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Scale 3237: "Raga Brindabani Sarang"

Scale 3237: Raga Brindabani Sarang, 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 Brindabani Sarang
Megh
Megh Malhar
Dozenal
Ugoian
Zeitler
Thatimic

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

{0,2,5,7,10,11}

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-Z47

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: 1191

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.

1 (uncohemitonic)

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: 663

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.

[2, 3, 2, 3, 1, 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, 3, 3, 2, 4, 1>

Interval Spectrum

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

p4m2n3s3d2t

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

Spectra Variation

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

2.333

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.

2.366

Polygon Perimeter

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

5.864

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.

(10, 16, 62)

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}221
A♯{10,2,5}221
Minor Triadsgm{7,10,2}221
Diminished Triads{11,2,5}221

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

Parsimonious Voice Leading Between Common Triads of Scale 3237. Created by Ian Ring ©2019 gm gm Parsimonious Voice Leading Between Common Triads of Scale 3237. Created by Ian Ring ©2019 G gm->G A# A# gm->A# G->b° A#->b°

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 3237 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1833
Scale 1833: Ionacrimic, Ian Ring Music TheoryIonacrimic
3rd mode:
Scale 741
Scale 741: Gathimic, Ian Ring Music TheoryGathimic
4th mode:
Scale 1209
Scale 1209: Raga Bhanumanjari, Ian Ring Music TheoryRaga Bhanumanjari
5th mode:
Scale 663
Scale 663: Phrynimic, Ian Ring Music TheoryPhrynimicThis is the prime mode
6th mode:
Scale 2379
Scale 2379: Raga Gurjari Todi, Ian Ring Music TheoryRaga Gurjari Todi

Prime

The prime form of this scale is Scale 663

Scale 663Scale 663: Phrynimic, Ian Ring Music TheoryPhrynimic

Complement

The hexatonic modal family [3237, 1833, 741, 1209, 663, 2379] (Forte: 6-Z47) is the complement of the hexatonic modal family [363, 1419, 1581, 1713, 2229, 2757] (Forte: 6-Z25)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3237 is 1191

Scale 1191Scale 1191: Pyrimic, Ian Ring Music TheoryPyrimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3237 is chiral, and its enantiomorph is scale 1191

Scale 1191Scale 1191: Pyrimic, Ian Ring Music TheoryPyrimic

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> 3237       T0I <11,0> 1191
T1 <1,1> 2379      T1I <11,1> 2382
T2 <1,2> 663      T2I <11,2> 669
T3 <1,3> 1326      T3I <11,3> 1338
T4 <1,4> 2652      T4I <11,4> 2676
T5 <1,5> 1209      T5I <11,5> 1257
T6 <1,6> 2418      T6I <11,6> 2514
T7 <1,7> 741      T7I <11,7> 933
T8 <1,8> 1482      T8I <11,8> 1866
T9 <1,9> 2964      T9I <11,9> 3732
T10 <1,10> 1833      T10I <11,10> 3369
T11 <1,11> 3666      T11I <11,11> 2643
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 3207      T0MI <7,0> 3111
T1M <5,1> 2319      T1MI <7,1> 2127
T2M <5,2> 543      T2MI <7,2> 159
T3M <5,3> 1086      T3MI <7,3> 318
T4M <5,4> 2172      T4MI <7,4> 636
T5M <5,5> 249      T5MI <7,5> 1272
T6M <5,6> 498      T6MI <7,6> 2544
T7M <5,7> 996      T7MI <7,7> 993
T8M <5,8> 1992      T8MI <7,8> 1986
T9M <5,9> 3984      T9MI <7,9> 3972
T10M <5,10> 3873      T10MI <7,10> 3849
T11M <5,11> 3651      T11MI <7,11> 3603

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 3239Scale 3239: Mela Tanarupi, Ian Ring Music TheoryMela Tanarupi
Scale 3233Scale 3233: Unbian, Ian Ring Music TheoryUnbian
Scale 3235Scale 3235: Pothimic, Ian Ring Music TheoryPothimic
Scale 3241Scale 3241: Dalimic, Ian Ring Music TheoryDalimic
Scale 3245Scale 3245: Mela Varunapriya, Ian Ring Music TheoryMela Varunapriya
Scale 3253Scale 3253: Mela Naganandini, Ian Ring Music TheoryMela Naganandini
Scale 3205Scale 3205: Utwian, Ian Ring Music TheoryUtwian
Scale 3221Scale 3221: Bycrimic, Ian Ring Music TheoryBycrimic
Scale 3269Scale 3269: Raga Malarani, Ian Ring Music TheoryRaga Malarani
Scale 3301Scale 3301: Chromatic Mixolydian Inverse, Ian Ring Music TheoryChromatic Mixolydian Inverse
Scale 3109Scale 3109: Tidian, Ian Ring Music TheoryTidian
Scale 3173Scale 3173: Zarimic, Ian Ring Music TheoryZarimic
Scale 3365Scale 3365: Katolimic, Ian Ring Music TheoryKatolimic
Scale 3493Scale 3493: Rathian, Ian Ring Music TheoryRathian
Scale 3749Scale 3749: Raga Sorati, Ian Ring Music TheoryRaga Sorati
Scale 2213Scale 2213: Raga Desh, Ian Ring Music TheoryRaga Desh
Scale 2725Scale 2725: Raga Nagagandhari, Ian Ring Music TheoryRaga Nagagandhari
Scale 1189Scale 1189: Suspended Pentatonic, Ian Ring Music TheorySuspended Pentatonic

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.