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Scale 949: "Mela Mararanjani"

Scale 949: Mela Mararanjani, 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

41161837294116105072918310504116183
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 Mela
Mela Mararanjani
Carnatic Raga
Raga Keseri
Jazz and Blues
Major Bebop Heptatonic
Zeitler
Ionagian

Analysis

Cardinality

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

7 (heptatonic)

Pitch Class Set

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

{0,2,4,5,7,8,9}

Forte Number

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

7-27

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: 1465

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.

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.

6

Prime Form

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

no
prime: 695

Deep Scale

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

no

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, 4, 4, 4, 5, 1]

Interval Spectrum

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

p5m4n4s4d3t

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

Spectra Variation

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

2.286

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.

2.549

Polygon Perimeter

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

5.967

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

Harmonic Chords

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}142.14
F{5,9,0}331.43
Minor Triadsdm{2,5,9}241.86
fm{5,8,0}321.29
am{9,0,4}231.57
Augmented TriadsC+{0,4,8}331.43
Diminished Triads{2,5,8}231.71
Parsimonious Voice Leading Between Common Triads of Scale 949. Created by Ian Ring ©2019 C C C+ C+ C->C+ fm fm C+->fm am am C+->am dm dm d°->dm d°->fm F F dm->F fm->F F->am

view full size

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 Verticesfm
Peripheral VerticesC, dm

Modes

Modes are the rotational transformation of this scale. Scale 949 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1261
Scale 1261: Modified Blues, Ian Ring Music TheoryModified Blues
3rd mode:
Scale 1339
Scale 1339: Kycrian, Ian Ring Music TheoryKycrian
4th mode:
Scale 2717
Scale 2717: Epygian, Ian Ring Music TheoryEpygian
5th mode:
Scale 1703
Scale 1703: Mela Vanaspati, Ian Ring Music TheoryMela Vanaspati
6th mode:
Scale 2899
Scale 2899: Kagian, Ian Ring Music TheoryKagian
7th mode:
Scale 3497
Scale 3497: Phrolian, Ian Ring Music TheoryPhrolian

Prime

The prime form of this scale is Scale 695

Scale 695Scale 695: Sarian, Ian Ring Music TheorySarian

Complement

The heptatonic modal family [949, 1261, 1339, 2717, 1703, 2899, 3497] (Forte: 7-27) is the complement of the pentatonic modal family [299, 689, 1417, 1573, 2197] (Forte: 5-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 949 is 1465

Scale 1465Scale 1465: Mela Ragavardhani, Ian Ring Music TheoryMela Ragavardhani

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 949 is chiral, and its enantiomorph is scale 1465

Scale 1465Scale 1465: Mela Ragavardhani, Ian Ring Music TheoryMela Ragavardhani

Transformations:

T0 949  T0I 1465
T1 1898  T1I 2930
T2 3796  T2I 1765
T3 3497  T3I 3530
T4 2899  T4I 2965
T5 1703  T5I 1835
T6 3406  T6I 3670
T7 2717  T7I 3245
T8 1339  T8I 2395
T9 2678  T9I 695
T10 1261  T10I 1390
T11 2522  T11I 2780

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 951Scale 951: Thogyllic, Ian Ring Music TheoryThogyllic
Scale 945Scale 945: Raga Saravati, Ian Ring Music TheoryRaga Saravati
Scale 947Scale 947: Mela Gayakapriya, Ian Ring Music TheoryMela Gayakapriya
Scale 953Scale 953: Mela Yagapriya, Ian Ring Music TheoryMela Yagapriya
Scale 957Scale 957: Phronyllic, Ian Ring Music TheoryPhronyllic
Scale 933Scale 933: Dadimic, Ian Ring Music TheoryDadimic
Scale 941Scale 941: Mela Jhankaradhvani, Ian Ring Music TheoryMela Jhankaradhvani
Scale 917Scale 917: Dygimic, Ian Ring Music TheoryDygimic
Scale 981Scale 981: Mela Kantamani, Ian Ring Music TheoryMela Kantamani
Scale 1013Scale 1013: Stydyllic, Ian Ring Music TheoryStydyllic
Scale 821Scale 821: Aeranimic, Ian Ring Music TheoryAeranimic
Scale 885Scale 885: Sathian, Ian Ring Music TheorySathian
Scale 693Scale 693: Arezzo Major Diatonic Hexachord, Ian Ring Music TheoryArezzo Major Diatonic Hexachord
Scale 437Scale 437: Ronimic, Ian Ring Music TheoryRonimic
Scale 1461Scale 1461: Major-Minor, Ian Ring Music TheoryMajor-Minor
Scale 1973Scale 1973: Zyryllic, Ian Ring Music TheoryZyryllic
Scale 2997Scale 2997: Major Bebop, Ian Ring Music TheoryMajor Bebop

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. 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.