# Is there a formula? BPM <---> cents?

Hi -

I have a portion of a project I’m thinking of increasing from about 65 BPM to 72 BPM. I’m trying to figure out a way to know how many cents the pitch of the project would be raised if I did that.

Is there a formula that anyone has seen for that?

Thanks!

Hi, is this a tape-based project? If it were, then if the tempo was 65 and the original tape was recorded at 15ips, if you ran it at 30ips, it would move up by one octave and sound like the chipmunks. A small increase from 65 bpm to 72 bpm, whatever percent increase that is, done with some kind of varispeed control, would yield a relatively small interval. I’d make a protection copy of the orginal project and then experiment with tape-style time stretching, but I’m not really sure about how this would work exactly. Cubase’s Time-stretching does a lot of things. If someone wanted to work in a tape-style way and ‘George Martin-out’ with loops, it’s probably possible. Greg Ondo might have some good ideas about this.

Why do you want to increase the tempo and have pitch increase? One of the beautiful things about digital audio is being able to change tempo without the pitch being effected, as it was with tape. Also, why not pitch shift and transpose the material using the usual Cubase functions for those things?

Very geeky question. heh.

P.S. – “Musical intervals are often expressed in cents, a unit of pitch based upon the equal tempered octave such that one equal tempered semitone is equal to 100 cents. An octave is then 1200¢ and the other equal tempered intervals can be obtained by adding semitones:…”

P.P.S. – The JND – “Just Noticeable Difference in Pitch”

"The just noticeable difference in pitch must be expressed as a ratio or musical interval since the human ear tends to respond equally to equal ratios of frequencies. It is convenient to express the just noticeable difference in cents since that notation was developed to express musical intervals. Although research reveals variations, a reasonable estimate of the JND is about five cents. One of the advantages of the cents notation is that it expresses the same musical interval, regardless of the frequency range. " (same link as in PS)

https://en.wikipedia.org/wiki/Cent_(music)

Just put BPM values to the first equation found in article and there you go.

Bpm time stretch
https://musiccalculator.com/#time-stretch-bpm

Very useful free on-line tool for questions similar to this and much more.

Hey guys, thanks for responding!

Here’s the part of the post where I ask for you to have mercy … I must be afflicted cognitively this morning … I can’t see how to get delta cents from delta BPM in either link!

1. http://hyperphysics.phy-astr.gsu.edu/hb … cents.html and https://en.wikipedia.org/wiki/Cent_(music) refer to the same formulae … but they appear to me to show the relationship between cents and frequency, am I missing the time dependency (changing BPM) there?

2. https://musiccalculator.com/#time-stretch-bpm gives me ratio/% change, but I think it’s referring to the amount of time stretch, not the pitch?

I will play with the Elastique options to increase BPM without affecting pitch, once I figure out which of the options that is, that’s a good idea, thank you Stephen57. My initial thought was to put the vocals in musical mode and let them get stretched/compressed as I increase the BPM. I know there will be degradation either way of course.

But I was looking for a formula to “know” how much sharper the vocals would be when I speed it up the “musical mode” way. I guess I could run a sine wave through and measure the before/after, but I’d love to see a formula!

Thanks again guys!

Frequency and BPM are 1:1 proportional when you speed up/slow down audio without doing any pitch correction. So formulas work for both BPM and frequency.

Double the BPM -> double the speed -> double the vibrations per second (frequency)

Ah, ok, thx!

Next challenge … how do I calculate “log base 2” of something? Do I need to look that up in a table?

The scientific calculator on windows has a log function.
That’s log base 10, so to find log base 2 of x use:
log(x)/log(2)

Or you can use any modern spreadsheet program (Excel, OpenOffice, …):
Put values on cells A1 and B1
Put following formula on cell C1
=1200*LOG(B1/A1;2)
You may need to use comma “,” instead of semicolon “;” depending on your locale settings.

OK, I’ll look at that, thank you.

When I tried to do that by hand for a slowdown from 74 BPM to 69 BPM, I got a huge # cents, so I know I did something wrong.

Surprised there isn’t a handy website to do this. I guess nobody cares about this but me!

BTW, I did a 3 BPM change using Musical Mode and and Elastique-Pitch. I was hopeful that I wouldn’t notice a change in the quality of the vocals, but alas, it was very clear that things were worse-sounding. And I don’t have golden ears! (More like tin, or even cardboard …).

Thanks again, everyone!

I slowed down a vocal track almost 10 BPM a while ago using the timestretch tool and I can’t hear the artifacts in the mix… Sure when you solo the track and listen for it you can pinpoint some things but it’s perfectly usable in my experience.

Interesting, what time stretch algorithm did you use?

The vocals here are quite exposed …

Good question… I think the default one, but I’m not sure.
Can I even see that somewhere?

Yes, in preferences. I have to check, but I think it might not have Elastique as an option. I looked into this at one time, and wound up choosing an MPEX option there.

I’m indeed quite sure it wasn’t Elastique.