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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

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 Rupavati
Dozenal
Utrian
Zeitler
Staptian
Carnatic Melakarta
Rupavati
Carnatic Numbered Melakarta
12th Melakarta raga

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

7 (heptatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,1,3,5,7,10,11}

Forte Number

A code assigned by theorist Allen Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

7-24

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

Reflection Axes

If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.

none

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

yes
enantiomorph: 2727

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

3 (trihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

2 (dicohemitonic)

Imperfections

An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.

3

Modes

Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.

6

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 687

Generator

Indicates if the scale can be constructed using a generator, and an origin.

none

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Structure

Defines the scale as the sequence of intervals between one tone and the next.

[1, 2, 2, 2, 3, 1, 1]

Interval Vector

Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.

<3, 5, 3, 4, 4, 2>

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hanson.

p4m4n3s5d3t2

Distribution Spectra

Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.

<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 Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

2.571

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

no

Maximal Area Set

A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.

no

Interior Area

Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.

2.549

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

5.967

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

no

Balanced

A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.

no

Ridge Tones

Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.

none

Propriety

Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".

Improper

Heteromorphic Profile

Defined by Norman Carey (2002), the heteromorphic profile is an ordered triple of (c, a, d) where c is the number of contradictions, a is the number of ambiguities, and d is the number of differences. When c is zero, the scale is Proper. When a is also zero, the scale is Strictly Proper.

(19, 38, 102)

Tertian Harmonic Chords

Tertian chords are made from alternating members of the scale, ie built from "stacked thirds". Not all scales lend themselves well to tertian harmony.

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:

In the abbreviation, the subscript number after "T" is the number of semitones of tranposition, "M" means the pitch class is multiplied by 5, and "I" means the result is inverted. Operation is an identical way to express the same thing; the syntax is <a,b> where each tone of the set x is transformed by the equation y = ax + b

Abbrev Operation Result Abbrev Operation Result
T0 <1,0> 3243       T0I <11,0> 2727
T1 <1,1> 2391      T1I <11,1> 1359
T2 <1,2> 687      T2I <11,2> 2718
T3 <1,3> 1374      T3I <11,3> 1341
T4 <1,4> 2748      T4I <11,4> 2682
T5 <1,5> 1401      T5I <11,5> 1269
T6 <1,6> 2802      T6I <11,6> 2538
T7 <1,7> 1509      T7I <11,7> 981
T8 <1,8> 3018      T8I <11,8> 1962
T9 <1,9> 1941      T9I <11,9> 3924
T10 <1,10> 3882      T10I <11,10> 3753
T11 <1,11> 3669      T11I <11,11> 3411
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2223      T0MI <7,0> 3747
T1M <5,1> 351      T1MI <7,1> 3399
T2M <5,2> 702      T2MI <7,2> 2703
T3M <5,3> 1404      T3MI <7,3> 1311
T4M <5,4> 2808      T4MI <7,4> 2622
T5M <5,5> 1521      T5MI <7,5> 1149
T6M <5,6> 3042      T6MI <7,6> 2298
T7M <5,7> 1989      T7MI <7,7> 501
T8M <5,8> 3978      T8MI <7,8> 1002
T9M <5,9> 3861      T9MI <7,9> 2004
T10M <5,10> 3627      T10MI <7,10> 4008
T11M <5,11> 3159      T11MI <7,11> 3921

The transformations that map this set to itself are: T0

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: Ulian, Ian Ring Music TheoryUlian
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: Tihian, Ian Ring Music TheoryTihian
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. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. All other diagrams and visualizations are © Ian Ring. 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, and George Howlett for assistance with the Carnatic ragas.