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Scale 403: "Raga Reva"

Scale 403: Raga Reva, 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 Reva
Revagupti
Vibhas (Bhairava)
Dozenal
Cigian
Hindustani
Ramkali
Zeitler
Daptitonic

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

{0,1,4,7,8}

Forte Number

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

5-22

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.

[4]

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.

no

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.

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 Structure

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

[1, 3, 3, 1, 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.

<2, 0, 2, 3, 2, 1>

Interval Spectrum

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

p2m3n2d2t

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

Spectra Variation

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

2

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.

1.933

Polygon Perimeter

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

5.596

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.

yes

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.

[8]

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, 5, 32)

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 TriadsC{0,4,7}221
Minor Triadsc♯m{1,4,8}221
Augmented TriadsC+{0,4,8}221
Diminished Triadsc♯°{1,4,7}221
Parsimonious Voice Leading Between Common Triads of Scale 403. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° c#m c#m C+->c#m c#°->c#m

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 403 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2249
Scale 2249: Raga Multani, Ian Ring Music TheoryRaga Multani
3rd mode:
Scale 793
Scale 793: Mocritonic, Ian Ring Music TheoryMocritonic
4th mode:
Scale 611
Scale 611: Anchihoye, Ian Ring Music TheoryAnchihoye
5th mode:
Scale 2353
Scale 2353: Raga Girija, Ian Ring Music TheoryRaga Girija

Prime

This is the prime form of this scale.

Complement

The pentatonic modal family [403, 2249, 793, 611, 2353] (Forte: 5-22) is the complement of the heptatonic modal family [871, 923, 1651, 2483, 2509, 2873, 3289] (Forte: 7-22)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 403 is 2353

Scale 2353Scale 2353: Raga Girija, Ian Ring Music TheoryRaga Girija

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> 403       T0I <11,0> 2353
T1 <1,1> 806      T1I <11,1> 611
T2 <1,2> 1612      T2I <11,2> 1222
T3 <1,3> 3224      T3I <11,3> 2444
T4 <1,4> 2353      T4I <11,4> 793
T5 <1,5> 611      T5I <11,5> 1586
T6 <1,6> 1222      T6I <11,6> 3172
T7 <1,7> 2444      T7I <11,7> 2249
T8 <1,8> 793      T8I <11,8> 403
T9 <1,9> 1586      T9I <11,9> 806
T10 <1,10> 3172      T10I <11,10> 1612
T11 <1,11> 2249      T11I <11,11> 3224
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2353      T0MI <7,0> 403
T1M <5,1> 611      T1MI <7,1> 806
T2M <5,2> 1222      T2MI <7,2> 1612
T3M <5,3> 2444      T3MI <7,3> 3224
T4M <5,4> 793      T4MI <7,4> 2353
T5M <5,5> 1586      T5MI <7,5> 611
T6M <5,6> 3172      T6MI <7,6> 1222
T7M <5,7> 2249      T7MI <7,7> 2444
T8M <5,8> 403       T8MI <7,8> 793
T9M <5,9> 806      T9MI <7,9> 1586
T10M <5,10> 1612      T10MI <7,10> 3172
T11M <5,11> 3224      T11MI <7,11> 2249

The transformations that map this set to itself are: T0, T8I, T8M, 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 401Scale 401: Epogic, Ian Ring Music TheoryEpogic
Scale 405Scale 405: Raga Bhupeshwari, Ian Ring Music TheoryRaga Bhupeshwari
Scale 407Scale 407: All-Trichord Hexachord, Ian Ring Music TheoryAll-Trichord Hexachord
Scale 411Scale 411: Lygimic, Ian Ring Music TheoryLygimic
Scale 387Scale 387: Ciwian, Ian Ring Music TheoryCiwian
Scale 395Scale 395: Phrygian Pentatonic, Ian Ring Music TheoryPhrygian Pentatonic
Scale 419Scale 419: Hon-kumoi-joshi, Ian Ring Music TheoryHon-kumoi-joshi
Scale 435Scale 435: Raga Purna Pancama, Ian Ring Music TheoryRaga Purna Pancama
Scale 467Scale 467: Raga Dhavalangam, Ian Ring Music TheoryRaga Dhavalangam
Scale 275Scale 275: Dalic, Ian Ring Music TheoryDalic
Scale 339Scale 339: Zaptitonic, Ian Ring Music TheoryZaptitonic
Scale 147Scale 147: Bafian, Ian Ring Music TheoryBafian
Scale 659Scale 659: Raga Rasika Ranjani, Ian Ring Music TheoryRaga Rasika Ranjani
Scale 915Scale 915: Raga Kalagada, Ian Ring Music TheoryRaga Kalagada
Scale 1427Scale 1427: Lolimic, Ian Ring Music TheoryLolimic
Scale 2451Scale 2451: Raga Bauli, Ian Ring Music TheoryRaga Bauli

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.