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Scale 965: "Ionothimic"

Scale 965: Ionothimic, 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

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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

Zeitler
Ionothimic

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

{0,2,6,7,8,9}

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-Z41

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: 1145

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.

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.

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.

no
prime: 335

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.

[3, 3, 2, 2, 3, 2]

Interval Spectrum

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

p3m2n2s3d3t2

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

Spectra Variation

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

3.333

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.

2.116

Polygon Perimeter

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

5.699

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

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}110.5
Diminished Triadsf♯°{6,9,0}110.5

The following pitch classes are not present in any of the common triads: {7,8}

Parsimonious Voice Leading Between Common Triads of Scale 965. Created by Ian Ring ©2019 D D f#° f#° D->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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 965 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1265
Scale 1265: Pynimic, Ian Ring Music TheoryPynimic
3rd mode:
Scale 335
Scale 335: Zanimic, Ian Ring Music TheoryZanimicThis is the prime mode
4th mode:
Scale 2215
Scale 2215: Ranimic, Ian Ring Music TheoryRanimic
5th mode:
Scale 3155
Scale 3155: Ladimic, Ian Ring Music TheoryLadimic
6th mode:
Scale 3625
Scale 3625: Podimic, Ian Ring Music TheoryPodimic

Prime

The prime form of this scale is Scale 335

Scale 335Scale 335: Zanimic, Ian Ring Music TheoryZanimic

Complement

The hexatonic modal family [965, 1265, 335, 2215, 3155, 3625] (Forte: 6-Z41) is the complement of the hexatonic modal family [215, 1475, 1805, 2155, 2785, 3125] (Forte: 6-Z12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 965 is 1145

Scale 1145Scale 1145: Zygimic, Ian Ring Music TheoryZygimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 965 is chiral, and its enantiomorph is scale 1145

Scale 1145Scale 1145: Zygimic, Ian Ring Music TheoryZygimic

Transformations:

T0 965  T0I 1145
T1 1930  T1I 2290
T2 3860  T2I 485
T3 3625  T3I 970
T4 3155  T4I 1940
T5 2215  T5I 3880
T6 335  T6I 3665
T7 670  T7I 3235
T8 1340  T8I 2375
T9 2680  T9I 655
T10 1265  T10I 1310
T11 2530  T11I 2620

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 967Scale 967: Mela Salaga, Ian Ring Music TheoryMela Salaga
Scale 961Scale 961, Ian Ring Music Theory
Scale 963Scale 963, Ian Ring Music Theory
Scale 969Scale 969: Ionogimic, Ian Ring Music TheoryIonogimic
Scale 973Scale 973: Mela Syamalangi, Ian Ring Music TheoryMela Syamalangi
Scale 981Scale 981: Mela Kantamani, Ian Ring Music TheoryMela Kantamani
Scale 997Scale 997: Rycrian, Ian Ring Music TheoryRycrian
Scale 901Scale 901, Ian Ring Music Theory
Scale 933Scale 933: Dadimic, Ian Ring Music TheoryDadimic
Scale 837Scale 837: Epaditonic, Ian Ring Music TheoryEpaditonic
Scale 709Scale 709: Raga Shri Kalyan, Ian Ring Music TheoryRaga Shri Kalyan
Scale 453Scale 453: Raditonic, Ian Ring Music TheoryRaditonic
Scale 1477Scale 1477: Raga Jaganmohanam, Ian Ring Music TheoryRaga Jaganmohanam
Scale 1989Scale 1989: Dydian, Ian Ring Music TheoryDydian
Scale 3013Scale 3013: Thynian, Ian Ring Music TheoryThynian

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.