The Exciting Universe Of Music Theory

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Scale 903

Scale 903, 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).


Cardinality6 (hexatonic)
Pitch Class Set{0,1,2,7,8,9}
Forte Number6-Z6
Rotational Symmetrynone
Reflection Axes4.5
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
prime: 231
Deep Scaleno
Interval Vector421242
Interval Spectrump4m2ns2d4t2
Distribution Spectra<1> = {1,3,5}
<2> = {2,4,6}
<3> = {5,7}
<4> = {6,8,10}
<5> = {7,9,11}
Spectra Variation3
Maximally Evenno
Maximal Area Setno
Interior Area1.75
Myhill Propertyno
Ridge Tones[9]

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 903 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2499
Scale 2499, Ian Ring Music Theory
3rd mode:
Scale 3297
Scale 3297, Ian Ring Music Theory
4th mode:
Scale 231
Scale 231, Ian Ring Music TheoryThis is the prime mode
5th mode:
Scale 2163
Scale 2163, Ian Ring Music Theory
6th mode:
Scale 3129
Scale 3129, Ian Ring Music Theory


The prime form of this scale is Scale 231

Scale 231Scale 231, Ian Ring Music Theory


The hexatonic modal family [903, 2499, 3297, 231, 2163, 3129] (Forte: 6-Z6) is the complement of the hexatonic modal family [399, 483, 2247, 2289, 3171, 3633] (Forte: 6-Z38)


The inverse of a scale is a reflection using the root as its axis. The inverse of 903 is 3129

Scale 3129Scale 3129, Ian Ring Music Theory


T0 903  T0I 3129
T1 1806  T1I 2163
T2 3612  T2I 231
T3 3129  T3I 462
T4 2163  T4I 924
T5 231  T5I 1848
T6 462  T6I 3696
T7 924  T7I 3297
T8 1848  T8I 2499
T9 3696  T9I 903
T10 3297  T10I 1806
T11 2499  T11I 3612

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 901Scale 901, Ian Ring Music Theory
Scale 899Scale 899, Ian Ring Music Theory
Scale 907Scale 907: Tholimic, Ian Ring Music TheoryTholimic
Scale 911Scale 911: Radian, Ian Ring Music TheoryRadian
Scale 919Scale 919: Chromatic Phrygian Inverse, Ian Ring Music TheoryChromatic Phrygian Inverse
Scale 935Scale 935: Chromatic Dorian, Ian Ring Music TheoryChromatic Dorian
Scale 967Scale 967: Mela Salaga, Ian Ring Music TheoryMela Salaga
Scale 775Scale 775: Raga Putrika, Ian Ring Music TheoryRaga Putrika
Scale 839Scale 839: Ionathimic, Ian Ring Music TheoryIonathimic
Scale 647Scale 647, Ian Ring Music Theory
Scale 391Scale 391, Ian Ring Music Theory
Scale 1415Scale 1415, Ian Ring Music Theory
Scale 1927Scale 1927, Ian Ring Music Theory
Scale 2951Scale 2951, 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.