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Scale 1315: "Pyritonic"

Scale 1315: Pyritonic, 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.

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



Cardinality5 (pentatonic)
Pitch Class Set{0,1,5,8,10}
Forte Number5-27
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 2197
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
prime: 299
Deep Scaleno
Interval Vector122230
Interval Spectrump3m2n2s2d
Distribution Spectra<1> = {1,2,3,4}
<2> = {3,4,5,7}
<3> = {5,7,8,9}
<4> = {8,9,10,11}
Spectra Variation2.8
Maximally Evenno
Myhill Propertyno
Ridge Tonesnone


Modes are the rotational transformation of this scale. Scale 1315 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2705
Scale 2705: Raga Mamata, Ian Ring Music TheoryRaga Mamata
3rd mode:
Scale 425
Scale 425: Raga Kokil Pancham, Ian Ring Music TheoryRaga Kokil Pancham
4th mode:
Scale 565
Scale 565: Aeolyphritonic, Ian Ring Music TheoryAeolyphritonic
5th mode:
Scale 1165
Scale 1165: Gycritonic, Ian Ring Music TheoryGycritonic


The prime form of this scale is Scale 299

Scale 299Scale 299: Raga Chitthakarshini, Ian Ring Music TheoryRaga Chitthakarshini


The pentatonic modal family [1315, 2705, 425, 565, 1165] (Forte: 5-27) is the complement of the heptatonic modal family [695, 1465, 1765, 1835, 2395, 2965, 3245] (Forte: 7-27)


The inverse of a scale is a reflection using the root as its axis. The inverse of 1315 is 2197

Scale 2197Scale 2197: Raga Hamsadhvani, Ian Ring Music TheoryRaga Hamsadhvani


Only scales that are chiral will have an enantiomorph. Scale 1315 is chiral, and its enantiomorph is scale 2197

Scale 2197Scale 2197: Raga Hamsadhvani, Ian Ring Music TheoryRaga Hamsadhvani


T0 1315  T0I 2197
T1 2630  T1I 299
T2 1165  T2I 598
T3 2330  T3I 1196
T4 565  T4I 2392
T5 1130  T5I 689
T6 2260  T6I 1378
T7 425  T7I 2756
T8 850  T8I 1417
T9 1700  T9I 2834
T10 3400  T10I 1573
T11 2705  T11I 3146

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 1313Scale 1313, Ian Ring Music Theory
Scale 1317Scale 1317: Chaio, Ian Ring Music TheoryChaio
Scale 1319Scale 1319: Phronimic, Ian Ring Music TheoryPhronimic
Scale 1323Scale 1323: Ritsu, Ian Ring Music TheoryRitsu
Scale 1331Scale 1331: Raga Vasantabhairavi, Ian Ring Music TheoryRaga Vasantabhairavi
Scale 1283Scale 1283, Ian Ring Music Theory
Scale 1299Scale 1299: Aerophitonic, Ian Ring Music TheoryAerophitonic
Scale 1347Scale 1347, Ian Ring Music Theory
Scale 1379Scale 1379: Kycrimic, Ian Ring Music TheoryKycrimic
Scale 1443Scale 1443: Raga Phenadyuti, Ian Ring Music TheoryRaga Phenadyuti
Scale 1059Scale 1059, Ian Ring Music Theory
Scale 1187Scale 1187: Kokin-joshi, Ian Ring Music TheoryKokin-joshi
Scale 1571Scale 1571: Lagitonic, Ian Ring Music TheoryLagitonic
Scale 1827Scale 1827: Katygimic, Ian Ring Music TheoryKatygimic
Scale 291Scale 291: Raga Lavangi, Ian Ring Music TheoryRaga Lavangi
Scale 803Scale 803: Loritonic, Ian Ring Music TheoryLoritonic
Scale 2339Scale 2339: Raga Kshanika, Ian Ring Music TheoryRaga Kshanika
Scale 3363Scale 3363: Rogimic, Ian Ring Music TheoryRogimic

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, and MIDI playback by MIDI.js. Bibliography