Scale 2889: "Thoptimic"

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).

Common Names

Zeitler: Thoptimic

Analysis

Cardinality	6 (hexatonic)
Pitch Class Set	{0,3,6,8,9,11}
Forte Number	6-27
Rotational Symmetry	none
Reflection Axes	none
Palindromic	no
Chirality	yes enantiomorph: 603
Hemitonia	2 (dihemitonic)
Cohemitonia	0 (ancohemitonic)
Imperfections	4
Modes	5
Prime?	no prime: 603
Deep Scale	no
Interval Vector	225222
Interval Spectrum	p²m²n⁵s²d²t²
Distribution Spectra	<1> = {1,2,3} <2> = {3,4,5,6} <3> = {4,5,6,7,8} <4> = {6,7,8,9} <5> = {9,10,11}
Spectra Variation	2.333
Maximally Even	no
Maximal Area Set	no
Interior Area	2.366
Myhill Property	no
Balanced	no
Ridge Tones	none
Propriety	Improper
Heliotonic	no

Modes

Modes are the rotational transformation of this scale. Scale 2889 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode: Scale 873				Bagimic
3rd mode: Scale 621				Pyramid Hexatonic
4th mode: Scale 1179				Sonimic
5th mode: Scale 2637				Raga Ranjani
6th mode: Scale 1683				Raga Malayamarutam

Prime

The prime form of this scale is Scale 603

Scale 603

Aeolygimic

Complement

The hexatonic modal family [2889, 873, 621, 1179, 2637, 1683] (Forte: 6-27) is the complement of the hexatonic modal family [603, 729, 1611, 1737, 2349, 2853] (Forte: 6-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2889 is 603

Scale 603

Aeolygimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2889 is chiral, and its enantiomorph is scale 603

Scale 603

Aeolygimic

Transformations:

T₀	2889	T₀I	603
T₁	1683	T₁I	1206
T₂	3366	T₂I	2412
T₃	2637	T₃I	729
T₄	1179	T₄I	1458
T₅	2358	T₅I	2916
T₆	621	T₆I	1737
T₇	1242	T₇I	3474
T₈	2484	T₈I	2853
T₉	873	T₉I	1611
T₁₀	1746	T₁₀I	3222
T₁₁	3492	T₁₁I	2349

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 2891				Phrogian
Scale 2893				Lylian
Scale 2881
Scale 2885				Byrimic
Scale 2897				Rycrimic
Scale 2905				Aeolian Flat 1
Scale 2921				Pogian
Scale 2825
Scale 2857				Stythimic
Scale 2953				Ionylimic
Scale 3017				Gacrian
Scale 2633				Bartók Beta Chord
Scale 2761				Dagimic
Scale 2377				Bartók Gamma Chord
Scale 3401				Palimic
Scale 3913				Bonian
Scale 841				Phrothitonic
Scale 1865				Thagimic

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, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.