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Scale 2213: "Raga Desh"

Scale 2213: Raga Desh, 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 Desh
Named After Composers
Tcherepnin Major Pentatonic
Unknown / Unsorted
Nam xuan
Zeitler
Daritonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,2,5,7,11}
Forte Number5-29
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1187
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections2
Modes4
Prime?no
prime: 331
Deep Scaleno
Interval Vector122131
Interval Spectrump3mn2s2dt
Distribution Spectra<1> = {1,2,3,4}
<2> = {3,5,6}
<3> = {6,7,9}
<4> = {8,9,10,11}
Spectra Variation2.4
Maximally Evenno
Maximal Area Setno
Interior Area2.049
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 TriadsG{7,11,2}110.5
Diminished Triads{11,2,5}110.5
Parsimonious Voice Leading Between Common Triads of Scale 2213. Created by Ian Ring ©2019 Parsimonious Voice Leading Between Common Triads of Scale 2213. Created by Ian Ring ©2019 G G->b°

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2213 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1577
Scale 1577: Raga Chandrakauns (Kafi), Ian Ring Music TheoryRaga Chandrakauns (Kafi)
3rd mode:
Scale 709
Scale 709: Raga Shri Kalyan, Ian Ring Music TheoryRaga Shri Kalyan
4th mode:
Scale 1201
Scale 1201: Mixolydian Pentatonic, Ian Ring Music TheoryMixolydian Pentatonic
5th mode:
Scale 331
Scale 331: Raga Chhaya Todi, Ian Ring Music TheoryRaga Chhaya TodiThis is the prime mode

Prime

The prime form of this scale is Scale 331

Scale 331Scale 331: Raga Chhaya Todi, Ian Ring Music TheoryRaga Chhaya Todi

Complement

The pentatonic modal family [2213, 1577, 709, 1201, 331] (Forte: 5-29) is the complement of the heptatonic modal family [727, 1483, 1721, 1837, 2411, 2789, 3253] (Forte: 7-29)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2213 is 1187

Scale 1187Scale 1187: Kokin-joshi, Ian Ring Music TheoryKokin-joshi

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2213 is chiral, and its enantiomorph is scale 1187

Scale 1187Scale 1187: Kokin-joshi, Ian Ring Music TheoryKokin-joshi

Transformations:

T0 2213  T0I 1187
T1 331  T1I 2374
T2 662  T2I 653
T3 1324  T3I 1306
T4 2648  T4I 2612
T5 1201  T5I 1129
T6 2402  T6I 2258
T7 709  T7I 421
T8 1418  T8I 842
T9 2836  T9I 1684
T10 1577  T10I 3368
T11 3154  T11I 2641

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 2215Scale 2215: Ranimic, Ian Ring Music TheoryRanimic
Scale 2209Scale 2209, Ian Ring Music Theory
Scale 2211Scale 2211: Raga Gauri, Ian Ring Music TheoryRaga Gauri
Scale 2217Scale 2217: Kagitonic, Ian Ring Music TheoryKagitonic
Scale 2221Scale 2221: Raga Sindhura Kafi, Ian Ring Music TheoryRaga Sindhura Kafi
Scale 2229Scale 2229: Raga Nalinakanti, Ian Ring Music TheoryRaga Nalinakanti
Scale 2181Scale 2181, Ian Ring Music Theory
Scale 2197Scale 2197: Raga Hamsadhvani, Ian Ring Music TheoryRaga Hamsadhvani
Scale 2245Scale 2245: Raga Vaijayanti, Ian Ring Music TheoryRaga Vaijayanti
Scale 2277Scale 2277: Kagimic, Ian Ring Music TheoryKagimic
Scale 2085Scale 2085, Ian Ring Music Theory
Scale 2149Scale 2149, Ian Ring Music Theory
Scale 2341Scale 2341: Raga Priyadharshini, Ian Ring Music TheoryRaga Priyadharshini
Scale 2469Scale 2469: Raga Bhinna Pancama, Ian Ring Music TheoryRaga Bhinna Pancama
Scale 2725Scale 2725: Raga Nagagandhari, Ian Ring Music TheoryRaga Nagagandhari
Scale 3237Scale 3237: Raga Brindabani Sarang, Ian Ring Music TheoryRaga Brindabani Sarang
Scale 165Scale 165: Genus Primum, Ian Ring Music TheoryGenus Primum
Scale 1189Scale 1189: Suspended Pentatonic, Ian Ring Music TheorySuspended Pentatonic

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.