THE RELATIONSHIP BETWEEN BPM & CPS (HZ)
The idea of an assumed relationship between Bpm (Beats Per Minute) and Cps (Cycles Per Second, a once-common English name for the unit of frequency now known as the hertz) is - in my opinion - a valid one. Both Bpm and Cps are a
particular number of occurrences + repeating event + time unit
In the case of Bpm the time unit is minutes, in the case of Cps the time unit is seconds.
From Cps to Bpm we need to multiply the number of cycles by 60.
From Bpm to Cps we need to devide the number of beats by 60.
EXAMPLE CPS TO BPM:
The tone C4=256Hz has 256 Cycles Per Second. In order to find a matching tempo (Bpm) we have to multiply 256 by 60 (turning second into minutes). 256 Cps · 60 = 15360 Cpm. Naturally 15360 Bpm would be too fast to use for any musical piece, so we have to halve the tempo until we get a usable tempo.
15360 /2/2/2/2/2/2/2 = 120 Cpm or Bpm
15360 /2/2/2/2/2/2/2/2 = 60 Cpm or Bpm
What if you find 60 Bpm or 120 Bpm too slow or fast for your composition?
Well, perhaps it would be worth exploring other tone frequencies of importance in your composition, for example the 3rd or 5th. Depending on the tonality (Major or minor) and Temperament used you create the following tempi with the 3rd and 5th, based in this example on Concert Pitch C4=256Hz:
|Scale Degree||CPS (Hz)||BPM||rounded-up|
|Equal Tempered minor Third||304.4370214406993||142,7048538 or 71,3524269||143 or 71|
|Just Intonation minor Third||307,2||144 or 72||144 or 72|
|Equal Tempered Major Third||322.5397887730913||151,190525987 or 75,595262994||151 or 76|
|Just Intonation Major Third||320||150 or 75||150 or 75|
Naturally you could select any tones you feel is important in your composition. If your melody has one tone that is used more often then any other, then you could experiment with adjusting the tempo to that tone as well.
You can convert Cps to Bpm online at www.convertworld.com
EXAMPLE BPM TO CPS:
If we like to use 130 bpm as tempo for a piece of (dance) music, what tone frequency would be "in sync"?. In order to find this tone, we have to divide 130 by 60 (turning 130 beats per minute into beats per second).
130 Bpm / 60 = 2,1666666667 Bps.
This tone of 2,1666666667 Cps (Hz) is too low to use as reference pitch (concert pitch) so we have to double it untill we reach a frequency between C4 and C5.
2,1666666667 ·2·2·2·2·2·2·2 = 277,333333338Hz
The tone in this example is pretty much the C♯4 or D♭4 (277.183Hz) when A4=440Hz and Equal Temperament is used.
You can convert Bpm to Cps online at www.convertworld.com