Dwarf: Difference between revisions
Too many problems in the last edit. We need to review it step by step Tag: Undo |
Re-install some changes that are valuable (1/) |
||
| Line 1: | Line 1: | ||
A '''dwarf''' is a [[period]]ic [[scale]] obtained by sequentially mapping odd [[harmonic]]s (1, 3, 5, 7, …) using a [[regular temperament]]. A dwarf is a kind of [[detempering|detempered scale]]. The name ''dwarf'' refers to the fact that you are choosing for each degree the smallest [[Tenney height]]. Dwarf scales often produce results which are rich harmonically, with | A '''dwarf''' is a [[period]]ic [[scale]] obtained by sequentially mapping odd [[harmonic]]s (1, 3, 5, 7, …) using a [[regular temperament]]. A dwarf is a kind of [[detempering|detempered scale]]. The name ''dwarf'' refers to the fact that you are choosing for each degree the smallest [[Tenney height]]. Dwarf scales often produce results which are rich harmonically. They are [[otonal]], with intervals expressible as [[octave reduction|octave-reduced]] forms of [[harmonic]]s, and may be flipped to provide [[utonal]] versions of the same scales. | ||
== Construction == | == Construction == | ||
| Line 14: | Line 14: | ||
And that is exactly [[Dwarf12 7]], the dwarf of 12et in the 7-limit. | And that is exactly [[Dwarf12 7]], the dwarf of 12et in the 7-limit. | ||
== Generalization == | |||
=== Symmetrical dwarf === | |||
For a symmetrical scale, we may consider for each odd harmonic both the octave reduction and octave complement, with equal priority. In the case of a tie, like in an even edo, either may be chosen. Unlike standard dwarves, which are strictly otonal, these are more balanced. For example, the symmetrical dwarf of 7et in the 5-limit is | |||
: 9/8, 5/4, 4/3, 3/2, 8/5, 16/9, 2/1 | |||
== See also == | == See also == | ||