Magic extensions: Difference between revisions
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[[Magic]] has various competing [[extension]]s to the [[11-limit|11-]] and [[13-limit]]. The following temperaments are discussed in this article: | [[Magic]] has various competing [[extension]]s to the [[11-limit|11-]] and [[13-limit]]. The following temperaments are discussed in this article: | ||
* '''Tridecimal magic''' (19 & 22f) – tempering out 100/99, 105/104, 144/143, and 196/195; | * '''Tridecimal magic''' ({{nowrap|19 & 22f}}) – tempering out 100/99, 105/104, 144/143, and 196/195; | ||
* '''Necromancy''' (19f & 22) – tempering out 100/99, 225/224, 245/243, and 275/273; | * '''Necromancy''' ({{nowrap|19f & 22}}) – tempering out 100/99, 225/224, 245/243, and 275/273; | ||
* '''Witchcraft''' (19e & 22ef) – tempering out 105/104, 196/195, 245/243, and 275/273; | * '''Witchcraft''' ({{nowrap|19e & 22ef}}) – tempering out 105/104, 196/195, 245/243, and 275/273; | ||
* '''Sorcery''' (19 & 22) – tempering out 65/64, 78/77, 91/90, and 100/99; | * '''Sorcery''' ({{nowrap|19 & 22}}) – tempering out 65/64, 78/77, 91/90, and 100/99; | ||
* '''Intuition''' (19e & 22f) – tempering out 55/54, 66/65, 99/98, and 105/104; | * '''Intuition''' ({{nowrap|19e & 22f}}) – tempering out 55/54, 66/65, 99/98, and 105/104; | ||
* '''Telepathy''' (19e & 22) – tempering out 55/54, 65/64, 91/90, and 99/98. | * '''Telepathy''' ({{nowrap|19e & 22}}) – tempering out 55/54, 65/64, 91/90, and 99/98. | ||
The most important of these is tridecimal magic, where primes 11 and 13 are mapped such that 10/9 and 11/10 are tempered together and that 14/13 and 16/15 are tempered together. Necromancy takes the same mapping of 11 as magic, but swaps in a more complex mapping for 13, enabling the possibility of a higher-accuracy harmony. Similarly, witchcraft takes the same mapping of 13 as magic, but swaps in a more complex mapping for 11. Necromancy is the {{nowrap| 41 & 63 }} temperament [[support]]ed by [[104edo]], whereas witchcraft is the {{nowrap| 41 & 60e }} temperament supported by [[101edo]] in the 101cd [[val]]. | The most important of these is tridecimal magic, where primes 11 and 13 are mapped such that 10/9 and 11/10 are tempered together and that 14/13 and 16/15 are tempered together. Necromancy takes the same mapping of 11 as magic, but swaps in a more complex mapping for 13, enabling the possibility of a higher-accuracy harmony. Similarly, witchcraft takes the same mapping of 13 as magic, but swaps in a more complex mapping for 11. Necromancy is the {{nowrap| 41 & 63 }} temperament [[support]]ed by [[104edo]], whereas witchcraft is the {{nowrap| 41 & 60e }} temperament supported by [[101edo]] in the 101cd [[val]]. | ||
Sorcery swaps in a less complex and less accurate mapping for prime 13, as it finds ~16/13 where magic will find ~26/21, which is of course conflated with ~5/4. Likewise, intuition uses a less complex and less accurate mapping for prime 11. Finally, telepathy adopts the changes of both sorcery and intuition, resulting in a very low-accuracy temperament. | Sorcery swaps in a less complex and less accurate mapping for prime 13, as it finds ~16/13 where magic will find ~26/21, which is of course conflated with ~5/4. Likewise, intuition uses a less complex and less accurate mapping for prime 11. Finally, telepathy adopts the changes of both sorcery and intuition, resulting in a very low-accuracy temperament. | ||
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