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Scale 2127

Scale 2127, 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

Cardinality6 (hexatonic)
Pitch Class Set{0,1,2,3,6,11}
Forte Number6-Z36
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3651
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes5
Prime?no
prime: 159
Deep Scaleno
Interval Vector433221
Interval Spectrump2m2n3s3d4t
Distribution Spectra<1> = {1,3,5}
<2> = {2,4,6,8}
<3> = {3,5,7,9}
<4> = {4,6,8,10}
<5> = {7,9,11}
Spectra Variation4.333
Maximally Evenno
Maximal Area Setno
Interior Area1.75
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
Major TriadsB{11,3,6}210.67
Minor Triadsbm{11,2,6}121
Diminished Triads{0,3,6}121
Parsimonious Voice Leading Between Common Triads of Scale 2127. Created by Ian Ring ©2019 B B c°->B bm bm bm->B

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter2
Radius1
Self-Centeredno
Central VerticesB
Peripheral Verticesc°, bm

Modes

Modes are the rotational transformation of this scale. Scale 2127 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3111
Scale 3111, Ian Ring Music Theory
3rd mode:
Scale 3603
Scale 3603, Ian Ring Music Theory
4th mode:
Scale 3849
Scale 3849, Ian Ring Music Theory
5th mode:
Scale 993
Scale 993, Ian Ring Music Theory
6th mode:
Scale 159
Scale 159, Ian Ring Music TheoryThis is the prime mode

Prime

The prime form of this scale is Scale 159

Scale 159Scale 159, Ian Ring Music Theory

Complement

The hexatonic modal family [2127, 3111, 3603, 3849, 993, 159] (Forte: 6-Z36) is the complement of the hexatonic modal family [111, 1923, 2103, 3009, 3099, 3597] (Forte: 6-Z3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2127 is 3651

Scale 3651Scale 3651, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2127 is chiral, and its enantiomorph is scale 3651

Scale 3651Scale 3651, Ian Ring Music Theory

Transformations:

T0 2127  T0I 3651
T1 159  T1I 3207
T2 318  T2I 2319
T3 636  T3I 543
T4 1272  T4I 1086
T5 2544  T5I 2172
T6 993  T6I 249
T7 1986  T7I 498
T8 3972  T8I 996
T9 3849  T9I 1992
T10 3603  T10I 3984
T11 3111  T11I 3873

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 2125Scale 2125, Ian Ring Music Theory
Scale 2123Scale 2123, Ian Ring Music Theory
Scale 2119Scale 2119, Ian Ring Music Theory
Scale 2135Scale 2135, Ian Ring Music Theory
Scale 2143Scale 2143, Ian Ring Music Theory
Scale 2159Scale 2159, Ian Ring Music Theory
Scale 2063Scale 2063, Ian Ring Music Theory
Scale 2095Scale 2095, Ian Ring Music Theory
Scale 2191Scale 2191: Thydimic, Ian Ring Music TheoryThydimic
Scale 2255Scale 2255: Dylian, Ian Ring Music TheoryDylian
Scale 2383Scale 2383: Katorian, Ian Ring Music TheoryKatorian
Scale 2639Scale 2639: Dothian, Ian Ring Music TheoryDothian
Scale 3151Scale 3151: Pacrian, Ian Ring Music TheoryPacrian
Scale 79Scale 79, Ian Ring Music Theory
Scale 1103Scale 1103: Lynimic, Ian Ring Music TheoryLynimic

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.