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Scale 2759: "Mela Pavani"

Scale 2759: Mela Pavani, 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 Pavani
Raga Kumbhini
Dozenal
Rixian
Zeitler
Aeraphian
Carnatic Melakarta
Pavani
Carnatic Numbered Melakarta
41st 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

{0,1,2,6,7,9,11}

Forte Number

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

7-14

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: 3179

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.

2

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: 431

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, 1, 4, 1, 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.

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

Interval Spectrum

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

p5m3n3s4d4t2

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

Spectra Variation

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

2.857

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.

2.299

Polygon Perimeter

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

5.803

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.

(25, 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{2,6,9}221.2
G{7,11,2}142
Minor Triadsf♯m{6,9,1}231.4
bm{11,2,6}231.4
Diminished Triadsf♯°{6,9,0}142
Parsimonious Voice Leading Between Common Triads of Scale 2759. Created by Ian Ring ©2019 D D f#m f#m D->f#m bm bm D->bm f#° f#° f#°->f#m Parsimonious Voice Leading Between Common Triads of Scale 2759. Created by Ian Ring ©2019 G G->bm

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 Verticesf♯°, G

Modes

Modes are the rotational transformation of this scale. Scale 2759 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3427
Scale 3427: Zacrian, Ian Ring Music TheoryZacrian
3rd mode:
Scale 3761
Scale 3761: Raga Madhuri, Ian Ring Music TheoryRaga Madhuri
4th mode:
Scale 491
Scale 491: Aeolyrian, Ian Ring Music TheoryAeolyrian
5th mode:
Scale 2293
Scale 2293: Gorian, Ian Ring Music TheoryGorian
6th mode:
Scale 1597
Scale 1597: Aeolodian, Ian Ring Music TheoryAeolodian
7th mode:
Scale 1423
Scale 1423: Doptian, Ian Ring Music TheoryDoptian

Prime

The prime form of this scale is Scale 431

Scale 431Scale 431: Epyrian, Ian Ring Music TheoryEpyrian

Complement

The heptatonic modal family [2759, 3427, 3761, 491, 2293, 1597, 1423] (Forte: 7-14) is the complement of the pentatonic modal family [167, 901, 1249, 2131, 3113] (Forte: 5-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2759 is 3179

Scale 3179Scale 3179: Daptian, Ian Ring Music TheoryDaptian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2759 is chiral, and its enantiomorph is scale 3179

Scale 3179Scale 3179: Daptian, Ian Ring Music TheoryDaptian

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> 2759       T0I <11,0> 3179
T1 <1,1> 1423      T1I <11,1> 2263
T2 <1,2> 2846      T2I <11,2> 431
T3 <1,3> 1597      T3I <11,3> 862
T4 <1,4> 3194      T4I <11,4> 1724
T5 <1,5> 2293      T5I <11,5> 3448
T6 <1,6> 491      T6I <11,6> 2801
T7 <1,7> 982      T7I <11,7> 1507
T8 <1,8> 1964      T8I <11,8> 3014
T9 <1,9> 3928      T9I <11,9> 1933
T10 <1,10> 3761      T10I <11,10> 3866
T11 <1,11> 3427      T11I <11,11> 3637
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 3809      T0MI <7,0> 239
T1M <5,1> 3523      T1MI <7,1> 478
T2M <5,2> 2951      T2MI <7,2> 956
T3M <5,3> 1807      T3MI <7,3> 1912
T4M <5,4> 3614      T4MI <7,4> 3824
T5M <5,5> 3133      T5MI <7,5> 3553
T6M <5,6> 2171      T6MI <7,6> 3011
T7M <5,7> 247      T7MI <7,7> 1927
T8M <5,8> 494      T8MI <7,8> 3854
T9M <5,9> 988      T9MI <7,9> 3613
T10M <5,10> 1976      T10MI <7,10> 3131
T11M <5,11> 3952      T11MI <7,11> 2167

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 2757Scale 2757: Raga Nishadi, Ian Ring Music TheoryRaga Nishadi
Scale 2755Scale 2755: Rivian, Ian Ring Music TheoryRivian
Scale 2763Scale 2763: Mela Suvarnangi, Ian Ring Music TheoryMela Suvarnangi
Scale 2767Scale 2767: Katydyllic, Ian Ring Music TheoryKatydyllic
Scale 2775Scale 2775: Godyllic, Ian Ring Music TheoryGodyllic
Scale 2791Scale 2791: Mixothyllic, Ian Ring Music TheoryMixothyllic
Scale 2695Scale 2695: Rakian, Ian Ring Music TheoryRakian
Scale 2727Scale 2727: Mela Manavati, Ian Ring Music TheoryMela Manavati
Scale 2631Scale 2631: Macrimic, Ian Ring Music TheoryMacrimic
Scale 2887Scale 2887: Gaptian, Ian Ring Music TheoryGaptian
Scale 3015Scale 3015: Laptyllic, Ian Ring Music TheoryLaptyllic
Scale 2247Scale 2247: Raga Vijayasri, Ian Ring Music TheoryRaga Vijayasri
Scale 2503Scale 2503: Mela Jhalavarali, Ian Ring Music TheoryMela Jhalavarali
Scale 3271Scale 3271: Mela Raghupriya, Ian Ring Music TheoryMela Raghupriya
Scale 3783Scale 3783: Phrygyllic, Ian Ring Music TheoryPhrygyllic
Scale 711Scale 711: Raga Chandrajyoti, Ian Ring Music TheoryRaga Chandrajyoti
Scale 1735Scale 1735: Mela Navanitam, Ian Ring Music TheoryMela Navanitam

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.