Your answer is of course the correct one. And it yeilds nearly exactly the same results as the 12th root of 2 in Duncans tables reprinted below. His question really had nothing to do with logrithmic scales, the pythagorean comma or any of the other interesting information given in reply. The question was actually nothing more then why he got two different results from multiplying the number 110 by first the 12th root of 2 ten times, and then by the 1200 hundreth root of 2 one thousand times. The answer of course was that something was wrongly calculated. No calculator can give as bad a divergence as the two tables below reveal given different ways of writing the same number. Altså----- the 1200th root of 2 is the exact same number as the 100th root of the 12th root of 2. Or taken the other way around.... the 12th root of 2 is the exact same number as the 1200th root of 2 to the 100th power. The two tables should have been essentially identical. Newton Hunt wrote: > I get a slightly different number for 1/1200 at 1.0005777895. That is > as far as my spread sheet will take it. > > The 1/12 root is the same. > > Newton > > 2^(1/1200) 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. > -- Richard Brekne RPT, N.P.T.F. Bergen, Norway mailto:Richard.Brekne@grieg.uib.no
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