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Scale 1355: "Raga Bhavani"

Scale 1355: Raga Bhavani, 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

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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 Bhavani
Zeitler
Aeolorimic

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

{0,1,3,6,8,10}

Forte Number

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

6-33

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: 2645

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.

5

Prime Form

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

no
prime: 685

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

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, 4, 3, 2, 4, 1]

Interval Spectrum

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

p4m2n3s4dt

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

Spectra Variation

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

1.667

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.

2.482

Polygon Perimeter

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

5.932

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".

Proper

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 TriadsF♯{6,10,1}131.5
G♯{8,0,3}131.5
Minor Triadsd♯m{3,6,10}221
Diminished Triads{0,3,6}221
Parsimonious Voice Leading Between Common Triads of Scale 1355. Created by Ian Ring ©2019 d#m d#m c°->d#m G# G# c°->G# F# F# d#m->F#

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.

Diameter3
Radius2
Self-Centeredno
Central Verticesc°, d♯m
Peripheral VerticesF♯, G♯

Modes

Modes are the rotational transformation of this scale. Scale 1355 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2725
Scale 2725: Raga Nagagandhari, Ian Ring Music TheoryRaga Nagagandhari
3rd mode:
Scale 1705
Scale 1705: Raga Manohari, Ian Ring Music TheoryRaga Manohari
4th mode:
Scale 725
Scale 725: Raga Yamuna Kalyani, Ian Ring Music TheoryRaga Yamuna Kalyani
5th mode:
Scale 1205
Scale 1205: Raga Siva Kambhoji, Ian Ring Music TheoryRaga Siva Kambhoji
6th mode:
Scale 1325
Scale 1325: Phradimic, Ian Ring Music TheoryPhradimic

Prime

The prime form of this scale is Scale 685

Scale 685Scale 685: Raga Suddha Bangala, Ian Ring Music TheoryRaga Suddha Bangala

Complement

The hexatonic modal family [1355, 2725, 1705, 725, 1205, 1325] (Forte: 6-33) is the complement of the hexatonic modal family [685, 1195, 1385, 1445, 1685, 2645] (Forte: 6-33)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1355 is 2645

Scale 2645Scale 2645: Raga Mruganandana, Ian Ring Music TheoryRaga Mruganandana

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1355 is chiral, and its enantiomorph is scale 2645

Scale 2645Scale 2645: Raga Mruganandana, Ian Ring Music TheoryRaga Mruganandana

Transformations:

T0 1355  T0I 2645
T1 2710  T1I 1195
T2 1325  T2I 2390
T3 2650  T3I 685
T4 1205  T4I 1370
T5 2410  T5I 2740
T6 725  T6I 1385
T7 1450  T7I 2770
T8 2900  T8I 1445
T9 1705  T9I 2890
T10 3410  T10I 1685
T11 2725  T11I 3370

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 1353Scale 1353: Raga Harikauns, Ian Ring Music TheoryRaga Harikauns
Scale 1357Scale 1357: Takemitsu Linea Mode 2, Ian Ring Music TheoryTakemitsu Linea Mode 2
Scale 1359Scale 1359: Aerygian, Ian Ring Music TheoryAerygian
Scale 1347Scale 1347, Ian Ring Music Theory
Scale 1351Scale 1351: Aeraptimic, Ian Ring Music TheoryAeraptimic
Scale 1363Scale 1363: Gygimic, Ian Ring Music TheoryGygimic
Scale 1371Scale 1371: Superlocrian, Ian Ring Music TheorySuperlocrian
Scale 1387Scale 1387: Locrian, Ian Ring Music TheoryLocrian
Scale 1291Scale 1291, Ian Ring Music Theory
Scale 1323Scale 1323: Ritsu, Ian Ring Music TheoryRitsu
Scale 1419Scale 1419: Raga Kashyapi, Ian Ring Music TheoryRaga Kashyapi
Scale 1483Scale 1483: Mela Bhavapriya, Ian Ring Music TheoryMela Bhavapriya
Scale 1099Scale 1099: Dyritonic, Ian Ring Music TheoryDyritonic
Scale 1227Scale 1227: Thacrimic, Ian Ring Music TheoryThacrimic
Scale 1611Scale 1611: Dacrimic, Ian Ring Music TheoryDacrimic
Scale 1867Scale 1867: Solian, Ian Ring Music TheorySolian
Scale 331Scale 331: Raga Chhaya Todi, Ian Ring Music TheoryRaga Chhaya Todi
Scale 843Scale 843: Molimic, Ian Ring Music TheoryMolimic
Scale 2379Scale 2379: Raga Gurjari Todi, Ian Ring Music TheoryRaga Gurjari Todi
Scale 3403Scale 3403: Bylian, Ian Ring Music TheoryBylian

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. 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.