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Scale 2739: "Mela Suryakanta"

Scale 2739: Mela Suryakanta, 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 Suryakanta
Mela Suryakantam
Raga Supradhipam
Dozenal
Relian
Hindustani
Bhairubahar That
Unknown / Unsorted
Sowrashtram
Jaganmohini
Western Modern
Major-Melodic Phrygian
Exoticisms
Hungarian Romani Inverse
Zeitler
Zanian
Carnatic Melakarta
Suryakantam
Carnatic Numbered Melakarta
17th 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

{0,1,4,5,7,9,11}

Forte Number

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

7-30

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: 2475

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.

1 (uncohemitonic)

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: 855

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, 3, 1, 2, 2, 2, 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, 4, 3, 5, 4, 2>

Interval Spectrum

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

p4m5n3s4d3t2

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}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {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.

1.714

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.

(2, 22, 86)

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{0,4,7}331.43
F{5,9,0}231.71
A{9,1,4}331.43
Minor Triadsem{4,7,11}142.14
am{9,0,4}321.29
Augmented TriadsC♯+{1,5,9}241.86
Diminished Triadsc♯°{1,4,7}231.57
Parsimonious Voice Leading Between Common Triads of Scale 2739. Created by Ian Ring ©2019 C C c#° c#° C->c#° em em C->em am am C->am A A c#°->A C#+ C#+ F F C#+->F C#+->A F->am am->A

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 Verticesam
Peripheral VerticesC♯+, em

Modes

Modes are the rotational transformation of this scale. Scale 2739 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3417
Scale 3417: Golian, Ian Ring Music TheoryGolian
3rd mode:
Scale 939
Scale 939: Mela Senavati, Ian Ring Music TheoryMela Senavati
4th mode:
Scale 2517
Scale 2517: Harmonic Lydian, Ian Ring Music TheoryHarmonic Lydian
5th mode:
Scale 1653
Scale 1653: Minor Romani Inverse, Ian Ring Music TheoryMinor Romani Inverse
6th mode:
Scale 1437
Scale 1437: Sabach ascending, Ian Ring Music TheorySabach ascending
7th mode:
Scale 1383
Scale 1383: Pynian, Ian Ring Music TheoryPynian

Prime

The prime form of this scale is Scale 855

Scale 855Scale 855: Porian, Ian Ring Music TheoryPorian

Complement

The heptatonic modal family [2739, 3417, 939, 2517, 1653, 1437, 1383] (Forte: 7-30) is the complement of the pentatonic modal family [339, 789, 1221, 1329, 2217] (Forte: 5-30)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2739 is 2475

Scale 2475Scale 2475: Neapolitan Minor, Ian Ring Music TheoryNeapolitan Minor

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2739 is chiral, and its enantiomorph is scale 2475

Scale 2475Scale 2475: Neapolitan Minor, Ian Ring Music TheoryNeapolitan Minor

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> 2739       T0I <11,0> 2475
T1 <1,1> 1383      T1I <11,1> 855
T2 <1,2> 2766      T2I <11,2> 1710
T3 <1,3> 1437      T3I <11,3> 3420
T4 <1,4> 2874      T4I <11,4> 2745
T5 <1,5> 1653      T5I <11,5> 1395
T6 <1,6> 3306      T6I <11,6> 2790
T7 <1,7> 2517      T7I <11,7> 1485
T8 <1,8> 939      T8I <11,8> 2970
T9 <1,9> 1878      T9I <11,9> 1845
T10 <1,10> 3756      T10I <11,10> 3690
T11 <1,11> 3417      T11I <11,11> 3285
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2979      T0MI <7,0> 2235
T1M <5,1> 1863      T1MI <7,1> 375
T2M <5,2> 3726      T2MI <7,2> 750
T3M <5,3> 3357      T3MI <7,3> 1500
T4M <5,4> 2619      T4MI <7,4> 3000
T5M <5,5> 1143      T5MI <7,5> 1905
T6M <5,6> 2286      T6MI <7,6> 3810
T7M <5,7> 477      T7MI <7,7> 3525
T8M <5,8> 954      T8MI <7,8> 2955
T9M <5,9> 1908      T9MI <7,9> 1815
T10M <5,10> 3816      T10MI <7,10> 3630
T11M <5,11> 3537      T11MI <7,11> 3165

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 2737Scale 2737: Raga Hari Nata, Ian Ring Music TheoryRaga Hari Nata
Scale 2741Scale 2741: Major, Ian Ring Music TheoryMajor
Scale 2743Scale 2743: Staptyllic, Ian Ring Music TheoryStaptyllic
Scale 2747Scale 2747: Stythyllic, Ian Ring Music TheoryStythyllic
Scale 2723Scale 2723: Raga Jivantika, Ian Ring Music TheoryRaga Jivantika
Scale 2731Scale 2731: Neapolitan Major, Ian Ring Music TheoryNeapolitan Major
Scale 2707Scale 2707: Banimic, Ian Ring Music TheoryBanimic
Scale 2771Scale 2771: Marva That, Ian Ring Music TheoryMarva That
Scale 2803Scale 2803: Raga Bhatiyar, Ian Ring Music TheoryRaga Bhatiyar
Scale 2611Scale 2611: Raga Vasanta, Ian Ring Music TheoryRaga Vasanta
Scale 2675Scale 2675: Chromatic Lydian, Ian Ring Music TheoryChromatic Lydian
Scale 2867Scale 2867: Socrian, Ian Ring Music TheorySocrian
Scale 2995Scale 2995: Raga Saurashtra, Ian Ring Music TheoryRaga Saurashtra
Scale 2227Scale 2227: Raga Gaula, Ian Ring Music TheoryRaga Gaula
Scale 2483Scale 2483: Double Harmonic, Ian Ring Music TheoryDouble Harmonic
Scale 3251Scale 3251: Mela Hatakambari, Ian Ring Music TheoryMela Hatakambari
Scale 3763Scale 3763: Modyllic, Ian Ring Music TheoryModyllic
Scale 691Scale 691: Raga Kalavati, Ian Ring Music TheoryRaga Kalavati
Scale 1715Scale 1715: Harmonic Minor Inverse, Ian Ring Music TheoryHarmonic Minor Inverse

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.