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Scale 4013: "Raga Pilu"

Scale 4013: Raga Pilu, 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

41161837294116105072918310504116183
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

Carnatic Raga
Raga Pilu
Western Modern
Full Minor
Zeitler
Dathygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,2,3,5,7,8,9,10,11}
Forte Number9-7
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1727
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections2
Modes8
Prime?no
prime: 1471
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
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsD♯{3,7,10}242.56
F{5,9,0}342.44
G{7,11,2}442.31
G♯{8,0,3}442.19
A♯{10,2,5}342.44
Minor Triadscm{0,3,7}242.38
dm{2,5,9}342.44
fm{5,8,0}442.31
gm{7,10,2}342.44
g♯m{8,11,3}442.13
Augmented TriadsD♯+{3,7,11}442.19
Diminished Triads{2,5,8}242.56
{5,8,11}242.44
g♯°{8,11,2}242.44
{9,0,3}242.56
{11,2,5}242.56
Parsimonious Voice Leading Between Common Triads of Scale 4013. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ G# G# cm->G# dm dm d°->dm fm fm d°->fm F F dm->F A# A# dm->A# D# D# D#->D#+ gm gm D#->gm Parsimonious Voice Leading Between Common Triads of Scale 4013. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m f°->fm f°->g#m fm->F fm->G# F->a° gm->G gm->A# g#° g#° G->g#° G->b° g#°->g#m g#m->G# G#->a° A#->b°

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Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter4
Radius4
Self-Centeredyes

Modes

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: Boptygic, Ian Ring Music TheoryBoptygic
3rd mode:
Scale 3061
Scale 3061: Apinygic, Ian Ring Music TheoryApinygic
4th mode:
Scale 1789
Scale 1789: Blues Enneatonic II, Ian Ring Music TheoryBlues Enneatonic II
5th mode:
Scale 1471
Scale 1471: Radygic, Ian Ring Music TheoryRadygicThis is the prime mode
6th mode:
Scale 2783
Scale 2783: Gothygic, Ian Ring Music TheoryGothygic
7th mode:
Scale 3439
Scale 3439: Lythygic, Ian Ring Music TheoryLythygic
8th mode:
Scale 3767
Scale 3767: Chromatic Bebop, Ian Ring Music TheoryChromatic Bebop
9th mode:
Scale 3931
Scale 3931: Aerygic, Ian Ring Music TheoryAerygic

Prime

The prime form of this scale is Scale 1471

Scale 1471Scale 1471: Radygic, Ian Ring Music TheoryRadygic

Complement

The nonatonic modal family [4013, 2027, 3061, 1789, 1471, 2783, 3439, 3767, 3931] (Forte: 9-7) is the complement of the tritonic modal family [37, 641, 1033] (Forte: 3-7)

Inverse

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

Scale 1727Scale 1727: Sydygic, Ian Ring Music TheorySydygic

Enantiomorph

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

Scale 1727Scale 1727: Sydygic, Ian Ring Music TheorySydygic

Transformations:

T0 4013  T0I 1727
T1 3931  T1I 3454
T2 3767  T2I 2813
T3 3439  T3I 1531
T4 2783  T4I 3062
T5 1471  T5I 2029
T6 2942  T6I 4058
T7 1789  T7I 4021
T8 3578  T8I 3947
T9 3061  T9I 3799
T10 2027  T10I 3503
T11 4054  T11I 2911

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: Phradyllian, Ian Ring Music TheoryPhradyllian
Scale 4009Scale 4009: Phranyllic, Ian Ring Music TheoryPhranyllic
Scale 4011Scale 4011: Styrygic, Ian Ring Music TheoryStyrygic
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: Phrycryllic, Ian Ring Music TheoryPhrycryllic
Scale 3997Scale 3997: Dogygic, Ian Ring Music TheoryDogygic
Scale 4045Scale 4045: Gyptygic, Ian Ring Music TheoryGyptygic
Scale 4077Scale 4077: Gothyllian, Ian Ring Music TheoryGothyllian
Scale 3885Scale 3885: Styryllic, Ian Ring Music TheoryStyryllic
Scale 3949Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic
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, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.