
T7 1156  T7I 145
T8 2312  T8I 290
T9 529  T9I 580
T10 1058  T10I 1160
T11 2116  T11I 2320

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 139Scale 139, Ian Ring Music Theory
Scale 141Scale 141, Ian Ring Music Theory
Scale 129Scale 129: Niagari, Ian Ring Music TheoryNiagari
Scale 133Scale 133, Ian Ring Music Theory
Scale 145Scale 145: Raga Malasri, Ian Ring Music TheoryRaga Malasri
Scale 153Scale 153, Ian Ring Music Theory
Scale 169Scale 169: Vietnamese Tetratonic, Ian Ring Music TheoryVietnamese Tetratonic
Scale 201Scale 201, Ian Ring Music Theory
Scale 9Scale 9, Ian Ring Music Theory
Scale 73Scale 73, Ian Ring Music Theory
Scale 265Scale 265, Ian Ring Music Theory
Scale 393Scale 393: Lothic, Ian Ring Music TheoryLothic
Scale 649Scale 649: Byptic, Ian Ring Music TheoryByptic
Scale 1161Scale 1161: Bi Yu, Ian Ring Music TheoryBi Yu
Scale 2185Scale 2185: Dygic, Ian Ring Music TheoryDygic

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.