The Exciting Universe Of Music Theory

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Scale 517

Scale 517, 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).


Cardinality3 (tritonic)
Pitch Class Set{0,2,9}
Forte Number3-7
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 1033
Hemitonia0 (anhemitonic)
Cohemitonia0 (ancohemitonic)
prime: 37
Deep Scaleno
Interval Vector011010
Interval Spectrumpns
Distribution Spectra<1> = {2,3,7}
<2> = {5,9,10}
Spectra Variation3.333
Maximally Evenno
Maximal Area Setno
Interior Area0.683
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 517 can be rotated to make 2 other scales. The 1st mode is itself.

2nd mode:
Scale 1153
Scale 1153, Ian Ring Music Theory
3rd mode:
Scale 41
Scale 41: Vietnamese Tritonic, Ian Ring Music TheoryVietnamese Tritonic


The prime form of this scale is Scale 37

Scale 37Scale 37, Ian Ring Music Theory


The tritonic modal family [517, 1153, 41] (Forte: 3-7) is the complement of the nonatonic modal family [1471, 1789, 2027, 2783, 3061, 3439, 3767, 3931, 4013] (Forte: 9-7)


The inverse of a scale is a reflection using the root as its axis. The inverse of 517 is 1033

Scale 1033Scale 1033, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 517 is chiral, and its enantiomorph is scale 1033

Scale 1033Scale 1033, Ian Ring Music Theory


T0 517  T0I 1033
T1 1034  T1I 2066
T2 2068  T2I 37
T3 41  T3I 74
T4 82  T4I 148
T5 164  T5I 296
T6 328  T6I 592
T7 656  T7I 1184
T8 1312  T8I 2368
T9 2624  T9I 641
T10 1153  T10I 1282
T11 2306  T11I 2564

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 519Scale 519, Ian Ring Music Theory
Scale 513Scale 513, Ian Ring Music Theory
Scale 515Scale 515, Ian Ring Music Theory
Scale 521Scale 521, Ian Ring Music Theory
Scale 525Scale 525, Ian Ring Music Theory
Scale 533Scale 533, Ian Ring Music Theory
Scale 549Scale 549: Raga Bhavani, Ian Ring Music TheoryRaga Bhavani
Scale 581Scale 581: Eporic 2, Ian Ring Music TheoryEporic 2
Scale 645Scale 645, Ian Ring Music Theory
Scale 773Scale 773, Ian Ring Music Theory
Scale 5Scale 5: Vietnamese ditonic, Ian Ring Music TheoryVietnamese ditonic
Scale 261Scale 261, Ian Ring Music Theory
Scale 1029Scale 1029, Ian Ring Music Theory
Scale 1541Scale 1541, Ian Ring Music Theory
Scale 2565Scale 2565, 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.