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Scale 2345: "Raga Chandrakauns"

Scale 2345: Raga Chandrakauns, 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
Raga Chandrakauns
Unknown / Unsorted
Kiravani
Zeitler
Gothitonic
Dozenal
Omsian

Analysis

Cardinality

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

5 (pentatonic)

Pitch Class Set

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

{0,3,5,8,11}

Forte Number

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

5-32

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: 659

Hemitonia

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

1 (unhemitonic)

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.

4

Prime Form

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

no
prime: 595

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, 2, 3, 3, 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.

<1, 1, 3, 2, 2, 1>

Interval Spectrum

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

p2m2n3sdt

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

Spectra Variation

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

1.6

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.

2.183

Polygon Perimeter

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

5.76

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".

Proper

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.

(0, 1, 30)

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}221
Minor Triadsfm{5,8,0}221
g♯m{8,11,3}221
Diminished Triads{5,8,11}221
Parsimonious Voice Leading Between Common Triads of Scale 2345. Created by Ian Ring ©2019 fm fm f°->fm g#m g#m f°->g#m G# G# fm->G# g#m->G#

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.

Diameter2
Radius2
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2345 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 805
Scale 805: Rothitonic, Ian Ring Music TheoryRothitonic
3rd mode:
Scale 1225
Scale 1225: Raga Samudhra Priya, Ian Ring Music TheoryRaga Samudhra Priya
4th mode:
Scale 665
Scale 665: Raga Mohanangi, Ian Ring Music TheoryRaga Mohanangi
5th mode:
Scale 595
Scale 595: Sogitonic, Ian Ring Music TheorySogitonicThis is the prime mode

Prime

The prime form of this scale is Scale 595

Scale 595Scale 595: Sogitonic, Ian Ring Music TheorySogitonic

Complement

The pentatonic modal family [2345, 805, 1225, 665, 595] (Forte: 5-32) is the complement of the heptatonic modal family [859, 1459, 1643, 1741, 2477, 2777, 2869] (Forte: 7-32)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2345 is 659

Scale 659Scale 659: Raga Rasika Ranjani, Ian Ring Music TheoryRaga Rasika Ranjani

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2345 is chiral, and its enantiomorph is scale 659

Scale 659Scale 659: Raga Rasika Ranjani, Ian Ring Music TheoryRaga Rasika Ranjani

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> 2345       T0I <11,0> 659
T1 <1,1> 595      T1I <11,1> 1318
T2 <1,2> 1190      T2I <11,2> 2636
T3 <1,3> 2380      T3I <11,3> 1177
T4 <1,4> 665      T4I <11,4> 2354
T5 <1,5> 1330      T5I <11,5> 613
T6 <1,6> 2660      T6I <11,6> 1226
T7 <1,7> 1225      T7I <11,7> 2452
T8 <1,8> 2450      T8I <11,8> 809
T9 <1,9> 805      T9I <11,9> 1618
T10 <1,10> 1610      T10I <11,10> 3236
T11 <1,11> 3220      T11I <11,11> 2377
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 155      T0MI <7,0> 2849
T1M <5,1> 310      T1MI <7,1> 1603
T2M <5,2> 620      T2MI <7,2> 3206
T3M <5,3> 1240      T3MI <7,3> 2317
T4M <5,4> 2480      T4MI <7,4> 539
T5M <5,5> 865      T5MI <7,5> 1078
T6M <5,6> 1730      T6MI <7,6> 2156
T7M <5,7> 3460      T7MI <7,7> 217
T8M <5,8> 2825      T8MI <7,8> 434
T9M <5,9> 1555      T9MI <7,9> 868
T10M <5,10> 3110      T10MI <7,10> 1736
T11M <5,11> 2125      T11MI <7,11> 3472

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 2347Scale 2347: Raga Viyogavarali, Ian Ring Music TheoryRaga Viyogavarali
Scale 2349Scale 2349: Raga Ghantana, Ian Ring Music TheoryRaga Ghantana
Scale 2337Scale 2337: Ogoian, Ian Ring Music TheoryOgoian
Scale 2341Scale 2341: Raga Priyadharshini, Ian Ring Music TheoryRaga Priyadharshini
Scale 2353Scale 2353: Raga Girija, Ian Ring Music TheoryRaga Girija
Scale 2361Scale 2361: Docrimic, Ian Ring Music TheoryDocrimic
Scale 2313Scale 2313: Osrian, Ian Ring Music TheoryOsrian
Scale 2329Scale 2329: Styditonic, Ian Ring Music TheoryStyditonic
Scale 2377Scale 2377: Bartók Gamma Chord, Ian Ring Music TheoryBartók Gamma Chord
Scale 2409Scale 2409: Zacrimic, Ian Ring Music TheoryZacrimic
Scale 2473Scale 2473: Raga Takka, Ian Ring Music TheoryRaga Takka
Scale 2089Scale 2089: Mujian, Ian Ring Music TheoryMujian
Scale 2217Scale 2217: Kagitonic, Ian Ring Music TheoryKagitonic
Scale 2601Scale 2601: Raga Chandrakauns, Ian Ring Music TheoryRaga Chandrakauns
Scale 2857Scale 2857: Stythimic, Ian Ring Music TheoryStythimic
Scale 3369Scale 3369: Mixolimic, Ian Ring Music TheoryMixolimic
Scale 297Scale 297: Mynic, Ian Ring Music TheoryMynic
Scale 1321Scale 1321: Blues Minor, Ian Ring Music TheoryBlues Minor

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.