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Scale 3653: "Sathimic"

Scale 3653: Sathimic, 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
Sathimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,6,9,10,11}
Forte Number6-Z39
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1103
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes5
Prime?no
prime: 317
Deep Scaleno
Interval Vector333321
Interval Spectrump2m3n3s3d3t
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,3,4,6,7}
<3> = {3,4,5,7,8,9}
<4> = {5,6,8,9,10}
<5> = {8,9,10,11}
Spectra Variation3.667
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}221
Minor Triadsbm{11,2,6}131.5
Augmented TriadsD+{2,6,10}221
Diminished Triadsf♯°{6,9,0}131.5
Parsimonious Voice Leading Between Common Triads of Scale 3653. Created by Ian Ring ©2019 D D D+ D+ D->D+ f#° f#° D->f#° bm bm D+->bm

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 VerticesD, D+
Peripheral Verticesf♯°, bm

Modes

Modes are the rotational transformation of this scale. Scale 3653 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1937
Scale 1937: Galimic, Ian Ring Music TheoryGalimic
3rd mode:
Scale 377
Scale 377: Kathimic, Ian Ring Music TheoryKathimic
4th mode:
Scale 559
Scale 559: Lylimic, Ian Ring Music TheoryLylimic
5th mode:
Scale 2327
Scale 2327: Epalimic, Ian Ring Music TheoryEpalimic
6th mode:
Scale 3211
Scale 3211: Epacrimic, Ian Ring Music TheoryEpacrimic

Prime

The prime form of this scale is Scale 317

Scale 317Scale 317: Korimic, Ian Ring Music TheoryKorimic

Complement

The hexatonic modal family [3653, 1937, 377, 559, 2327, 3211] (Forte: 6-Z39) is the complement of the hexatonic modal family [187, 1559, 1889, 2141, 2827, 3461] (Forte: 6-Z10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3653 is 1103

Scale 1103Scale 1103: Lynimic, Ian Ring Music TheoryLynimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3653 is chiral, and its enantiomorph is scale 1103

Scale 1103Scale 1103: Lynimic, Ian Ring Music TheoryLynimic

Transformations:

T0 3653  T0I 1103
T1 3211  T1I 2206
T2 2327  T2I 317
T3 559  T3I 634
T4 1118  T4I 1268
T5 2236  T5I 2536
T6 377  T6I 977
T7 754  T7I 1954
T8 1508  T8I 3908
T9 3016  T9I 3721
T10 1937  T10I 3347
T11 3874  T11I 2599

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 3655Scale 3655: Mathian, Ian Ring Music TheoryMathian
Scale 3649Scale 3649, Ian Ring Music Theory
Scale 3651Scale 3651, Ian Ring Music Theory
Scale 3657Scale 3657: Epynimic, Ian Ring Music TheoryEpynimic
Scale 3661Scale 3661: Mixodorian, Ian Ring Music TheoryMixodorian
Scale 3669Scale 3669: Mothian, Ian Ring Music TheoryMothian
Scale 3685Scale 3685: Kodian, Ian Ring Music TheoryKodian
Scale 3589Scale 3589, Ian Ring Music Theory
Scale 3621Scale 3621: Gylimic, Ian Ring Music TheoryGylimic
Scale 3717Scale 3717, Ian Ring Music Theory
Scale 3781Scale 3781: Gyphian, Ian Ring Music TheoryGyphian
Scale 3909Scale 3909: Rydian, Ian Ring Music TheoryRydian
Scale 3141Scale 3141: Kanitonic, Ian Ring Music TheoryKanitonic
Scale 3397Scale 3397: Sydimic, Ian Ring Music TheorySydimic
Scale 2629Scale 2629: Raga Shubravarni, Ian Ring Music TheoryRaga Shubravarni
Scale 1605Scale 1605: Zanitonic, Ian Ring Music TheoryZanitonic

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.