The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 2229: "Raga Nalinakanti"

Scale 2229: Raga Nalinakanti, 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 Raga
Raga Nalinakanti
Unknown / Unsorted
Kedaram
Vilasini
Zeitler
Ionyptimic

Analysis

Cardinality

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

6 (hexatonic)

Pitch Class Set

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

{0,2,4,5,7,11}

Forte Number

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

6-Z25

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: 1443

Hemitonia

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

2 (dihemitonic)

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.

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.

5

Prime Form

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

no
prime: 363

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.

[2, 3, 3, 2, 4, 1]

Interval Spectrum

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

p4m2n3s3d2t

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> = {1,2,4}
<2> = {3,4,5,6}
<3> = {5,7}
<4> = {6,7,8,9}
<5> = {8,10,11}

Spectra Variation

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

2.333

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.

2.232

Polygon Perimeter

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

5.767

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

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}131.5
G{7,11,2}221
Minor Triadsem{4,7,11}221
Diminished Triads{11,2,5}131.5
Parsimonious Voice Leading Between Common Triads of Scale 2229. Created by Ian Ring ©2019 C C em em C->em Parsimonious Voice Leading Between Common Triads of Scale 2229. Created by Ian Ring ©2019 G em->G G->b°

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
Radius2
Self-Centeredno
Central Verticesem, G
Peripheral VerticesC, b°

Modes

Modes are the rotational transformation of this scale. Scale 2229 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1581
Scale 1581: Raga Bagesri, Ian Ring Music TheoryRaga Bagesri
3rd mode:
Scale 1419
Scale 1419: Raga Kashyapi, Ian Ring Music TheoryRaga Kashyapi
4th mode:
Scale 2757
Scale 2757: Raga Nishadi, Ian Ring Music TheoryRaga Nishadi
5th mode:
Scale 1713
Scale 1713: Raga Khamas, Ian Ring Music TheoryRaga Khamas
6th mode:
Scale 363
Scale 363: Soptimic, Ian Ring Music TheorySoptimicThis is the prime mode

Prime

The prime form of this scale is Scale 363

Scale 363Scale 363: Soptimic, Ian Ring Music TheorySoptimic

Complement

The hexatonic modal family [2229, 1581, 1419, 2757, 1713, 363] (Forte: 6-Z25) is the complement of the hexatonic modal family [663, 741, 1209, 1833, 2379, 3237] (Forte: 6-Z47)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2229 is 1443

Scale 1443Scale 1443: Raga Phenadyuti, Ian Ring Music TheoryRaga Phenadyuti

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2229 is chiral, and its enantiomorph is scale 1443

Scale 1443Scale 1443: Raga Phenadyuti, Ian Ring Music TheoryRaga Phenadyuti

Transformations:

T0 2229  T0I 1443
T1 363  T1I 2886
T2 726  T2I 1677
T3 1452  T3I 3354
T4 2904  T4I 2613
T5 1713  T5I 1131
T6 3426  T6I 2262
T7 2757  T7I 429
T8 1419  T8I 858
T9 2838  T9I 1716
T10 1581  T10I 3432
T11 3162  T11I 2769

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 2231Scale 2231: Macrian, Ian Ring Music TheoryMacrian
Scale 2225Scale 2225: Ionian Pentatonic, Ian Ring Music TheoryIonian Pentatonic
Scale 2227Scale 2227: Raga Gaula, Ian Ring Music TheoryRaga Gaula
Scale 2233Scale 2233: Donimic, Ian Ring Music TheoryDonimic
Scale 2237Scale 2237: Epothian, Ian Ring Music TheoryEpothian
Scale 2213Scale 2213: Raga Desh, Ian Ring Music TheoryRaga Desh
Scale 2221Scale 2221: Raga Sindhura Kafi, Ian Ring Music TheoryRaga Sindhura Kafi
Scale 2197Scale 2197: Raga Hamsadhvani, Ian Ring Music TheoryRaga Hamsadhvani
Scale 2261Scale 2261: Raga Caturangini, Ian Ring Music TheoryRaga Caturangini
Scale 2293Scale 2293: Gorian, Ian Ring Music TheoryGorian
Scale 2101Scale 2101, Ian Ring Music Theory
Scale 2165Scale 2165, Ian Ring Music Theory
Scale 2357Scale 2357: Raga Sarasanana, Ian Ring Music TheoryRaga Sarasanana
Scale 2485Scale 2485: Harmonic Major, Ian Ring Music TheoryHarmonic Major
Scale 2741Scale 2741: Major, Ian Ring Music TheoryMajor
Scale 3253Scale 3253: Mela Naganandini, Ian Ring Music TheoryMela Naganandini
Scale 181Scale 181: Raga Budhamanohari, Ian Ring Music TheoryRaga Budhamanohari
Scale 1205Scale 1205: Raga Siva Kambhoji, Ian Ring Music TheoryRaga Siva Kambhoji

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.