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Scale 2889: "Thoptimic"

Scale 2889: Thoptimic, 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

41161837294116105072918310504116183
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

Cardinality6 (hexatonic)
Pitch Class Set{0,3,6,8,9,11}
Forte Number6-27
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 603
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes5
Prime?no
prime: 603
Deep Scaleno
Interval Vector225222
Interval Spectrump2m2n5s2d2t2
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 Variation2.333
Maximally Evenno
Maximal Area Setno
Interior Area2.366
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 TriadsG♯{8,0,3}331.43
B{11,3,6}331.43
Minor Triadsg♯m{8,11,3}231.57
Diminished Triads{0,3,6}231.57
d♯°{3,6,9}231.57
f♯°{6,9,0}231.71
{9,0,3}231.57
Parsimonious Voice Leading Between Common Triads of Scale 2889. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B d#° d#° f#° f#° d#°->f#° d#°->B f#°->a° g#m g#m g#m->G# g#m->B G#->a°

view full size

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.

Diameter3
Radius3
Self-Centeredyes

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
Scale 873: Bagimic, Ian Ring Music TheoryBagimic
3rd mode:
Scale 621
Scale 621: Pyramid Hexatonic, Ian Ring Music TheoryPyramid Hexatonic
4th mode:
Scale 1179
Scale 1179: Sonimic, Ian Ring Music TheorySonimic
5th mode:
Scale 2637
Scale 2637: Raga Ranjani, Ian Ring Music TheoryRaga Ranjani
6th mode:
Scale 1683
Scale 1683: Raga Malayamarutam, Ian Ring Music TheoryRaga Malayamarutam

Prime

The prime form of this scale is Scale 603

Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic

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 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic

Enantiomorph

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

Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic

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 2891Scale 2891: Phrogian, Ian Ring Music TheoryPhrogian
Scale 2893Scale 2893: Lylian, Ian Ring Music TheoryLylian
Scale 2881Scale 2881, Ian Ring Music Theory
Scale 2885Scale 2885: Byrimic, Ian Ring Music TheoryByrimic
Scale 2897Scale 2897: Rycrimic, Ian Ring Music TheoryRycrimic
Scale 2905Scale 2905: Aeolian Flat 1, Ian Ring Music TheoryAeolian Flat 1
Scale 2921Scale 2921: Pogian, Ian Ring Music TheoryPogian
Scale 2825Scale 2825, Ian Ring Music Theory
Scale 2857Scale 2857: Stythimic, Ian Ring Music TheoryStythimic
Scale 2953Scale 2953: Ionylimic, Ian Ring Music TheoryIonylimic
Scale 3017Scale 3017: Gacrian, Ian Ring Music TheoryGacrian
Scale 2633Scale 2633: Bartók Beta Chord, Ian Ring Music TheoryBartók Beta Chord
Scale 2761Scale 2761: Dagimic, Ian Ring Music TheoryDagimic
Scale 2377Scale 2377: Bartók Gamma Chord, Ian Ring Music TheoryBartók Gamma Chord
Scale 3401Scale 3401: Palimic, Ian Ring Music TheoryPalimic
Scale 3913Scale 3913: Bonian, Ian Ring Music TheoryBonian
Scale 841Scale 841: Phrothitonic, Ian Ring Music TheoryPhrothitonic
Scale 1865Scale 1865: Thagimic, Ian Ring Music TheoryThagimic

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.