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Scale 2547: "Raga Ramkali"

Scale 2547: Raga Ramkali, 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 Ramkali
Raga Ramakri
Zeitler
Bythyllic
Dozenal
Povian

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

8 (octatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,1,4,5,6,7,8,11}

Forte Number

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

8-8

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.

[0]

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

yes

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.

6 (multihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

4 (multicohemitonic)

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.

7

Prime Form

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

no
prime: 927

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, 1, 1, 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.

<6, 4, 4, 5, 6, 3>

Interval Spectrum

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

p6m5n4s4d6t3

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

Spectra Variation

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

2

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.

2.5

Polygon Perimeter

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

5.934

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.

[0]

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.

(44, 16, 93)

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{0,4,7}331.67
C♯{1,5,8}242
E{4,8,11}331.67
Minor Triadsc♯m{1,4,8}331.67
em{4,7,11}242
fm{5,8,0}331.67
Augmented TriadsC+{0,4,8}421.33
Diminished Triadsc♯°{1,4,7}242
{5,8,11}242

The following pitch classes are not present in any of the common triads: {6}

Parsimonious Voice Leading Between Common Triads of Scale 2547. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E fm fm C+->fm c#°->c#m C# C# c#m->C# C#->fm em->E E->f° f°->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.

Diameter4
Radius2
Self-Centeredno
Central VerticesC+
Peripheral Verticesc♯°, C♯, em, f°

Modes

Modes are the rotational transformation of this scale. Scale 2547 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3321
Scale 3321: Epagyllic, Ian Ring Music TheoryEpagyllic
3rd mode:
Scale 927
Scale 927: Gaptyllic, Ian Ring Music TheoryGaptyllicThis is the prime mode
4th mode:
Scale 2511
Scale 2511: Aeroptyllic, Ian Ring Music TheoryAeroptyllic
5th mode:
Scale 3303
Scale 3303: Mylyllic, Ian Ring Music TheoryMylyllic
6th mode:
Scale 3699
Scale 3699: Galyllic, Ian Ring Music TheoryGalyllic
7th mode:
Scale 3897
Scale 3897: Kalyllic, Ian Ring Music TheoryKalyllic
8th mode:
Scale 999
Scale 999: Ionodyllic, Ian Ring Music TheoryIonodyllic

Prime

The prime form of this scale is Scale 927

Scale 927Scale 927: Gaptyllic, Ian Ring Music TheoryGaptyllic

Complement

The octatonic modal family [2547, 3321, 927, 2511, 3303, 3699, 3897, 999] (Forte: 8-8) is the complement of the tetratonic modal family [99, 387, 2097, 2241] (Forte: 4-8)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2547 is itself, because it is a palindromic scale!

Scale 2547Scale 2547: Raga Ramkali, Ian Ring Music TheoryRaga Ramkali

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> 2547       T0I <11,0> 2547
T1 <1,1> 999      T1I <11,1> 999
T2 <1,2> 1998      T2I <11,2> 1998
T3 <1,3> 3996      T3I <11,3> 3996
T4 <1,4> 3897      T4I <11,4> 3897
T5 <1,5> 3699      T5I <11,5> 3699
T6 <1,6> 3303      T6I <11,6> 3303
T7 <1,7> 2511      T7I <11,7> 2511
T8 <1,8> 927      T8I <11,8> 927
T9 <1,9> 1854      T9I <11,9> 1854
T10 <1,10> 3708      T10I <11,10> 3708
T11 <1,11> 3321      T11I <11,11> 3321
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2547       T0MI <7,0> 2547
T1M <5,1> 999      T1MI <7,1> 999
T2M <5,2> 1998      T2MI <7,2> 1998
T3M <5,3> 3996      T3MI <7,3> 3996
T4M <5,4> 3897      T4MI <7,4> 3897
T5M <5,5> 3699      T5MI <7,5> 3699
T6M <5,6> 3303      T6MI <7,6> 3303
T7M <5,7> 2511      T7MI <7,7> 2511
T8M <5,8> 927      T8MI <7,8> 927
T9M <5,9> 1854      T9MI <7,9> 1854
T10M <5,10> 3708      T10MI <7,10> 3708
T11M <5,11> 3321      T11MI <7,11> 3321

The transformations that map this set to itself are: T0, T0I, T0M, T0MI

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 2545Scale 2545: Thycrian, Ian Ring Music TheoryThycrian
Scale 2549Scale 2549: Rydyllic, Ian Ring Music TheoryRydyllic
Scale 2551Scale 2551: Thocrygic, Ian Ring Music TheoryThocrygic
Scale 2555Scale 2555: Bythygic, Ian Ring Music TheoryBythygic
Scale 2531Scale 2531: Danian, Ian Ring Music TheoryDanian
Scale 2539Scale 2539: Half-Diminished Bebop, Ian Ring Music TheoryHalf-Diminished Bebop
Scale 2515Scale 2515: Chromatic Hypolydian, Ian Ring Music TheoryChromatic Hypolydian
Scale 2483Scale 2483: Double Harmonic, Ian Ring Music TheoryDouble Harmonic
Scale 2419Scale 2419: Raga Lalita, Ian Ring Music TheoryRaga Lalita
Scale 2291Scale 2291: Zydian, Ian Ring Music TheoryZydian
Scale 2803Scale 2803: Raga Bhatiyar, Ian Ring Music TheoryRaga Bhatiyar
Scale 3059Scale 3059: Madygic, Ian Ring Music TheoryMadygic
Scale 3571Scale 3571: Dyrygic, Ian Ring Music TheoryDyrygic
Scale 499Scale 499: Ionaptian, Ian Ring Music TheoryIonaptian
Scale 1523Scale 1523: Zothyllic, Ian Ring Music TheoryZothyllic

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.