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.