reducing notes to the octave

Someone just had a post which mentioned, as part of the message,
reducing notes mathematically to bring them into the range of an octave.
Needless to say, this has been done for a long time, and is the only way
to hear notes which are way up in the harmonic series, or cycle of 5ths.
What has always fascinated me is this: when notes are brought into the
octave in this way, we are not actually hearing the sound of the note
itself...it's "up there" somewhere, and our ears are not capable of
hearing the real tone. Where are these notes? How different it would be
if we could actually hear them, as they really sound. As it is now, the
actual notes are theoretical, since no one (no human, anyway) can hear
them in reality...Hstick

Dave Hill wrote:

>I've read that accuracy of tuning of the fifth is more critical than
accuracy
>of tuning of the major third for the overall harmoniousness etc. of the
music.

Yes, a lot of people say this, but I've never seen any evidence. Really,
experiments should be done on musically naive subjects. My brother, Neil,
fulfils this criterion, so I tried some meantones out on him played with
my AWE64's "Acoustic Grand Piano" voice. I quickly played him a scale and
a couple of chords in each tuning -- a first impressions thing.

First, on 1/6-comma and 1/9-comma (should have been 12-equal, but I got
the number wrong), he said there wasn't much difference. With a few
seconds more listening he concluded that 1/6 comma was better.

On Pythagorean tuning he had no comment. However, he concluded very
quickly that 1/4-comma meantone sounded best.

So, the usual rules seem to apply -- all consonant intervals should be
treated equal. However, the fact that he didn't immediately reject
Pythagorean tuning suggests there's more to it than that. 1/9 is far
greater than the difference between 1/6 and 1/9. In fact, my microtonally
experienced ears concluded a long time ago that Pythagorean tuning works
unusually well with piano samples. I assume this is because the pure
fifths dominate the sound. It could also be why well temperaments, and
eventually equal temperament, became so well established on the piano.

I think, with 1/9-comma meantone, I blundered onto the dullest piano
tuning around. No wonder my ears accepted it as 12-equal!

Dave, your postings on this subject are very reassuring. I agree with
most of your conclusions, so perhaps I'm not mad after all.

How do you think the sound of digital pianos compare to that of an
acoustic? I ask because these are the only instruments I've seen that
advertise their tuning capability, although nobody on this list has ever
mentioned using one. To me, they sound great. I don't like acoustic
pianos much, though, so I'm probably not the person to ask.

Graham Breed
gbreed@cix.co.uk www.cix.co.uk/~gbreed/