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Scale 4013: "Raga Pilu"

Also known as: Full Minor

Scale 4013: Raga Pilu, Ian Ring Music Theory

i = imperfections

Tones9 (nonatonic)
Pitch Class Set{0,2,3,5,7,8,9,10,11}
Forte Number9-7
Rotational Symmetrynone
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
prime: 1471
enantiomorph: 1727
Deep Scaleno
Interval Vector677673
Interval Spectrump7m6n7s7d6t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {10,11}
Spectra Variation1.778
Myhill Propertyno


Modes are the rotational transformation of this scale. Scale 4013 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2027
Scale 2027, Ian Ring Music Theory
3rd mode:
Scale 3061
Scale 3061, Ian Ring Music Theory
4th mode:
Scale 1789
Scale 1789: Blues Enneatonic II, Ian Ring Music TheoryBlues Enneatonic II
5th mode:
Scale 1471
Scale 1471, Ian Ring Music TheoryThis is the prime mode
6th mode:
Scale 2783
Scale 2783, Ian Ring Music Theory
7th mode:
Scale 3439
Scale 3439, Ian Ring Music Theory
8th mode:
Scale 3767
Scale 3767: Chromatic Bebop, Ian Ring Music TheoryChromatic Bebop
9th mode:
Scale 3931
Scale 3931, Ian Ring Music Theory


The prime form of this scale is Scale 1471

Scale 1471Scale 1471, Ian Ring Music Theory


The nonatonic modal family [4013, 2027, 3061, 1789, 1471, 2783, 3439, 3767, 3931] is the negative of the tritonic modal family [37, 641, 1033]


The inverse of a scale is a reflection using the root as its axis. The inverse of 4013 is 1727

Scale 1727Scale 1727, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 4013 is chiral, and its enantiomorph is scale 1727

Scale 1727Scale 1727, Ian Ring Music Theory

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 4015Scale 4015, Ian Ring Music Theory
Scale 4009Scale 4009, Ian Ring Music Theory
Scale 4011Scale 4011, Ian Ring Music Theory
Scale 4005Scale 4005, Ian Ring Music Theory
Scale 4021Scale 4021: Raga Pahadi, Ian Ring Music TheoryRaga Pahadi
Scale 4029Scale 4029: Major/Minor mixed, Ian Ring Music TheoryMajor/Minor mixed
Scale 3981Scale 3981, Ian Ring Music Theory
Scale 3997Scale 3997, Ian Ring Music Theory
Scale 4045Scale 4045, Ian Ring Music Theory
Scale 4077Scale 4077, Ian Ring Music Theory
Scale 3885Scale 3885, Ian Ring Music Theory
Scale 3949Scale 3949, Ian Ring Music Theory
Scale 3757Scale 3757: Raga Mian Ki Malhar, Ian Ring Music TheoryRaga Mian Ki Malhar
Scale 3501Scale 3501: Maqam Nahawand, Ian Ring Music TheoryMaqam Nahawand
Scale 2989Scale 2989: Bebop Minor, Ian Ring Music TheoryBebop Minor
Scale 1965Scale 1965: Raga Mukhari, Ian Ring Music TheoryRaga Mukhari

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