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Scale 869: "Kothimic"

Scale 869: Kothimic, 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

Zeitler
Kothimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,5,6,8,9}
Forte Number6-Z49
Rotational Symmetrynone
Reflection Axes1
Palindromicno
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes5
Prime?no
prime: 667
Deep Scaleno
Interval Vector224322
Interval Spectrump2m3n4s2d2t2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {4,6,8}
<4> = {7,8,9}
<5> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.366
Myhill Propertyno
Balancedno
Ridge Tones[2]
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 869 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1241
Scale 1241: Pygimic, Ian Ring Music TheoryPygimic
3rd mode:
Scale 667
Scale 667: Rodimic, Ian Ring Music TheoryRodimicThis is the prime mode
4th mode:
Scale 2381
Scale 2381: Takemitsu Linea Mode 1, Ian Ring Music TheoryTakemitsu Linea Mode 1
5th mode:
Scale 1619
Scale 1619: Prometheus Neapolitan, Ian Ring Music TheoryPrometheus Neapolitan
6th mode:
Scale 2857
Scale 2857: Stythimic, Ian Ring Music TheoryStythimic

Prime

The prime form of this scale is Scale 667

Scale 667Scale 667: Rodimic, Ian Ring Music TheoryRodimic

Complement

The hexatonic modal family [869, 1241, 667, 2381, 1619, 2857] (Forte: 6-Z49) is the complement of the hexatonic modal family [619, 857, 1427, 1613, 2357, 2761] (Forte: 6-Z28)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 869 is 1241

Scale 1241Scale 1241: Pygimic, Ian Ring Music TheoryPygimic

Transformations:

T0 869  T0I 1241
T1 1738  T1I 2482
T2 3476  T2I 869
T3 2857  T3I 1738
T4 1619  T4I 3476
T5 3238  T5I 2857
T6 2381  T6I 1619
T7 667  T7I 3238
T8 1334  T8I 2381
T9 2668  T9I 667
T10 1241  T10I 1334
T11 2482  T11I 2668

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 871Scale 871: Locrian Double-flat 3 Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 3 Double-flat 7
Scale 865Scale 865, Ian Ring Music Theory
Scale 867Scale 867: Phrocrimic, Ian Ring Music TheoryPhrocrimic
Scale 873Scale 873: Bagimic, Ian Ring Music TheoryBagimic
Scale 877Scale 877: Moravian Pistalkova, Ian Ring Music TheoryMoravian Pistalkova
Scale 885Scale 885: Sathian, Ian Ring Music TheorySathian
Scale 837Scale 837: Epaditonic, Ian Ring Music TheoryEpaditonic
Scale 853Scale 853: Epothimic, Ian Ring Music TheoryEpothimic
Scale 805Scale 805: Rothitonic, Ian Ring Music TheoryRothitonic
Scale 933Scale 933: Dadimic, Ian Ring Music TheoryDadimic
Scale 997Scale 997: Rycrian, Ian Ring Music TheoryRycrian
Scale 613Scale 613: Phralitonic, Ian Ring Music TheoryPhralitonic
Scale 741Scale 741: Gathimic, Ian Ring Music TheoryGathimic
Scale 357Scale 357: Banitonic, Ian Ring Music TheoryBanitonic
Scale 1381Scale 1381: Padimic, Ian Ring Music TheoryPadimic
Scale 1893Scale 1893: Ionylian, Ian Ring Music TheoryIonylian
Scale 2917Scale 2917: Nohkan Flute Scale, Ian Ring Music TheoryNohkan Flute Scale

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, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.