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Scale 717: "Raga Vijayanagari"

Scale 717: Raga Vijayanagari, 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 Vijayanagari
Zeitler
Gythimic

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

{0,2,3,6,7,9}

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-Z29

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.

[4.5]

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.

no

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.

3

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.

yes

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, 2, 4, 2, 3, 2]

Interval Spectrum

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

p3m2n4s2d2t2

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

Spectra Variation

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

1.667

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.

2.366

Polygon Perimeter

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

5.864

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.

[9]

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".

Proper

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{2,6,9}231.5
Minor Triadscm{0,3,7}231.5
Diminished Triads{0,3,6}231.5
d♯°{3,6,9}231.5
f♯°{6,9,0}231.5
{9,0,3}231.5
Parsimonious Voice Leading Between Common Triads of Scale 717. Created by Ian Ring ©2019 cm cm c°->cm d#° d#° c°->d#° cm->a° D D D->d#° f#° f#° D->f#° f#°->a°

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 717 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1203
Scale 1203: Pagimic, Ian Ring Music TheoryPagimic
3rd mode:
Scale 2649
Scale 2649: Aeolythimic, Ian Ring Music TheoryAeolythimic
4th mode:
Scale 843
Scale 843: Molimic, Ian Ring Music TheoryMolimic
5th mode:
Scale 2469
Scale 2469: Raga Bhinna Pancama, Ian Ring Music TheoryRaga Bhinna Pancama
6th mode:
Scale 1641
Scale 1641: Bocrimic, Ian Ring Music TheoryBocrimic

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [717, 1203, 2649, 843, 2469, 1641] (Forte: 6-Z29) is the complement of the hexatonic modal family [723, 813, 1227, 1689, 2409, 2661] (Forte: 6-Z50)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 717 is 1641

Scale 1641Scale 1641: Bocrimic, Ian Ring Music TheoryBocrimic

Transformations:

T0 717  T0I 1641
T1 1434  T1I 3282
T2 2868  T2I 2469
T3 1641  T3I 843
T4 3282  T4I 1686
T5 2469  T5I 3372
T6 843  T6I 2649
T7 1686  T7I 1203
T8 3372  T8I 2406
T9 2649  T9I 717
T10 1203  T10I 1434
T11 2406  T11I 2868

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 719Scale 719: Kanian, Ian Ring Music TheoryKanian
Scale 713Scale 713: Thoptitonic, Ian Ring Music TheoryThoptitonic
Scale 715Scale 715: Messiaen Truncated Mode 2, Ian Ring Music TheoryMessiaen Truncated Mode 2
Scale 709Scale 709: Raga Shri Kalyan, Ian Ring Music TheoryRaga Shri Kalyan
Scale 725Scale 725: Raga Yamuna Kalyani, Ian Ring Music TheoryRaga Yamuna Kalyani
Scale 733Scale 733: Donian, Ian Ring Music TheoryDonian
Scale 749Scale 749: Aeologian, Ian Ring Music TheoryAeologian
Scale 653Scale 653: Dorian Pentatonic, Ian Ring Music TheoryDorian Pentatonic
Scale 685Scale 685: Raga Suddha Bangala, Ian Ring Music TheoryRaga Suddha Bangala
Scale 589Scale 589: Ionalitonic, Ian Ring Music TheoryIonalitonic
Scale 845Scale 845: Raga Neelangi, Ian Ring Music TheoryRaga Neelangi
Scale 973Scale 973: Mela Syamalangi, Ian Ring Music TheoryMela Syamalangi
Scale 205Scale 205, Ian Ring Music Theory
Scale 461Scale 461: Raga Syamalam, Ian Ring Music TheoryRaga Syamalam
Scale 1229Scale 1229: Raga Simharava, Ian Ring Music TheoryRaga Simharava
Scale 1741Scale 1741: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
Scale 2765Scale 2765: Lydian Flat 3, Ian Ring Music TheoryLydian Flat 3

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.