Calculating Cents from String Ratios Using Your Computer's Calculator

Set up Calculator.

- Find the Windows Calculator under Accessories (Start > Programs >Accessories) or the Mac Calculator (in the Applications folder). - Under "View," make sure you have the "Scientific" version of the Calculator selected.

Enter	Function — result
	Step One
1200	1200 cents per octave (12 semitones at 100 cents per semitone)
/	divide by
2	compare two pitches
Log	logarithmically (use Log10 in a Mac environment)
=	calculate [3986.313713865]
M+	store the above calculation for later use
	Step Two
C	Clear the calculator screen.
X	The larger of the two numbers in your ratio (representing the full length of the string)
/	divided by
Y	the smaller of the two numbers in your ratio (representing the portion of the string you wish to calculate).
=	calculate —
Log	Apply the logarithmic function of the above value (use Log10 in a Mac environment)
*	multiplied by
MR	recall the previous calculation [3986.31371386483481744438331538727]
=	to calculate the interval in terms of cents.

Once you have made the first calculation, you can leave the first value stored in the memory and repeat the process for other intervals. Below shows how to calculate one of the most important intervals, the fifth.

	Step Two (example)
C	Clear the calculator screen
36"	The larger of the two numbers in your ratio representing the full length of the string, in this case, the full length is thirty-six inches (the "denominator")
/	divided by
24"	the smaller of the two numbers in your ratio representing the portion of the string you wish to calculate, in this case, twenty-four inches of the thirty-six inches (the "numerator").
=	calculate [1.5]
Log	Apply the logarithmic function of the above value [0.1760912590556812420812890085] (use Log10 in a Mac environment)
*	multiplied by
MR	recall the previous calculation [3986.31371386483481744438331538727]
=	to calculate the interval in terms of cents. [701.95500086538741774448673273738]

Pythagoras Redux

9 May, 2011