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Scale 2221: "Raga Sindhura Kafi"

Scale 2221: Raga Sindhura Kafi, 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 Raga
Raga Sindhura Kafi
Zeitler
Poptimic

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

6 (hexatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,2,3,5,7,11}

Forte Number

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

6-Z24

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: 1699

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

2 (dihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

0 (ancohemitonic)

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.

5

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 347

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.

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

Interval Spectrum

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

p3m3n3s3d2t

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> = {1,2,4}
<2> = {3,4,5,6}
<3> = {4,5,7,8}
<4> = {6,7,8,9}
<5> = {8,10,11}

Spectra Variation

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

2.667

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.

2.232

Polygon Perimeter

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

5.767

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

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}221
Minor Triadscm{0,3,7}131.5
Augmented TriadsD♯+{3,7,11}221
Diminished Triads{11,2,5}131.5
Parsimonious Voice Leading Between Common Triads of Scale 2221. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ Parsimonious Voice Leading Between Common Triads of Scale 2221. Created by Ian Ring ©2019 G D#+->G G->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 VerticesD♯+, G
Peripheral Verticescm, b°

Modes

Modes are the rotational transformation of this scale. Scale 2221 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1579
Scale 1579: Sagimic, Ian Ring Music TheorySagimic
3rd mode:
Scale 2837
Scale 2837: Aelothimic, Ian Ring Music TheoryAelothimic
4th mode:
Scale 1733
Scale 1733: Raga Sarasvati, Ian Ring Music TheoryRaga Sarasvati
5th mode:
Scale 1457
Scale 1457: Raga Kamalamanohari, Ian Ring Music TheoryRaga Kamalamanohari
6th mode:
Scale 347
Scale 347: Barimic, Ian Ring Music TheoryBarimicThis is the prime mode

Prime

The prime form of this scale is Scale 347

Scale 347Scale 347: Barimic, Ian Ring Music TheoryBarimic

Complement

The hexatonic modal family [2221, 1579, 2837, 1733, 1457, 347] (Forte: 6-Z24) is the complement of the hexatonic modal family [599, 697, 1481, 1829, 2347, 3221] (Forte: 6-Z46)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2221 is 1699

Scale 1699Scale 1699: Raga Rasavali, Ian Ring Music TheoryRaga Rasavali

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2221 is chiral, and its enantiomorph is scale 1699

Scale 1699Scale 1699: Raga Rasavali, Ian Ring Music TheoryRaga Rasavali

Transformations:

T0 2221  T0I 1699
T1 347  T1I 3398
T2 694  T2I 2701
T3 1388  T3I 1307
T4 2776  T4I 2614
T5 1457  T5I 1133
T6 2914  T6I 2266
T7 1733  T7I 437
T8 3466  T8I 874
T9 2837  T9I 1748
T10 1579  T10I 3496
T11 3158  T11I 2897

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 2223Scale 2223: Konian, Ian Ring Music TheoryKonian
Scale 2217Scale 2217: Kagitonic, Ian Ring Music TheoryKagitonic
Scale 2219Scale 2219: Phrydimic, Ian Ring Music TheoryPhrydimic
Scale 2213Scale 2213: Raga Desh, Ian Ring Music TheoryRaga Desh
Scale 2229Scale 2229: Raga Nalinakanti, Ian Ring Music TheoryRaga Nalinakanti
Scale 2237Scale 2237: Epothian, Ian Ring Music TheoryEpothian
Scale 2189Scale 2189: Zagitonic, Ian Ring Music TheoryZagitonic
Scale 2205Scale 2205: Ionocrimic, Ian Ring Music TheoryIonocrimic
Scale 2253Scale 2253: Raga Amarasenapriya, Ian Ring Music TheoryRaga Amarasenapriya
Scale 2285Scale 2285: Aerogian, Ian Ring Music TheoryAerogian
Scale 2093Scale 2093, Ian Ring Music Theory
Scale 2157Scale 2157, Ian Ring Music Theory
Scale 2349Scale 2349: Raga Ghantana, Ian Ring Music TheoryRaga Ghantana
Scale 2477Scale 2477: Harmonic Minor, Ian Ring Music TheoryHarmonic Minor
Scale 2733Scale 2733: Melodic Minor Ascending, Ian Ring Music TheoryMelodic Minor Ascending
Scale 3245Scale 3245: Mela Varunapriya, Ian Ring Music TheoryMela Varunapriya
Scale 173Scale 173: Raga Purnalalita, Ian Ring Music TheoryRaga Purnalalita
Scale 1197Scale 1197: Minor Hexatonic, Ian Ring Music TheoryMinor Hexatonic

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.