The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1965: "Raga Mukhari"

Scale 1965: Raga Mukhari, 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 Mukhari
Hindustani
Anandabhairavi
Unknown / Unsorted
Deshi
Manji
Gregorian Numbered
Gregorian Number 1
Western Mixed
Dorian/Aeolian Mixed
Zeitler
Gadyllic

Analysis

Cardinality

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

8 (octatonic)

Pitch Class Set

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

{0,2,3,5,7,8,9,10}

Forte Number

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

8-23

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.

[2.5]

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.

4 (multihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

2 (dicohemitonic)

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.

1

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.

7

Prime Form

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

no
prime: 1455

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.

[4, 6, 5, 4, 7, 2]

Interval Spectrum

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

p7m4n5s6d4t2

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

Spectra Variation

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

1.5

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.

yes

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.

2.732

Polygon Perimeter

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

6.071

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.

[5]

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 TriadsD♯{3,7,10}242.3
F{5,9,0}341.9
G♯{8,0,3}341.9
A♯{10,2,5}242.1
Minor Triadscm{0,3,7}242.1
dm{2,5,9}341.9
fm{5,8,0}341.9
gm{7,10,2}242.3
Diminished Triads{2,5,8}242.1
{9,0,3}242.1
Parsimonious Voice Leading Between Common Triads of Scale 1965. Created by Ian Ring ©2019 cm cm D# D# cm->D# G# G# cm->G# dm dm d°->dm fm fm d°->fm F F dm->F A# A# dm->A# gm gm D#->gm fm->F fm->G# F->a° gm->A# G#->a°

view full size

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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1965 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1515
Scale 1515: Phrygian/Locrian Mixed, Ian Ring Music TheoryPhrygian/Locrian Mixed
3rd mode:
Scale 2805
Scale 2805: Ishikotsucho, Ian Ring Music TheoryIshikotsucho
4th mode:
Scale 1725
Scale 1725: Minor Bebop, Ian Ring Music TheoryMinor Bebop
5th mode:
Scale 1455
Scale 1455: Quartal Octamode, Ian Ring Music TheoryQuartal OctamodeThis is the prime mode
6th mode:
Scale 2775
Scale 2775: Godyllic, Ian Ring Music TheoryGodyllic
7th mode:
Scale 3435
Scale 3435: Prokofiev, Ian Ring Music TheoryProkofiev
8th mode:
Scale 3765
Scale 3765: Dominant Bebop, Ian Ring Music TheoryDominant Bebop

Prime

The prime form of this scale is Scale 1455

Scale 1455Scale 1455: Quartal Octamode, Ian Ring Music TheoryQuartal Octamode

Complement

The octatonic modal family [1965, 1515, 2805, 1725, 1455, 2775, 3435, 3765] (Forte: 8-23) is the complement of the tetratonic modal family [165, 645, 1065, 1185] (Forte: 4-23)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1965 is 1725

Scale 1725Scale 1725: Minor Bebop, Ian Ring Music TheoryMinor Bebop

Transformations:

T0 1965  T0I 1725
T1 3930  T1I 3450
T2 3765  T2I 2805
T3 3435  T3I 1515
T4 2775  T4I 3030
T5 1455  T5I 1965
T6 2910  T6I 3930
T7 1725  T7I 3765
T8 3450  T8I 3435
T9 2805  T9I 2775
T10 1515  T10I 1455
T11 3030  T11I 2910

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 1967Scale 1967: Diatonic Dorian Mixed, Ian Ring Music TheoryDiatonic Dorian Mixed
Scale 1961Scale 1961: Soptian, Ian Ring Music TheorySoptian
Scale 1963Scale 1963: Epocryllic, Ian Ring Music TheoryEpocryllic
Scale 1957Scale 1957: Pyrian, Ian Ring Music TheoryPyrian
Scale 1973Scale 1973: Zyryllic, Ian Ring Music TheoryZyryllic
Scale 1981Scale 1981: Houseini, Ian Ring Music TheoryHouseini
Scale 1933Scale 1933: Mocrian, Ian Ring Music TheoryMocrian
Scale 1949Scale 1949: Mathyllic, Ian Ring Music TheoryMathyllic
Scale 1997Scale 1997: Raga Cintamani, Ian Ring Music TheoryRaga Cintamani
Scale 2029Scale 2029: Kiourdi, Ian Ring Music TheoryKiourdi
Scale 1837Scale 1837: Dalian, Ian Ring Music TheoryDalian
Scale 1901Scale 1901: Ionidyllic, Ian Ring Music TheoryIonidyllic
Scale 1709Scale 1709: Dorian, Ian Ring Music TheoryDorian
Scale 1453Scale 1453: Aeolian, Ian Ring Music TheoryAeolian
Scale 941Scale 941: Mela Jhankaradhvani, Ian Ring Music TheoryMela Jhankaradhvani
Scale 2989Scale 2989: Bebop Minor, Ian Ring Music TheoryBebop Minor
Scale 4013Scale 4013: Raga Pilu, Ian Ring Music TheoryRaga Pilu

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.