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Scale 3243: "Mela Rupavati"

Scale 3243: Mela Rupavati, 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 Mela
Mela Rupavati
Zeitler
Staptian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,5,7,10,11}
Forte Number7-24
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2727
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 687
Deep Scaleno
Interval Vector353442
Interval Spectrump4m4n3s5d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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}221.2
Minor Triadscm{0,3,7}142
a♯m{10,1,5}142
Augmented TriadsD♯+{3,7,11}231.4
Diminished Triads{7,10,1}231.4
Parsimonious Voice Leading Between Common Triads of Scale 3243. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ D# D# D#->D#+ D#->g° a#m a#m g°->a#m

view full size

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
Radius2
Self-Centeredno
Central VerticesD♯
Peripheral Verticescm, a♯m

Modes

Modes are the rotational transformation of this scale. Scale 3243 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3669
Scale 3669: Mothian, Ian Ring Music TheoryMothian
3rd mode:
Scale 1941
Scale 1941: Aeranian, Ian Ring Music TheoryAeranian
4th mode:
Scale 1509
Scale 1509: Ragian, Ian Ring Music TheoryRagian
5th mode:
Scale 1401
Scale 1401: Pagian, Ian Ring Music TheoryPagian
6th mode:
Scale 687
Scale 687: Aeolythian, Ian Ring Music TheoryAeolythianThis is the prime mode
7th mode:
Scale 2391
Scale 2391: Molian, Ian Ring Music TheoryMolian

Prime

The prime form of this scale is Scale 687

Scale 687Scale 687: Aeolythian, Ian Ring Music TheoryAeolythian

Complement

The heptatonic modal family [3243, 3669, 1941, 1509, 1401, 687, 2391] (Forte: 7-24) is the complement of the pentatonic modal family [171, 1377, 1413, 1557, 2133] (Forte: 5-24)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3243 is 2727

Scale 2727Scale 2727: Mela Manavati, Ian Ring Music TheoryMela Manavati

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3243 is chiral, and its enantiomorph is scale 2727

Scale 2727Scale 2727: Mela Manavati, Ian Ring Music TheoryMela Manavati

Transformations:

T0 3243  T0I 2727
T1 2391  T1I 1359
T2 687  T2I 2718
T3 1374  T3I 1341
T4 2748  T4I 2682
T5 1401  T5I 1269
T6 2802  T6I 2538
T7 1509  T7I 981
T8 3018  T8I 1962
T9 1941  T9I 3924
T10 3882  T10I 3753
T11 3669  T11I 3411

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 3241Scale 3241: Dalimic, Ian Ring Music TheoryDalimic
Scale 3245Scale 3245: Mela Varunapriya, Ian Ring Music TheoryMela Varunapriya
Scale 3247Scale 3247: Aeolonyllic, Ian Ring Music TheoryAeolonyllic
Scale 3235Scale 3235: Pothimic, Ian Ring Music TheoryPothimic
Scale 3239Scale 3239: Mela Tanarupi, Ian Ring Music TheoryMela Tanarupi
Scale 3251Scale 3251: Mela Hatakambari, Ian Ring Music TheoryMela Hatakambari
Scale 3259Scale 3259, Ian Ring Music Theory
Scale 3211Scale 3211: Epacrimic, Ian Ring Music TheoryEpacrimic
Scale 3227Scale 3227: Aeolocrian, Ian Ring Music TheoryAeolocrian
Scale 3275Scale 3275: Mela Divyamani, Ian Ring Music TheoryMela Divyamani
Scale 3307Scale 3307: Boptyllic, Ian Ring Music TheoryBoptyllic
Scale 3115Scale 3115, Ian Ring Music Theory
Scale 3179Scale 3179: Daptian, Ian Ring Music TheoryDaptian
Scale 3371Scale 3371: Aeolylian, Ian Ring Music TheoryAeolylian
Scale 3499Scale 3499: Hamel, Ian Ring Music TheoryHamel
Scale 3755Scale 3755: Phryryllic, Ian Ring Music TheoryPhryryllic
Scale 2219Scale 2219: Phrydimic, Ian Ring Music TheoryPhrydimic
Scale 2731Scale 2731: Neapolitan Major, Ian Ring Music TheoryNeapolitan Major
Scale 1195Scale 1195: Raga Gandharavam, Ian Ring Music TheoryRaga Gandharavam

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.