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Scale 2151

Scale 2151, 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{0,1,2,5,6,11}
Forte Number6-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3267
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes5
Prime?no
prime: 207
Deep Scaleno
Interval Vector422232
Interval Spectrump3m2n2s2d4t2
Distribution Spectra<1> = {1,3,5}
<2> = {2,4,6}
<3> = {3,5,7,9}
<4> = {6,8,10}
<5> = {7,9,11}
Spectra Variation3.667
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
Minor Triadsbm{11,2,6}110.5
Diminished Triads{11,2,5}110.5
Parsimonious Voice Leading Between Common Triads of Scale 2151. Created by Ian Ring ©2019 bm bm b°->bm

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2151 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3123
Scale 3123, Ian Ring Music Theory
3rd mode:
Scale 3609
Scale 3609, Ian Ring Music Theory
4th mode:
Scale 963
Scale 963, Ian Ring Music Theory
5th mode:
Scale 2529
Scale 2529, Ian Ring Music Theory
6th mode:
Scale 207
Scale 207, Ian Ring Music TheoryThis is the prime mode

Prime

The prime form of this scale is Scale 207

Scale 207Scale 207, Ian Ring Music Theory

Complement

The hexatonic modal family [2151, 3123, 3609, 963, 2529, 207] (Forte: 6-5) is the complement of the hexatonic modal family [207, 963, 2151, 2529, 3123, 3609] (Forte: 6-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2151 is 3267

Scale 3267Scale 3267, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2151 is chiral, and its enantiomorph is scale 3267

Scale 3267Scale 3267, Ian Ring Music Theory

Transformations:

T0 2151  T0I 3267
T1 207  T1I 2439
T2 414  T2I 783
T3 828  T3I 1566
T4 1656  T4I 3132
T5 3312  T5I 2169
T6 2529  T6I 243
T7 963  T7I 486
T8 1926  T8I 972
T9 3852  T9I 1944
T10 3609  T10I 3888
T11 3123  T11I 3681

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 2149Scale 2149, Ian Ring Music Theory
Scale 2147Scale 2147, Ian Ring Music Theory
Scale 2155Scale 2155, Ian Ring Music Theory
Scale 2159Scale 2159, Ian Ring Music Theory
Scale 2167Scale 2167, Ian Ring Music Theory
Scale 2119Scale 2119, Ian Ring Music Theory
Scale 2135Scale 2135, Ian Ring Music Theory
Scale 2087Scale 2087, Ian Ring Music Theory
Scale 2215Scale 2215: Ranimic, Ian Ring Music TheoryRanimic
Scale 2279Scale 2279: Dyrian, Ian Ring Music TheoryDyrian
Scale 2407Scale 2407: Zylian, Ian Ring Music TheoryZylian
Scale 2663Scale 2663: Lalian, Ian Ring Music TheoryLalian
Scale 3175Scale 3175: Eponian, Ian Ring Music TheoryEponian
Scale 103Scale 103, Ian Ring Music Theory
Scale 1127Scale 1127: Eparimic, Ian Ring Music TheoryEparimic

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.