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Scale 1721: "Mela Vagadhisvari"

Scale 1721: Mela Vagadhisvari, 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 Vagadhisvari
Raga Bhogachayanata
Dozenal
Korian
Western Altered
Mixolydian Sharp 2
Unknown / Unsorted
Nandkauns
Ganavaridhi
Chayanata
Jazz and Blues
Bluesy Rock 'n Roll
Zeitler
Ionycrian
Carnatic Melakarta
Vagadheeswari
Carnatic Numbered Melakarta
34th 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

{0,3,4,5,7,9,10}

Forte Number

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

7-29

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: 941

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.

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: 727

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.

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

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, 4, 3, 5, 2>

Interval Spectrum

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

p5m3n4s4d3t2

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

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.

(4, 28, 92)

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}321.29
D♯{3,7,10}241.86
F{5,9,0}142.14
Minor Triadscm{0,3,7}331.43
am{9,0,4}331.43
Diminished Triads{4,7,10}231.71
{9,0,3}231.57
Parsimonious Voice Leading Between Common Triads of Scale 1721. Created by Ian Ring ©2019 cm cm C C cm->C D# D# cm->D# cm->a° C->e° am am C->am D#->e° F F F->am a°->am

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 VerticesC
Peripheral VerticesD♯, F

Modes

Modes are the rotational transformation of this scale. Scale 1721 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 727
Scale 727: Phradian, Ian Ring Music TheoryPhradianThis is the prime mode
3rd mode:
Scale 2411
Scale 2411: Aeolorian, Ian Ring Music TheoryAeolorian
4th mode:
Scale 3253
Scale 3253: Mela Naganandini, Ian Ring Music TheoryMela Naganandini
5th mode:
Scale 1837
Scale 1837: Dalian, Ian Ring Music TheoryDalian
6th mode:
Scale 1483
Scale 1483: Mela Bhavapriya, Ian Ring Music TheoryMela Bhavapriya
7th mode:
Scale 2789
Scale 2789: Zolian, Ian Ring Music TheoryZolian

Prime

The prime form of this scale is Scale 727

Scale 727Scale 727: Phradian, Ian Ring Music TheoryPhradian

Complement

The heptatonic modal family [1721, 727, 2411, 3253, 1837, 1483, 2789] (Forte: 7-29) is the complement of the pentatonic modal family [331, 709, 1201, 1577, 2213] (Forte: 5-29)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1721 is 941

Scale 941Scale 941: Mela Jhankaradhvani, Ian Ring Music TheoryMela Jhankaradhvani

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1721 is chiral, and its enantiomorph is scale 941

Scale 941Scale 941: Mela Jhankaradhvani, Ian Ring Music TheoryMela Jhankaradhvani

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> 1721       T0I <11,0> 941
T1 <1,1> 3442      T1I <11,1> 1882
T2 <1,2> 2789      T2I <11,2> 3764
T3 <1,3> 1483      T3I <11,3> 3433
T4 <1,4> 2966      T4I <11,4> 2771
T5 <1,5> 1837      T5I <11,5> 1447
T6 <1,6> 3674      T6I <11,6> 2894
T7 <1,7> 3253      T7I <11,7> 1693
T8 <1,8> 2411      T8I <11,8> 3386
T9 <1,9> 727      T9I <11,9> 2677
T10 <1,10> 1454      T10I <11,10> 1259
T11 <1,11> 2908      T11I <11,11> 2518
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2831      T0MI <7,0> 3611
T1M <5,1> 1567      T1MI <7,1> 3127
T2M <5,2> 3134      T2MI <7,2> 2159
T3M <5,3> 2173      T3MI <7,3> 223
T4M <5,4> 251      T4MI <7,4> 446
T5M <5,5> 502      T5MI <7,5> 892
T6M <5,6> 1004      T6MI <7,6> 1784
T7M <5,7> 2008      T7MI <7,7> 3568
T8M <5,8> 4016      T8MI <7,8> 3041
T9M <5,9> 3937      T9MI <7,9> 1987
T10M <5,10> 3779      T10MI <7,10> 3974
T11M <5,11> 3463      T11MI <7,11> 3853

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 1723Scale 1723: JG Octatonic, Ian Ring Music TheoryJG Octatonic
Scale 1725Scale 1725: Minor Bebop, Ian Ring Music TheoryMinor Bebop
Scale 1713Scale 1713: Raga Khamas, Ian Ring Music TheoryRaga Khamas
Scale 1717Scale 1717: Mixolydian, Ian Ring Music TheoryMixolydian
Scale 1705Scale 1705: Raga Manohari, Ian Ring Music TheoryRaga Manohari
Scale 1689Scale 1689: Lorimic, Ian Ring Music TheoryLorimic
Scale 1753Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major
Scale 1785Scale 1785: Tharyllic, Ian Ring Music TheoryTharyllic
Scale 1593Scale 1593: Zogimic, Ian Ring Music TheoryZogimic
Scale 1657Scale 1657: Ionothian, Ian Ring Music TheoryIonothian
Scale 1849Scale 1849: Chromatic Hypodorian Inverse, Ian Ring Music TheoryChromatic Hypodorian Inverse
Scale 1977Scale 1977: Dagyllic, Ian Ring Music TheoryDagyllic
Scale 1209Scale 1209: Raga Bhanumanjari, Ian Ring Music TheoryRaga Bhanumanjari
Scale 1465Scale 1465: Mela Ragavardhani, Ian Ring Music TheoryMela Ragavardhani
Scale 697Scale 697: Lagimic, Ian Ring Music TheoryLagimic
Scale 2745Scale 2745: Mela Sulini, Ian Ring Music TheoryMela Sulini
Scale 3769Scale 3769: Eponyllic, Ian Ring Music TheoryEponyllic

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.