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Scale 2247: "Raga Vijayasri"

Scale 2247: Raga Vijayasri, 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 Vijayasri
Zeitler
Aeolimic
Dozenal
Nobian

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

{0,1,2,6,7,11}

Forte Number

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

6-Z38

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.

[0.5]

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.

4 (multihemitonic)

Cohemitonia

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

2 (dicohemitonic)

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.

2

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: 399

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, 1, 4, 1, 4, 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.

<4, 2, 1, 2, 4, 2>

Interval Spectrum

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

p4m2ns2d4t2

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

Spectra Variation

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

3

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.

1.866

Polygon Perimeter

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

5.535

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.

[1]

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.

(20, 0, 41)

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}110.5
Minor Triadsbm{11,2,6}110.5

The following pitch classes are not present in any of the common triads: {0,1}

Parsimonious Voice Leading Between Common Triads of Scale 2247. Created by Ian Ring ©2019 Parsimonious Voice Leading Between Common Triads of Scale 2247. Created by Ian Ring ©2019 G bm bm G->bm

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2247 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3171
Scale 3171: Zythimic, Ian Ring Music TheoryZythimic
3rd mode:
Scale 3633
Scale 3633: Daptimic, Ian Ring Music TheoryDaptimic
4th mode:
Scale 483
Scale 483: Kygimic, Ian Ring Music TheoryKygimic
5th mode:
Scale 2289
Scale 2289: Mocrimic, Ian Ring Music TheoryMocrimic
6th mode:
Scale 399
Scale 399: Zynimic, Ian Ring Music TheoryZynimicThis is the prime mode

Prime

The prime form of this scale is Scale 399

Scale 399Scale 399: Zynimic, Ian Ring Music TheoryZynimic

Complement

The hexatonic modal family [2247, 3171, 3633, 483, 2289, 399] (Forte: 6-Z38) is the complement of the hexatonic modal family [231, 903, 2163, 2499, 3129, 3297] (Forte: 6-Z6)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2247 is 3171

Scale 3171Scale 3171: Zythimic, Ian Ring Music TheoryZythimic

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> 2247       T0I <11,0> 3171
T1 <1,1> 399      T1I <11,1> 2247
T2 <1,2> 798      T2I <11,2> 399
T3 <1,3> 1596      T3I <11,3> 798
T4 <1,4> 3192      T4I <11,4> 1596
T5 <1,5> 2289      T5I <11,5> 3192
T6 <1,6> 483      T6I <11,6> 2289
T7 <1,7> 966      T7I <11,7> 483
T8 <1,8> 1932      T8I <11,8> 966
T9 <1,9> 3864      T9I <11,9> 1932
T10 <1,10> 3633      T10I <11,10> 3864
T11 <1,11> 3171      T11I <11,11> 3633
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 3297      T0MI <7,0> 231
T1M <5,1> 2499      T1MI <7,1> 462
T2M <5,2> 903      T2MI <7,2> 924
T3M <5,3> 1806      T3MI <7,3> 1848
T4M <5,4> 3612      T4MI <7,4> 3696
T5M <5,5> 3129      T5MI <7,5> 3297
T6M <5,6> 2163      T6MI <7,6> 2499
T7M <5,7> 231      T7MI <7,7> 903
T8M <5,8> 462      T8MI <7,8> 1806
T9M <5,9> 924      T9MI <7,9> 3612
T10M <5,10> 1848      T10MI <7,10> 3129
T11M <5,11> 3696      T11MI <7,11> 2163

The transformations that map this set to itself are: T0, T1I

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 2245Scale 2245: Raga Vaijayanti, Ian Ring Music TheoryRaga Vaijayanti
Scale 2243Scale 2243: Noyian, Ian Ring Music TheoryNoyian
Scale 2251Scale 2251: Zodimic, Ian Ring Music TheoryZodimic
Scale 2255Scale 2255: Dylian, Ian Ring Music TheoryDylian
Scale 2263Scale 2263: Lycrian, Ian Ring Music TheoryLycrian
Scale 2279Scale 2279: Dyrian, Ian Ring Music TheoryDyrian
Scale 2183Scale 2183: Nenian, Ian Ring Music TheoryNenian
Scale 2215Scale 2215: Ranimic, Ian Ring Music TheoryRanimic
Scale 2119Scale 2119: Mubian, Ian Ring Music TheoryMubian
Scale 2375Scale 2375: Aeolaptimic, Ian Ring Music TheoryAeolaptimic
Scale 2503Scale 2503: Mela Jhalavarali, Ian Ring Music TheoryMela Jhalavarali
Scale 2759Scale 2759: Mela Pavani, Ian Ring Music TheoryMela Pavani
Scale 3271Scale 3271: Mela Raghupriya, Ian Ring Music TheoryMela Raghupriya
Scale 199Scale 199: Raga Nabhomani, Ian Ring Music TheoryRaga Nabhomani
Scale 1223Scale 1223: Phryptimic, Ian Ring Music TheoryPhryptimic

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.