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Scale 971: "Mela Gavambodhi"

Scale 971: Mela Gavambodhi, 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 Gavambodhi
Raga Girvani
Zeitler
Ladian
Dozenal
Gahian
Carnatic Melakarta
Gavambhodi
Carnatic Numbered Melakarta
43rd 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

{0,1,3,6,7,8,9}

Forte Number

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

7-19

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: 2681

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.

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: 719

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

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, 3, 4, 3, 4, 3>

Interval Spectrum

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

p4m3n4s3d4t3

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> = {3,5,6}
<4> = {6,7,9}
<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.

2.433

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.

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.

(16, 29, 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 TriadsG♯{8,0,3}231.71
Minor Triadscm{0,3,7}231.71
f♯m{6,9,1}231.71
Diminished Triads{0,3,6}231.71
d♯°{3,6,9}231.71
f♯°{6,9,0}231.71
{9,0,3}231.71
Parsimonious Voice Leading Between Common Triads of Scale 971. Created by Ian Ring ©2019 cm cm c°->cm d#° d#° c°->d#° G# G# cm->G# f#m f#m d#°->f#m f#° f#° f#°->f#m f#°->a° G#->a°

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
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 971 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2533
Scale 2533: Podian, Ian Ring Music TheoryPodian
3rd mode:
Scale 1657
Scale 1657: Ionothian, Ian Ring Music TheoryIonothian
4th mode:
Scale 719
Scale 719: Kanian, Ian Ring Music TheoryKanianThis is the prime mode
5th mode:
Scale 2407
Scale 2407: Zylian, Ian Ring Music TheoryZylian
6th mode:
Scale 3251
Scale 3251: Mela Hatakambari, Ian Ring Music TheoryMela Hatakambari
7th mode:
Scale 3673
Scale 3673: Ranian, Ian Ring Music TheoryRanian

Prime

The prime form of this scale is Scale 719

Scale 719Scale 719: Kanian, Ian Ring Music TheoryKanian

Complement

The heptatonic modal family [971, 2533, 1657, 719, 2407, 3251, 3673] (Forte: 7-19) is the complement of the pentatonic modal family [203, 707, 1561, 2149, 2401] (Forte: 5-19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 971 is 2681

Scale 2681Scale 2681: Aerycrian, Ian Ring Music TheoryAerycrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 971 is chiral, and its enantiomorph is scale 2681

Scale 2681Scale 2681: Aerycrian, Ian Ring Music TheoryAerycrian

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> 971       T0I <11,0> 2681
T1 <1,1> 1942      T1I <11,1> 1267
T2 <1,2> 3884      T2I <11,2> 2534
T3 <1,3> 3673      T3I <11,3> 973
T4 <1,4> 3251      T4I <11,4> 1946
T5 <1,5> 2407      T5I <11,5> 3892
T6 <1,6> 719      T6I <11,6> 3689
T7 <1,7> 1438      T7I <11,7> 3283
T8 <1,8> 2876      T8I <11,8> 2471
T9 <1,9> 1657      T9I <11,9> 847
T10 <1,10> 3314      T10I <11,10> 1694
T11 <1,11> 2533      T11I <11,11> 3388
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2681      T0MI <7,0> 971
T1M <5,1> 1267      T1MI <7,1> 1942
T2M <5,2> 2534      T2MI <7,2> 3884
T3M <5,3> 973      T3MI <7,3> 3673
T4M <5,4> 1946      T4MI <7,4> 3251
T5M <5,5> 3892      T5MI <7,5> 2407
T6M <5,6> 3689      T6MI <7,6> 719
T7M <5,7> 3283      T7MI <7,7> 1438
T8M <5,8> 2471      T8MI <7,8> 2876
T9M <5,9> 847      T9MI <7,9> 1657
T10M <5,10> 1694      T10MI <7,10> 3314
T11M <5,11> 3388      T11MI <7,11> 2533

The transformations that map this set to itself are: T0, T0MI

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 969Scale 969: Ionogimic, Ian Ring Music TheoryIonogimic
Scale 973Scale 973: Mela Syamalangi, Ian Ring Music TheoryMela Syamalangi
Scale 975Scale 975: Messiaen Mode 4, Ian Ring Music TheoryMessiaen Mode 4
Scale 963Scale 963: Gacian, Ian Ring Music TheoryGacian
Scale 967Scale 967: Mela Salaga, Ian Ring Music TheoryMela Salaga
Scale 979Scale 979: Mela Dhavalambari, Ian Ring Music TheoryMela Dhavalambari
Scale 987Scale 987: Aeraptyllic, Ian Ring Music TheoryAeraptyllic
Scale 1003Scale 1003: Ionyryllic, Ian Ring Music TheoryIonyryllic
Scale 907Scale 907: Tholimic, Ian Ring Music TheoryTholimic
Scale 939Scale 939: Mela Senavati, Ian Ring Music TheoryMela Senavati
Scale 843Scale 843: Molimic, Ian Ring Music TheoryMolimic
Scale 715Scale 715: Messiaen Truncated Mode 2, Ian Ring Music TheoryMessiaen Truncated Mode 2
Scale 459Scale 459: Zaptimic, Ian Ring Music TheoryZaptimic
Scale 1483Scale 1483: Mela Bhavapriya, Ian Ring Music TheoryMela Bhavapriya
Scale 1995Scale 1995: Sideways Scale, Ian Ring Music TheorySideways Scale
Scale 3019Scale 3019: Subian, Ian Ring Music TheorySubian

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.