Gulp! here we go.

Firstly i got to set out a few basics.

*example*

100hz = 100 cycles of a wavelength per second
therefore (herin known as TF)

TF 0.1 cycles per ms
TF 1 cycle = 10ms[oops put 1ms in first edit..]

*musical delay basics*

QTR bar delay times

60 x 1000 / Tempo = number of ms in a qtr bar of whatever tempo

eg. 60 x 1000 / 140bpm = 428.57142857142857142857142857143


Calculation

Precept - getting frequencies to run in line with a tempo. This means an equal number of wave cycles in a 16th, 32nd 1/2 bar etc etc. This is especially important in the bass end. Getting the compression and rarefaction waves to push the speakers forward in time with the music releases some power in the bottom end.


f#3 = 1000ms/184.997hz = 5.40549306204965485 cycles per ms

(this next bit is a bit hit and miss - understand im not a maths expert ;) )

The figure we are trying to reach is around 200-800ms depending on your prefered tempo. in this case we will try and reach around 428 as in the previous example.

5.40549306204965485 cycles per ms x 80 (this figure is reached by experimentation) = 432.439444963972388

we can now transpose the formulae

60000 / 432.439444963972388 = 138.7477bpm

This tempo cannot be reached by most sequencers (except logic and i think digital performer) but the difference of 1 decimal place is almost negligable especially over short distances such as 4 bars.

if we were to use 128 cycles we would use this tempo 86.7173bpm.


These are just my calculations and are totally open for people to attack/ pull apart. If you find them useful then im pleased, if you dont understand them please ask for clarification. If you want to criticise, please tell me where i went wrong.

I dont really use these much, but it was fun doing the workings.