source file: m1428.txt Date: Tue, 26 May 1998 17:19:55 -0500 (CDT) Subject: Re: Basic Just Intervals? From: Paul Hahn 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. <*>