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Scale 985: "Mela Sucaritra"

Scale 985: Mela Sucaritra, 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 Sucaritra
Raga Santanamanjari
Dozenal
Gaqian
Zeitler
Raptian
Carnatic Melakarta
Sucharitra
Carnatic Numbered Melakarta
67th 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

{0,3,4,6,7,8,9}

Forte Number

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

7-16

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: 889

Hemitonia

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

4 (multihemitonic)

Cohemitonia

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

2 (dicohemitonic)

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: 623

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.

[3, 1, 2, 1, 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.

<4, 3, 5, 4, 3, 2>

Interval Spectrum

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

p3m4n5s3d4t2

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

Spectra Variation

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

2.857

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.

2.433

Polygon Perimeter

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

5.899

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.

(32, 38, 102)

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{0,4,7}231.89
G♯{8,0,3}331.67
Minor Triadscm{0,3,7}331.67
am{9,0,4}331.67
Augmented TriadsC+{0,4,8}331.67
Diminished Triads{0,3,6}231.89
d♯°{3,6,9}232
f♯°{6,9,0}231.89
{9,0,3}231.89
Parsimonious Voice Leading Between Common Triads of Scale 985. Created by Ian Ring ©2019 cm cm c°->cm d#° d#° c°->d#° C C cm->C G# G# cm->G# C+ C+ C->C+ C+->G# am am C+->am f#° f#° d#°->f#° f#°->am G#->a° a°->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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 985 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 635
Scale 635: Epolian, Ian Ring Music TheoryEpolian
3rd mode:
Scale 2365
Scale 2365: Sythian, Ian Ring Music TheorySythian
4th mode:
Scale 1615
Scale 1615: Sydian, Ian Ring Music TheorySydian
5th mode:
Scale 2855
Scale 2855: Epocrain, Ian Ring Music TheoryEpocrain
6th mode:
Scale 3475
Scale 3475: Kylian, Ian Ring Music TheoryKylian
7th mode:
Scale 3785
Scale 3785: Epagian, Ian Ring Music TheoryEpagian

Prime

The prime form of this scale is Scale 623

Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian

Complement

The heptatonic modal family [985, 635, 2365, 1615, 2855, 3475, 3785] (Forte: 7-16) is the complement of the pentatonic modal family [155, 865, 1555, 2125, 2825] (Forte: 5-16)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 985 is 889

Scale 889Scale 889: Borian, Ian Ring Music TheoryBorian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 985 is chiral, and its enantiomorph is scale 889

Scale 889Scale 889: Borian, Ian Ring Music TheoryBorian

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> 985       T0I <11,0> 889
T1 <1,1> 1970      T1I <11,1> 1778
T2 <1,2> 3940      T2I <11,2> 3556
T3 <1,3> 3785      T3I <11,3> 3017
T4 <1,4> 3475      T4I <11,4> 1939
T5 <1,5> 2855      T5I <11,5> 3878
T6 <1,6> 1615      T6I <11,6> 3661
T7 <1,7> 3230      T7I <11,7> 3227
T8 <1,8> 2365      T8I <11,8> 2359
T9 <1,9> 635      T9I <11,9> 623
T10 <1,10> 1270      T10I <11,10> 1246
T11 <1,11> 2540      T11I <11,11> 2492
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2905      T0MI <7,0> 859
T1M <5,1> 1715      T1MI <7,1> 1718
T2M <5,2> 3430      T2MI <7,2> 3436
T3M <5,3> 2765      T3MI <7,3> 2777
T4M <5,4> 1435      T4MI <7,4> 1459
T5M <5,5> 2870      T5MI <7,5> 2918
T6M <5,6> 1645      T6MI <7,6> 1741
T7M <5,7> 3290      T7MI <7,7> 3482
T8M <5,8> 2485      T8MI <7,8> 2869
T9M <5,9> 875      T9MI <7,9> 1643
T10M <5,10> 1750      T10MI <7,10> 3286
T11M <5,11> 3500      T11MI <7,11> 2477

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 987Scale 987: Aeraptyllic, Ian Ring Music TheoryAeraptyllic
Scale 989Scale 989: Phrolyllic, Ian Ring Music TheoryPhrolyllic
Scale 977Scale 977: Kocrimic, Ian Ring Music TheoryKocrimic
Scale 981Scale 981: Mela Kantamani, Ian Ring Music TheoryMela Kantamani
Scale 969Scale 969: Ionogimic, Ian Ring Music TheoryIonogimic
Scale 1001Scale 1001: Badian, Ian Ring Music TheoryBadian
Scale 1017Scale 1017: Dythyllic, Ian Ring Music TheoryDythyllic
Scale 921Scale 921: Bogimic, Ian Ring Music TheoryBogimic
Scale 953Scale 953: Mela Yagapriya, Ian Ring Music TheoryMela Yagapriya
Scale 857Scale 857: Aeolydimic, Ian Ring Music TheoryAeolydimic
Scale 729Scale 729: Stygimic, Ian Ring Music TheoryStygimic
Scale 473Scale 473: Aeralimic, Ian Ring Music TheoryAeralimic
Scale 1497Scale 1497: Mela Jyotisvarupini, Ian Ring Music TheoryMela Jyotisvarupini
Scale 2009Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic
Scale 3033Scale 3033: Doptyllic, Ian Ring Music TheoryDoptyllic

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.