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Scale 1129: "Raga Jayakauns"

Scale 1129: Raga Jayakauns, 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 Jayakauns
Dozenal
Gubian
Zeitler
Phrynitonic

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

{0,3,5,6,10}

Forte Number

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

5-29

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: 709

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.

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.

4

Prime Form

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

no
prime: 331

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, 1, 4, 2]

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, 2, 1, 3, 1>

Interval Spectrum

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

p3mn2s2dt

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}
<3> = {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.

2.4

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.

(2, 3, 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
Minor Triadsd♯m{3,6,10}110.5
Diminished Triads{0,3,6}110.5

The following pitch classes are not present in any of the common triads: {5}

Parsimonious Voice Leading Between Common Triads of Scale 1129. Created by Ian Ring ©2019 d#m d#m c°->d#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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1129 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 653
Scale 653: Dorian Pentatonic, Ian Ring Music TheoryDorian Pentatonic
3rd mode:
Scale 1187
Scale 1187: Kokin-joshi, Ian Ring Music TheoryKokin-joshi
4th mode:
Scale 2641
Scale 2641: Raga Hindol, Ian Ring Music TheoryRaga Hindol
5th mode:
Scale 421
Scale 421: Han-kumoi, Ian Ring Music TheoryHan-kumoi

Prime

The prime form of this scale is Scale 331

Scale 331Scale 331: Raga Chhaya Todi, Ian Ring Music TheoryRaga Chhaya Todi

Complement

The pentatonic modal family [1129, 653, 1187, 2641, 421] (Forte: 5-29) is the complement of the heptatonic modal family [727, 1483, 1721, 1837, 2411, 2789, 3253] (Forte: 7-29)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1129 is 709

Scale 709Scale 709: Raga Shri Kalyan, Ian Ring Music TheoryRaga Shri Kalyan

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1129 is chiral, and its enantiomorph is scale 709

Scale 709Scale 709: Raga Shri Kalyan, Ian Ring Music TheoryRaga Shri Kalyan

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> 1129       T0I <11,0> 709
T1 <1,1> 2258      T1I <11,1> 1418
T2 <1,2> 421      T2I <11,2> 2836
T3 <1,3> 842      T3I <11,3> 1577
T4 <1,4> 1684      T4I <11,4> 3154
T5 <1,5> 3368      T5I <11,5> 2213
T6 <1,6> 2641      T6I <11,6> 331
T7 <1,7> 1187      T7I <11,7> 662
T8 <1,8> 2374      T8I <11,8> 1324
T9 <1,9> 653      T9I <11,9> 2648
T10 <1,10> 1306      T10I <11,10> 1201
T11 <1,11> 2612      T11I <11,11> 2402
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 79      T0MI <7,0> 3649
T1M <5,1> 158      T1MI <7,1> 3203
T2M <5,2> 316      T2MI <7,2> 2311
T3M <5,3> 632      T3MI <7,3> 527
T4M <5,4> 1264      T4MI <7,4> 1054
T5M <5,5> 2528      T5MI <7,5> 2108
T6M <5,6> 961      T6MI <7,6> 121
T7M <5,7> 1922      T7MI <7,7> 242
T8M <5,8> 3844      T8MI <7,8> 484
T9M <5,9> 3593      T9MI <7,9> 968
T10M <5,10> 3091      T10MI <7,10> 1936
T11M <5,11> 2087      T11MI <7,11> 3872

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 1131Scale 1131: Honchoshi Plagal Form, Ian Ring Music TheoryHonchoshi Plagal Form
Scale 1133Scale 1133: Stycrimic, Ian Ring Music TheoryStycrimic
Scale 1121Scale 1121: Guwian, Ian Ring Music TheoryGuwian
Scale 1125Scale 1125: Ionaritonic, Ian Ring Music TheoryIonaritonic
Scale 1137Scale 1137: Stonitonic, Ian Ring Music TheoryStonitonic
Scale 1145Scale 1145: Zygimic, Ian Ring Music TheoryZygimic
Scale 1097Scale 1097: Aeraphic, Ian Ring Music TheoryAeraphic
Scale 1113Scale 1113: Locrian Pentatonic 2, Ian Ring Music TheoryLocrian Pentatonic 2
Scale 1065Scale 1065: Gonian, Ian Ring Music TheoryGonian
Scale 1193Scale 1193: Minor Pentatonic, Ian Ring Music TheoryMinor Pentatonic
Scale 1257Scale 1257: Blues Scale, Ian Ring Music TheoryBlues Scale
Scale 1385Scale 1385: Phracrimic, Ian Ring Music TheoryPhracrimic
Scale 1641Scale 1641: Bocrimic, Ian Ring Music TheoryBocrimic
Scale 105Scale 105, Ian Ring Music Theory
Scale 617Scale 617: Katycritonic, Ian Ring Music TheoryKatycritonic
Scale 2153Scale 2153: Navian, Ian Ring Music TheoryNavian
Scale 3177Scale 3177: Rothimic, Ian Ring Music TheoryRothimic

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.