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Scale 2723: "Raga Jivantika"

Scale 2723: Raga Jivantika, 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
Raga Jivantika
Zeitler
Epylimic
Dozenal
Rebian

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

{0,1,5,7,9,11}

Forte Number

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

6-22

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: 2219

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.

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.

5

Prime Form

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

no
prime: 343

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, 4, 2, 2, 2, 1]

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, 4, 1, 4, 2, 2>

Interval Spectrum

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

p2m4ns4d2t2

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

Spectra Variation

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

3

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

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.

(10, 23, 64)

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 TriadsF{5,9,0}110.5
Augmented TriadsC♯+{1,5,9}110.5

The following pitch classes are not present in any of the common triads: {7,11}

Parsimonious Voice Leading Between Common Triads of Scale 2723. Created by Ian Ring ©2019 C#+ C#+ F F C#+->F

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2723 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3409
Scale 3409: Katanimic, Ian Ring Music TheoryKatanimic
3rd mode:
Scale 469
Scale 469: Katyrimic, Ian Ring Music TheoryKatyrimic
4th mode:
Scale 1141
Scale 1141: Rynimic, Ian Ring Music TheoryRynimic
5th mode:
Scale 1309
Scale 1309: Pogimic, Ian Ring Music TheoryPogimic
6th mode:
Scale 1351
Scale 1351: Aeraptimic, Ian Ring Music TheoryAeraptimic

Prime

The prime form of this scale is Scale 343

Scale 343Scale 343: Ionorimic, Ian Ring Music TheoryIonorimic

Complement

The hexatonic modal family [2723, 3409, 469, 1141, 1309, 1351] (Forte: 6-22) is the complement of the hexatonic modal family [343, 1393, 1477, 1813, 2219, 3157] (Forte: 6-22)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2723 is 2219

Scale 2219Scale 2219: Phrydimic, Ian Ring Music TheoryPhrydimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2723 is chiral, and its enantiomorph is scale 2219

Scale 2219Scale 2219: Phrydimic, Ian Ring Music TheoryPhrydimic

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> 2723       T0I <11,0> 2219
T1 <1,1> 1351      T1I <11,1> 343
T2 <1,2> 2702      T2I <11,2> 686
T3 <1,3> 1309      T3I <11,3> 1372
T4 <1,4> 2618      T4I <11,4> 2744
T5 <1,5> 1141      T5I <11,5> 1393
T6 <1,6> 2282      T6I <11,6> 2786
T7 <1,7> 469      T7I <11,7> 1477
T8 <1,8> 938      T8I <11,8> 2954
T9 <1,9> 1876      T9I <11,9> 1813
T10 <1,10> 3752      T10I <11,10> 3626
T11 <1,11> 3409      T11I <11,11> 3157
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2723       T0MI <7,0> 2219
T1M <5,1> 1351      T1MI <7,1> 343
T2M <5,2> 2702      T2MI <7,2> 686
T3M <5,3> 1309      T3MI <7,3> 1372
T4M <5,4> 2618      T4MI <7,4> 2744
T5M <5,5> 1141      T5MI <7,5> 1393
T6M <5,6> 2282      T6MI <7,6> 2786
T7M <5,7> 469      T7MI <7,7> 1477
T8M <5,8> 938      T8MI <7,8> 2954
T9M <5,9> 1876      T9MI <7,9> 1813
T10M <5,10> 3752      T10MI <7,10> 3626
T11M <5,11> 3409      T11MI <7,11> 3157

The transformations that map this set to itself are: T0, T0M

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 2721Scale 2721: Raga Puruhutika, Ian Ring Music TheoryRaga Puruhutika
Scale 2725Scale 2725: Raga Nagagandhari, Ian Ring Music TheoryRaga Nagagandhari
Scale 2727Scale 2727: Mela Manavati, Ian Ring Music TheoryMela Manavati
Scale 2731Scale 2731: Neapolitan Major, Ian Ring Music TheoryNeapolitan Major
Scale 2739Scale 2739: Mela Suryakanta, Ian Ring Music TheoryMela Suryakanta
Scale 2691Scale 2691: Rahian, Ian Ring Music TheoryRahian
Scale 2707Scale 2707: Banimic, Ian Ring Music TheoryBanimic
Scale 2755Scale 2755: Rivian, Ian Ring Music TheoryRivian
Scale 2787Scale 2787: Zyrian, Ian Ring Music TheoryZyrian
Scale 2595Scale 2595: Rolitonic, Ian Ring Music TheoryRolitonic
Scale 2659Scale 2659: Katynimic, Ian Ring Music TheoryKatynimic
Scale 2851Scale 2851: Katoptimic, Ian Ring Music TheoryKatoptimic
Scale 2979Scale 2979: Gyptian, Ian Ring Music TheoryGyptian
Scale 2211Scale 2211: Raga Gauri, Ian Ring Music TheoryRaga Gauri
Scale 2467Scale 2467: Raga Padi, Ian Ring Music TheoryRaga Padi
Scale 3235Scale 3235: Pothimic, Ian Ring Music TheoryPothimic
Scale 3747Scale 3747: Myrian, Ian Ring Music TheoryMyrian
Scale 675Scale 675: Altered Pentatonic, Ian Ring Music TheoryAltered Pentatonic
Scale 1699Scale 1699: Raga Rasavali, Ian Ring Music TheoryRaga Rasavali

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.