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Scale 775: "Raga Putrika"

Scale 775: Raga Putrika, 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 Putrika
Dozenal
Ermian

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

{0,1,2,8,9}

Forte Number

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

5-6

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: 3097

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.

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.

4

Prime Form

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

no
prime: 103

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, 1, 6, 1, 3]

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, 1, 1, 2, 2, 1>

Interval Spectrum

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

p2m2nsd3t

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

Spectra Variation

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

4

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.

1.25

Polygon Perimeter

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

4.967

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.

(16, 1, 30)

Common Triads

There are no common triads (major, minor, augmented and diminished) that can be formed using notes in this scale.

Modes

Modes are the rotational transformation of this scale. Scale 775 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2435
Scale 2435: Raga Deshgaur, Ian Ring Music TheoryRaga Deshgaur
3rd mode:
Scale 3265
Scale 3265: Urrian, Ian Ring Music TheoryUrrian
4th mode:
Scale 115
Scale 115: Ashian, Ian Ring Music TheoryAshian
5th mode:
Scale 2105
Scale 2105: Rigian, Ian Ring Music TheoryRigian

Prime

The prime form of this scale is Scale 103

Scale 103Scale 103: Apuian, Ian Ring Music TheoryApuian

Complement

The pentatonic modal family [775, 2435, 3265, 115, 2105] (Forte: 5-6) is the complement of the heptatonic modal family [415, 995, 2255, 2545, 3175, 3635, 3865] (Forte: 7-6)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 775 is 3097

Scale 3097Scale 3097: Tiwian, Ian Ring Music TheoryTiwian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 775 is chiral, and its enantiomorph is scale 3097

Scale 3097Scale 3097: Tiwian, Ian Ring Music TheoryTiwian

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> 775       T0I <11,0> 3097
T1 <1,1> 1550      T1I <11,1> 2099
T2 <1,2> 3100      T2I <11,2> 103
T3 <1,3> 2105      T3I <11,3> 206
T4 <1,4> 115      T4I <11,4> 412
T5 <1,5> 230      T5I <11,5> 824
T6 <1,6> 460      T6I <11,6> 1648
T7 <1,7> 920      T7I <11,7> 3296
T8 <1,8> 1840      T8I <11,8> 2497
T9 <1,9> 3680      T9I <11,9> 899
T10 <1,10> 3265      T10I <11,10> 1798
T11 <1,11> 2435      T11I <11,11> 3596
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 1585      T0MI <7,0> 397
T1M <5,1> 3170      T1MI <7,1> 794
T2M <5,2> 2245      T2MI <7,2> 1588
T3M <5,3> 395      T3MI <7,3> 3176
T4M <5,4> 790      T4MI <7,4> 2257
T5M <5,5> 1580      T5MI <7,5> 419
T6M <5,6> 3160      T6MI <7,6> 838
T7M <5,7> 2225      T7MI <7,7> 1676
T8M <5,8> 355      T8MI <7,8> 3352
T9M <5,9> 710      T9MI <7,9> 2609
T10M <5,10> 1420      T10MI <7,10> 1123
T11M <5,11> 2840      T11MI <7,11> 2246

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 773Scale 773: Esuian, Ian Ring Music TheoryEsuian
Scale 771Scale 771: Esoian, Ian Ring Music TheoryEsoian
Scale 779Scale 779: Etrian, Ian Ring Music TheoryEtrian
Scale 783Scale 783: Etuian, Ian Ring Music TheoryEtuian
Scale 791Scale 791: Aeoloptimic, Ian Ring Music TheoryAeoloptimic
Scale 807Scale 807: Raga Suddha Mukhari, Ian Ring Music TheoryRaga Suddha Mukhari
Scale 839Scale 839: Ionathimic, Ian Ring Music TheoryIonathimic
Scale 903Scale 903: Fosian, Ian Ring Music TheoryFosian
Scale 519Scale 519: Deyian, Ian Ring Music TheoryDeyian
Scale 647Scale 647: Duzian, Ian Ring Music TheoryDuzian
Scale 263Scale 263, Ian Ring Music Theory
Scale 1287Scale 1287: Hutian, Ian Ring Music TheoryHutian
Scale 1799Scale 1799: Lamian, Ian Ring Music TheoryLamian
Scale 2823Scale 2823: Rulian, Ian Ring Music TheoryRulian

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.