BPM Math Question...

[tomhartman]

A song is in the key of G and at a certain tempo.

The guitars were recorded one whole step up (A) at a faster tempo.

So how would you find out what the original tempo of the "A" guitars was in order to arrive at the "G" guitars in the final result?

Yikes, I really hate math a lot.

Thanks for any input...

Tom

[jeremyroberts]

A truck leaves New York City at 1pm on Monday heading West. It never exceeds the posted speed limit.
A Bus leaves Los Angeles at 2pm on Tuesday heading East. The bus driver always exceeds the speed limit.
What color is the uniform of the Denver Broncos?

Tom, based on your info, it appears that:

The song was recorded in G at tempo #1; also recorded in A @ tempo #2;

Why should there be any relationship between these events?

NOW -- could it be that there was a clocking/sample rate issue? - as in, original session was 44.1; engineer took the session to a 48k rig and assumed the song was in A...

The math kinda works out...

The ratio of G-->A is .89090909
The ration of 44.1k --. 48k is .91875

Fairly close -- so that if someone screwed up and clocked the session incorrectly, and assumed the session was in A - and HOPEFULLY tuned to the track (which was not exactly in A) - then it should all be just fine.

You can always do the math...

I googled a "frequency pitch chart" and found one of many: Frequency chart - the math works out.

If all you need to do is convert the guitar recorded in A to G (and assuming sample rate is the same) - then use the ratio of .89090909

But -- tempo is an entirely different animal... you will need to figure out your source and destination tempi.

Was this enough info? Hope so...

jr

[studiostuff]

The guitars were recorded one whole step up (A) at a faster tempo.
So how would you find out what the original tempo of the "A" guitars was in order to arrive at the "G" guitars in the final result?

Well, if you hate math, you're gonna really hate this answer!

The difference between any given note and the note ONE octave above it is a ratio of 1:2. To determine the frequency of the octave above "A-440" you multiply by two. The answer is "A-880".

That means the the distance between the notes in an octave is 1/12th of the 1:2 ration... or the 12th ROOT of 2.

So, if you're in the key of G, and you want to know the tempo of the key of A... all you do is multiply the tempo of the key of G by the 12th root of 2 for each 1/2 step.

If the 12th root of 2 is 1.059463 (it is), then if you are in the tempo "quarter note = 120 bpm" in the key of G... the tempo in the key of A will be figured like this: 120 bpm x 1.059463= the tempo of the key of G# or 127.13556 bpm. Then 127.13556 bpm x 1.059463 = the tempo of the key of A or 134.69542 (approximately, of course).

If you're goin' the other way: If A is 120 bpm... then A flat tempo will be 120 divided by 1.059463 or 113.26492 and then the key of G tempo is 113.26492 divided by 1.059463 or 106.90785 (approximately).

1.059463... The twelth root of two... our musical friend.

[tomhartman]

Whoa, you guys are just too scary.

Thanks so much.

The reason I asked, is that the song "Rain" by The Beatles, features some slowed down guitars and drums. It is in the key of G.

The Beatles said "We played the song faster, and they slowed down the track." Best guess judging from the guitar riff is that the original, faster version was played in A. So I was trying to figure out how fast they would have to have been playing it on that original "A" track to arrive at the final version. I will now go do some calculating, if my head doesn't explode first

Thanks again!

Tom

[jeremyroberts]

Oh - VSO --- that's an entirely different animal.

We used to do stuff like that all the time... with TAPE (anyone remember what that was?)

We'd simply (ala Martha Stewart) VSO the tape machine until it was in tune, then play the song fast. No math needed. We always did it by ear.

In PT, it's not so easy to do this...

On this subject: anyone ever mess with midi transpositions and what a 1/2 step does to your keyboard voicings? i.e. play the song in B major, then transpose it to Bb -- you'd NEVER play those notes in Bb (or vice versa). Makes for an interesting sound...

If the VSO is what you're after, the SYNC I/O may be able to help you ????