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Scale 2155

Scale 2155, 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{0,1,3,5,6,11}
Forte Number6-Z12
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2755
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 215
Deep Scaleno
Interval Vector332232
Interval Spectrump3m2n2s3d3t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,4,6}
<3> = {4,5,7,8}
<4> = {6,8,9,10}
<5> = {7,10,11}
Spectra Variation3.333
Maximally Evenno
Maximal Area Setno
Interior Area1.866
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}110.5
Diminished Triads{0,3,6}110.5
Parsimonious Voice Leading Between Common Triads of Scale 2155. Created by Ian Ring ©2019 B B c°->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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2155 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3125
Scale 3125, Ian Ring Music Theory
3rd mode:
Scale 1805
Scale 1805, Ian Ring Music Theory
4th mode:
Scale 1475
Scale 1475, Ian Ring Music Theory
5th mode:
Scale 2785
Scale 2785, Ian Ring Music Theory
6th mode:
Scale 215
Scale 215, Ian Ring Music TheoryThis is the prime mode

Prime

The prime form of this scale is Scale 215

Scale 215Scale 215, Ian Ring Music Theory

Complement

The hexatonic modal family [2155, 3125, 1805, 1475, 2785, 215] (Forte: 6-Z12) is the complement of the hexatonic modal family [335, 965, 1265, 2215, 3155, 3625] (Forte: 6-Z41)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2155 is 2755

Scale 2755Scale 2755, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2155 is chiral, and its enantiomorph is scale 2755

Scale 2755Scale 2755, Ian Ring Music Theory

Transformations:

T0 2155  T0I 2755
T1 215  T1I 1415
T2 430  T2I 2830
T3 860  T3I 1565
T4 1720  T4I 3130
T5 3440  T5I 2165
T6 2785  T6I 235
T7 1475  T7I 470
T8 2950  T8I 940
T9 1805  T9I 1880
T10 3610  T10I 3760
T11 3125  T11I 3425

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 2153Scale 2153, Ian Ring Music Theory
Scale 2157Scale 2157, Ian Ring Music Theory
Scale 2159Scale 2159, Ian Ring Music Theory
Scale 2147Scale 2147, Ian Ring Music Theory
Scale 2151Scale 2151, Ian Ring Music Theory
Scale 2163Scale 2163, Ian Ring Music Theory
Scale 2171Scale 2171, Ian Ring Music Theory
Scale 2123Scale 2123, Ian Ring Music Theory
Scale 2139Scale 2139, Ian Ring Music Theory
Scale 2091Scale 2091, Ian Ring Music Theory
Scale 2219Scale 2219: Phrydimic, Ian Ring Music TheoryPhrydimic
Scale 2283Scale 2283: Aeolyptian, Ian Ring Music TheoryAeolyptian
Scale 2411Scale 2411: Aeolorian, Ian Ring Music TheoryAeolorian
Scale 2667Scale 2667: Byrian, Ian Ring Music TheoryByrian
Scale 3179Scale 3179: Daptian, Ian Ring Music TheoryDaptian
Scale 107Scale 107, Ian Ring Music Theory
Scale 1131Scale 1131: Honchoshi Plagal Form, Ian Ring Music TheoryHonchoshi Plagal Form

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.