41edo: Difference between revisions
→Theory: rework (we don't need to insist 16\41 or 12\31 be ~13/10) |
→Theory: 205edo |
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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]] due to a much better approximation to the 7th harmonic, 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 [[100/99]]. Note that this equivalence is especially nice in 41edo due to also giving a more accurate interpretation of this comma-flat whole tone as a [[21/19]]. | 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]] due to a much better approximation to the 7th harmonic, 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 [[100/99]]. Note that this equivalence is especially nice in 41edo due to also giving a more accurate interpretation of this comma-flat whole tone as a [[21/19]]. | ||
41et is used by the [[Kite Guitar]], see below in [[#Instruments]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
41edo is the 13th [[prime edo]], following [[37edo]] and coming before [[43edo]]. | 41edo is the 13th [[prime edo]], following [[37edo]] and coming before [[43edo]]. | ||
[[205edo]], which slices each step of 41edo into five, corrects some approximations of 41edo to near-just quality. As such, 41edo forms the foundation of the [http://www.h-pi.com/theory/huntsystem1.html H-System], which uses the scale degrees of 41edo as the basic [[13-limit]] intervals requiring fine tuning +/- 1 [http://www.h-pi.com/theory/huntsystem2.html average JND] from the 41edo circle in 205edo. | |||
== Intervals == | == Intervals == | ||