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Scale 1417: "Raga Shailaja"

Scale 1417: Raga Shailaja, 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 Shailaja
Unknown / Unsorted
Varini
Zeitler
Zoptitonic
Dozenal
Irkian

Analysis

Cardinality

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

5 (pentatonic)

Pitch Class Set

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

{0,3,7,8,10}

Forte Number

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

5-27

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: 565

Hemitonia

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

1 (unhemitonic)

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.

4

Prime Form

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

no
prime: 299

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, 4, 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.

<1, 2, 2, 2, 3, 0>

Interval Spectrum

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

p3m2n2s2d

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

Spectra Variation

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

2.8

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.

2.049

Polygon Perimeter

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

5.664

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.

(3, 8, 36)

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♯{3,7,10}121
G♯{8,0,3}121
Minor Triadscm{0,3,7}210.67
Parsimonious Voice Leading Between Common Triads of Scale 1417. Created by Ian Ring ©2019 cm cm D# D# cm->D# G# G# cm->G#

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.

Diameter2
Radius1
Self-Centeredno
Central Verticescm
Peripheral VerticesD♯, G♯

Modes

Modes are the rotational transformation of this scale. Scale 1417 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 689
Scale 689: Raga Nagasvaravali, Ian Ring Music TheoryRaga Nagasvaravali
3rd mode:
Scale 299
Scale 299: Raga Chitthakarshini, Ian Ring Music TheoryRaga ChitthakarshiniThis is the prime mode
4th mode:
Scale 2197
Scale 2197: Raga Hamsadhvani, Ian Ring Music TheoryRaga Hamsadhvani
5th mode:
Scale 1573
Scale 1573: Raga Guhamanohari, Ian Ring Music TheoryRaga Guhamanohari

Prime

The prime form of this scale is Scale 299

Scale 299Scale 299: Raga Chitthakarshini, Ian Ring Music TheoryRaga Chitthakarshini

Complement

The pentatonic modal family [1417, 689, 299, 2197, 1573] (Forte: 5-27) is the complement of the heptatonic modal family [695, 1465, 1765, 1835, 2395, 2965, 3245] (Forte: 7-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1417 is 565

Scale 565Scale 565: Aeolyphritonic, Ian Ring Music TheoryAeolyphritonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1417 is chiral, and its enantiomorph is scale 565

Scale 565Scale 565: Aeolyphritonic, Ian Ring Music TheoryAeolyphritonic

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> 1417       T0I <11,0> 565
T1 <1,1> 2834      T1I <11,1> 1130
T2 <1,2> 1573      T2I <11,2> 2260
T3 <1,3> 3146      T3I <11,3> 425
T4 <1,4> 2197      T4I <11,4> 850
T5 <1,5> 299      T5I <11,5> 1700
T6 <1,6> 598      T6I <11,6> 3400
T7 <1,7> 1196      T7I <11,7> 2705
T8 <1,8> 2392      T8I <11,8> 1315
T9 <1,9> 689      T9I <11,9> 2630
T10 <1,10> 1378      T10I <11,10> 1165
T11 <1,11> 2756      T11I <11,11> 2330
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2077      T0MI <7,0> 1795
T1M <5,1> 59      T1MI <7,1> 3590
T2M <5,2> 118      T2MI <7,2> 3085
T3M <5,3> 236      T3MI <7,3> 2075
T4M <5,4> 472      T4MI <7,4> 55
T5M <5,5> 944      T5MI <7,5> 110
T6M <5,6> 1888      T6MI <7,6> 220
T7M <5,7> 3776      T7MI <7,7> 440
T8M <5,8> 3457      T8MI <7,8> 880
T9M <5,9> 2819      T9MI <7,9> 1760
T10M <5,10> 1543      T10MI <7,10> 3520
T11M <5,11> 3086      T11MI <7,11> 2945

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 1419Scale 1419: Raga Kashyapi, Ian Ring Music TheoryRaga Kashyapi
Scale 1421Scale 1421: Raga Trimurti, Ian Ring Music TheoryRaga Trimurti
Scale 1409Scale 1409: Imsian, Ian Ring Music TheoryImsian
Scale 1413Scale 1413: Iruian, Ian Ring Music TheoryIruian
Scale 1425Scale 1425: Ryphitonic, Ian Ring Music TheoryRyphitonic
Scale 1433Scale 1433: Dynimic, Ian Ring Music TheoryDynimic
Scale 1449Scale 1449: Raga Gopikavasantam, Ian Ring Music TheoryRaga Gopikavasantam
Scale 1481Scale 1481: Zagimic, Ian Ring Music TheoryZagimic
Scale 1289Scale 1289: Huvian, Ian Ring Music TheoryHuvian
Scale 1353Scale 1353: Raga Harikauns, Ian Ring Music TheoryRaga Harikauns
Scale 1161Scale 1161: Bi Yu, Ian Ring Music TheoryBi Yu
Scale 1673Scale 1673: Thocritonic, Ian Ring Music TheoryThocritonic
Scale 1929Scale 1929: Aeolycrimic, Ian Ring Music TheoryAeolycrimic
Scale 393Scale 393: Lothic, Ian Ring Music TheoryLothic
Scale 905Scale 905: Bylitonic, Ian Ring Music TheoryBylitonic
Scale 2441Scale 2441: Kyritonic, Ian Ring Music TheoryKyritonic
Scale 3465Scale 3465: Katathimic, Ian Ring Music TheoryKatathimic

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.