What is the percent change achieved in pitch for every percent change in speed. I am looking for an equation that help me compensate the pitch for changes in different speeds ±50%. I could only manage a crude table to get near perfect original soundtrack (I know tempo does this too, in a way).

The relationship between speed and frequency is very simple:

Double the speed and you double the frequency.

Double the frequency and you double the speed.

The change in speed is directly proportional to the change in frequency.

Converting from frequency to pitch is a bit tricky, but there are tables of pitch frequencies available on the internet, for example: http://www.phy.mtu.edu/~suits/notefreqs.html

Well, it doesn’t appear that straightforward. I have enclosed a graph that displays the compensation in pitch (percent) for certain discrete changes in playback speeds. These were achieved using a musical keyboard (for detecting the levels of changes) and a spreadsheet to compute the variations. Besides using the spreadsheet to give me a ‘best fit’ equation I am looking for the actual one so that I can achieve ideal restoration of the original playback pitch.

As this is the Audacity forum, and as you didn’t specify otherwise, I assumed that you were referring to speed and pitch change as they occur in the Audacity effect (Change Speed, Change Tempo, Change Pitch). If that is not what you are talking about, please describe what you are doing and how you are doing it - in particular, how you are measuring the change in speed, the change in pitch, and what the practical task is that you are trying to achieve.

Yes I should have mentioned that. As you said, I am using the ‘change speed’ and the resultant change in pitch.

As for the methodology, I take a recording and change the speed (for example, to get the nuances while singing). Since the pitch is obviously affected I note down the new scale using the keys of a musical keyboard and thus the resultant level of change from the original scale. Using 2^(1/12) as the basis for each note I compute the percent change compared to the original recording. Quite obviously, sometimes, the exact scale will tend to lie in between the two keys but I go ahead with the one that’s close enough. Then I compensate by either increasing or decreasing the pitch. I do so by using the ‘change pitch’ and change the percentage to make the recording sound ‘normal’.

Change tempo only seems to go so far unlike change speed. Also I am interested for the sake of it since this seems to software related and I hope to see from the code if I can get any clues.

Ah ha! I think that’s where the difference is occurring.

There are two ways that the % can be calculated:

(change/original) * 100

or

(change/new) * 100

You’re using the former. Audacity uses the latter.

See here: http://manual.audacityteam.org/o/man/change_speed.html#percent