EXS 24 Logic Sampler Users Group

Dear Fellow EXS users

	I used to have a chart that gave you the change in beats per
minute per note transposition. I can't find the chart or remember the
formula.  I know a 1/2 step is 8.3% difference.  But I can't figure out
what the formula would be for other intervals.  Anyone remember?

Thanks

Gary Pozner
www.whirledmusic.com

On a fine day, 11-10-2003, gary pozner wrote:

>	I used to have a chart that gave you the change in beats per
>minute per note transposition. I can't find the chart or remember the
>formula.  I know a 1/2 step is 8.3% difference.  But I can't figure out
>what the formula would be for other intervals.  Anyone remember?

Not sure what you mean exactly, but...   If you go up an octave, the 
frequency (or the speed of a sample) is increased by a factor of 2. 
If you go up a semitone, that's a factor of 2^(1/12) (where ^ means 
'to the power') which is roughly 1.0595 (or a 5.95% increase).  For x 
semitones, that would become 2^(x/12).  Is that what you're looking 
for?

-- 
Hendrik Jan Veenstra   h @ k n o w a r e . n l
Omega Art: http://www.omega-art.com/

Guys thank you for your responses.  I am not sure I explained myself

Here is a reel world example.  I have a loop in my exs that is running
at 120 BPM when I play middle C(C3).  What I want to figure out is the
tempo when I play different intervals.  Let's say I play the same loop
on Bb2, a 1/2 step down.  How do I figure out it's tempo mathematically.
And then of course easily figure out the other speeds at other
intervals.  

Lets say C3=120 beats per minute
	   C4=240 beats per minute
	Now how do I get the other notes in between.  

	Thanks

	Gary Pozner

Hi Gary!

Easy this one, especially with the example you used. Just divide the 
difference between the C3 and C4 by 12.

a) 240 bpm - 120 bpm = 120 bpm

b) 120 bpm / 12 = 10 bpm

c) 10 bpm per semitone. C#3 = 130 bpm, F3 = 170 bpm

d) with 96 bpm, for eg, you'll divide 96 by 12, and get 8. Just add 8 
bpm for every semitone.

C'est tout!

Best,

Ned

On Sunday, October 12, 2003, at 11:44  AM, gary pozner wrote:

> Guys thank you for your responses.  I am not sure I explained myself
>
> Here is a reel world example.  I have a loop in my exs that is running
> at 120 BPM when I play middle C(C3).  What I want to figure out is the
> tempo when I play different intervals.  Let's say I play the same loop
> on Bb2, a 1/2 step down.  How do I figure out it's tempo 
> mathematically.
> And then of course easily figure out the other speeds at other
> intervals. 
>
> Lets say C3=120 beats per minute
>          C4=240 beats per minute
>       Now how do I get the other notes in between. 
>
>       Thanks
>
>       Gary Pozner     
>
>
>
>
>
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>
>
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http://www.nedfx.com

    Ned Bouhalassa

n e d @ n e d f x . c o m


[Non-text portions of this message have been removed]

I dont think he means the change in frequency as you change the pitch. I 
think he is just asking the the percentage of change in length of the entire 
sample would be for every 1/2 step increment in pitch. For example, if the sample 
is is 1 second long and if the sample becomes .8 seconds after increasing the 
pitch a 1/2 step, the percentage of change is 20% of the original sample.  
Again, this is only an example. Not sure if this is what you are asking. I would 
also like to know the answer.

Pete

Thanks Ned,

It is hard to believe we used to have to this kind of math all the time
and now, it is gone with the brain cells.  The weird thing is, when I
add 100 cents to a loop in Logic running at 120 it gives me the tempo as
127.1346. It only works out the same as your formula when I add 1200
cents to make it an octave?  I have been Doing the formula as (BPM) x
8.333 % x (the number of semitones) + (BPM) 

So 120 x 8.333 x 1 + 120 = 129.99996  for one semi tone.  Yours is much
easier.  I wanted to build an excel chart for this. So I wanted to make
the formula as simple as possible.  I seem to remember making a chart
like this when I bought my Ensoniq Mirage.

