On a casio calculator the 1200 root of 2 is 1.00057779. This would implement a rounding off due to the figure that Newton gave. On the other hand it matches the 12 root when taken to the 100th power (sorry for the English translation). In that case you get the exact same values. (which of course should have been there, due to the equasions): 1.059463094. And also: rounding offs don't make so much differences as wrong figures do. greetings, John Meulendijks Tilburg. ----- Original Message ----- From: D.Martens <cybertuner@planet.nl> To: <pianotech@ptg.org> Sent: Sunday, March 11, 2001 12:18 PM 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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