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Scale 2353: "Raga Girija"

Scale 2353: Raga Girija, 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 Girija
East European
Bacovia Pentatonic
Ethiopian
Batti Major Sharp 5
Zeitler
Lycritonic
Dozenal
ORTian

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

{0,4,5,8,11}

Forte Number

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

5-22

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.

[2]

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 Starr/Rahn algorithm.

no
prime: 403

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, an indicator of maximum hierarchization.

no

Interval Structure

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

[4, 1, 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.

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

Proportional Saturation Vector

First described by Michael Buchler (2001), this is a vector showing the prominence of intervals relative to the maximum and minimum possible for the scale's cardinality. A saturation of 0 means the interval is present minimally, a saturation of 1 means it is the maximum possible.

<0.5, 0, 0.5, 0.667, 0.5, 0.5>

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 Distribution Spectra have 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.

[4]

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)

Coherence Quotient

The Coherence Quotient is a score between 0 and 1, indicating the proportion of coherence failures (ambiguity or contradiction) in the scale, against the maximum possible for a cardinality. A high coherence quotient indicates a less complex scale, whereas a quotient of 0 indicates a maximally complex scale.

0.8

Sameness Quotient

The Sameness Quotient is a score between 0 and 1, indicating the proportion of differences in the heteromorphic profile, against the maximum possible for a cardinality. A higher quotient indicates a less complex scale, whereas a quotient of 0 indicates a scale with maximum complexity.

0.2

Generator

This scale has no generator.

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 TriadsE{4,8,11}221
Minor Triadsfm{5,8,0}221
Augmented TriadsC+{0,4,8}221
Diminished Triads{5,8,11}221
Parsimonious Voice Leading Between Common Triads of Scale 2353. Created by Ian Ring ©2019 C+ C+ E E C+->E fm fm C+->fm E->f° f°->fm

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 2353 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 403
Scale 403: Raga Reva, Ian Ring Music TheoryRaga RevaThis is the prime mode
3rd mode:
Scale 2249
Scale 2249: Raga Multani, Ian Ring Music TheoryRaga Multani
4th mode:
Scale 793
Scale 793: Mocritonic, Ian Ring Music TheoryMocritonic
5th mode:
Scale 611
Scale 611: Anchihoye, Ian Ring Music TheoryAnchihoye

Prime

The prime form of this scale is Scale 403

Scale 403Scale 403: Raga Reva, Ian Ring Music TheoryRaga Reva

Complement

The pentatonic modal family [2353, 403, 2249, 793, 611] (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 2353 is 403

Scale 403Scale 403: Raga Reva, Ian Ring Music TheoryRaga Reva

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

The transformations that map this set to itself are: T0, T4I, T4M, 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 2355Scale 2355: Raga Lalita, Ian Ring Music TheoryRaga Lalita
Scale 2357Scale 2357: Raga Sarasanana, Ian Ring Music TheoryRaga Sarasanana
Scale 2361Scale 2361: Docrimic, Ian Ring Music TheoryDocrimic
Scale 2337Scale 2337: OGOian, Ian Ring Music TheoryOGOian
Scale 2345Scale 2345: Gothitonic, Ian Ring Music TheoryGothitonic
Scale 2321Scale 2321: Zyphic, Ian Ring Music TheoryZyphic
Scale 2385Scale 2385: Karen 5tone Type 2, Ian Ring Music TheoryKaren 5tone Type 2
Scale 2417Scale 2417: Kanimic, Ian Ring Music TheoryKanimic
Scale 2481Scale 2481: Raga Paraju, Ian Ring Music TheoryRaga Paraju
Scale 2097Scale 2097: MUNian, Ian Ring Music TheoryMUNian
Scale 2225Scale 2225: Ionian Pentatonic, Ian Ring Music TheoryIonian Pentatonic
Scale 2609Scale 2609: Raga Bhinna Shadja, Ian Ring Music TheoryRaga Bhinna Shadja
Scale 2865Scale 2865: Solimic, Ian Ring Music TheorySolimic
Scale 3377Scale 3377: Phralimic, Ian Ring Music TheoryPhralimic
Scale 305Scale 305: Gonic, Ian Ring Music TheoryGonic
Scale 1329Scale 1329: Epygitonic, Ian Ring Music TheoryEpygitonic

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. Scale notation generated by VexFlow and Lilypond, graph visualization by Graphviz, audio by TiMIDIty and FFMPEG. 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.