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Scale 301: "Raga Audav Tukhari"

Scale 301: Raga Audav Tukhari, 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
Raga Audav Tukhari
Zeitler
Zythitonic

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

{0,2,3,5,8}

Forte Number

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

5-25

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: 1681

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.

yes

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 Formula

Defines the scale as the sequence of intervals between one tone and the next.

[2, 1, 2, 3, 4]

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, 2, 3, 1, 2, 1>

Interval Spectrum

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

p2mn3s2dt

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

Spectra Variation

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

2.8

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.

2.049

Polygon Perimeter

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

5.664

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.

(7, 7, 36)

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}121
Minor Triadsfm{5,8,0}210.67
Diminished Triads{2,5,8}121
Parsimonious Voice Leading Between Common Triads of Scale 301. Created by Ian Ring ©2019 fm fm d°->fm G# G# fm->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
Radius1
Self-Centeredno
Central Verticesfm
Peripheral Verticesd°, G♯

Modes

Modes are the rotational transformation of this scale. Scale 301 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1099
Scale 1099: Dyritonic, Ian Ring Music TheoryDyritonic
3rd mode:
Scale 2597
Scale 2597: Raga Rasranjani, Ian Ring Music TheoryRaga Rasranjani
4th mode:
Scale 1673
Scale 1673: Thocritonic, Ian Ring Music TheoryThocritonic
5th mode:
Scale 721
Scale 721: Raga Dhavalashri, Ian Ring Music TheoryRaga Dhavalashri

Prime

This is the prime form of this scale.

Complement

The pentatonic modal family [301, 1099, 2597, 1673, 721] (Forte: 5-25) is the complement of the heptatonic modal family [733, 1207, 1769, 1867, 2651, 2981, 3373] (Forte: 7-25)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 301 is 1681

Scale 1681Scale 1681: Raga Valaji, Ian Ring Music TheoryRaga Valaji

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 301 is chiral, and its enantiomorph is scale 1681

Scale 1681Scale 1681: Raga Valaji, Ian Ring Music TheoryRaga Valaji

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> 301       T0I <11,0> 1681
T1 <1,1> 602      T1I <11,1> 3362
T2 <1,2> 1204      T2I <11,2> 2629
T3 <1,3> 2408      T3I <11,3> 1163
T4 <1,4> 721      T4I <11,4> 2326
T5 <1,5> 1442      T5I <11,5> 557
T6 <1,6> 2884      T6I <11,6> 1114
T7 <1,7> 1673      T7I <11,7> 2228
T8 <1,8> 3346      T8I <11,8> 361
T9 <1,9> 2597      T9I <11,9> 722
T10 <1,10> 1099      T10I <11,10> 1444
T11 <1,11> 2198      T11I <11,11> 2888
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 1051      T0MI <7,0> 2821
T1M <5,1> 2102      T1MI <7,1> 1547
T2M <5,2> 109      T2MI <7,2> 3094
T3M <5,3> 218      T3MI <7,3> 2093
T4M <5,4> 436      T4MI <7,4> 91
T5M <5,5> 872      T5MI <7,5> 182
T6M <5,6> 1744      T6MI <7,6> 364
T7M <5,7> 3488      T7MI <7,7> 728
T8M <5,8> 2881      T8MI <7,8> 1456
T9M <5,9> 1667      T9MI <7,9> 2912
T10M <5,10> 3334      T10MI <7,10> 1729
T11M <5,11> 2573      T11MI <7,11> 3458

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 303Scale 303: Golimic, Ian Ring Music TheoryGolimic
Scale 297Scale 297: Mynic, Ian Ring Music TheoryMynic
Scale 299Scale 299: Raga Chitthakarshini, Ian Ring Music TheoryRaga Chitthakarshini
Scale 293Scale 293: Raga Haripriya, Ian Ring Music TheoryRaga Haripriya
Scale 309Scale 309: Palitonic, Ian Ring Music TheoryPalitonic
Scale 317Scale 317: Korimic, Ian Ring Music TheoryKorimic
Scale 269Scale 269, Ian Ring Music Theory
Scale 285Scale 285: Zaritonic, Ian Ring Music TheoryZaritonic
Scale 333Scale 333: Bogitonic, Ian Ring Music TheoryBogitonic
Scale 365Scale 365: Marimic, Ian Ring Music TheoryMarimic
Scale 429Scale 429: Koptimic, Ian Ring Music TheoryKoptimic
Scale 45Scale 45, Ian Ring Music Theory
Scale 173Scale 173: Raga Purnalalita, Ian Ring Music TheoryRaga Purnalalita
Scale 557Scale 557: Raga Abhogi, Ian Ring Music TheoryRaga Abhogi
Scale 813Scale 813: Larimic, Ian Ring Music TheoryLarimic
Scale 1325Scale 1325: Phradimic, Ian Ring Music TheoryPhradimic
Scale 2349Scale 2349: Raga Ghantana, Ian Ring Music TheoryRaga Ghantana

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.