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Scale 2943: "Dathyllian"
Bracelet Diagram
Tonnetz Diagram
Common Names
- Zeitler
- Dathyllian
Analysis
| Cardinality | 10 (decatonic) |
|---|---|
| Pitch Class Set | {0,1,2,3,4,5,6,8,9,11} |
| Forte Number | 10-3 |
| Rotational Symmetry | none |
| Reflection Axes | 2.5 |
| Palindromic | no |
| Chirality | no |
| Hemitonia | 8 (multihemitonic) |
| Cohemitonia | 6 (multicohemitonic) |
| Imperfections | 2 |
| Modes | 9 |
| Prime? | no prime: 1791 |
| Deep Scale | no |
| Interval Vector | 889884 |
| Interval Spectrum | p8m8n9s8d8t4 |
| Distribution Spectra | <1> = {1,2} <2> = {2,3} <3> = {3,4,5} <4> = {4,5,6} <5> = {5,6,7} <6> = {6,7,8} <7> = {7,8,9} <8> = {9,10} <9> = {10,11} |
| Spectra Variation | 1.4 |
| Maximally Even | no |
| Maximal Area Set | yes |
| Interior Area | 2.866 |
| Myhill Property | no |
| Balanced | no |
| Ridge Tones | [5] |
| 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 | C♯ | {1,5,8} | 4 | 5 | 2.67 |
| D | {2,6,9} | 4 | 5 | 2.75 | |
| E | {4,8,11} | 3 | 5 | 2.75 | |
| F | {5,9,0} | 4 | 5 | 2.58 | |
| G♯ | {8,0,3} | 4 | 5 | 2.67 | |
| A | {9,1,4} | 3 | 5 | 2.75 | |
| B | {11,3,6} | 4 | 5 | 2.83 | |
| Minor Triads | c♯m | {1,4,8} | 3 | 5 | 2.75 |
| dm | {2,5,9} | 4 | 5 | 2.67 | |
| fm | {5,8,0} | 4 | 5 | 2.58 | |
| f♯m | {6,9,1} | 3 | 5 | 2.75 | |
| g♯m | {8,11,3} | 4 | 5 | 2.75 | |
| am | {9,0,4} | 4 | 5 | 2.67 | |
| bm | {11,2,6} | 4 | 5 | 2.83 | |
| Augmented Triads | C+ | {0,4,8} | 5 | 5 | 2.5 |
| C♯+ | {1,5,9} | 5 | 5 | 2.5 | |
| Diminished Triads | c° | {0,3,6} | 2 | 5 | 3 |
| d° | {2,5,8} | 2 | 5 | 3 | |
| d♯° | {3,6,9} | 2 | 5 | 3 | |
| f° | {5,8,11} | 2 | 5 | 3 | |
| f♯° | {6,9,0} | 2 | 5 | 3 | |
| g♯° | {8,11,2} | 2 | 5 | 3 | |
| a° | {9,0,3} | 2 | 5 | 3 | |
| b° | {11,2,5} | 2 | 5 | 3 |
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 | 5 |
|---|---|
| Radius | 5 |
| Self-Centered | yes |
Modes
Modes are the rotational transformation of this scale. Scale 2943 can be rotated to make 9 other scales. The 1st mode is itself.
| 2nd mode: Scale 3519 |  | Raga Sindhi-Bhairavi | |||
| 3rd mode: Scale 3807 |  | Bagyllian | |||
| 4th mode: Scale 3951 |  | Mathyllian | |||
| 5th mode: Scale 4023 |  | Styptyllian | |||
| 6th mode: Scale 4059 |  | Zolyllian | |||
| 7th mode: Scale 4077 |  | Gothyllian | |||
| 8th mode: Scale 2043 |  | Maqam Tarzanuyn | |||
| 9th mode: Scale 3069 |  | Maqam Shawq Afza | |||
| 10th mode: Scale 1791 |  | Aerygyllian | This is the prime mode |
Prime
The prime form of this scale is Scale 1791
| Scale 1791 | | Aerygyllian |
Complement
The decatonic modal family [2943, 3519, 3807, 3951, 4023, 4059, 4077, 2043, 3069, 1791] (Forte: 10-3) is the complement of the modal family [9, 513] (Forte: 2-3)
Inverse
The inverse of a scale is a reflection using the root as its axis. The inverse of 2943 is 4059
| Scale 4059 | | Zolyllian |
Transformations:
| T0 | 2943 | T0I | 4059 | |||||
| T1 | 1791 | T1I | 4023 | |||||
| T2 | 3582 | T2I | 3951 | |||||
| T3 | 3069 | T3I | 3807 | |||||
| T4 | 2043 | T4I | 3519 | |||||
| T5 | 4086 | T5I | 2943 | |||||
| T6 | 4077 | T6I | 1791 | |||||
| T7 | 4059 | T7I | 3582 | |||||
| T8 | 4023 | T8I | 3069 | |||||
| T9 | 3951 | T9I | 2043 | |||||
| T10 | 3807 | T10I | 4086 | |||||
| T11 | 3519 | T11I | 4077 |
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 2941 |  | Laptygic | ||
| Scale 2939 |  | Goptygic | ||
| Scale 2935 |  | Modygic | ||
| Scale 2927 |  | Rodygic | ||
| Scale 2911 |  | Katygic | ||
| Scale 2879 |  | Stadygic | ||
| Scale 3007 |  | Zyryllian | ||
| Scale 3071 |  | Solatic | ||
| Scale 2687 |  | Thacrygic | ||
| Scale 2815 |  | Aeradyllian | ||
| Scale 2431 |  | Gythygic | ||
| Scale 3455 |  | Ryptyllian | ||
| Scale 3967 |  | Soratic | ||
| Scale 895 |  | Aeolathygic | ||
| Scale 1919 |  | Rocryllian |
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.