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java.lang.Object com.softsynth.jmsl.util.LinearAccelerator
public class LinearAccelerator
Calculate the accelerated duration of an event, given the acceleration, the event's starting time, and its duration.
Accelerando is expressed as beats/sec change over some number of beats. EXPLANATION... Formula for instantaneous tempo v as a function of unaccelerated time x. v(x) = Vi + Dx / (n) Where: Vi is initial tempo in b/s, D is the amount the tempo changes n is the number of beats over which the tempo changes. For example: to calculate instantaneous tempo which accelerates from 1 b/s to 2 b/s over 4 beats: V(x) = 1 + (1)x/4 To find instantaeous tempo at beat 2, V(2) = 1 + 2/4 = 1.5 We can not apply instanteous tempo to the duration of an event to get its accelerated duration. Easiest to see this if you imagine that the first event would not have its tempo altered, since the tempo at accelerando time 0 is equal to Vinitial. You can also imagine easily that an event list containing one event of 1.0 would fall out of synch with an event list containing 2 events of 0.5 seconds each. Instead we need to take the integral of 1/V(x) between the x initial and x final. For example, for an event of duration 1.0 beginning at time x=1.0, we'd need the integral between x=2.0 and x=3.0 (since it starts at x=2 and lasts until x=3). 1/V(x) = n/(nVi + Dx) The integral of this with respect to dx is: n ln(nVi + Dx) EXAMPLE PROBLEM: A MusicShape has four elements each of whose durations is 1.0. The initial tempo is 1 b/s (ie 1.0 lasts 1 second) The final tempo is 2 b/s The duration over which this acceleration takes place is 4.0 Calculate the duration of the third event. SOLUTION: n=4 Vi=1 D=1 Evaluate the integral 4 ln(4 + 1x) at x=2.0 (the event's starting time) and at x=3.0 (the events finishing time). Find the difference. The accelerated duration is 0.61660271930903321717150154024991
Constructor Summary  

LinearAccelerator(double startTempo,
double endTempo,
double numBeats)
Create a new accelerando calculator given the starting tempo (beats per second), the ending tempo, and the number of "beats" over which to linearly interpolate this change. 
Method Summary  

double 
acceleratedDuration(double startTime,
double dur)
Calculate the new duration of an event starting at startTime with duration dur. 
static void 
main(java.lang.String[] args)
Test accelerando. 
Methods inherited from class java.lang.Object 

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Constructor Detail 

public LinearAccelerator(double startTempo, double endTempo, double numBeats)
Method Detail 

public double acceleratedDuration(double startTime, double dur)
public static void main(java.lang.String[] args)
public static void main(String args[]) { // accelerate from 1 bps to 2 bps over 4 beats LinearAccelerator accel = new LinearAccelerator(1, 2, 4); double[] eventDurations = {1.0, 1.0, 1.0, 1.0}; double nonAccelStartTime=0.0; // needed to calculate double acceleratedStartTime = 0.0; // just for fun for (int i=0; i < eventDurations.length; i++) { double nonAccelDur = eventDurations[i]; double accelDur = accel.acceleratedDuration(nonAccelStartTime, nonAccelDur); System.out.println("event " + i); System.out.print("Nonaccelerated starting time=" + nonAccelStartTime ); System.out.print(", Nonaccelerated dur= " + nonAccelDur); System.out.print(", Accelerated starting time=" + acceleratedStartTime ); System.out.println(", Accelerated dur = " + accelDur); nonAccelStartTime += nonAccelDur; acceleratedStartTime += accelDur; } System.out.println("Total duration of accelerando =" + acceleratedStartTime); }


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