On Fri, Jul 13, 2012 at 9:55 PM, Burkhard Wölfel <versuchsanstalt@gmx.de> wrote:

Am 12.07.2012 um 17:42 schrieb Rustom Mody <rustompmody@gmail.com>:

I recently got into an argument (on the python list so more OT there than here :-) ) about whether a B# is the same as C.

They are different pointers to the same acoustic phenomenon. Which can be useful to have in one context and confusing in another one.

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

It's the listening ear that turns sound into music.

Nice quote!