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Scale 2837: "Aelothimic"
Bracelet Diagram
Tonnetz Diagram
Common Names
- Zeitler
- Aelothimic
Analysis
| Cardinality | 6 (hexatonic) |
|---|---|
| Pitch Class Set | {0,2,4,8,9,11} |
| Forte Number | 6-Z24 |
| Rotational Symmetry | none |
| Reflection Axes | none |
| Palindromic | no |
| Chirality | yes enantiomorph: 1307 |
| Hemitonia | 2 (dihemitonic) |
| Cohemitonia | 0 (ancohemitonic) |
| Imperfections | 3 |
| Modes | 5 |
| Prime? | no prime: 347 |
| Deep Scale | no |
| Interval Vector | 233331 |
| Interval Spectrum | p3m3n3s3d2t |
| Distribution Spectra | <1> = {1,2,4} <2> = {3,4,5,6} <3> = {4,5,7,8} <4> = {6,7,8,9} <5> = {8,10,11} |
| Spectra Variation | 2.667 |
| Maximally Even | no |
| Maximal Area Set | no |
| Interior Area | 2.232 |
| 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 | E | {4,8,11} | 2 | 2 | 1 |
| Minor Triads | am | {9,0,4} | 1 | 3 | 1.5 |
| Augmented Triads | C+ | {0,4,8} | 2 | 2 | 1 |
| Diminished Triads | g♯° | {8,11,2} | 1 | 3 | 1.5 |
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 | 2 |
| Self-Centered | no |
| Central Vertices | C+, E |
| Peripheral Vertices | g♯°, am |
Modes
Modes are the rotational transformation of this scale. Scale 2837 can be rotated to make 5 other scales. The 1st mode is itself.
| 2nd mode: Scale 1733 |  | Raga Sarasvati | |||
| 3rd mode: Scale 1457 |  | Raga Kamalamanohari | |||
| 4th mode: Scale 347 |  | Barimic | This is the prime mode | ||
| 5th mode: Scale 2221 |  | Raga Sindhura Kafi | |||
| 6th mode: Scale 1579 |  | Sagimic |
Prime
The prime form of this scale is Scale 347
| Scale 347 | | Barimic |
Complement
The hexatonic modal family [2837, 1733, 1457, 347, 2221, 1579] (Forte: 6-Z24) is the complement of the hexatonic modal family [599, 697, 1481, 1829, 2347, 3221] (Forte: 6-Z46)
Inverse
The inverse of a scale is a reflection using the root as its axis. The inverse of 2837 is 1307
| Scale 1307 |  | Katorimic |
Enantiomorph
Only scales that are chiral will have an enantiomorph. Scale 2837 is chiral, and its enantiomorph is scale 1307
| Scale 1307 | | Katorimic |
Transformations:
| T0 | 2837 | T0I | 1307 | |||||
| T1 | 1579 | T1I | 2614 | |||||
| T2 | 3158 | T2I | 1133 | |||||
| T3 | 2221 | T3I | 2266 | |||||
| T4 | 347 | T4I | 437 | |||||
| T5 | 694 | T5I | 874 | |||||
| T6 | 1388 | T6I | 1748 | |||||
| T7 | 2776 | T7I | 3496 | |||||
| T8 | 1457 | T8I | 2897 | |||||
| T9 | 2914 | T9I | 1699 | |||||
| T10 | 1733 | T10I | 3398 | |||||
| T11 | 3466 | T11I | 2701 |
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 2839 |  | Lyptian | ||
| Scale 2833 |  | Dolitonic | ||
| Scale 2835 |  | Ionygimic | ||
| Scale 2841 |  | Sothimic | ||
| Scale 2845 |  | Baptian | ||
| Scale 2821 |  | |||
| Scale 2829 |  | |||
| Scale 2853 |  | Baptimic | ||
| Scale 2869 |  | Major Augmented | ||
| Scale 2901 |  | Lydian Augmented | ||
| Scale 2965 |  | Darian | ||
| Scale 2581 |  | Raga Neroshta | ||
| Scale 2709 |  | Raga Kumud | ||
| Scale 2325 |  | Pynitonic | ||
| Scale 3349 |  | Aeolocrimic | ||
| Scale 3861 |  | Phroptian | ||
| Scale 789 |  | Zogitonic | ||
| Scale 1813 |  | Katothimic |
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.