A problem continually arises when, for instance, I need to put eleven 32nd notes into the space of a single quarter note. While NoteWorthy Composer provides for triplets, eleven is not divisible by 3 and is literally impossible to duplicate precisely within these parameters. Then the thought occurred to me to change the tempo of the song for the duration of the odd notes. In order to fit eleven 32nd notes into one beat, in which normally you will find eight 32nd notes, the tempo must be increased to accommodate the extra 3 notes. But how much of an increase? It took a little number-crunching on my part, but the tempo increase worked out to 22.5 beats per minute (bpm). A 60 bpm song would increase to about 82 bpm for the duration of the eleven 32nd notes, and then revert back to 60 bpm if that's what the music calls for, after the end of the 11th note.
How did I work that out? 60 beats per minute, in 4/4 or common time, is equal to 1 beat per second. A 32nd note is 1/8 of a beat. 1/8 of a beat requires 1/8 of a second to play. I need to accommodate 3 more of these 32nd notes (1/8 beats), 1/8 * 3 = 3/8. Therefore I must add 3/8 of a second to the beat. How many beats per minute tempo increase does this give? In 60 bpm tempo, 3/8 * 60 = 22.5 bpm. Add 22.5 to 60, and the tempo increase works out to 82.5 bpm, or just 82 bpm since the program only works with whole numbers. In this fashion you can play your 11 32nd notes without missing a beat!
Supposing your values over here are correct:
Let's name tempo the tempo (say 60 beats per minute);
Let's name standard the number of the notes of the type you use that fits into a beat (say 8, if you use 32ths in 4/4);
Let's name extra the number of the notes that are over standard, so extra + standard = the number of notes you want; (say 3 for a 11-uplet)
Then the tempo must be added by:
tempo*extra/standard
In other words, the new tempo = tempo * (1 + extra/standard).
Am I correct, Mal?