ndenton434@bigwave.ca

Perhaps the best place to start for Web resources on tuning is:

http://www-math.cudenver.edu/~jstarret/microtone.html

On Tue, 26 May 1998, Just Intonation wrote:
> 12TET Just
> Semitones Ratio Common Name Cents Value
>
> 7 3/2 Perfect Fifth 701.96
> 5 4/3 Perfect Fourth 498.04
> 8 8/5 Minor Sixth 813.69
> 4 5/4 Major Third 386.31
> 9 5/3 Major Sixth 884.36
> 3 6/5 Minor Third 315.64
> 10 16/9 Minor Seventh
> 2 9/8 Major Second
> 11 15/8 Major Seventh
> 1 16/15 Minor Second
> 6 45/32 Tritone 600.0
>
> Please let me know if I made any mistakes, or if you have some of the
> missing cents values. Thanks.

Point the first, part one: if you have the cents values for the primary
intervals, you can derive them for the secondaries by adding and
subtracting. Example: let's say you want the cents value for 16/15.
That's a 4/3 less a 5/4, so take 498.04 - 386.31 = 111.73. Simple.

Point the first, part two: cents are simply 1200 times the log, base 2,
of the ratio. So grab your scientific calculator (let's do 16/15
again): enter 16/15 (1.0666666...) and press log, /, 2, log, =. The
display should now read 0.09310904... which is the log base 2 of 16/15.
(What we just did was to divide the common log of 16/15 by the common
log of 2, to get the log base 2 of 16/15.) Then multiply by 1200 to get
111.731285... which agrees with what we got the other way.

Point the second: your tritone value is wrong. 45/32 in cents is
590.22. Another 5-limit ratio often used for tritones is 6/5 * 6/5 =
36/25, which is 631.28 cents. And either of those can be inverted, of
course.

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