41edo: Difference between revisions

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A step of 41edo is close and consistently mapped to [[64/63]], the septimal comma.

41edo can be seen as a tuning of the [[garibaldi temperament|garibaldi]] temperament<ref>[http://x31eq.com/schismic.htm Schismic Temperaments] at x31eq.com, the website of [[Graham Breed]]</ref><ref>[http://x31eq.com/decimal_lattice.htm Lattices with Decimal Notation] at x31eq.com</ref>, the [[magic]] temperament, the [[superkleismic]] temperament and multiple temperaments in the [[tetracot family]]. Various 13-limit [[magic family|magic extensions]] are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in [[22edo]]. 41edo is also a great [[tetracot]] tuning, and works as an alternative to [[34edo]], providing proper approximations to the 7th and 11th harmonic (at the cost of the 13th), and supporting [[monkey]], [[bunya]] and [[octacot]] simultaneously. All three of these extend to the [[11-limit]] by way of interpreting the flat [[10/9]] as an [[11/10]] by tempering out [[100/99]]. Note that this equivalence is especially useful in 41edo, wherein this comma-flat whole tone (a.k.a. the tetracot 2nd) can also be more accurately interpreted as [[21/19]] — which is equated with [[32/29]] above [[31/28]] below (both very near) — providing an explanation of the accuracy of primes 29 and 31 so that it is a uniquely good/versatile choice for interpreting the harmony of tetracot.

41edo can be seen as a tuning of the [[garibaldi temperament|garibaldi]] temperament<ref>[http://x31eq.com/schismic.htm Schismic Temperaments] at x31eq.com, the website of [[Graham Breed]]</ref><ref>[http://x31eq.com/decimal_lattice.htm Lattices with Decimal Notation] at x31eq.com</ref>, the [[magic]] temperament, the [[superkleismic]] temperament and multiple temperaments in the [[tetracot family]]. Various 13-limit [[magic family|magic extensions]] are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in [[22edo]]. 41edo is also a great [[tetracot]] tuning, and works as an alternative to [[34edo]], providing proper approximations to the 7th and 11th harmonic (at the cost of the 13th), and supporting [[monkey]], [[bunya]] and [[octacot]] simultaneously. All three of these extend to the [[11-limit]] by way of interpreting the flat [[10/9]] as an [[11/10]] by tempering out [[100/99]]. Note that this equivalence is especially useful in 41edo, wherein this comma-flat whole tone (a.k.a. the tetracot 2nd) can also be more accurately interpreted as [[21/19]] — which is equated with [[32/29]] above [[31/28]] below (both very near) — providing an explanation of the accuracy of primes 29 and 31 so that it is a uniquely good/versatile choice for (interpreting the harmony) of tetracot.

41et is used by the [[Kite Guitar]], see below in [[#Instruments]].

@@ Line 14: / Line 14: @@
 A step of 41edo is close and consistently mapped to [[64/63]], the septimal comma.
-edo can be seen as a tuning of the [[garibaldi temperament|garibaldi]] temperament<ref>[http://x31eq.com/schismic.htm Schismic Temperaments] at x31eq.com, the website of [[Graham Breed]]</ref><ref>[http://x31eq.com/decimal_lattice.htm Lattices with Decimal Notation] at x31eq.com</ref>, the [[magic]] temperament, the [[superkleismic]] temperament and multiple temperaments in the [[tetracot family]]. Various 13-limit [[magic family|magic extensions]] are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in [[22edo]]. 41edo is also a great [[tetracot]] tuning, and works as an alternative to [[34edo]], providing proper approximations to the 7th and 11th harmonic (at the cost of the 13th), and supporting [[monkey]], [[bunya]] and [[octacot]] simultaneously. All three of these extend to the [[11-limit]] by way of interpreting the flat [[10/9]] as an [[11/10]] by tempering out [[100/99]]. Note that this equivalence is especially useful in 41edo, wherein this comma-flat whole tone (a.k.a. the tetracot 2nd) can also be more accurately interpreted as [[21/19]] — which is equated with [[32/29]] above [[31/28]] below (both very near) — providing an explanation of the accuracy of primes 29 and 31 so that it is a uniquely good/versatile choice for interpreting the harmony of tetracot.
+edo can be seen as a tuning of the [[garibaldi temperament|garibaldi]] temperament<ref>[http://x31eq.com/schismic.htm Schismic Temperaments] at x31eq.com, the website of [[Graham Breed]]</ref><ref>[http://x31eq.com/decimal_lattice.htm Lattices with Decimal Notation] at x31eq.com</ref>, the [[magic]] temperament, the [[superkleismic]] temperament and multiple temperaments in the [[tetracot family]]. Various 13-limit [[magic family|magic extensions]] are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in [[22edo]]. 41edo is also a great [[tetracot]] tuning, and works as an alternative to [[34edo]], providing proper approximations to the 7th and 11th harmonic (at the cost of the 13th), and supporting [[monkey]], [[bunya]] and [[octacot]] simultaneously. All three of these extend to the [[11-limit]] by way of interpreting the flat [[10/9]] as an [[11/10]] by tempering out [[100/99]]. Note that this equivalence is especially useful in 41edo, wherein this comma-flat whole tone (a.k.a. the tetracot 2nd) can also be more accurately interpreted as [[21/19]] — which is equated with [[32/29]] above [[31/28]] below (both very near) — providing an explanation of the accuracy of primes 29 and 31 so that it is a uniquely good/versatile choice for (interpreting the harmony) of tetracot.
 et is used by the [[Kite Guitar]], see below in [[#Instruments]].