The Exciting Universe Of Music Theory

more than you ever wanted to know about...

Scale 167

Scale 167, 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{0,1,2,5,7}
Forte Number5-14
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 3233
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
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 167 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2131
Scale 2131, Ian Ring Music Theory
3rd mode:
Scale 3113
Scale 3113, Ian Ring Music Theory
4th mode:
Scale 901
Scale 901, Ian Ring Music Theory
5th mode:
Scale 1249
Scale 1249, Ian Ring Music Theory


This is the prime form of this scale.


The pentatonic modal family [167, 2131, 3113, 901, 1249] (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 167 is 3233

Scale 3233Scale 3233, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 167 is chiral, and its enantiomorph is scale 3233

Scale 3233Scale 3233, Ian Ring Music Theory


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

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 165Scale 165: Genus Primum, Ian Ring Music TheoryGenus Primum
Scale 163Scale 163, Ian Ring Music Theory
Scale 171Scale 171, Ian Ring Music Theory
Scale 175Scale 175, Ian Ring Music Theory
Scale 183Scale 183, Ian Ring Music Theory
Scale 135Scale 135, Ian Ring Music Theory
Scale 151Scale 151, Ian Ring Music Theory
Scale 199Scale 199: Raga Nabhomani, Ian Ring Music TheoryRaga Nabhomani
Scale 231Scale 231, Ian Ring Music Theory
Scale 39Scale 39, Ian Ring Music Theory
Scale 103Scale 103, Ian Ring Music Theory
Scale 295Scale 295: Gyritonic, Ian Ring Music TheoryGyritonic
Scale 423Scale 423: Sogimic, Ian Ring Music TheorySogimic
Scale 679Scale 679: Lanimic, Ian Ring Music TheoryLanimic
Scale 1191Scale 1191: Pyrimic, Ian Ring Music TheoryPyrimic
Scale 2215Scale 2215: Ranimic, Ian Ring Music TheoryRanimic

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.