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Math Help - Synchronize accelerations and decelerations

  1. #1
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    Synchronize accelerations and decelerations

    Halo everybody!

    first of all I want to say that I am not a Mathematician but a Musician-Composer and I am using Maths for the design of my works and for programming electronic music. I have a problem witch seems very simple but it is really difficult to solve it. Also it is related with geometry that's way I am posting it here.

    The problem is: I want a metronome that makes accelerations and decelerations from x b.p.s. to y b.p.s. in z time and be synchronized!!! That means that the metronome starts with a beat at time t=0 and finish at time t=z also with a beat. B.p.s. means beat per second (60bps is a beat every 1 second).

    Another thing is that we are hearing all aspects of music logarithmic but we (the musicians) are organize them in power of 2 in order to have a liner result and to control them. For example the frequencies 200, 400, 800, 1600... are the same notes what we call octaves.[IMG]file:///Users/Koularas/Library/Caches/TemporaryItems/moz-screenshot.jpg[/IMG][IMG]file:///Users/Koularas/Library/Caches/TemporaryItems/moz-screenshot-1.jpg[/IMG][IMG]file:///Users/Koularas/Library/Caches/TemporaryItems/moz-screenshot-2.jpg[/IMG] Our linear units, called MIDI notes, come from the equation:[IMG]file:///Users/Koularas/Library/Caches/TemporaryItems/moz-screenshot-3.jpg[/IMG][IMG]file:///Users/Koularas/Library/Caches/TemporaryItems/moz-screenshot-4.jpg[/IMG] m=69+12*log(f/440). (log with base 2). That is because we want the 69 midi note equals 440Hz.

    When we make a glissando (is a glide from one frequency to another) we are making it in the MIDI form in order to have a acoustic linear change. Correspondingly when I make a acceleration with b.p.s. and metronomes I want the same result. But how can I calculate it? And also take into account the synchronicity issue?

    In geometric means can be said like this. I have a line with z length and I want do divide it in smaller parts. The first part (x) is the bigger from all the other parts and the last the smallest (y), or the opposite (acceleration and deceleration correspondingly). And all these length of the parts must follow a power/logarithmic curve of 2.
    I think this problem can be solved!

    Finally I want to thanks in advance the people who'll help me and apologize if somehow I didn't made myself clear.

    Have fun,
    Skatias
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  2. #2
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    Sep 2010
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    Yes you can do it but the time z will depend on x and y.

    It's like those physics questions about velocity. To see that - suppose you have a bike with a (small) wheel that turns round once every meter and clicks once on each turn.

    Then, start with the bicycle travelling at say 60 bpm (velocity one meter per second but let's use meters per minute so that units are same as for tempo),

    Then, it accelarates at constant speed to say 120 bpm over some time period (doesn't matter what).

    It will travel at 60 m per minute, accelerating to 120 bpm and just as for velocity questions, you can then say that it would go the same distance (so same number of ticks of the wheel) if it travelled at the average speed, here 90 bpm.

    So - in this case, its going to average 90 bpm, no matter how large or small z is. So to get it to work, z has to be an integral multiple of 60/90. So e.g. z = one minute would do fine. Also z = one minute and 2/3 seconds. Any multiple of 2/3 seconds in this particular case will work okay. Any other value of z won't - unless you change the requirements so that it goes at non constant acceleration.

    BTW you can play rhythms like this with my Bounce Metronome Pro - lets you set the start and finish tempo and it will do a gradual tempo change from one to the other.
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  3. #3
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    Thank you Robert for your reply. For me is very important to have a fixed z time because I have to synchronize different voices. What you have described is a linear acceleration from 60 bpm to 120 bpm. As I said before I want the acceleration to follow a curve of power of 2. And yes maybe the time t depends from x and y but I want a way to trick it in a way that it is closer to the power of 2 curve in order to achieve the time t! It should have not so easy maths but I don't know if there is an algorithm that can be used for all cases (I hope there is!!!). Your Bounce Metronome Pro looks very handy but I am working in a mac so when you'll release a mac version please contact me.
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