Beat

package cas.cs4tb3.mellowd;

A Beat represent a classical definition of a note duration. Each beat has the number of quarter notes it is equivalent to (possibly a fraction), for converting from PPQN (ticks per quarter note) to a duration in ticks that the beat should be held for.

public class Beat {

All beats must start out as one of the following durations which can then later on be manipulated via dots to extend the duration or wrapping inside a tuplet.

    public static final Beat WHOLE          = new Beat(4d);
    public static final Beat HALF           = new Beat(2d);
    public static final Beat QUARTER        = new Beat(1d);
    public static final Beat EIGHTH         = new Beat(1/2d);
    public static final Beat SIXTEENTH      = new Beat(1/4d);
    public static final Beat THIRTYSECOND   = new Beat(1/8d);

    private final double numQuarters;

    private Beat(double numQuarters) {
        this.numQuarters = numQuarters;
    }

Each dot following a beat extends the duration by the original duration times ¹⁄_2ⁿ. Where n is the index of the dot. This means that a quarter note with 3 dots has the equivalent duration of

 1 + 1·1⁄21 + 1·1⁄22 + 1·1⁄23
 = 1 + 1·1⁄2 + 1·1⁄4 + 1·1⁄8
 = 1 6⁄8
 = 1 3⁄4 quarter notes

    public Beat dot(int amount) {
        double numQuarters = this.numQuarters;
        double prevAdded = this.numQuarters;
        for (int i = 0; i < amount; i++) {
            numQuarters += prevAdded/2;
        }
        return new Beat(numQuarters);
    }

A tuplet is a sequence of equivalent notes played in the time it takes to play fewer of those notes. A 5:3 quarter note tuplet plays 5 quarter notes in the time it takes to play 3. A common tuplet is a triplet.

A triplet squeezes 3 of the wrapped beat into the same time frame that 2 of that beat would fit. For example an eighth note triplet will result in the performance of 3 eighth notes in 2 eight notes, equivalent of a quarter note. This is the same as scaling down the numQuarters by ²⁄₃ or ^div&fracsl;_num

For example: an eight note is ¹⁄₂ quarter notes.

1⁄2 + 1⁄2 = 1 quarter note

Now if we want an eight note triple we need to fit 3 eight notes into a quarter note

1⁄2 · 2⁄3 + 1⁄2 · 2⁄3 + 1⁄2 · 2⁄3 = 6⁄6 = 1 quarter note

    public Beat tuplet(int num) {
        if (num <= 1)
            throw new IllegalArgumentException("Cannot create a tuplet of "+num);
        return tuplet(num, num - 1);
    }

    public Beat tuplet(int num, int div) {
        if (num <= 0 || div <= 0)
            throw new IllegalArgumentException("Cannot create a tuplet of "+num+":"+div);
        return new Beat(numQuarters * (div / (double) num));
    }

    public double getNumQuarters() {
        return this.numQuarters;
    }
}