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Scale 865

Scale 865, 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).

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,5,6,8,9}
Forte Number5-16
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 217
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes4
Prime?no
prime: 155
Deep Scaleno
Interval Vector213211
Interval Spectrumpm2n3sd2t
Distribution Spectra<1> = {1,2,3,5}
<2> = {3,4,6,8}
<3> = {4,6,8,9}
<4> = {7,9,10,11}
Spectra Variation3.6
Maximally Evenno
Maximal Area Setno
Interior Area1.683
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 865 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 155
Scale 155, Ian Ring Music TheoryThis is the prime mode
3rd mode:
Scale 2125
Scale 2125, Ian Ring Music Theory
4th mode:
Scale 1555
Scale 1555, Ian Ring Music Theory
5th mode:
Scale 2825
Scale 2825, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 155

Scale 155Scale 155, Ian Ring Music Theory

Complement

The pentatonic modal family [865, 155, 2125, 1555, 2825] (Forte: 5-16) is the complement of the heptatonic modal family [623, 889, 1939, 2359, 3017, 3227, 3661] (Forte: 7-16)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 865 is 217

Scale 217Scale 217, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 865 is chiral, and its enantiomorph is scale 217

Scale 217Scale 217, Ian Ring Music Theory

Transformations:

T0 865  T0I 217
T1 1730  T1I 434
T2 3460  T2I 868
T3 2825  T3I 1736
T4 1555  T4I 3472
T5 3110  T5I 2849
T6 2125  T6I 1603
T7 155  T7I 3206
T8 310  T8I 2317
T9 620  T9I 539
T10 1240  T10I 1078
T11 2480  T11I 2156

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 867Scale 867: Phrocrimic, Ian Ring Music TheoryPhrocrimic
Scale 869Scale 869: Kothimic, Ian Ring Music TheoryKothimic
Scale 873Scale 873: Bagimic, Ian Ring Music TheoryBagimic
Scale 881Scale 881: Aerothimic, Ian Ring Music TheoryAerothimic
Scale 833Scale 833, Ian Ring Music Theory
Scale 849Scale 849: Aerynitonic, Ian Ring Music TheoryAerynitonic
Scale 801Scale 801, Ian Ring Music Theory
Scale 929Scale 929, Ian Ring Music Theory
Scale 993Scale 993, Ian Ring Music Theory
Scale 609Scale 609, Ian Ring Music Theory
Scale 737Scale 737, Ian Ring Music Theory
Scale 353Scale 353, Ian Ring Music Theory
Scale 1377Scale 1377, Ian Ring Music Theory
Scale 1889Scale 1889, Ian Ring Music Theory
Scale 2913Scale 2913, Ian Ring Music Theory

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.