<HTML>In a message dated 12/23/02 12:25:08 PM Central Standard Time, joegarrett@earthlink.net writes: <BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">Alan, Thanks for the link! Nice to have. One thing struck me: As this is a chart to convert Cents TO Hertz,(CPS), there is nothing that shows the exact cents to achieve frequencies such as 435cps or 425cps. I wonder if there is a reverse of this chart somewhere? Oh, as an aside, on the bottom of the chart is the statement that this chart is copyrighted by "International Piano Suppy". Who/what is that? Best Regards, Joe Garrett, RPT, (Oregon) </BLOCKQUOTE> Joe Technically, the chart doesn't convert cents to Hertz. You cannot convert cents to Hertz, because cents are not a frequency. What this chart is showing is at what frequency, (or Hertz), a particular note is beating a certain number of cents above or below that particular note. If you look at A, and zero cents, it shows the frequency, or Hertz, is 440.00. (It is presumed that A on this chart is A4.) Then for every cents below A, it give the frequency.   Cents are the measurement between intervals, and there are 100 cents between each interval. There are 100 cents between A0 and A#0 and between B7 and C8, and between every interval all the way up and down the piano. The higher you go up the scale, the difference in the number of Htz between notes gets greater and greater. The greater the difference, the fewer cents there will be between beats. And the opposite, there are fewer beats difference between intervals as you go down the scale, so there will be more cents between beats. That is what this chart illustrates. A 440 is at 440.000 Htz. A# is at a frequency of 466.164. That mean A# beats 26.164 faster than A. There are 100 cents between A and A#. That means the difference between each beat is about 3.82 cents. G# beats at 415.305 beats per second, which is 24.95 beats less than A. There also 100 cents between G# and A. But because it is lower, there are more cents between beats. (4.01 to be exact).   So if you want tune a piano to A435, considering there are about 4 cents difference between beats at A4, you multiply 5 beats times 4 cents, and you get 20 cents. If you want to go down to A425, you multiply 4 cents time 15 beats, or 45 cents. According to the chart, the closest you can get to A 435 is 435.197 at 19 cents below A or 434.916 at 20 cents below A.  So if you want to get super accurate, you'll have to off set your machine to 19.5. But I don't think any one will hear the difference if you play it safe at 19 or 20 cents below A. Quite frankly, someone spent a lot of time on a chart that is virtually useless. Why would any one want to know the frequency of D#  50 cents below pitch? Whoever put this together at the International Piano Supply Company either had too much time on their hands, or is trying to impress piano tuners that they know something others don't. But as far as I'm concerned, this is useless information. Wim </HTML>