Richard Moody asks: >Is 2 cents the same as 2% of an interval. Yes, if that interval is a half-step (semitone). >If I read that a third is flat by 3.5 cents, how do I translate that to >cycles per second. Other wise how would one figure the beat rates for >different temperaments? It depends on which third you are talking about. In any case, it means 3.5% of a half step and a half-step is 5.946% of the frequency in question. So if the third you are talking about is A4 - C#5, then the most prominent beat comes from the 5th partial of A4 and the 4th partial of C#5, which is near 440 x 5 = 2200 Hz. At this frequency, 3.5 cents is 2200 x .035 x .05946 = 4.6 Hz so the beat rate would be 4.6 beats per second. However, I don't think this is what you meant. I suspect that you really meant to suppose that a third is 3.5 cents flat as compared to Equal Temperment. In that case the 4.6 Hz means that this interval will beat 4.6 beats less per second than an Equal Tempered third. >I know little about logs other than the ones that heat my house. Can cents >be calculated with out them.? Yes. It took logarithms to get that 5.946% of a frequency change is 100 cents, but once you know that and write that down, you can forget about logs. >Here are some calculations I have tried. Looking for confirmation or >corrections, or suggestions. > >Distance between one interval 100 cents. > >Freq of Middle C (mC) 261.626 >Difference between mC and C# in cps. 277.183 - 261.626= 15.557 >Difference between mC and C# in cents > 100 > >Question: Does one cent here mean a value of .15557 cycles per second? Yes, you have it exactly right. >If I want to tune mC sharp by 4 cents. Do I >multiply .15556 by 4 and add it to the freq of mC ? > 261.626 + 0.62224 = 262.24824 Yup, right again. >I ask this because I have seen some tables that give different temperaments >in cents differing from Equal Temperament. To tune by ear one needs to >know the beat rates of the intervals, and to figure these the cycles per >second have to be known. Then the partials must be figured, and then >the beats from them. OR is there a way to figure beat rates from cents? No, you have to do as you said. If want to use a temperment that is described in terms of cents deviation from Equal Temperment, then you have to figure the individual frequencies from that, and then calculate the partials by multiplying by 2, 3, 4, etc. Of course this assumes no inharmonicity. If you know the inharmonicity, or have an estimate for it, then you will be multiplying by 2.001, 3.004, etc., or something like that. Then, knowing which partials create the beats for each interval, you can finally calculate the beats for tuning by ear. -Bob Scott Ann Arbor, Michigan
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