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Scale 3253: "Mela Naganandini"

Scale 3253: Mela Naganandini, 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 Naganandini
Raga Nagabharanam
Sāmanta
Zeitler
Gonian
Dozenal
Uchian
Carnatic Melakarta
Naganandini
Carnatic Numbered Melakarta
30th 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

{0,2,4,5,7,10,11}

Forte Number

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

7-29

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: 1447

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.

[2, 2, 1, 2, 3, 1, 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, 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}142.14
G{7,11,2}321.29
A♯{10,2,5}241.86
Minor Triadsem{4,7,11}331.43
gm{7,10,2}331.43
Diminished Triads{4,7,10}231.57
{11,2,5}231.71
Parsimonious Voice Leading Between Common Triads of Scale 3253. Created by Ian Ring ©2019 C C em em C->em e°->em gm gm e°->gm Parsimonious Voice Leading Between Common Triads of Scale 3253. Created by Ian Ring ©2019 G em->G gm->G A# A# gm->A# G->b° A#->b°

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 VerticesG
Peripheral VerticesC, A♯

Modes

Modes are the rotational transformation of this scale. Scale 3253 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1837
Scale 1837: Dalian, Ian Ring Music TheoryDalian
3rd mode:
Scale 1483
Scale 1483: Mela Bhavapriya, Ian Ring Music TheoryMela Bhavapriya
4th mode:
Scale 2789
Scale 2789: Zolian, Ian Ring Music TheoryZolian
5th mode:
Scale 1721
Scale 1721: Mela Vagadhisvari, Ian Ring Music TheoryMela Vagadhisvari
6th mode:
Scale 727
Scale 727: Phradian, Ian Ring Music TheoryPhradianThis is the prime mode
7th mode:
Scale 2411
Scale 2411: Aeolorian, Ian Ring Music TheoryAeolorian

Prime

The prime form of this scale is Scale 727

Scale 727Scale 727: Phradian, Ian Ring Music TheoryPhradian

Complement

The heptatonic modal family [3253, 1837, 1483, 2789, 1721, 727, 2411] (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 3253 is 1447

Scale 1447Scale 1447: Mela Ratnangi, Ian Ring Music TheoryMela Ratnangi

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3253 is chiral, and its enantiomorph is scale 1447

Scale 1447Scale 1447: Mela Ratnangi, Ian Ring Music TheoryMela Ratnangi

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

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 3255Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic
Scale 3249Scale 3249: Raga Tilang, Ian Ring Music TheoryRaga Tilang
Scale 3251Scale 3251: Mela Hatakambari, Ian Ring Music TheoryMela Hatakambari
Scale 3257Scale 3257: Mela Calanata, Ian Ring Music TheoryMela Calanata
Scale 3261Scale 3261: Dodyllic, Ian Ring Music TheoryDodyllic
Scale 3237Scale 3237: Raga Brindabani Sarang, Ian Ring Music TheoryRaga Brindabani Sarang
Scale 3245Scale 3245: Mela Varunapriya, Ian Ring Music TheoryMela Varunapriya
Scale 3221Scale 3221: Bycrimic, Ian Ring Music TheoryBycrimic
Scale 3285Scale 3285: Mela Citrambari, Ian Ring Music TheoryMela Citrambari
Scale 3317Scale 3317: Katynyllic, Ian Ring Music TheoryKatynyllic
Scale 3125Scale 3125: Tonian, Ian Ring Music TheoryTonian
Scale 3189Scale 3189: Aeolonian, Ian Ring Music TheoryAeolonian
Scale 3381Scale 3381: Katanian, Ian Ring Music TheoryKatanian
Scale 3509Scale 3509: Stogyllic, Ian Ring Music TheoryStogyllic
Scale 3765Scale 3765: Dominant Bebop, Ian Ring Music TheoryDominant Bebop
Scale 2229Scale 2229: Raga Nalinakanti, Ian Ring Music TheoryRaga Nalinakanti
Scale 2741Scale 2741: Major, Ian Ring Music TheoryMajor
Scale 1205Scale 1205: Raga Siva Kambhoji, Ian Ring Music TheoryRaga Siva Kambhoji

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.