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Scale 1739: "Mela Sadvidhamargini"

Scale 1739: Mela Sadvidhamargini, 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 Sadvidhamargini
Raga Sthavarajam
Dozenal
Kocian
Unknown / Unsorted
Tivravahini
Zeitler
Phrylian
Carnatic Melakarta
Shadvidamargini
Carnatic Numbered Melakarta
46th Melakarta raga

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

{0,1,3,6,7,9,10}

Forte Number

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

7-31

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: 2669

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.

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.

4

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: 731

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, 3, 1, 2, 1, 2]

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, 3, 6, 3, 3, 3>

Interval Spectrum

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

p3m3n6s3d3t3

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> = {3,4,5}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {7,8,9}
<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.

(4, 27, 84)

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 TriadsD♯{3,7,10}331.7
F♯{6,10,1}331.7
Minor Triadscm{0,3,7}331.8
d♯m{3,6,10}431.6
f♯m{6,9,1}331.8
Diminished Triads{0,3,6}231.9
d♯°{3,6,9}231.9
f♯°{6,9,0}232
{7,10,1}232
{9,0,3}232
Parsimonious Voice Leading Between Common Triads of Scale 1739. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m D# D# cm->D# cm->a° d#° d#° d#°->d#m f#m f#m d#°->f#m d#m->D# F# F# d#m->F# D#->g° f#° f#° f#°->f#m f#°->a° f#m->F# F#->g°

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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1739 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2917
Scale 2917: Nohkan Flute Scale, Ian Ring Music TheoryNohkan Flute Scale
3rd mode:
Scale 1753
Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major
4th mode:
Scale 731
Scale 731: Alternating Heptamode, Ian Ring Music TheoryAlternating HeptamodeThis is the prime mode
5th mode:
Scale 2413
Scale 2413: Locrian Natural 2, Ian Ring Music TheoryLocrian Natural 2
6th mode:
Scale 1627
Scale 1627: Zyptian, Ian Ring Music TheoryZyptian
7th mode:
Scale 2861
Scale 2861: Katothian, Ian Ring Music TheoryKatothian

Prime

The prime form of this scale is Scale 731

Scale 731Scale 731: Alternating Heptamode, Ian Ring Music TheoryAlternating Heptamode

Complement

The heptatonic modal family [1739, 2917, 1753, 731, 2413, 1627, 2861] (Forte: 7-31) is the complement of the pentatonic modal family [587, 601, 713, 1609, 2341] (Forte: 5-31)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1739 is 2669

Scale 2669Scale 2669: Jeths' Mode, Ian Ring Music TheoryJeths' Mode

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1739 is chiral, and its enantiomorph is scale 2669

Scale 2669Scale 2669: Jeths' Mode, Ian Ring Music TheoryJeths' Mode

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> 1739       T0I <11,0> 2669
T1 <1,1> 3478      T1I <11,1> 1243
T2 <1,2> 2861      T2I <11,2> 2486
T3 <1,3> 1627      T3I <11,3> 877
T4 <1,4> 3254      T4I <11,4> 1754
T5 <1,5> 2413      T5I <11,5> 3508
T6 <1,6> 731      T6I <11,6> 2921
T7 <1,7> 1462      T7I <11,7> 1747
T8 <1,8> 2924      T8I <11,8> 3494
T9 <1,9> 1753      T9I <11,9> 2893
T10 <1,10> 3506      T10I <11,10> 1691
T11 <1,11> 2917      T11I <11,11> 3382
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2669      T0MI <7,0> 1739
T1M <5,1> 1243      T1MI <7,1> 3478
T2M <5,2> 2486      T2MI <7,2> 2861
T3M <5,3> 877      T3MI <7,3> 1627
T4M <5,4> 1754      T4MI <7,4> 3254
T5M <5,5> 3508      T5MI <7,5> 2413
T6M <5,6> 2921      T6MI <7,6> 731
T7M <5,7> 1747      T7MI <7,7> 1462
T8M <5,8> 3494      T8MI <7,8> 2924
T9M <5,9> 2893      T9MI <7,9> 1753
T10M <5,10> 1691      T10MI <7,10> 3506
T11M <5,11> 3382      T11MI <7,11> 2917

The transformations that map this set to itself are: T0, 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 1737Scale 1737: Raga Madhukauns, Ian Ring Music TheoryRaga Madhukauns
Scale 1741Scale 1741: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
Scale 1743Scale 1743: Epigyllic, Ian Ring Music TheoryEpigyllic
Scale 1731Scale 1731: Koxian, Ian Ring Music TheoryKoxian
Scale 1735Scale 1735: Mela Navanitam, Ian Ring Music TheoryMela Navanitam
Scale 1747Scale 1747: Mela Ramapriya, Ian Ring Music TheoryMela Ramapriya
Scale 1755Scale 1755: Octatonic, Ian Ring Music TheoryOctatonic
Scale 1771Scale 1771: Kuwian, Ian Ring Music TheoryKuwian
Scale 1675Scale 1675: Raga Salagavarali, Ian Ring Music TheoryRaga Salagavarali
Scale 1707Scale 1707: Dorian Flat 2, Ian Ring Music TheoryDorian Flat 2
Scale 1611Scale 1611: Dacrimic, Ian Ring Music TheoryDacrimic
Scale 1867Scale 1867: Solian, Ian Ring Music TheorySolian
Scale 1995Scale 1995: Sideways Scale, Ian Ring Music TheorySideways Scale
Scale 1227Scale 1227: Thacrimic, Ian Ring Music TheoryThacrimic
Scale 1483Scale 1483: Mela Bhavapriya, Ian Ring Music TheoryMela Bhavapriya
Scale 715Scale 715: Messiaen Truncated Mode 2, Ian Ring Music TheoryMessiaen Truncated Mode 2
Scale 2763Scale 2763: Mela Suvarnangi, Ian Ring Music TheoryMela Suvarnangi
Scale 3787Scale 3787: Kagyllic, Ian Ring Music TheoryKagyllic

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.