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Scale 2471: "Mela Ganamurti"

Scale 2471: Mela Ganamurti, 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
Mela Ganamurti
Carnatic Raga
Raga Ganasamavarali
Zeitler
Eparian

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

{0,1,2,5,7,8,11}

Forte Number

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

7-19

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: 3251

Hemitonia

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

4 (multihemitonic)

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: 719

Deep Scale

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

no

Interval Formula

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

[1, 1, 3, 2, 1, 3, 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.

<4, 3, 4, 3, 4, 3>

Interval Spectrum

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

p4m3n4s3d4t3

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> = {3,5,6}
<4> = {6,7,9}
<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.

2.286

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.

2.433

Polygon Perimeter

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

5.899

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

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 TriadsC♯{1,5,8}231.71
G{7,11,2}231.71
Minor Triadsfm{5,8,0}231.71
Diminished Triads{2,5,8}231.71
{5,8,11}231.71
g♯°{8,11,2}231.71
{11,2,5}231.71
Parsimonious Voice Leading Between Common Triads of Scale 2471. Created by Ian Ring ©2019 C# C# C#->d° fm fm C#->fm d°->b° f°->fm g#° g#° f°->g#° Parsimonious Voice Leading Between Common Triads of Scale 2471. Created by Ian Ring ©2019 G G->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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2471 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3283
Scale 3283: Mela Visvambhari, Ian Ring Music TheoryMela Visvambhari
3rd mode:
Scale 3689
Scale 3689: Katocrian, Ian Ring Music TheoryKatocrian
4th mode:
Scale 973
Scale 973: Mela Syamalangi, Ian Ring Music TheoryMela Syamalangi
5th mode:
Scale 1267
Scale 1267: Katynian, Ian Ring Music TheoryKatynian
6th mode:
Scale 2681
Scale 2681: Aerycrian, Ian Ring Music TheoryAerycrian
7th mode:
Scale 847
Scale 847: Ganian, Ian Ring Music TheoryGanian

Prime

The prime form of this scale is Scale 719

Scale 719Scale 719: Kanian, Ian Ring Music TheoryKanian

Complement

The heptatonic modal family [2471, 3283, 3689, 973, 1267, 2681, 847] (Forte: 7-19) is the complement of the pentatonic modal family [203, 707, 1561, 2149, 2401] (Forte: 5-19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2471 is 3251

Scale 3251Scale 3251: Mela Hatakambari, Ian Ring Music TheoryMela Hatakambari

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2471 is chiral, and its enantiomorph is scale 3251

Scale 3251Scale 3251: Mela Hatakambari, Ian Ring Music TheoryMela Hatakambari

Transformations:

T0 2471  T0I 3251
T1 847  T1I 2407
T2 1694  T2I 719
T3 3388  T3I 1438
T4 2681  T4I 2876
T5 1267  T5I 1657
T6 2534  T6I 3314
T7 973  T7I 2533
T8 1946  T8I 971
T9 3892  T9I 1942
T10 3689  T10I 3884
T11 3283  T11I 3673

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 2469Scale 2469: Raga Bhinna Pancama, Ian Ring Music TheoryRaga Bhinna Pancama
Scale 2467Scale 2467: Raga Padi, Ian Ring Music TheoryRaga Padi
Scale 2475Scale 2475: Neapolitan Minor, Ian Ring Music TheoryNeapolitan Minor
Scale 2479Scale 2479: Harmonic and Neapolitan Minor Mixed, Ian Ring Music TheoryHarmonic and Neapolitan Minor Mixed
Scale 2487Scale 2487: Dothyllic, Ian Ring Music TheoryDothyllic
Scale 2439Scale 2439, Ian Ring Music Theory
Scale 2455Scale 2455: Bothian, Ian Ring Music TheoryBothian
Scale 2503Scale 2503: Mela Jhalavarali, Ian Ring Music TheoryMela Jhalavarali
Scale 2535Scale 2535: Messiaen Mode 4, Ian Ring Music TheoryMessiaen Mode 4
Scale 2343Scale 2343: Tharimic, Ian Ring Music TheoryTharimic
Scale 2407Scale 2407: Zylian, Ian Ring Music TheoryZylian
Scale 2215Scale 2215: Ranimic, Ian Ring Music TheoryRanimic
Scale 2727Scale 2727: Mela Manavati, Ian Ring Music TheoryMela Manavati
Scale 2983Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic
Scale 3495Scale 3495: Banyllic, Ian Ring Music TheoryBanyllic
Scale 423Scale 423: Sogimic, Ian Ring Music TheorySogimic
Scale 1447Scale 1447: Mela Ratnangi, Ian Ring Music TheoryMela Ratnangi

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. 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.