Scale 3089

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	4 (tetratonic)
Pitch Class Set	{0,4,10,11}
Forte Number	4-5
Rotational Symmetry	none
Reflection Axes	none
Palindromic	no
Chirality	yes enantiomorph: 263
Hemitonia	2 (dihemitonic)
Cohemitonia	1 (uncohemitonic)
Imperfections	3
Modes	3
Prime?	no prime: 71
Deep Scale	no
Interval Vector	210111
Interval Spectrum	pmsd²t
Distribution Spectra	<1> = {1,4,6} <2> = {2,5,7,10} <3> = {6,8,11}
Spectra Variation	4.5
Maximally Even	no
Maximal Area Set	no
Interior Area	0.933
Myhill Property	no
Balanced	no
Ridge Tones	none
Propriety	Improper
Heliotonic	no

Common Triads

There are no common triads (major, minor, augmented and diminished) that can be formed using notes in this scale.

Modes

Modes are the rotational transformation of this scale. Scale 3089 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode: Scale 449
3rd mode: Scale 71					This is the prime mode
4th mode: Scale 2083

Prime

The prime form of this scale is Scale 71

Scale 71

Complement

The tetratonic modal family [3089, 449, 71, 2083] (Forte: 4-5) is the complement of the octatonic modal family [479, 1991, 2287, 3043, 3191, 3569, 3643, 3869] (Forte: 8-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3089 is 263

Scale 263

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3089 is chiral, and its enantiomorph is scale 263

Scale 263

Transformations:

T₀	3089	T₀I	263
T₁	2083	T₁I	526
T₂	71	T₂I	1052
T₃	142	T₃I	2104
T₄	284	T₄I	113
T₅	568	T₅I	226
T₆	1136	T₆I	452
T₇	2272	T₇I	904
T₈	449	T₈I	1808
T₉	898	T₉I	3616
T₁₀	1796	T₁₀I	3137
T₁₁	3592	T₁₁I	2179

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 3091
Scale 3093
Scale 3097
Scale 3073
Scale 3081
Scale 3105
Scale 3121
Scale 3153				Zathitonic
Scale 3217				Molitonic
Scale 3345				Zylitonic
Scale 3601
Scale 2065
Scale 2577
Scale 1041

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.