The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 2469: "Raga Bhinna Pancama"

Scale 2469: Raga Bhinna Pancama, 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 Bhinna Pancama
Dozenal
Peyian
Zeitler
Staptimic

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

{0,2,5,7,8,11}

Forte Number

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

6-Z29

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.

[3.5]

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.

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.

5

Prime Form

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

no
prime: 717

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

Interval Spectrum

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

p3m2n4s2d2t2

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.

2.366

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.

[7]

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, 12, 57)

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}231.5
Minor Triadsfm{5,8,0}231.5
Diminished Triads{2,5,8}231.5
{5,8,11}231.5
g♯°{8,11,2}231.5
{11,2,5}231.5
Parsimonious Voice Leading Between Common Triads of Scale 2469. Created by Ian Ring ©2019 fm fm d°->fm d°->b° f°->fm g#° g#° f°->g#° Parsimonious Voice Leading Between Common Triads of Scale 2469. Created by Ian Ring ©2019 G G->g#° G->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.

Diameter3
Radius3
Self-Centeredyes

Triad Polychords

Also known as Bi-Triadic Hexatonics (a term coined by mDecks), and related to Generic Modality Compression (a method for guitar by Mick Goodrick and Tim Miller), these are two common triads that when combined use all the tones in this scale.

There is 1 way that this hexatonic scale can be split into two common triads.


Minor: {5, 8, 0}
Major: {7, 11, 2}

Modes

Modes are the rotational transformation of this scale. Scale 2469 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1641
Scale 1641: Bocrimic, Ian Ring Music TheoryBocrimic
3rd mode:
Scale 717
Scale 717: Raga Vijayanagari, Ian Ring Music TheoryRaga VijayanagariThis is the prime mode
4th mode:
Scale 1203
Scale 1203: Pagimic, Ian Ring Music TheoryPagimic
5th mode:
Scale 2649
Scale 2649: Aeolythimic, Ian Ring Music TheoryAeolythimic
6th mode:
Scale 843
Scale 843: Molimic, Ian Ring Music TheoryMolimic

Prime

The prime form of this scale is Scale 717

Scale 717Scale 717: Raga Vijayanagari, Ian Ring Music TheoryRaga Vijayanagari

Complement

The hexatonic modal family [2469, 1641, 717, 1203, 2649, 843] (Forte: 6-Z29) is the complement of the hexatonic modal family [723, 813, 1227, 1689, 2409, 2661] (Forte: 6-Z50)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2469 is 1203

Scale 1203Scale 1203: Pagimic, Ian Ring Music TheoryPagimic

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> 2469       T0I <11,0> 1203
T1 <1,1> 843      T1I <11,1> 2406
T2 <1,2> 1686      T2I <11,2> 717
T3 <1,3> 3372      T3I <11,3> 1434
T4 <1,4> 2649      T4I <11,4> 2868
T5 <1,5> 1203      T5I <11,5> 1641
T6 <1,6> 2406      T6I <11,6> 3282
T7 <1,7> 717      T7I <11,7> 2469
T8 <1,8> 1434      T8I <11,8> 843
T9 <1,9> 2868      T9I <11,9> 1686
T10 <1,10> 1641      T10I <11,10> 3372
T11 <1,11> 3282      T11I <11,11> 2649
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 3219      T0MI <7,0> 2343
T1M <5,1> 2343      T1MI <7,1> 591
T2M <5,2> 591      T2MI <7,2> 1182
T3M <5,3> 1182      T3MI <7,3> 2364
T4M <5,4> 2364      T4MI <7,4> 633
T5M <5,5> 633      T5MI <7,5> 1266
T6M <5,6> 1266      T6MI <7,6> 2532
T7M <5,7> 2532      T7MI <7,7> 969
T8M <5,8> 969      T8MI <7,8> 1938
T9M <5,9> 1938      T9MI <7,9> 3876
T10M <5,10> 3876      T10MI <7,10> 3657
T11M <5,11> 3657      T11MI <7,11> 3219

The transformations that map this set to itself are: T0, T7I

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 2471Scale 2471: Mela Ganamurti, Ian Ring Music TheoryMela Ganamurti
Scale 2465Scale 2465: Raga Devaranjani, Ian Ring Music TheoryRaga Devaranjani
Scale 2467Scale 2467: Raga Padi, Ian Ring Music TheoryRaga Padi
Scale 2473Scale 2473: Raga Takka, Ian Ring Music TheoryRaga Takka
Scale 2477Scale 2477: Harmonic Minor, Ian Ring Music TheoryHarmonic Minor
Scale 2485Scale 2485: Harmonic Major, Ian Ring Music TheoryHarmonic Major
Scale 2437Scale 2437: Pafian, Ian Ring Music TheoryPafian
Scale 2453Scale 2453: Raga Latika, Ian Ring Music TheoryRaga Latika
Scale 2501Scale 2501: Ralimic, Ian Ring Music TheoryRalimic
Scale 2533Scale 2533: Podian, Ian Ring Music TheoryPodian
Scale 2341Scale 2341: Raga Priyadharshini, Ian Ring Music TheoryRaga Priyadharshini
Scale 2405Scale 2405: Katalimic, Ian Ring Music TheoryKatalimic
Scale 2213Scale 2213: Raga Desh, Ian Ring Music TheoryRaga Desh
Scale 2725Scale 2725: Raga Nagagandhari, Ian Ring Music TheoryRaga Nagagandhari
Scale 2981Scale 2981: Ionolian, Ian Ring Music TheoryIonolian
Scale 3493Scale 3493: Rathian, Ian Ring Music TheoryRathian
Scale 421Scale 421: Han-kumoi, Ian Ring Music TheoryHan-kumoi
Scale 1445Scale 1445: Raga Navamanohari, Ian Ring Music TheoryRaga Navamanohari

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.