Chinese banjo?

I took part in a festival in Chinatown this weekend (I play with a
Chinese-American singer-songwriter). Before us was an ensemble that
played what sounded to me like traditional Chinese opera. The orchestra
played in a very rough kind of unison. They had one Western instrument,
a saxophone, and many traditional Chinese instruments. Finally they had
what appeared to be a ukelele and banjo, which were refretted to
something close to 7-tone equal temperament. I was very surprised by
this, as I thought Chinese music used Pythagorean scales at least for 5
of the notes, and I thought that 7-tET-like tunings were restricted to
Thailand and Cambodia. Anyone else heard of this kind of refretting?

On Tue, 4 Aug 1998, Mark Wilkes wrote:
> I'm looking for a formula which will let me convert from cents to hertz.
> Any ideas?

First of all, cents are a measure of interval size, which is to say a
frequency _ratio_, while Hertz are a measure of absolute frequency.
While we often use intervals and notes almost interchangably on the
list, it's understood that you would multiply the interval by whatever
the frequency is of the note you're using as your 1/1 or keynote.

That said, cents are just the log, base 2, of an intervals (frequency
ratio) times 1200. So to go the other direction, just divide by 1200
and take the antilog base 2. Of course, most calculators don't do
logarithms in base 2, only base e and base 10 (natural and common log).
So before you take the antilog you have to multiply by the log of 2 in
the same base to get the right answer.

Example: to convert 386 cents to a frequency ratio, divide 386 by 1200,
getting 0.321666... Multiply by the log of 2--I'll use natural logs, so
the natural log of 2 is 0.693147...; multiplying that with the previous
number gives 0.2229623... Then taking the antilog of that (base e
again--don't switch to common log now, or it'll screw stuff up!) gives
1.24977..., which is very close to 1.25 or the frequency ratio of 5/4
that we all know 386 cents approximates.

--pH http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

------------------------------

End of TUNING Digest 1493
*************************

> I'm looking for a formula which will let me convert from cents to hertz.

Well, that's a tricky question, because (unless you're talking about
beat frequencies) Hertz is a unit of absolute pitch (or frequency to be
more accurate), and cents are a unit of pitch change. So that's a little
bit like asking "what's the conversion formula between miles and the North
Pole". The North Pole defines a particular place (like a frequency in Hz),
where as a mile defines a distance between two places (like a number of
cents between two pitches).

But perhaps this is what you're looking for: Given two frequencies, f1
and f2, you can find the number of cents interval between them by the
formula:

n = 1200 * log (f1/f2) / log (2)