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Scale 1497: "Mela Jyotisvarupini"

Scale 1497: Mela Jyotisvarupini, 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 Jyotisvarupini
Raga Jotismatti
Jyothisvarupini
Zeitler
Ionanian
Dozenal
JEKian
Carnatic Melakarta
Jyoti Swarupini
Carnatic Numbered Melakarta
68th 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

 {0,3,4,6,7,8,10}

Forte Number

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

 7-26

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: 885

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.

 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 Starr/Rahn algorithm.

 no
prime: 699

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, an indicator of maximum hierarchization.

 no

Interval Structure

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

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

Proportional Saturation Vector

First described by Michael Buchler (2001), this is a vector showing the prominence of intervals relative to the maximum and minimum possible for the scale's cardinality. A saturation of 0 means the interval is present minimally, a saturation of 1 means it is the maximum possible.

<0.25, 0.5, 0.5, 0.667, 0.25, 0.5>

Interval Spectrum

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

 p3m5n4s4d3t2

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 Distribution Spectra have 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.

(13, 34, 98)

Coherence Quotient

The Coherence Quotient is a score between 0 and 1, indicating the proportion of coherence failures (ambiguity or contradiction) in the scale, against the maximum possible for a cardinality. A high coherence quotient indicates a less complex scale, whereas a quotient of 0 indicates a maximally complex scale.

0.664

Sameness Quotient

The Sameness Quotient is a score between 0 and 1, indicating the proportion of differences in the heteromorphic profile, against the maximum possible for a cardinality. A higher quotient indicates a less complex scale, whereas a quotient of 0 indicates a scale with maximum complexity.

0.222

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.

Generator

This scale has no generator.

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}331.5
D♯{3,7,10}331.5
G♯{8,0,3}231.75
Minor Triadscm{0,3,7}421.25
d♯m{3,6,10}242
Augmented TriadsC+{0,4,8}242
Diminished Triadsc°{0,3,6}231.75
e°{4,7,10}231.75
Parsimonious Voice Leading Between Common Triads of Scale 1497. Created by Ian Ring ©2019 c° c° cm cm c°->cm d#m d#m c°->d#m C C cm->C D# D# cm->D# G# G# cm->G# C+ C+ C->C+ e° e° C->e° C+->G# d#m->D# D#->e°

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 Verticescm
Peripheral VerticesC+, d♯m

Modes

Modes are the rotational transformation of this scale. Scale 1497 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 699		Scale 699: Aerothian, Ian Ring Music TheoryAerothianThis is the prime mode
3rd mode:
Scale 2397		Scale 2397: Stagian, Ian Ring Music TheoryStagian
4th mode:
Scale 1623		Scale 1623: Lothian, Ian Ring Music TheoryLothian
5th mode:
Scale 2859		Scale 2859: Phrycrian, Ian Ring Music TheoryPhrycrian
6th mode:
Scale 3477		Scale 3477: Kyptian, Ian Ring Music TheoryKyptian
7th mode:
Scale 1893		Scale 1893: Ionylian, Ian Ring Music TheoryIonylian

Prime

The prime form of this scale is Scale 699

Scale 699Scale 699: Aerothian, Ian Ring Music TheoryAerothian

Complement

The heptatonic modal family [1497, 699, 2397, 1623, 2859, 3477, 1893] (Forte: 7-26) is the complement of the pentatonic modal family [309, 849, 1101, 1299, 2697] (Forte: 5-26)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1497 is 885

Scale 885Scale 885: Sathian, Ian Ring Music TheorySathian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1497 is chiral, and its enantiomorph is scale 885

Scale 885Scale 885: Sathian, Ian Ring Music TheorySathian

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> 1497       T0I <11,0> 885
T1 <1,1> 2994      T1I <11,1> 1770
T2 <1,2> 1893      T2I <11,2> 3540
T3 <1,3> 3786      T3I <11,3> 2985
T4 <1,4> 3477      T4I <11,4> 1875
T5 <1,5> 2859      T5I <11,5> 3750
T6 <1,6> 1623      T6I <11,6> 3405
T7 <1,7> 3246      T7I <11,7> 2715
T8 <1,8> 2397      T8I <11,8> 1335
T9 <1,9> 699      T9I <11,9> 2670
T10 <1,10> 1398      T10I <11,10> 1245
T11 <1,11> 2796      T11I <11,11> 2490
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2397      T0MI <7,0> 1875
T1M <5,1> 699      T1MI <7,1> 3750
T2M <5,2> 1398      T2MI <7,2> 3405
T3M <5,3> 2796      T3MI <7,3> 2715
T4M <5,4> 1497       T4MI <7,4> 1335
T5M <5,5> 2994      T5MI <7,5> 2670
T6M <5,6> 1893      T6MI <7,6> 1245
T7M <5,7> 3786      T7MI <7,7> 2490
T8M <5,8> 3477      T8MI <7,8> 885
T9M <5,9> 2859      T9MI <7,9> 1770
T10M <5,10> 1623      T10MI <7,10> 3540
T11M <5,11> 3246      T11MI <7,11> 2985

The transformations that map this set to itself are: T0, T4M

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 1499Scale 1499: Bebop Locrian, Ian Ring Music TheoryBebop Locrian
Scale 1501Scale 1501: Stygyllic, Ian Ring Music TheoryStygyllic
Scale 1489Scale 1489: Raga Jyoti, Ian Ring Music TheoryRaga Jyoti
Scale 1493Scale 1493: Lydian Minor, Ian Ring Music TheoryLydian Minor
Scale 1481Scale 1481: Zagimic, Ian Ring Music TheoryZagimic
Scale 1513Scale 1513: Stathian, Ian Ring Music TheoryStathian
Scale 1529Scale 1529: Kataryllic, Ian Ring Music TheoryKataryllic
Scale 1433Scale 1433: Dynimic, Ian Ring Music TheoryDynimic
Scale 1465Scale 1465: Mela Ragavardhani, Ian Ring Music TheoryMela Ragavardhani
Scale 1369Scale 1369: Boptimic, Ian Ring Music TheoryBoptimic
Scale 1241Scale 1241: Pygimic, Ian Ring Music TheoryPygimic
Scale 1753Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major
Scale 2009Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic
Scale 473Scale 473: Aeralimic, Ian Ring Music TheoryAeralimic
Scale 985Scale 985: Mela Sucaritra, Ian Ring Music TheoryMela Sucaritra
Scale 2521Scale 2521: Mela Dhatuvardhani, Ian Ring Music TheoryMela Dhatuvardhani
Scale 3545Scale 3545: Thyptyllic, Ian Ring Music TheoryThyptyllic

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. Scale notation generated by VexFlow and Lilypond, graph visualization by Graphviz, audio by TiMIDIty and FFMPEG. 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.