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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

Cardinality6 (hexatonic)
Pitch Class Set{0,2,6,7,8,9}
Forte Number6-Z41
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1145
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes5
Prime?no
prime: 335
Deep Scaleno
Interval Vector332232
Interval Spectrump3m2n2s3d3t2
Distribution Spectra<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 Variation3.333
Maximally Evenno
Maximal Area Setno
Interior Area2.116
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

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
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.