On Fri, Jul 13, 2012 at 6:55 PM, Rustom Mody <rustompmody@xxxxxxxxx> wrote: > On Fri, Jul 13, 2012 at 9:55 PM, Burkhard Wölfel <versuchsanstalt@xxxxxx> > wrote: > > I dont have a B# vs C example ready offhand but here is an example where G# > is a different acoustical phenomenon from Ab in C major context. > > In Beethoven piano sonata no 32 2nd movement there is a Ab and a G# within a > couple of bars of each other. > > If I put my keyboard in 'Just major-C' tuning, the G# sounds right, the Ab > sounds wrong > If I put it into 'Just minor-C' tuning the Ab sounds right the G# sounds > wrong > > My explanation (to be taken with liberal salt given my music theory and > tuning theory novice status): > The augmented fifth (G#) is a different note from the minor sixth (Ab) > Equal temperament chooses a midpoint between the two as an approximation to > both > They are 772 800 813 cents in http://www.kylegann.com/Octave.html > > The above is a more theoretical discussion. > Pragmatically, one cannot play Beethoven in Just intonation. > But equally(!) Equal temperament is suboptimal But wasn't Beethoven writing long after Bach had figured out the tempered piano tuning? Besides, assuming that Beethoven was playing a keyed instrument ... well, unless he had some extra keys ... Yes, you are right that equal temperament is less that perfect ... but on keyed instruments (and this will include fretted stuff as well) one doesn't have much choice when playing. BTW, what does all this have to do with my original request for a little software program :) -- **** Listen to my CD at http://www.mellowood.ca/music/cedars **** Bob van der Poel ** Wynndel, British Columbia, CANADA ** EMAIL: bob@xxxxxxxxxxxx WWW: http://www.mellowood.ca _______________________________________________ Linux-audio-user mailing list Linux-audio-user@xxxxxxxxxxxxxxxxxxxx http://lists.linuxaudio.org/listinfo/linux-audio-user
