Hi All I think my own confusion about cents has to do with whether the number is referring to an exact pitch or to the size of an interval. I think you have to keep both in mind to understand what is going on. If you start from middle C4 and go up by half steps in equal temperament it looks like this. NOTE C4 C#4 D4 D#4 E4 F4 F#4 G4 G#4 A4 CENTS 0 100 200 300 400 500 600 700 800 900 etc. SAT 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 So from C4 to G4 is 700 cents, an equal tempered fifth. And from D4 to A4 is also 700 cents. 900-200=700 A pure or just fifth is 702 cents. >From C4 to E4 is 400 cents, an equal tempered 3rd. >From E4 to G#4 is also 400 cents. 800-400=400 A pure or just third is 386 cents. Now then the SAT says all note are 0.0 if they do not vary from the mathematically correct equal temperament. So if you tuned C4 to 0.0 and then wanted to tune a pure fifth above you would set the SAT to tune G4 +2.0 cents, that is to say 702 cents. Or if you wanted to tune a pure third then C4 0.0 and E4 -14.0 400 cents - 386 cents = 14 Now I know there ain't no Santa. So of course the SAT will most likely have different numbers on display because of the partial it is listening to. Even more confusing is comparing temperaments from two different sources. Suppose you found a table for 1/4 comma meantone that says something like this. NOTE C D E G A CENTS 0 193 386 696.5 889.5 SAT 0.0 -7.0 -14.0 -3.5 -10.5 >From another source it say this: NOTE C D E G A CENTS 10.5 203.5 397 707 900 SAT +10.5 +3.5 -3.0 +7.0 0.0 They are both right of course. The intervals are the same size. It just depends on where you start. With A or C. That is to say do you want A=440 or C=261.6255. And of course once you put it into the machine you can reset the machine up or down as needed to get the pitch you want. As to converting cents to beats I think others have answered that well enough. I think it has also been mentioned before that people offen confuse beats and cents when talking about pitch. What bugs me is when people talk about the pitch being A440 (or A415.3) and use cents that are for C261.6255 And they will talk about temperaments being different when they are in fact the same. Most of Owen's work uses cents that go with C=261.6255. But if you tune aurally and want a A=440 you have to redo the temperament scheme before you can get the results you want. It is no wonder people get confused when they tune and things don't work out right. Sorry if this is too long for some of you. Phil Sloffer psloffer@ucs.indiana.edu
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