A Small and Quick program for calculating Cyclic Cents for Relative Frequencies
If you have been reading articles on music you may often meet with the tern 'cent' or 'cyclic cent'. From this page you can download (see end of this page) a small free program for calculating cyclic cents for any relative frequency quickly. Below is a explanation of the cent system.
In music the relation between any 2 notes (interval) is their ratio and not the actual difference in the number of cycles. This makes it difficult to appreciate intervals correctly. For instance it is difficult to say at a glance whether 16/15 is higher or lower than 256/243 and how much do they differ actually. The cyclic cents system converts the relationship of ratios into one of arithmetic addition or subtraction by using the logarithms
As the octave is a basic interval and as most systems use 12 notes in an octave the relative frequency ratio of 2 of the octave is equated to the 1200 cents. The interval between 2 adjacent notes (a semitone) then becomes 100 cents in the Equally Tempered Scale (a scale where the relative frequency between 2 adjacent notes in the 12 note system is twelfth root of 2).
To calculate the cent value of any relative frequency ratio the following formula is used:
cent value = 1200 X log(rf) / log(2) where rf is the relative frequency ratio. The cent can be calculated using any scientific calculator which provides for logarithms or using the program that can be downloaded from this page.
Some cent values of common relative frequency ratios are given below:
To obtain a note which is at an interval of 3/2 (sa to pa) we have to add 701.96 in the cent system. For moving up by 4/3 (sa to ma interval) we have to add 498.05. Thus, the note with r.f. 9/8 (203.91 cents) when increased by 4/3 will give a note of 203.91 + 498.05 = 701.96 (which is 3/2). The above table shows that the equally tempered fifth (pa) with a cent value of 700 is very close to the natural pa (701.96 cents). However, the natural r.f 5/4 (ga) has a cent value of 386.31 is somewhat lower than the equally tempered third with a cent value of 400.
Download cents32.zip. Right click on the link and save the zip file (383 kb). Extract the 2 files "cents32.exe" and "vb40032.dll" into any folder and then run cents32.exe. No installation. You have to manually create short cut on the Desk Top or Start Menu. If you have "vb40032.dll" in your windows\system folder (system32 folder in case you use WindowsMe or XP) then you do not need the "vb40032.dll" file along with "cents32.exe"
This is how the program window looks like. Enter the fraction in the first window and press 'Enter' key. Cent value appears on the second window. In the sample screen below the r.f. entered is 5/4 and cent value is 386.31