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Scale 2167

Scale 2167, 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

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,5,6,11}
Forte Number7-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3523
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes6
Prime?no
prime: 239
Deep Scaleno
Interval Vector543342
Interval Spectrump4m3n3s4d5t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6}
<3> = {3,4,7}
<4> = {5,8,9}
<5> = {6,9,10}
<6> = {7,10,11}
Spectra Variation3.429
Maximally Evenno
Maximal Area Setno
Interior Area1.933
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 2167. 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 2167 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3131
Scale 3131, Ian Ring Music Theory
3rd mode:
Scale 3613
Scale 3613, Ian Ring Music Theory
4th mode:
Scale 1927
Scale 1927, Ian Ring Music Theory
5th mode:
Scale 3011
Scale 3011, Ian Ring Music Theory
6th mode:
Scale 3553
Scale 3553, Ian Ring Music Theory
7th mode:
Scale 239
Scale 239, Ian Ring Music TheoryThis is the prime mode

Prime

The prime form of this scale is Scale 239

Scale 239Scale 239, Ian Ring Music Theory

Complement

The heptatonic modal family [2167, 3131, 3613, 1927, 3011, 3553, 239] (Forte: 7-5) is the complement of the pentatonic modal family [143, 481, 2119, 3107, 3601] (Forte: 5-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2167 is 3523

Scale 3523Scale 3523, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2167 is chiral, and its enantiomorph is scale 3523

Scale 3523Scale 3523, Ian Ring Music Theory

Transformations:

T0 2167  T0I 3523
T1 239  T1I 2951
T2 478  T2I 1807
T3 956  T3I 3614
T4 1912  T4I 3133
T5 3824  T5I 2171
T6 3553  T6I 247
T7 3011  T7I 494
T8 1927  T8I 988
T9 3854  T9I 1976
T10 3613  T10I 3952
T11 3131  T11I 3809

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 2165Scale 2165, Ian Ring Music Theory
Scale 2163Scale 2163, Ian Ring Music Theory
Scale 2171Scale 2171, Ian Ring Music Theory
Scale 2175Scale 2175, Ian Ring Music Theory
Scale 2151Scale 2151, Ian Ring Music Theory
Scale 2159Scale 2159, Ian Ring Music Theory
Scale 2135Scale 2135, Ian Ring Music Theory
Scale 2103Scale 2103, Ian Ring Music Theory
Scale 2231Scale 2231: Macrian, Ian Ring Music TheoryMacrian
Scale 2295Scale 2295: Kogyllic, Ian Ring Music TheoryKogyllic
Scale 2423Scale 2423, Ian Ring Music Theory
Scale 2679Scale 2679: Rathyllic, Ian Ring Music TheoryRathyllic
Scale 3191Scale 3191: Bynyllic, Ian Ring Music TheoryBynyllic
Scale 119Scale 119, Ian Ring Music Theory
Scale 1143Scale 1143: Styrian, Ian Ring Music TheoryStyrian

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.