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Scale 935: "Chromatic Dorian"

Scale 935: Chromatic Dorian, 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

Western Chromatic
Chromatic Dorian
Carnatic Mela
Mela Kanakangi
Carnatic Raga
Raga Kanakambari
Zeitler
Katarian

Analysis

Cardinality

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

7 (heptatonic)

Pitch Class Set

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

{0,1,2,5,7,8,9}

Forte Number

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

7-20

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: 3257

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.

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.

6

Prime Form

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

no
prime: 743

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Formula

Defines the scale as the sequence of intervals between one tone and the next.

[1, 1, 3, 2, 1, 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.

<4, 3, 3, 4, 5, 2>

Interval Spectrum

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

p5m4n3s3d4t2

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

Spectra Variation

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

2

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.

2.433

Polygon Perimeter

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

5.899

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

Tertian Harmonic Chords

Tertian chords are made from alternating members of the scale, ie built from "stacked thirds". Not all scales lend themselves well to tertian harmony.

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 TriadsC♯{1,5,8}321.17
F{5,9,0}231.5
Minor Triadsdm{2,5,9}231.5
fm{5,8,0}231.5
Augmented TriadsC♯+{1,5,9}321.17
Diminished Triads{2,5,8}231.5

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

Parsimonious Voice Leading Between Common Triads of Scale 935. Created by Ian Ring ©2019 C# C# C#+ C#+ C#->C#+ C#->d° fm fm C#->fm dm dm C#+->dm F F C#+->F d°->dm fm->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.

Diameter3
Radius2
Self-Centeredno
Central VerticesC♯, C♯+
Peripheral Verticesd°, dm, fm, F

Modes

Modes are the rotational transformation of this scale. Scale 935 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2515
Scale 2515: Chromatic Hypolydian, Ian Ring Music TheoryChromatic Hypolydian
3rd mode:
Scale 3305
Scale 3305: Chromatic Hypophrygian, Ian Ring Music TheoryChromatic Hypophrygian
4th mode:
Scale 925
Scale 925: Chromatic Hypodorian, Ian Ring Music TheoryChromatic Hypodorian
5th mode:
Scale 1255
Scale 1255: Chromatic Mixolydian, Ian Ring Music TheoryChromatic Mixolydian
6th mode:
Scale 2675
Scale 2675: Chromatic Lydian, Ian Ring Music TheoryChromatic Lydian
7th mode:
Scale 3385
Scale 3385: Chromatic Phrygian, Ian Ring Music TheoryChromatic Phrygian

Prime

The prime form of this scale is Scale 743

Scale 743Scale 743: Chromatic Hypophrygian Inverse, Ian Ring Music TheoryChromatic Hypophrygian Inverse

Complement

The heptatonic modal family [935, 2515, 3305, 925, 1255, 2675, 3385] (Forte: 7-20) is the complement of the pentatonic modal family [355, 395, 1585, 2225, 2245] (Forte: 5-20)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 935 is 3257

Scale 3257Scale 3257: Mela Calanata, Ian Ring Music TheoryMela Calanata

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 935 is chiral, and its enantiomorph is scale 3257

Scale 3257Scale 3257: Mela Calanata, Ian Ring Music TheoryMela Calanata

Transformations:

T0 935  T0I 3257
T1 1870  T1I 2419
T2 3740  T2I 743
T3 3385  T3I 1486
T4 2675  T4I 2972
T5 1255  T5I 1849
T6 2510  T6I 3698
T7 925  T7I 3301
T8 1850  T8I 2507
T9 3700  T9I 919
T10 3305  T10I 1838
T11 2515  T11I 3676

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 933Scale 933: Dadimic, Ian Ring Music TheoryDadimic
Scale 931Scale 931: Raga Kalakanthi, Ian Ring Music TheoryRaga Kalakanthi
Scale 939Scale 939: Mela Senavati, Ian Ring Music TheoryMela Senavati
Scale 943Scale 943: Aerygyllic, Ian Ring Music TheoryAerygyllic
Scale 951Scale 951: Thogyllic, Ian Ring Music TheoryThogyllic
Scale 903Scale 903, Ian Ring Music Theory
Scale 919Scale 919: Chromatic Phrygian Inverse, Ian Ring Music TheoryChromatic Phrygian Inverse
Scale 967Scale 967: Mela Salaga, Ian Ring Music TheoryMela Salaga
Scale 999Scale 999: Ionodyllic, Ian Ring Music TheoryIonodyllic
Scale 807Scale 807: Raga Suddha Mukhari, Ian Ring Music TheoryRaga Suddha Mukhari
Scale 871Scale 871: Locrian Double-flat 3 Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 3 Double-flat 7
Scale 679Scale 679: Lanimic, Ian Ring Music TheoryLanimic
Scale 423Scale 423: Sogimic, Ian Ring Music TheorySogimic
Scale 1447Scale 1447: Mela Ratnangi, Ian Ring Music TheoryMela Ratnangi
Scale 1959Scale 1959: Katolyllic, Ian Ring Music TheoryKatolyllic
Scale 2983Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic

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. 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.