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Scale 2057

Scale 2057, 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

Cardinality3 (tritonic)
Pitch Class Set{0,3,11}
Forte Number3-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 515
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes2
Prime?no
prime: 19
Deep Scaleno
Interval Vector101100
Interval Spectrummnd
Distribution Spectra<1> = {1,3,8}
<2> = {4,9,11}
Spectra Variation4.667
Maximally Evenno
Maximal Area Setno
Interior Area0.317
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 2057 can be rotated to make 2 other scales. The 1st mode is itself.

2nd mode:
Scale 769
Scale 769, Ian Ring Music Theory
3rd mode:
Scale 19
Scale 19, Ian Ring Music TheoryThis is the prime mode

Prime

The prime form of this scale is Scale 19

Scale 19Scale 19, Ian Ring Music Theory

Complement

The tritonic modal family [2057, 769, 19] (Forte: 3-3) is the complement of the nonatonic modal family [895, 2035, 2495, 3065, 3295, 3695, 3895, 3995, 4045] (Forte: 9-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2057 is 515

Scale 515Scale 515, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2057 is chiral, and its enantiomorph is scale 515

Scale 515Scale 515, Ian Ring Music Theory

Transformations:

T0 2057  T0I 515
T1 19  T1I 1030
T2 38  T2I 2060
T3 76  T3I 25
T4 152  T4I 50
T5 304  T5I 100
T6 608  T6I 200
T7 1216  T7I 400
T8 2432  T8I 800
T9 769  T9I 1600
T10 1538  T10I 3200
T11 3076  T11I 2305

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 2059Scale 2059, Ian Ring Music Theory
Scale 2061Scale 2061, Ian Ring Music Theory
Scale 2049Scale 2049, Ian Ring Music Theory
Scale 2053Scale 2053, Ian Ring Music Theory
Scale 2065Scale 2065, Ian Ring Music Theory
Scale 2073Scale 2073, Ian Ring Music Theory
Scale 2089Scale 2089, Ian Ring Music Theory
Scale 2121Scale 2121, Ian Ring Music Theory
Scale 2185Scale 2185: Dygic, Ian Ring Music TheoryDygic
Scale 2313Scale 2313, Ian Ring Music Theory
Scale 2569Scale 2569, Ian Ring Music Theory
Scale 3081Scale 3081, Ian Ring Music Theory
Scale 9Scale 9, 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.