Merci Beaucoup

T'ami

Gary

on 10/12/03 9:44 AM, Ned Bouhalassa at ned@... wrote:

> Hi Gary!
> 
> Easy this one, especially with the example you used. Just divide the
> difference between the C3 and C4 by 12.
> 
> a) 240 bpm - 120 bpm = 120 bpm
> 
> b) 120 bpm / 12 = 10 bpm
> 
> c) 10 bpm per semitone. C#3 = 130 bpm, F3 = 170 bpm
> 
> d) with 96 bpm, for eg, you'll divide 96 by 12, and get 8. Just add 8
> bpm for every semitone.

Sorry, Ned. I don't think this can be correct. If it were, then you'd have
one fixed increment for going up between 120 and 240 and a different one for
going down from 120 to 60. I think you have to use the twelfth-root of two
business.

Don

> Sorry, Ned. I don't think this can be correct. If it were, then you'd 
> have
> one fixed increment for going up between 120 and 240 and a different 
> one for
> going down from 120 to 60. I think you have to use the twelfth-root of 
> two
> business.
>
> Don
>

Right Don (I thought it might be too easy...)

So let's go with x or / by 1.059 and see what happens! ;-)

Ned

http://www.nedfx.com

    Ned Bouhalassa

n e d @ n e d f x . c o m


[Non-text portions of this message have been removed]

On a fine day, 12-10-2003, gary pozner wrote:

>It is hard to believe we used to have to this kind of math all the time
>and now, it is gone with the brain cells.  The weird thing is, when I
>add 100 cents to a loop in Logic running at 120 it gives me the tempo as
>127.1346. It only works out the same as your formula when I add 1200
>cents to make it an octave?  I have been Doing the formula as (BPM) x
>8.333 % x (the number of semitones) + (BPM)

Well, again, 1 semitone increase is a frequency change by a factor of 
2^(1/12).  So that then also means the audio file tempo increases by 
the same factor.  Makes sense: if you have a loop with a root note of 
C3, and you play C4, it'll all sound 1 octave higher -- i.e. double 
the pitch and double the bpm.

So transposing a 120 bmp loop 1 semitone up would yield a tempo of 
120 x 2^(1/12) = 127.13557 -- almost exactly what Logic gives you. 
Two semitones up gives 120*2^(2/12) = 134.7, et cetera.

The 8.3 percentage is wrong.  If you divide 100 by 12, you get 8.333% 
alright, but that's not how exponential growth works.  If your bank 
gives you 5% interest per year, you *don't* get 10% interest in 2 
years, but a wee bit more (since you also get 5% over the 1st year's 
5%).  Likewise you also don't get 100% in 20 years, but way more 
(1.05^20 = 2.65, so that's a 165% increase).  Now apply the same to a 
12-tone scale :-).

>I wanted to build an excel chart for this. So I wanted to make
>the formula as simple as possible.

Easy.  Let's suppose you want to use tuning in cents instead of 
semitones (for accuracy).  Type the original bpm in cell A1.  Type 
the transposition in cents in cell A2 (I.e. -1200 is an octave down). 
In A3 enter the formula:
=A1*2^(A2/1200).  That's your target bpm.

The other way round also isn't very hard: given a source bpm and a 
target bpm, how much do you have to transpose the loop to reach the 
target?
In A1: source bpm.  In A2: target bpm.  In A3: = log(A2/A1,2)*1200. 
A3 now contains the transposition you need in cents.

If this fails (I've installed some extra Excel packages, and am not 
sure whether this log(num,base) function is one of them), this also 
works in A3:
= log10(A2/A1)/log10(2)*1200.


-- 
Hendrik Jan Veenstra   h @ k n o w a r e . n l
Omega Art: http://www.omega-art.com/

On a fine day, 12-10-2003, Ned Bouhalassa wrote:

>Easy this one, especially with the example you used. Just divide the
>difference between the C3 and C4 by 12.
>
>a) 240 bpm - 120 bpm = 120 bpm
>
>b) 120 bpm / 12 = 10 bpm
>
>c) 10 bpm per semitone. C#3 = 130 bpm, F3 = 170 bpm
>
>d) with 96 bpm, for eg, you'll divide 96 by 12, and get 8. Just add 8
>bpm for every semitone.
>
>C'est tout!

Very wrong, sorry.  See my other post.  It's not a linear scale (a 10 
bpm increase per semitone) but an exponential scale (a factor of 
2^(1/12) per semitone).

-- 
Hendrik Jan Veenstra   h @ k n o w a r e . n l
Omega Art: http://www.omega-art.com/