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Scale 939: "Mela Senavati"

Scale 939: Mela Senavati, 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
Mela Senavati
Raga Senagrani
Malini
Dozenal
Fupian
Zeitler
Dyptian
Carnatic Numbered Melakarta
7th Melakarta raga
Carnatic Melakarta
Senavati

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

{0,1,3,5,7,8,9}

Forte Number

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

7-30

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: 2745

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.

6

Prime Form

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

no
prime: 855

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, 2, 2, 2, 1, 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, 4, 3, 5, 4, 2>

Interval Spectrum

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

p4m5n3s4d3t2

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}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {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.

1.714

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

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.

(2, 22, 86)

Tertian Harmonic Chords

Tertian chords are made from alternating members of the scale, ie built from "stacked thirds". Not all scales lend themselves well to tertian harmony.

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}231.71
F{5,9,0}331.43
G♯{8,0,3}331.43
Minor Triadscm{0,3,7}142.14
fm{5,8,0}321.29
Augmented TriadsC♯+{1,5,9}241.86
Diminished Triads{9,0,3}231.57
Parsimonious Voice Leading Between Common Triads of Scale 939. Created by Ian Ring ©2019 cm cm G# G# cm->G# C# C# C#+ C#+ C#->C#+ fm fm C#->fm F F C#+->F fm->F fm->G# F->a° G#->a°

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 Verticescm, C♯+

Modes

Modes are the rotational transformation of this scale. Scale 939 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2517
Scale 2517: Harmonic Lydian, Ian Ring Music TheoryHarmonic Lydian
3rd mode:
Scale 1653
Scale 1653: Minor Romani Inverse, Ian Ring Music TheoryMinor Romani Inverse
4th mode:
Scale 1437
Scale 1437: Sabach ascending, Ian Ring Music TheorySabach ascending
5th mode:
Scale 1383
Scale 1383: Pynian, Ian Ring Music TheoryPynian
6th mode:
Scale 2739
Scale 2739: Mela Suryakanta, Ian Ring Music TheoryMela Suryakanta
7th mode:
Scale 3417
Scale 3417: Golian, Ian Ring Music TheoryGolian

Prime

The prime form of this scale is Scale 855

Scale 855Scale 855: Porian, Ian Ring Music TheoryPorian

Complement

The heptatonic modal family [939, 2517, 1653, 1437, 1383, 2739, 3417] (Forte: 7-30) is the complement of the pentatonic modal family [339, 789, 1221, 1329, 2217] (Forte: 5-30)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 939 is 2745

Scale 2745Scale 2745: Mela Sulini, Ian Ring Music TheoryMela Sulini

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 939 is chiral, and its enantiomorph is scale 2745

Scale 2745Scale 2745: Mela Sulini, Ian Ring Music TheoryMela Sulini

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> 939       T0I <11,0> 2745
T1 <1,1> 1878      T1I <11,1> 1395
T2 <1,2> 3756      T2I <11,2> 2790
T3 <1,3> 3417      T3I <11,3> 1485
T4 <1,4> 2739      T4I <11,4> 2970
T5 <1,5> 1383      T5I <11,5> 1845
T6 <1,6> 2766      T6I <11,6> 3690
T7 <1,7> 1437      T7I <11,7> 3285
T8 <1,8> 2874      T8I <11,8> 2475
T9 <1,9> 1653      T9I <11,9> 855
T10 <1,10> 3306      T10I <11,10> 1710
T11 <1,11> 2517      T11I <11,11> 3420
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2619      T0MI <7,0> 2955
T1M <5,1> 1143      T1MI <7,1> 1815
T2M <5,2> 2286      T2MI <7,2> 3630
T3M <5,3> 477      T3MI <7,3> 3165
T4M <5,4> 954      T4MI <7,4> 2235
T5M <5,5> 1908      T5MI <7,5> 375
T6M <5,6> 3816      T6MI <7,6> 750
T7M <5,7> 3537      T7MI <7,7> 1500
T8M <5,8> 2979      T8MI <7,8> 3000
T9M <5,9> 1863      T9MI <7,9> 1905
T10M <5,10> 3726      T10MI <7,10> 3810
T11M <5,11> 3357      T11MI <7,11> 3525

The transformations that map this set to itself are: T0

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 937Scale 937: Stothimic, Ian Ring Music TheoryStothimic
Scale 941Scale 941: Mela Jhankaradhvani, Ian Ring Music TheoryMela Jhankaradhvani
Scale 943Scale 943: Aerygyllic, Ian Ring Music TheoryAerygyllic
Scale 931Scale 931: Raga Kalakanthi, Ian Ring Music TheoryRaga Kalakanthi
Scale 935Scale 935: Chromatic Dorian, Ian Ring Music TheoryChromatic Dorian
Scale 947Scale 947: Mela Gayakapriya, Ian Ring Music TheoryMela Gayakapriya
Scale 955Scale 955: Ionogyllic, Ian Ring Music TheoryIonogyllic
Scale 907Scale 907: Tholimic, Ian Ring Music TheoryTholimic
Scale 923Scale 923: Ultraphrygian, Ian Ring Music TheoryUltraphrygian
Scale 971Scale 971: Mela Gavambodhi, Ian Ring Music TheoryMela Gavambodhi
Scale 1003Scale 1003: Ionyryllic, Ian Ring Music TheoryIonyryllic
Scale 811Scale 811: Radimic, Ian Ring Music TheoryRadimic
Scale 875Scale 875: Locrian Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 7
Scale 683Scale 683: Stogimic, Ian Ring Music TheoryStogimic
Scale 427Scale 427: Raga Suddha Simantini, Ian Ring Music TheoryRaga Suddha Simantini
Scale 1451Scale 1451: Phrygian, Ian Ring Music TheoryPhrygian
Scale 1963Scale 1963: Epocryllic, Ian Ring Music TheoryEpocryllic
Scale 2987Scale 2987: Neapolitan Major and Minor Mixed, Ian Ring Music TheoryNeapolitan Major and Minor Mixed

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.