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Scale 3271: "Mela Raghupriya"

Scale 3271: Mela Raghupriya, 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 Raghupriya
Carnatic Raga
Raga Ravikriya
Hindustani
Ghandarva
Zeitler
Kolian

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

{0,1,2,6,7,10,11}

Forte Number

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

7-6

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: 3175

Hemitonia

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

5 (multihemitonic)

Cohemitonia

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

3 (tricohemitonic)

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: 415

Deep Scale

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

no

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.

[5, 3, 3, 4, 4, 2]

Interval Spectrum

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

p4m4n3s3d5t2

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> = {1,3,4}
<2> = {2,4,5}
<3> = {3,5,6,8}
<4> = {4,6,7,9}
<5> = {7,8,10}
<6> = {8,9,11}

Spectra Variation

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

3.143

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.

2.183

Polygon Perimeter

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

5.734

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

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 TriadsF♯{6,10,1}231.5
G{7,11,2}231.5
Minor Triadsgm{7,10,2}321.17
bm{11,2,6}231.5
Augmented TriadsD+{2,6,10}321.17
Diminished Triads{7,10,1}231.5

The following pitch classes are not present in any of the common triads: {0}

Parsimonious Voice Leading Between Common Triads of Scale 3271. Created by Ian Ring ©2019 D+ D+ F# F# D+->F# gm gm D+->gm bm bm D+->bm F#->g° g°->gm Parsimonious Voice Leading Between Common Triads of Scale 3271. Created by Ian Ring ©2019 G gm->G G->bm

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.

Diameter3
Radius2
Self-Centeredno
Central VerticesD+, gm
Peripheral VerticesF♯, g°, G, bm

Modes

Modes are the rotational transformation of this scale. Scale 3271 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3683
Scale 3683: Dycrian, Ian Ring Music TheoryDycrian
3rd mode:
Scale 3889
Scale 3889: Parian, Ian Ring Music TheoryParian
4th mode:
Scale 499
Scale 499: Ionaptian, Ian Ring Music TheoryIonaptian
5th mode:
Scale 2297
Scale 2297: Thylian, Ian Ring Music TheoryThylian
6th mode:
Scale 799
Scale 799: Lolian, Ian Ring Music TheoryLolian
7th mode:
Scale 2447
Scale 2447: Thagian, Ian Ring Music TheoryThagian

Prime

The prime form of this scale is Scale 415

Scale 415Scale 415: Aeoladian, Ian Ring Music TheoryAeoladian

Complement

The heptatonic modal family [3271, 3683, 3889, 499, 2297, 799, 2447] (Forte: 7-6) is the complement of the pentatonic modal family [103, 899, 2099, 2497, 3097] (Forte: 5-6)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3271 is 3175

Scale 3175Scale 3175: Eponian, Ian Ring Music TheoryEponian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3271 is chiral, and its enantiomorph is scale 3175

Scale 3175Scale 3175: Eponian, Ian Ring Music TheoryEponian

Transformations:

T0 3271  T0I 3175
T1 2447  T1I 2255
T2 799  T2I 415
T3 1598  T3I 830
T4 3196  T4I 1660
T5 2297  T5I 3320
T6 499  T6I 2545
T7 998  T7I 995
T8 1996  T8I 1990
T9 3992  T9I 3980
T10 3889  T10I 3865
T11 3683  T11I 3635

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 3269Scale 3269: Raga Malarani, Ian Ring Music TheoryRaga Malarani
Scale 3267Scale 3267, Ian Ring Music Theory
Scale 3275Scale 3275: Mela Divyamani, Ian Ring Music TheoryMela Divyamani
Scale 3279Scale 3279: Pythyllic, Ian Ring Music TheoryPythyllic
Scale 3287Scale 3287: Phrathyllic, Ian Ring Music TheoryPhrathyllic
Scale 3303Scale 3303: Mylyllic, Ian Ring Music TheoryMylyllic
Scale 3207Scale 3207, Ian Ring Music Theory
Scale 3239Scale 3239: Mela Tanarupi, Ian Ring Music TheoryMela Tanarupi
Scale 3143Scale 3143: Polimic, Ian Ring Music TheoryPolimic
Scale 3399Scale 3399: Zonian, Ian Ring Music TheoryZonian
Scale 3527Scale 3527: Ronyllic, Ian Ring Music TheoryRonyllic
Scale 3783Scale 3783: Phrygyllic, Ian Ring Music TheoryPhrygyllic
Scale 2247Scale 2247: Raga Vijayasri, Ian Ring Music TheoryRaga Vijayasri
Scale 2759Scale 2759: Mela Pavani, Ian Ring Music TheoryMela Pavani
Scale 1223Scale 1223: Phryptimic, Ian Ring Music TheoryPhryptimic

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.