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Scale 807: "Raga Suddha Mukhari"

Scale 807: Raga Suddha Mukhari, 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
Raga Suddha Mukhari
Zeitler
Epadimic

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

{0,1,2,5,8,9}

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-Z44

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: 3225

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

3 (trihemitonic)

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.

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: 615

Deep Scale

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

no

Interval Formula

Defines the scale as the sequence of intervals between one tone and the next.

[1, 1, 3, 3, 1, 3]

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.

<3, 1, 3, 4, 3, 1>

Interval Spectrum

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

p3m4n3sd3t

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

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.

2.25

Polygon Perimeter

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

5.796

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

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}321.17
F{5,9,0}231.5
Minor Triadsdm{2,5,9}231.5
fm{5,8,0}231.5
Augmented TriadsC♯+{1,5,9}321.17
Diminished Triads{2,5,8}231.5
Parsimonious Voice Leading Between Common Triads of Scale 807. Created by Ian Ring ©2019 C# C# C#+ C#+ C#->C#+ C#->d° fm fm C#->fm dm dm C#+->dm F F C#+->F d°->dm fm->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♯, C♯+
Peripheral Verticesd°, dm, fm, F

Modes

Modes are the rotational transformation of this scale. Scale 807 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2451
Scale 2451: Raga Bauli, Ian Ring Music TheoryRaga Bauli
3rd mode:
Scale 3273
Scale 3273: Raga Jivantini, Ian Ring Music TheoryRaga Jivantini
4th mode:
Scale 921
Scale 921: Bogimic, Ian Ring Music TheoryBogimic
5th mode:
Scale 627
Scale 627: Mogimic, Ian Ring Music TheoryMogimic
6th mode:
Scale 2361
Scale 2361: Docrimic, Ian Ring Music TheoryDocrimic

Prime

The prime form of this scale is Scale 615

Scale 615Scale 615: Phrothimic, Ian Ring Music TheoryPhrothimic

Complement

The hexatonic modal family [807, 2451, 3273, 921, 627, 2361] (Forte: 6-Z44) is the complement of the hexatonic modal family [411, 867, 1587, 2253, 2481, 2841] (Forte: 6-Z19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 807 is 3225

Scale 3225Scale 3225: Ionalimic, Ian Ring Music TheoryIonalimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 807 is chiral, and its enantiomorph is scale 3225

Scale 3225Scale 3225: Ionalimic, Ian Ring Music TheoryIonalimic

Transformations:

T0 807  T0I 3225
T1 1614  T1I 2355
T2 3228  T2I 615
T3 2361  T3I 1230
T4 627  T4I 2460
T5 1254  T5I 825
T6 2508  T6I 1650
T7 921  T7I 3300
T8 1842  T8I 2505
T9 3684  T9I 915
T10 3273  T10I 1830
T11 2451  T11I 3660

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 805Scale 805: Rothitonic, Ian Ring Music TheoryRothitonic
Scale 803Scale 803: Loritonic, Ian Ring Music TheoryLoritonic
Scale 811Scale 811: Radimic, Ian Ring Music TheoryRadimic
Scale 815Scale 815: Bolian, Ian Ring Music TheoryBolian
Scale 823Scale 823: Stodian, Ian Ring Music TheoryStodian
Scale 775Scale 775: Raga Putrika, Ian Ring Music TheoryRaga Putrika
Scale 791Scale 791: Aeoloptimic, Ian Ring Music TheoryAeoloptimic
Scale 839Scale 839: Ionathimic, Ian Ring Music TheoryIonathimic
Scale 871Scale 871: Locrian Double-flat 3 Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 3 Double-flat 7
Scale 935Scale 935: Chromatic Dorian, Ian Ring Music TheoryChromatic Dorian
Scale 551Scale 551: Aeoloditonic, Ian Ring Music TheoryAeoloditonic
Scale 679Scale 679: Lanimic, Ian Ring Music TheoryLanimic
Scale 295Scale 295: Gyritonic, Ian Ring Music TheoryGyritonic
Scale 1319Scale 1319: Phronimic, Ian Ring Music TheoryPhronimic
Scale 1831Scale 1831: Pothian, Ian Ring Music TheoryPothian
Scale 2855Scale 2855: Epocrain, Ian Ring Music TheoryEpocrain

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. 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.