User:Unque/Dhembrwood
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Dhembrwood is a temperament originally presented as a joke, which was later refined into a scale that could debatably be considered usable.
Technical Data
Dhembrwood belongs to the Subgroup 2.9/5.Kleven. It is defined by tempering such that nine Komornik-Loreti Constants (MissMagenta calls this interval the Kleventh, a clipping of "Komornik-Loreti Seventh") reduce to an octave; this maps the Kleventh (somewhat inaccurately) to 8\9.
Dhembrwood has a period of 2\9 (Seven Klevenths, octave-reduced) and a generator of 10/9.
Dhembrwood[18]
The parent scale for Dhembrwood is the Dhembrwood[18] scale. This scale repeats every other octave, generating a 4/1-equivalent form of the MOS scale 9L 9s.
If disambiguation is necessary, the two modes of this scale can be referred to "Bright Dhembrwood[18]" and "Dark Dhembrwood[18]."
Dhembrwood[9]
Dhembrwood[9] is generated by taking the first eight notes of the Bright Dhembrwood[18] mode, and adding the octave above the root; this provides a single step that is not equivalent to the Large or Small step of Dhembrewood[18], but rather equal to the average thereof. Since the large and small steps always add up to 2\9, the average of the two steps (and therefore the size of the Medium step) will always be exactly 1\9.
Because of that medium step, all nine modes of Dhembrwood[9] are unique; these modes can be named after the Eight or Nine Dwarves from Rapunzel:
- Clumsy (LsLsLsLsM)
- Snoozy (sLsLsLsML)
- Cheerful (LsLsLsMLs)
- Fearful (sLsLsMLsL)
- Hyper (LsLsMLsLs)
- Hungry (sLsMLsLsL)
- Griselda (LsMLsLsLs)
- Ambidextrous (sMLsLsLsL)
- Sometimes Bewildered (MLsLsLsLs)
Dhembrwood[9]
If we use the Dark Dhembrwood[18] mode instead of the Light mode, we generate Dhembrwood[9] instead; this scale also has a single medium step, and thus provides nine more unique modes to explore. These modes can be named after the nine planets of the Solar System:
- Quicksilver (sLsLsLsLM)
- Cythera (LsLsLsLMs)
- America (sLsLsLMsL)
- The Moon (LsLsLMsLs)
- Big Jim (sLsLMsLsL)
- Mount Olympus (LsLMsLsLs)
- Urecrtum (sLMsLsLsL)
- SpongeBob (LMsLsLsLs)
- Pluto (MsLsLsLsL)
Tuning Ranges
Below are listed several sequences that support the Dhembrwood scales:
| Bright Gen | Dark Gen | Notes |
|---|---|---|
| 1\9 | 1\9 | Equalized |
| 6\45 | 4\45 | Not 45edo's optimal tuning of 9/5 |
| 4\27 | 2\27 | Basic Dhembrwood |
| 10/9 | ~84.3c | Untempered 10/9 |
| 7\45 | 3\45 | |
| 3\18 | 1\18 | |
| ~195.9c | 25/24 | Scales harder than this are debatably not true Dhembrwood |
| 9/8 | ~62.8c | |
| 2\9 | 0 | Collapsed |
Music
Due to first and foremost being a joke, music written in Dhembrwood is scarce, but not entirely unheard of.