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Scale 2889: "Thoptimic"
Bracelet Diagram
Tonnetz Diagram
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 |
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 |
|---|---|---|---|---|---|
| Major Triads | G♯ | {8,0,3} | 3 | 3 | 1.43 |
| B | {11,3,6} | 3 | 3 | 1.43 | |
| Minor Triads | g♯m | {8,11,3} | 2 | 3 | 1.57 |
| Diminished Triads | c° | {0,3,6} | 2 | 3 | 1.57 |
| d♯° | {3,6,9} | 2 | 3 | 1.57 | |
| f♯° | {6,9,0} | 2 | 3 | 1.71 | |
| a° | {9,0,3} | 2 | 3 | 1.57 |
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.
| Diameter | 3 |
|---|---|
| Radius | 3 |
| Self-Centered | yes |
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, 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.