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Scale 307: "Raga Megharanjani"

Scale 307: Raga Megharanjani, 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 Megharanjani
Dozenal
Buzian
Exoticisms
Syrian Pentatonic
Zeitler
Phrolitonic

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

{0,1,4,5,8}

Forte Number

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

5-21

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: 2449

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.

4

Prime Form

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

yes

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, 3, 1, 3, 4]

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, 0, 2, 4, 2, 0>

Interval Spectrum

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

p2m4n2d2

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

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.

1.933

Polygon Perimeter

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

5.596

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.

(1, 8, 30)

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 TriadsC♯{1,5,8}221
Minor Triadsc♯m{1,4,8}221
fm{5,8,0}221
Augmented TriadsC+{0,4,8}221
Parsimonious Voice Leading Between Common Triads of Scale 307. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m fm fm C+->fm C# C# c#m->C# C#->fm

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 307 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2201
Scale 2201: Ionagitonic, Ian Ring Music TheoryIonagitonic
3rd mode:
Scale 787
Scale 787: Aeolapritonic, Ian Ring Music TheoryAeolapritonic
4th mode:
Scale 2441
Scale 2441: Kyritonic, Ian Ring Music TheoryKyritonic
5th mode:
Scale 817
Scale 817: Zothitonic, Ian Ring Music TheoryZothitonic

Prime

This is the prime form of this scale.

Complement

The pentatonic modal family [307, 2201, 787, 2441, 817] (Forte: 5-21) is the complement of the heptatonic modal family [823, 883, 1843, 2459, 2489, 2969, 3277] (Forte: 7-21)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 307 is 2449

Scale 2449Scale 2449: Zacritonic, Ian Ring Music TheoryZacritonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 307 is chiral, and its enantiomorph is scale 2449

Scale 2449Scale 2449: Zacritonic, Ian Ring Music TheoryZacritonic

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> 307       T0I <11,0> 2449
T1 <1,1> 614      T1I <11,1> 803
T2 <1,2> 1228      T2I <11,2> 1606
T3 <1,3> 2456      T3I <11,3> 3212
T4 <1,4> 817      T4I <11,4> 2329
T5 <1,5> 1634      T5I <11,5> 563
T6 <1,6> 3268      T6I <11,6> 1126
T7 <1,7> 2441      T7I <11,7> 2252
T8 <1,8> 787      T8I <11,8> 409
T9 <1,9> 1574      T9I <11,9> 818
T10 <1,10> 3148      T10I <11,10> 1636
T11 <1,11> 2201      T11I <11,11> 3272
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 307       T0MI <7,0> 2449
T1M <5,1> 614      T1MI <7,1> 803
T2M <5,2> 1228      T2MI <7,2> 1606
T3M <5,3> 2456      T3MI <7,3> 3212
T4M <5,4> 817      T4MI <7,4> 2329
T5M <5,5> 1634      T5MI <7,5> 563
T6M <5,6> 3268      T6MI <7,6> 1126
T7M <5,7> 2441      T7MI <7,7> 2252
T8M <5,8> 787      T8MI <7,8> 409
T9M <5,9> 1574      T9MI <7,9> 818
T10M <5,10> 3148      T10MI <7,10> 1636
T11M <5,11> 2201      T11MI <7,11> 3272

The transformations that map this set to itself are: T0, T0M

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 305Scale 305: Gonic, Ian Ring Music TheoryGonic
Scale 309Scale 309: Palitonic, Ian Ring Music TheoryPalitonic
Scale 311Scale 311: Stagimic, Ian Ring Music TheoryStagimic
Scale 315Scale 315: Stodimic, Ian Ring Music TheoryStodimic
Scale 291Scale 291: Raga Lavangi, Ian Ring Music TheoryRaga Lavangi
Scale 299Scale 299: Raga Chitthakarshini, Ian Ring Music TheoryRaga Chitthakarshini
Scale 275Scale 275: Dalic, Ian Ring Music TheoryDalic
Scale 339Scale 339: Zaptitonic, Ian Ring Music TheoryZaptitonic
Scale 371Scale 371: Rythimic, Ian Ring Music TheoryRythimic
Scale 435Scale 435: Raga Purna Pancama, Ian Ring Music TheoryRaga Purna Pancama
Scale 51Scale 51: Arfian, Ian Ring Music TheoryArfian
Scale 179Scale 179: Beyian, Ian Ring Music TheoryBeyian
Scale 563Scale 563: Thacritonic, Ian Ring Music TheoryThacritonic
Scale 819Scale 819: Augmented Inverse, Ian Ring Music TheoryAugmented Inverse
Scale 1331Scale 1331: Raga Vasantabhairavi, Ian Ring Music TheoryRaga Vasantabhairavi
Scale 2355Scale 2355: Raga Lalita, Ian Ring Music TheoryRaga Lalita

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.