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Scale 1465: "Mela Ragavardhani"

Scale 1465: Mela Ragavardhani, 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 Ragavardhani
Raga Cudamani
Dozenal
Jaqian
Zeitler
Aerathian
Carnatic Melakarta
Ragavardhini
Carnatic Numbered Melakarta
32nd 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

{0,3,4,5,7,8,10}

Forte Number

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

7-27

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: 949

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: 695

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

Interval Spectrum

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

p5m4n4s4d3t

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

2.286

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.

2.549

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.

(9, 35, 98)

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
G♯{8,0,3}231.57
Minor Triadscm{0,3,7}331.43
fm{5,8,0}142.14
Augmented TriadsC+{0,4,8}331.43
Diminished Triads{4,7,10}231.71
Parsimonious Voice Leading Between Common Triads of Scale 1465. Created by Ian Ring ©2019 cm cm C C cm->C D# D# cm->D# G# G# cm->G# C+ C+ C->C+ C->e° fm fm C+->fm C+->G# D#->e°

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♯, fm

Modes

Modes are the rotational transformation of this scale. Scale 1465 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 695
Scale 695: Sarian, Ian Ring Music TheorySarianThis is the prime mode
3rd mode:
Scale 2395
Scale 2395: Zoptian, Ian Ring Music TheoryZoptian
4th mode:
Scale 3245
Scale 3245: Mela Varunapriya, Ian Ring Music TheoryMela Varunapriya
5th mode:
Scale 1835
Scale 1835: Byptian, Ian Ring Music TheoryByptian
6th mode:
Scale 2965
Scale 2965: Darian, Ian Ring Music TheoryDarian
7th mode:
Scale 1765
Scale 1765: Lonian, Ian Ring Music TheoryLonian

Prime

The prime form of this scale is Scale 695

Scale 695Scale 695: Sarian, Ian Ring Music TheorySarian

Complement

The heptatonic modal family [1465, 695, 2395, 3245, 1835, 2965, 1765] (Forte: 7-27) is the complement of the pentatonic modal family [299, 689, 1417, 1573, 2197] (Forte: 5-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1465 is 949

Scale 949Scale 949: Mela Mararanjani, Ian Ring Music TheoryMela Mararanjani

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1465 is chiral, and its enantiomorph is scale 949

Scale 949Scale 949: Mela Mararanjani, Ian Ring Music TheoryMela Mararanjani

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> 1465       T0I <11,0> 949
T1 <1,1> 2930      T1I <11,1> 1898
T2 <1,2> 1765      T2I <11,2> 3796
T3 <1,3> 3530      T3I <11,3> 3497
T4 <1,4> 2965      T4I <11,4> 2899
T5 <1,5> 1835      T5I <11,5> 1703
T6 <1,6> 3670      T6I <11,6> 3406
T7 <1,7> 3245      T7I <11,7> 2717
T8 <1,8> 2395      T8I <11,8> 1339
T9 <1,9> 695      T9I <11,9> 2678
T10 <1,10> 1390      T10I <11,10> 1261
T11 <1,11> 2780      T11I <11,11> 2522
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2335      T0MI <7,0> 3859
T1M <5,1> 575      T1MI <7,1> 3623
T2M <5,2> 1150      T2MI <7,2> 3151
T3M <5,3> 2300      T3MI <7,3> 2207
T4M <5,4> 505      T4MI <7,4> 319
T5M <5,5> 1010      T5MI <7,5> 638
T6M <5,6> 2020      T6MI <7,6> 1276
T7M <5,7> 4040      T7MI <7,7> 2552
T8M <5,8> 3985      T8MI <7,8> 1009
T9M <5,9> 3875      T9MI <7,9> 2018
T10M <5,10> 3655      T10MI <7,10> 4036
T11M <5,11> 3215      T11MI <7,11> 3977

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 1467Scale 1467: Spanish Phrygian, Ian Ring Music TheorySpanish Phrygian
Scale 1469Scale 1469: Epiryllic, Ian Ring Music TheoryEpiryllic
Scale 1457Scale 1457: Raga Kamalamanohari, Ian Ring Music TheoryRaga Kamalamanohari
Scale 1461Scale 1461: Major-Minor, Ian Ring Music TheoryMajor-Minor
Scale 1449Scale 1449: Raga Gopikavasantam, Ian Ring Music TheoryRaga Gopikavasantam
Scale 1433Scale 1433: Dynimic, Ian Ring Music TheoryDynimic
Scale 1497Scale 1497: Mela Jyotisvarupini, Ian Ring Music TheoryMela Jyotisvarupini
Scale 1529Scale 1529: Kataryllic, Ian Ring Music TheoryKataryllic
Scale 1337Scale 1337: Epogimic, Ian Ring Music TheoryEpogimic
Scale 1401Scale 1401: Pagian, Ian Ring Music TheoryPagian
Scale 1209Scale 1209: Raga Bhanumanjari, Ian Ring Music TheoryRaga Bhanumanjari
Scale 1721Scale 1721: Mela Vagadhisvari, Ian Ring Music TheoryMela Vagadhisvari
Scale 1977Scale 1977: Dagyllic, Ian Ring Music TheoryDagyllic
Scale 441Scale 441: Thycrimic, Ian Ring Music TheoryThycrimic
Scale 953Scale 953: Mela Yagapriya, Ian Ring Music TheoryMela Yagapriya
Scale 2489Scale 2489: Mela Gangeyabhusani, Ian Ring Music TheoryMela Gangeyabhusani
Scale 3513Scale 3513: Dydyllic, Ian Ring Music TheoryDydyllic

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.