Fantasy detempers
Fantasy detempers are a collection of algorithms for forming detemperaments of edos to just intonation, or to a higher-rank regular temperament. They have in common that the simplest interval mapped to each step of the edo is chosen, using some measure of complexity. The name "fantasy detemper" derives from the nomenclature of fantasy races for these methods.
| Scale type | Detemperament to | Complexity measure |
|---|---|---|
| Hobbit | Temperament which the edo supports | Tenney-Euclidean octave-equivalent seminorm |
| Elf | Any temperament, including temperaments which the edo does not support | Temperament complexity of representative simple JI intervals (chosen by Benedetti height) |
| Dwarf | JI otonalities | Size of the odd number in the numerator |
Types
Hobbit
A hobbit consists of the simplest intervals in a temperament which map to the steps of an edo (or any rank-1 temperament) that supports the temperament. Since a hobbit is octave-equivalent, an octave-equivalent measure of complexity is used. For a rank-2 temperament, the hobbit is the MOS of the EDO's size.
Elf
An elf consists of the simplest intervals in a temperament which map to the steps of an edo that does NOT support the temperament. In order to do this, a simple JI representative (by Benedetti height) is chosen for each interval of the temperament. Then the simplest of those intervals is chosen for each step of the edo, and then tempered by the temperament to produce the elf.
Dwarf
A dwarf consists of the simplest (by odd-limit) octave-reduced JI otonal intervals that map to each step of the EDO.