Re: Re: Re: Re: Re: Re: Know any good D's?
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Posted by Chuck(G) on October 22, 2003 at 19:26:39:
In Reply to: Re: Re: Re: Re: Re: Know any good D's? posted by Rick Denney on October 22, 2003 at 17:07:15:
John, Rick's after the same thing that I've been trying to get at.
Let's take three notes from your chart to form a I-III-V major triad and play them on three euphoniums:
C4 261.63
E4 329.63
G4 392.00
(I've rounded things off to 2 decimals because I doubt that anyone can hear differences in the range of a thounsandth of a Hz).
The result is a C major chord all right, but it's not very pretty because equal temperament will cause the notes as sounded above to give rise beat frequencies. The C4-G4 isn't too bad; in relation to a "pure" beatless fifth, the G is only 2 cents too flat. However, the third C4-E4 is terrible; compared to a beatless pure third, the E is 14 cents too sharp. A more "just" tuning that shows a beatless major triad is:
C4 261.63
E4 327.03
G4 392.44
Ëqual temperament (or what I refer to as "piano pitch" is a deal with the devil that produces uniformly somewhat out-of-tune intervals because of the limitation of having only 12 keys per octave and dealing with 18th century technology. Keyboards have been proposed over the intervening centuries with 31 or 51 divisions per octave and various methods for "bending" the pitch of individual notes. (In fact, B# is Lower in pitch than C is lower in pitch than Dbb.)
Not being limited by a keyboard, instrumentalists and singers can adjust their intervals to be purer than those the piano generates, since the ivory-tickler can't adjust the tuning of individual notes on the fly. On the other hand, a piano can play many notes simultaneously.
A pure third is a joy to the ears, no matter what your tuner tells you. Absolute fixed pitch has very little to do with anything musical--good intervals are the very soul of harmony.
And this is what I was getting at. Do "perfect pitchers" in fact hear their major thirds as being 14 cents out of tune? If so, I'll take a good ear for relative pitch and intervals any day over "piano ears".
Below is a link to a little Java applet that will let you entertain your ears with various intervals and temperaments.
Hope this helps.
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