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Scale 2135

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

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

Cardinality	6 (hexatonic)
Pitch Class Set	{0,1,2,4,6,11}
Forte Number	6-9
Rotational Symmetry	none
Reflection Axes	none
Palindromic	no
Chirality	yes enantiomorph: 3395
Hemitonia	3 (trihemitonic)
Cohemitonia	2 (dicohemitonic)
Imperfections	3
Modes	5
Prime?	no prime: 175
Deep Scale	no
Interval Vector	342231
Interval Spectrum	p³m²n²s⁴d³t
Distribution Spectra	<1> = {1,2,5} <2> = {2,3,4,6,7} <3> = {3,4,5,7,8,9} <4> = {5,6,8,9,10} <5> = {7,10,11}
Spectra Variation	4
Maximally Even	no
Maximal Area Set	no
Interior Area	1.866
Myhill Property	no
Balanced	no
Ridge Tones	none
Propriety	Improper
Heliotonic	no

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 Type	Triad^*	Pitch Classes	Degree	Eccentricity	Closeness Centrality
Minor Triads	bm	{11,2,6}	0	0	0

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 2135 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode: Scale 3115
3rd mode: Scale 3605
4th mode: Scale 1925
5th mode: Scale 1505
6th mode: Scale 175					This is the prime mode

Prime

The prime form of this scale is Scale 175

Scale 175

Complement

The hexatonic modal family [2135, 3115, 3605, 1925, 1505, 175] (Forte: 6-9) is the complement of the hexatonic modal family [175, 1505, 1925, 2135, 3115, 3605] (Forte: 6-9)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2135 is 3395

Scale 3395

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2135 is chiral, and its enantiomorph is scale 3395

Scale 3395

Transformations:

T₀	2135	T₀I	3395
T₁	175	T₁I	2695
T₂	350	T₂I	1295
T₃	700	T₃I	2590
T₄	1400	T₄I	1085
T₅	2800	T₅I	2170
T₆	1505	T₆I	245
T₇	3010	T₇I	490
T₈	1925	T₈I	980
T₉	3850	T₉I	1960
T₁₀	3605	T₁₀I	3920
T₁₁	3115	T₁₁I	3745

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 2133				Raga Kumurdaki
Scale 2131
Scale 2139
Scale 2143
Scale 2119
Scale 2127
Scale 2151
Scale 2167
Scale 2071
Scale 2103
Scale 2199				Dyptimic
Scale 2263				Lycrian
Scale 2391				Molian
Scale 2647				Dadian
Scale 3159				Stocrian
Scale 87
Scale 1111				Sycrimic

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.