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Scale 3081

Scale 3081, 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{0,3,10,11}
Forte Number4-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 519
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 3081 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 897
Scale 897, Ian Ring Music Theory
3rd mode:
Scale 39
Scale 39, Ian Ring Music TheoryThis is the prime mode
4th mode:
Scale 2067
Scale 2067, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 39

Scale 39Scale 39, Ian Ring Music Theory

Complement

The tetratonic modal family [3081, 897, 39, 2067] (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 3081 is 519

Scale 519Scale 519, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3081 is chiral, and its enantiomorph is scale 519

Scale 519Scale 519, Ian Ring Music Theory

Transformations:

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

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 3083Scale 3083, Ian Ring Music Theory
Scale 3085Scale 3085, Ian Ring Music Theory
Scale 3073Scale 3073, Ian Ring Music Theory
Scale 3077Scale 3077, Ian Ring Music Theory
Scale 3089Scale 3089, Ian Ring Music Theory
Scale 3097Scale 3097, Ian Ring Music Theory
Scale 3113Scale 3113, Ian Ring Music Theory
Scale 3145Scale 3145: Stolitonic, Ian Ring Music TheoryStolitonic
Scale 3209Scale 3209: Aeraphitonic, Ian Ring Music TheoryAeraphitonic
Scale 3337Scale 3337, Ian Ring Music Theory
Scale 3593Scale 3593, Ian Ring Music Theory
Scale 2057Scale 2057, Ian Ring Music Theory
Scale 2569Scale 2569, Ian Ring Music Theory
Scale 1033Scale 1033, 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.