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Scale 2109

Scale 2109, 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

Cardinality6 (hexatonic)
Pitch Class Set{0,2,3,4,5,11}
Forte Number6-Z3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1923
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes5
Prime?no
prime: 111
Deep Scaleno
Interval Vector433221
Interval Spectrump2m2n3s3d4t
Distribution Spectra<1> = {1,2,6}
<2> = {2,3,7}
<3> = {3,4,8,9}
<4> = {5,9,10}
<5> = {6,10,11}
Spectra Variation4.333
Maximally Evenno
Maximal Area Setno
Interior Area1.433
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Diminished Triads{11,2,5}000

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.

Modes

Modes are the rotational transformation of this scale. Scale 2109 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1551
Scale 1551, Ian Ring Music Theory
3rd mode:
Scale 2823
Scale 2823, Ian Ring Music Theory
4th mode:
Scale 3459
Scale 3459, Ian Ring Music Theory
5th mode:
Scale 3777
Scale 3777, Ian Ring Music Theory
6th mode:
Scale 123
Scale 123, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 111

Scale 111Scale 111, Ian Ring Music Theory

Complement

The hexatonic modal family [2109, 1551, 2823, 3459, 3777, 123] (Forte: 6-Z3) is the complement of the hexatonic modal family [159, 993, 2127, 3111, 3603, 3849] (Forte: 6-Z36)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2109 is 1923

Scale 1923Scale 1923, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2109 is chiral, and its enantiomorph is scale 1923

Scale 1923Scale 1923, Ian Ring Music Theory

Transformations:

T0 2109  T0I 1923
T1 123  T1I 3846
T2 246  T2I 3597
T3 492  T3I 3099
T4 984  T4I 2103
T5 1968  T5I 111
T6 3936  T6I 222
T7 3777  T7I 444
T8 3459  T8I 888
T9 2823  T9I 1776
T10 1551  T10I 3552
T11 3102  T11I 3009

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 2111Scale 2111, Ian Ring Music Theory
Scale 2105Scale 2105, Ian Ring Music Theory
Scale 2107Scale 2107, Ian Ring Music Theory
Scale 2101Scale 2101, Ian Ring Music Theory
Scale 2093Scale 2093, Ian Ring Music Theory
Scale 2077Scale 2077, Ian Ring Music Theory
Scale 2141Scale 2141, Ian Ring Music Theory
Scale 2173Scale 2173, Ian Ring Music Theory
Scale 2237Scale 2237: Epothian, Ian Ring Music TheoryEpothian
Scale 2365Scale 2365: Sythian, Ian Ring Music TheorySythian
Scale 2621Scale 2621: Ionogian, Ian Ring Music TheoryIonogian
Scale 3133Scale 3133, Ian Ring Music Theory
Scale 61Scale 61, Ian Ring Music Theory
Scale 1085Scale 1085, 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.