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Scale 4021: "Raga Pahadi"

Scale 4021: Raga Pahadi, 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

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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 Pahadi
Zeitler
Bagygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,2,4,5,7,8,9,10,11}
Forte Number9-7
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1471
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 TriadsC{0,4,7}242.38
E{4,8,11}442.13
F{5,9,0}342.44
G{7,11,2}442.31
A♯{10,2,5}342.44
Minor Triadsdm{2,5,9}342.44
em{4,7,11}442.19
fm{5,8,0}442.31
gm{7,10,2}342.44
am{9,0,4}242.56
Augmented TriadsC+{0,4,8}442.19
Diminished Triads{2,5,8}242.56
{4,7,10}242.56
{5,8,11}242.44
g♯°{8,11,2}242.44
{11,2,5}242.56
Parsimonious Voice Leading Between Common Triads of Scale 4021. Created by Ian Ring ©2019 C C C+ C+ C->C+ em em C->em E E C+->E fm fm C+->fm am am C+->am dm dm d°->dm d°->fm F F dm->F A# A# dm->A# e°->em gm gm e°->gm em->E Parsimonious Voice Leading Between Common Triads of Scale 4021. Created by Ian Ring ©2019 G em->G E->f° g#° g#° E->g#° f°->fm fm->F F->am gm->G gm->A# G->g#° G->b° 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 4021 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2029
Scale 2029: Kiourdi, Ian Ring Music TheoryKiourdi
3rd mode:
Scale 1531
Scale 1531: Styptygic, Ian Ring Music TheoryStyptygic
4th mode:
Scale 2813
Scale 2813: Zolygic, Ian Ring Music TheoryZolygic
5th mode:
Scale 1727
Scale 1727: Sydygic, Ian Ring Music TheorySydygic
6th mode:
Scale 2911
Scale 2911: Katygic, Ian Ring Music TheoryKatygic
7th mode:
Scale 3503
Scale 3503: Zyphygic, Ian Ring Music TheoryZyphygic
8th mode:
Scale 3799
Scale 3799: Aeralygic, Ian Ring Music TheoryAeralygic
9th mode:
Scale 3947
Scale 3947: Ryptygic, Ian Ring Music TheoryRyptygic

Prime

The prime form of this scale is Scale 1471

Scale 1471Scale 1471: Radygic, Ian Ring Music TheoryRadygic

Complement

The nonatonic modal family [4021, 2029, 1531, 2813, 1727, 2911, 3503, 3799, 3947] (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 4021 is 1471

Scale 1471Scale 1471: Radygic, Ian Ring Music TheoryRadygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 4021 is chiral, and its enantiomorph is scale 1471

Scale 1471Scale 1471: Radygic, Ian Ring Music TheoryRadygic

Transformations:

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

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 4023Scale 4023: Styptyllian, Ian Ring Music TheoryStyptyllian
Scale 4017Scale 4017: Dolyllic, Ian Ring Music TheoryDolyllic
Scale 4019Scale 4019: Lonygic, Ian Ring Music TheoryLonygic
Scale 4025Scale 4025: Kalygic, Ian Ring Music TheoryKalygic
Scale 4029Scale 4029: Major/Minor Mixed, Ian Ring Music TheoryMajor/Minor Mixed
Scale 4005Scale 4005, Ian Ring Music Theory
Scale 4013Scale 4013: Raga Pilu, Ian Ring Music TheoryRaga Pilu
Scale 3989Scale 3989: Sythyllic, Ian Ring Music TheorySythyllic
Scale 4053Scale 4053: Kyrygic, Ian Ring Music TheoryKyrygic
Scale 4085Scale 4085: Sydyllian, Ian Ring Music TheorySydyllian
Scale 3893Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic
Scale 3957Scale 3957: Porygic, Ian Ring Music TheoryPorygic
Scale 3765Scale 3765: Dominant Bebop, Ian Ring Music TheoryDominant Bebop
Scale 3509Scale 3509: Stogyllic, Ian Ring Music TheoryStogyllic
Scale 2997Scale 2997: Major Bebop, Ian Ring Music TheoryMajor Bebop
Scale 1973Scale 1973: Zyryllic, Ian Ring Music TheoryZyryllic

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.

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.