It looks simple but it isn't. For example I want to make an acceleration from 75 b.p.m to 263 b.p.m in 7,3 seconds (7300ms), and the most important to be synchronized. That means to start the metronome (metro object or whatever) with a beat and ending after exactly 7300ms with a beat! I think this problem can be sold. I would like to know if there is an algorithm for general because I want different accel., decel. in various times.
The guy who'll solve he'll get my love! (....appreciation I want to say 
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Synchronize accelerations and decelerations
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have fun figuring out the maths behind this
i bet no one knows a formula for this and wants to solve it for you
but if you do it please sharepd redefining mathematics |expr fact(0)|==0
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do you mean something like that?
does it help?i forgot the stop bang...
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do you mean something like that?
does it help?i forgot the stop bang...
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Thank you Alistair but I've count 30.0239 ms delay between the the point that reaches the 263 and the beat that follows. It should be exactly a beat in the point it gets at 263.
Also I didn't mention that I want a linear audible accel. and decel. and not an logarithmic. So the ramp of b.p.m must be in power in order to have a linear audible accel. and decel. Maybe with the use of mtof and ftom or there is a better way? (it gets really complex eh?) -
oh my gob... 30.0239 ms are ages...try subctract em from 7300
dunno how to help with ogarithmic stuff...
tell us if u find out.
cheers -
maybe the exponential sums (http://en.wikipedia.org/wiki/Exponential_sum) can solve this problem but unfortunately I don't have so strong mathematical background. Have we a mathematical expert here?
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I've wondered about this same problem in the past, and I'm not sure it's necessarily possible in the general case. I'm not sure the acceleration has enough degrees of freedom to satisfy both conditions at one (unless you're lucky enough that they coincide, which is unlikely). Might try and think about it a little more and get back to you with a definite answer, though.
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It depends on a few things:-
1. Does the acceleration need to be linear ie, constant
2. What are the start and end conditions? Is the acceleration zero at 75bpm and also zero when reaching 263bpm? If so, the acceleration can't be constant but should follow an S-curve instead, unless you don't mind an abrupt change.
3. Is there a fixed number of beats that you want to occur during the 7.3 seconds? If not, then there should be a number of different solutions to the problem, depending on the shape of the curve you wish to follow.I'm sure it must involve some integration/differentiation somewhere along the way. I'll have a think about it ~ it's similar to sth I was trying to do, but I didn't get as far as matching the beat at the other end!
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I am trying to trick it by changing the curve factor but oddly there is no difference. The only solution I think is changing the curve factor while it is processes. But with witch values??? That's why I think should someone solve this problem in the table (theoretically) and then we can program it. Otherwise is like searching in the ocean!!!
And also in Pd there is a huge difference between metro object and phasor~ as you can see! -
http://myweb.fsu.edu/ccallender/formalizedaccelerando.pdf
Clifton Callender has worked it out for you.
