It is becuase 1x1=1 Joe Goss imatunr@primenet.com http://www.primenet.com/~imatunr/ ----- Original Message ----- From: "D.Martens" <cybertuner@planet.nl> To: <pianotech@ptg.org> Sent: Sunday, March 11, 2001 4:18 AM Subject: Roots, Cents and Herz and ETD's > Hi, apparently I wasn't clear enough in my last post, > I'll rephrase the problem : > > Suppose you want to divide an octave in 1200 steps (cents), 100 for each, > note, what should be the correct number if the first note is 110 Hz, and the > last 220 Hz ? (the last ofcourse, is exactly double the amount of the first) > > Suppose you want to divide an octave in 12 steps, 1 for each note, what > should be the correct number if the first note is 110 Hz, and the last 220 > Hz ? (the last ofcourse, is exactly double the amount of the first) > > I filled this in in a spreadsheet, and had the 110 Hz multiplied 1200 times > by the number 1.0005782715387 in 1200 cells in a row. > 220 came out to be the answer in the 1200th cell, NOT rounded off. > > I did the same for the twelfth root of two. > again no surprise , the answer is 220 Hz in 12th cell in the other row, > again NOT rounded off. > > I figured that if both numbers are exactly correct, they must have 12 places > that exactly match: the 100th, the 200th,......the 12hunredth cell of the > first row vs. the cells in the second row. > > 1200 row 12row > A 110 110 > A# 116.4791983 116.5409404 > B 123.4113571 123.4708253 > C 130.7560774 130.8127827 > C# 138.5379123 138.5913155 > D 146.7828764 146.832384 > D# 155.5185324 155.5634919 > E 164.7740834 164.8137785 > F 174.5804706 174.6141157 > F# 184.9704764 184.9972114 > G 195.9788344 195.997718 > G# 207.6423453 207.6523488 > A 220 220 > > As you can see in the above table, differences are between 0.06 Hz and 0.01 > Hz, which is too much. > > 1.05946309436 for the 12 > 1.0005782715387 for the 1200 > > My question is: Why don't these two rows exactly match ? > Did I overlook something, or is it the computer's processor, > > Does anyone have a clue ? > > > Duncan. > > > > >
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