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
>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/