Someone correct me if I'm wrong here, but my understanding was that the pitch of any note is
determined by the volume of the air column. Since the relationship is proportional, as you
increase the length of the instrument--without increasing the diameter of the bore, mind you--you
must add proportionally to effect the pitch. So going down a fourth from a 2.4 is going to require
a lot more length than going down a fourth from a 1.4. I don't know for sure, but I would think
that if you measured a series of flutes with the same bore profile in lengths from 1.3 to 3.0, or
whatever, you'd find that the length required to lower the pitch a half tone increased
proportionally, with the difference being more or less one sun at the 1.8 length. I would think
the increase would be proportional, and only seems to jump due to rounding off until around
2.0/2.1 and then rounding up to 2.4 after that.
In Japan, an A flute is usually called a 2.3, and a G flute is sometimes called a 2.6, more
usually a 2.7. In the US you usually hear 2.4 and 2.7 or 2.8. Most A flutes are in fact over 2.4
in length, and 2.8 is more accurate for a G flute. So if you order a chohkan, especially from
Japan, make sure you specify what pitch you want.
Something unrelated about pitch, but which has intrigued me for years, so I'll throw it out there:
The chi on almost all old flutes is quite sharp, (as is the re, but my only theory for that is
that it sounded better that way!). Since going from a note to the fifth above it gives a
proportion, in cycles per second, of 3/2, or 1.5, a sharp chi note would give a ratio around 1.6.
The golden mean is 1.618034...(If you're new to the golden mean, try dividing 1 by 1.61803399.
Cool huh?), and that proportion was supposedly in the ancient Pythagorean scale, which may well
have been incorporated into ancient Persian scales, which is supposed to have had at least an
indirect influence on East Asian music, so I've often wondered if this wasn't a factor in the
pitch of that note before contact with the diatonic scale. Probably not, but it's something else
to wonder about...
Peter
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