A handy calculation to help you convert consistent-sounding notes while changing the tempo.
Have you ever written anything that started with continuous eighth-notes, for example, and you wanted those eighths to become eighth-note-triplets by only using a tempo change? The most clear-cut way to do this would be to change the tempo, and if you know this calculation you can figure it out fast!
In the above example if you started out with eighth-notes at 180bpm and wanted to change them to eighth-note-triplets without it sounding any different you would have to write the eighth-note-triplets at 120bpm. Eighth-note triplets at 120 sound exactly the same as eighth-notes at 180.
Easier example: If you have eighth-notes and want to switch to quarter-notes you need to multiply the first tempo by 2. To go the other direction you need to divide by 2. If your note value would be slower if you stayed the same tempo you’ll need to multiply, if it would be faster at the original tempo you’ll need to divide.
Here’s a foolproof list of calculations for you to use with most standard note values, just find the conversion you’re looking for with your tempo change…
Now, if you want to get crazier with any extreme conversions I left off you can do this pretty easily by taking a number you know and cross-multiplying it to find the answer you don’t know. But first, you need to understand how the math works. Basically, I’m breaking down how many note values fit in a standard 4/4 measure (common time), which is a very simple way to remember how to do this. If you have quarter-notes, for example, you’ll represent them with the number 4, because there are 4 quarter-notes in a measure. So whole-notes are 1, half-notes are 2, eighth-notes are 8, sixteenth-notes are 16, etc. But what about the triplet variations? Well just see how many fit in a single measure: quarter-note triplets is 6, eighth-note triplets is 12, and sixteenth-note triplets is 24. Technically instead of calling any of these triplets, we could just use the term of the number like all the standard values. So if you wanted to call eighth-note-triplets “twelfth-notes” you could, but most people won’t understand what that means on the fly.
Now, back to the math. If you currently have quarter-notes and you want to convert them to eighth-notes you can cross multiply by taking the first number and dividing it by the number of where you want to go. So your current note value is the numerator and your target note value is the denominator. This example would be 4/8 which equals 0.5, and you can go ahead and multiply the tempo by that answer! Done!
