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Scale 1621: "Scriabin's Prometheus"
Bracelet Diagram
Tonnetz Diagram
Common Names
- Named After Composers
- Scriabin's Prometheus
- Mystic
- Carnatic Raga
- Raga Barbara
- Zeitler
- Aeolathimic
Analysis
| Cardinality | 6 (hexatonic) |
|---|---|
| Pitch Class Set | {0,2,4,6,9,10} |
| Forte Number | 6-34 |
| Rotational Symmetry | none |
| Reflection Axes | none |
| Palindromic | no |
| Chirality | yes enantiomorph: 1357 |
| Hemitonia | 1 (unhemitonic) |
| Cohemitonia | 0 (ancohemitonic) |
| Imperfections | 4 |
| Modes | 5 |
| Prime? | no prime: 683 |
| Deep Scale | no |
| Interval Vector | 142422 |
| Interval Spectrum | p2m4n2s4dt2 |
| Distribution Spectra | <1> = {1,2,3} <2> = {3,4,5} <3> = {5,6,7} <4> = {7,8,9} <5> = {9,10,11} |
| Spectra Variation | 1.667 |
| Maximally Even | no |
| Maximal Area Set | no |
| Interior Area | 2.482 |
| Myhill Property | no |
| Balanced | no |
| Ridge Tones | none |
| Propriety | Proper |
| 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 | D | {2,6,9} | 2 | 2 | 1 |
| Minor Triads | am | {9,0,4} | 1 | 3 | 1.5 |
| Augmented Triads | D+ | {2,6,10} | 1 | 3 | 1.5 |
| Diminished Triads | f♯° | {6,9,0} | 2 | 2 | 1 |
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 | D, f♯° |
| Peripheral Vertices | D+, am |
Modes
Modes are the rotational transformation of this scale. Scale 1621 can be rotated to make 5 other scales. The 1st mode is itself.
| 2nd mode: Scale 1429 |  | Bythimic | |||
| 3rd mode: Scale 1381 |  | Padimic | |||
| 4th mode: Scale 1369 |  | Boptimic | |||
| 5th mode: Scale 683 |  | Stogimic | This is the prime mode | ||
| 6th mode: Scale 2389 |  | Eskimo Hexatonic 2 |
Prime
The prime form of this scale is Scale 683
| Scale 683 | | Stogimic |
Complement
The hexatonic modal family [1621, 1429, 1381, 1369, 683, 2389] (Forte: 6-34) is the complement of the hexatonic modal family [683, 1369, 1381, 1429, 1621, 2389] (Forte: 6-34)
Inverse
The inverse of a scale is a reflection using the root as its axis. The inverse of 1621 is 1357
| Scale 1357 |  | Takemitsu Linea Mode 2 |
Enantiomorph
Only scales that are chiral will have an enantiomorph. Scale 1621 is chiral, and its enantiomorph is scale 1357
| Scale 1357 | | Takemitsu Linea Mode 2 |
Transformations:
| T0 | 1621 | T0I | 1357 | |||||
| T1 | 3242 | T1I | 2714 | |||||
| T2 | 2389 | T2I | 1333 | |||||
| T3 | 683 | T3I | 2666 | |||||
| T4 | 1366 | T4I | 1237 | |||||
| T5 | 2732 | T5I | 2474 | |||||
| T6 | 1369 | T6I | 853 | |||||
| T7 | 2738 | T7I | 1706 | |||||
| T8 | 1381 | T8I | 3412 | |||||
| T9 | 2762 | T9I | 2729 | |||||
| T10 | 1429 | T10I | 1363 | |||||
| T11 | 2858 | T11I | 2726 |
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 1623 |  | Lothian | ||
| Scale 1617 |  | Phronitonic | ||
| Scale 1619 |  | Prometheus Neapolitan | ||
| Scale 1625 |  | Lythimic | ||
| Scale 1629 |  | Synian | ||
| Scale 1605 |  | Zanitonic | ||
| Scale 1613 |  | Thylimic | ||
| Scale 1637 |  | Syptimic | ||
| Scale 1653 |  | Minor Romani Inverse | ||
| Scale 1557 |  | |||
| Scale 1589 |  | Raga Rageshri | ||
| Scale 1685 |  | Zeracrimic | ||
| Scale 1749 |  | Acoustic | ||
| Scale 1877 |  | Aeroptian | ||
| Scale 1109 |  | Kataditonic | ||
| Scale 1365 |  | Whole Tone | ||
| Scale 597 |  | Kung | ||
| Scale 2645 |  | Raga Mruganandana | ||
| Scale 3669 |  | Mothian |
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.