EDT: Difference between revisions
category rename; catsort for same-name cat |
No edit summary |
||
| Line 29: | Line 29: | ||
'''One should bear in mind that, assuming tritave equivalence, when determining which harmonics are represented, the ratios of 3 in the denominator are fungible instead of those of 2.''' For example making the fifth harmonic 5:3 a "major sixth" by conventional (and arbitrarily silly for the purposes of xenharmony, even with octaves) pitch class terminology. | '''One should bear in mind that, assuming tritave equivalence, when determining which harmonics are represented, the ratios of 3 in the denominator are fungible instead of those of 2.''' For example making the fifth harmonic 5:3 a "major sixth" by conventional (and arbitrarily silly for the purposes of xenharmony, even with octaves) pitch class terminology. | ||
There are other uses, or conceptualizations, of tritave-based tunings. Purely intuitive use of these myriad, assuredly xenharmonic structures comes to mind (see "EDO" versus "equal temperament"). Another intent might be to find or define temperaments (such as Magic, Hanson, etc.), or to provide exact formulae for stretching/compressing what would musically be used as an "ordinary" octave of ~2:1. (And given the stable nature of octave-based systems, some aesthetic overlap even in the most tritave-equivalent of music, would be forseeable.) For instance, the Bernhard-Stopper (19edt) temperament, might for instance be found useful in tuning pianoforti, being equivalent to 12edo, except for a 2c sharp octave which is relevant to inharmonicity. | There are other uses, or conceptualizations, of tritave-based tunings. Purely intuitive use of these myriad, assuredly xenharmonic structures comes to mind (see "EDO" versus "equal temperament"). Another intent might be to find or define temperaments (such as Magic, Hanson, etc.), or to provide exact formulae for stretching/compressing what would musically be used as an "ordinary" octave of ~2:1. (And given the stable nature of octave-based systems, some aesthetic overlap even in the most tritave-equivalent of music, would be forseeable.) For instance, the Bernhard-Stopper (19edt) temperament, might for instance be found useful in tuning pianoforti, being equivalent to 12edo, except for a 1.2c sharp octave which is relevant to inharmonicity. | ||
Below is a large list of EDTs; additionally, some equal divisions of the tritave are known by alternate names or have special interest: | Below is a large list of EDTs; additionally, some equal divisions of the tritave are known by alternate names or have special interest: | ||
| Line 396: | Line 396: | ||
A list of [[Tritave_Reduced_Harmonics|tritave reduced harmonics]] for easy comparison of JI and temperaments in tritave based systems. | A list of [[Tritave_Reduced_Harmonics|tritave reduced harmonics]] for easy comparison of JI and temperaments in tritave based systems. | ||
Also may be found convenient: | Also may be found convenient: http://www.nonoctave.com/tuning/twelfth.html | ||
=EDO-EDT correspondences= | =EDO-EDT correspondences= | ||
| Line 621: | Line 621: | ||
Patent vals match through the 89 limit. (Really! I checked!) | Patent vals match through the 89 limit. (Really! I checked!) | ||
|} | |} | ||
=Multiples of 13EDT which approximate EDO= | =Multiples of 13EDT which approximate EDO= | ||
| Line 627: | Line 626: | ||
=See also= | =See also= | ||
Heinz Bohlen's work: | Heinz Bohlen's work: http://www.huygens-fokker.org/bpsite/otherscales.html | ||
[[Category:Edt| ]] <!-- main article --> | [[Category:Edt| ]] <!-- main article --> | ||