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Scale 3239: "Mela Tanarupi"

Scale 3239: Mela Tanarupi, 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

41161837294116105072918310504116183
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
Mela Tanarupi
Carnatic Raga
Raga Tanukirti
Zeitler
Epythian

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

{0,1,2,5,7,10,11}

Forte Number

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

7-Z12

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.

[0]

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

yes

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

no

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.

3 (tricohemitonic)

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: 671

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

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, 4, 3, 4, 2]

Interval Spectrum

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

p4m3n4s4d4t2

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

Spectra Variation

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

2.857

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.

2.433

Polygon Perimeter

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

5.899

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.

[0]

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

Harmonic Chords

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 TriadsG{7,11,2}231.5
A♯{10,2,5}321.17
Minor Triadsgm{7,10,2}321.17
a♯m{10,1,5}231.5
Diminished Triads{7,10,1}231.5
{11,2,5}231.5

The following pitch classes are not present in any of the common triads: {0}

Parsimonious Voice Leading Between Common Triads of Scale 3239. Created by Ian Ring ©2019 gm gm g°->gm a#m a#m g°->a#m Parsimonious Voice Leading Between Common Triads of Scale 3239. Created by Ian Ring ©2019 G gm->G A# A# gm->A# G->b° a#m->A# A#->b°

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.

Diameter3
Radius2
Self-Centeredno
Central Verticesgm, A♯
Peripheral Verticesg°, G, a♯m, b°

Modes

Modes are the rotational transformation of this scale. Scale 3239 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3667
Scale 3667: Kaptian, Ian Ring Music TheoryKaptian
3rd mode:
Scale 3881
Scale 3881: Morian, Ian Ring Music TheoryMorian
4th mode:
Scale 997
Scale 997: Rycrian, Ian Ring Music TheoryRycrian
5th mode:
Scale 1273
Scale 1273: Ronian, Ian Ring Music TheoryRonian
6th mode:
Scale 671
Scale 671: Stycrian, Ian Ring Music TheoryStycrianThis is the prime mode
7th mode:
Scale 2383
Scale 2383: Katorian, Ian Ring Music TheoryKatorian

Prime

The prime form of this scale is Scale 671

Scale 671Scale 671: Stycrian, Ian Ring Music TheoryStycrian

Complement

The heptatonic modal family [3239, 3667, 3881, 997, 1273, 671, 2383] (Forte: 7-Z12) is the complement of the pentatonic modal family [107, 1411, 1549, 2101, 2753] (Forte: 5-Z12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3239 is itself, because it is a palindromic scale!

Scale 3239Scale 3239: Mela Tanarupi, Ian Ring Music TheoryMela Tanarupi

Transformations:

T0 3239  T0I 3239
T1 2383  T1I 2383
T2 671  T2I 671
T3 1342  T3I 1342
T4 2684  T4I 2684
T5 1273  T5I 1273
T6 2546  T6I 2546
T7 997  T7I 997
T8 1994  T8I 1994
T9 3988  T9I 3988
T10 3881  T10I 3881
T11 3667  T11I 3667

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 3237Scale 3237: Raga Brindabani Sarang, Ian Ring Music TheoryRaga Brindabani Sarang
Scale 3235Scale 3235: Pothimic, Ian Ring Music TheoryPothimic
Scale 3243Scale 3243: Mela Rupavati, Ian Ring Music TheoryMela Rupavati
Scale 3247Scale 3247: Aeolonyllic, Ian Ring Music TheoryAeolonyllic
Scale 3255Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic
Scale 3207Scale 3207, Ian Ring Music Theory
Scale 3223Scale 3223: Thyphian, Ian Ring Music TheoryThyphian
Scale 3271Scale 3271: Mela Raghupriya, Ian Ring Music TheoryMela Raghupriya
Scale 3303Scale 3303: Mylyllic, Ian Ring Music TheoryMylyllic
Scale 3111Scale 3111, Ian Ring Music Theory
Scale 3175Scale 3175: Eponian, Ian Ring Music TheoryEponian
Scale 3367Scale 3367: Moptian, Ian Ring Music TheoryMoptian
Scale 3495Scale 3495: Banyllic, Ian Ring Music TheoryBanyllic
Scale 3751Scale 3751: Aerathyllic, Ian Ring Music TheoryAerathyllic
Scale 2215Scale 2215: Ranimic, Ian Ring Music TheoryRanimic
Scale 2727Scale 2727: Mela Manavati, Ian Ring Music TheoryMela Manavati
Scale 1191Scale 1191: Pyrimic, Ian Ring Music TheoryPyrimic

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. 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.