Hi Aaron, Aaron Krister Johnson escreveu: > On Wednesday 08 February 2006 6:28 pm, Hudson Lacerda wrote: > > >>For an equal tempered scale, one can: >> >>- Define the tuning for the base pitches C D E F G A B (pitches C and c >>are equivalent mod N, but N doesn't have to be the 2/1 octave); >> >>- Define the number of steps included in a whole tone (C to D); the >>number of steps involved in a specific accidental can be represented by >>its ratio numerator. > > > Hi Hudson, > > The above assumes a regular meantone-type ET (or EDO as they are sometimes > called). Sometimes, as in a non-meantone ET like 22-tet or 53-tet, there are > two sizes of major 2nd--one for the 9/8 approximation, the other, a smaller > major 2nd, representing 10/9. > > So, the above only works for temperaments that temper out the 81/80 syntonic > comma (i.e. meantone-family temperaments) > > Best, > Aaron.
Fortunately, I think not. I can agree with that it works *better* for meantone-like temperaments. If one uses the suggested notations provided by the program scala, there is no such a limitation, although some pitches are rather roughly approximated (e.g. E vs. E\ in E22). For 22-ET using E22 notation, a whole tone is always 4 steps: 0: 1/1 C unison, perfect prime 1: 54.545 cents C/ Db 2: 109.091 cents C#\ Db/ 3: 163.636 cents C# D\ 4: 218.182 cents D 5: 272.727 cents D/ Eb 6: 327.273 cents D#\ Eb/ 7: 381.818 cents D# E\ 8: 436.364 cents E 9: 490.909 cents F 10: 545.455 cents F/ Gb 11: 600.000 cents F#\ Gb/ 12: 654.545 cents F# G\ 13: 709.091 cents G 14: 763.636 cents G/ Ab 15: 818.182 cents G#\ Ab/ 16: 872.727 cents G# A\ 17: 927.273 cents A 18: 981.818 cents A/ Bb 19: 1036.364 cents A#\ Bb/ 20: 1090.909 cents A# B\ 21: 1145.455 cents B 22: 2/1 C octave For 53-ET, a whole tone is always 9 steps. Cheers, Hudson -- '-------------------------------------------------------------------. Hudson Lacerda <http://geocities.yahoo.com.br/hfmlacerda/> *Não deixe seu voto sumir! http://www.votoseguro.org/ *Apóie o Manifesto: http://www.votoseguro.com/alertaprofessores/ == THE WAR IN IRAQ COSTS == http://nationalpriorities.org/index.php?option=com_wrapper&Itemid=182 .-------------------------------------------------------------------' -- _______________________________________________________ Yahoo! doce lar. Faça do Yahoo! sua homepage. http://br.yahoo.com/homepageset.html Yahoo! Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/abcusers/ <*> To unsubscribe from this group, send an email to: [EMAIL PROTECTED] <*> Your use of Yahoo! Groups is subject to: http://docs.yahoo.com/info/terms/
