Elf: Difference between revisions
No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
An '''elf''' is a scale in a [[regular temperament]] which is tempered from a [[just intonation]] (JI) scale in the group of the temperament which is a one-to-one [[detempering]] of ''n''-edo via a val ''V'' which may not be, and characteristically is not, a val supporting the temperament. This allows the elf to have more freedom in scale size and structure but still to possess the coherence induced by the epimorphic mapping. | An '''elf''' is a scale in a [[regular temperament]] which is tempered from a [[just intonation]] (JI) scale in the group of the temperament which is a one-to-one [[detempering]] of ''n''-edo via a val ''V'' which may not be, and characteristically is not, a val supporting the temperament. This allows the elf to have more freedom in scale size and structure but still to possess the coherence induced by the epimorphic mapping. | ||
To construct an elf, the following steps are used: | To construct an elf given an ''n''-edo val ''V'' and a temperament, the following steps are used: | ||
# Take all intervals in the JI group of the temperament which lie within an octave. | # Take all intervals in the JI group of the temperament which lie within an octave. | ||
# For each interval of the temperament, keep only the least complex (in terms of [[Benedetti height]]) JI interpretation of that interval. | # For each interval of the temperament, keep only the least complex (in terms of [[Benedetti height]]) JI interpretation of that interval. | ||