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Scale 2067

Scale 2067, 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).

Analysis

Cardinality4 (tetratonic)
Pitch Class Set{0,1,4,11}
Forte Number4-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2307
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes3
Prime?no
prime: 39
Deep Scaleno
Interval Vector211110
Interval Spectrumpmnsd2
Distribution Spectra<1> = {1,3,7}
<2> = {2,4,8,10}
<3> = {5,9,11}
Spectra Variation5
Maximally Evenno
Maximal Area Setno
Interior Area0.75
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Common Triads

There are no common triads (major, minor, augmented and diminished) that can be formed using notes in this scale.

Modes

Modes are the rotational transformation of this scale. Scale 2067 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 3081
Scale 3081, Ian Ring Music Theory
3rd mode:
Scale 897
Scale 897, Ian Ring Music Theory
4th mode:
Scale 39
Scale 39, Ian Ring Music TheoryThis is the prime mode

Prime

The prime form of this scale is Scale 39

Scale 39Scale 39, Ian Ring Music Theory

Complement

The tetratonic modal family [2067, 3081, 897, 39] (Forte: 4-4) is the complement of the octatonic modal family [447, 2019, 2271, 3057, 3183, 3639, 3867, 3981] (Forte: 8-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2067 is 2307

Scale 2307Scale 2307, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2067 is chiral, and its enantiomorph is scale 2307

Scale 2307Scale 2307, Ian Ring Music Theory

Transformations:

T0 2067  T0I 2307
T1 39  T1I 519
T2 78  T2I 1038
T3 156  T3I 2076
T4 312  T4I 57
T5 624  T5I 114
T6 1248  T6I 228
T7 2496  T7I 456
T8 897  T8I 912
T9 1794  T9I 1824
T10 3588  T10I 3648
T11 3081  T11I 3201

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 2065Scale 2065, Ian Ring Music Theory
Scale 2069Scale 2069, Ian Ring Music Theory
Scale 2071Scale 2071, Ian Ring Music Theory
Scale 2075Scale 2075, Ian Ring Music Theory
Scale 2051Scale 2051, Ian Ring Music Theory
Scale 2059Scale 2059, Ian Ring Music Theory
Scale 2083Scale 2083, Ian Ring Music Theory
Scale 2099Scale 2099: Raga Megharanji, Ian Ring Music TheoryRaga Megharanji
Scale 2131Scale 2131, Ian Ring Music Theory
Scale 2195Scale 2195: Zalitonic, Ian Ring Music TheoryZalitonic
Scale 2323Scale 2323: Doptitonic, Ian Ring Music TheoryDoptitonic
Scale 2579Scale 2579, Ian Ring Music Theory
Scale 3091Scale 3091, Ian Ring Music Theory
Scale 19Scale 19, Ian Ring Music Theory
Scale 1043Scale 1043, 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, 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.