tuning accuracy - more thoughts

Hola,

Regarding wavetable engines I wrote:

> * Lower frequencies have less pitch resolution.

This is true in cents' but not in Hz - which is where it matters.

Examples below are table in previous post. Calculations show
smallest possible detuned unison at a given fundamental frequency in Hz. Figure
in seconds is number of seconds for one beat between partials
at the fundamental frequency to occur. Assuming a perfectly
harmonic overtone series such as you're likely to get with a
simple wavetable oscillator, you'd hear faster beats between
the upper partials. But even so!

Cycle Length: 128 samples
1/(86.13806962967 Hz - 86.1328125 Hz) = 190.235 seconds
1/(689.0677571297 Hz - 689.0625 Hz) = 190.512 seconds

Cycle Length: 512 samples
1/(86.13412678242 Hz - 86.1328125 Hz) = 762.047 seconds
1/(689.0638142824 Hz - 689.0625 Hz) = 780.190 seconds

So the tuning resolution in Hz is seen to be slightly less
for lower frequencies - but the length of a cycle in the wave
table is a major contributor to tuning accuracy. Longer tables
(requiring more memory and suggesting a higher initial sampling
rate when creating the waveform banks) = more accuracy.

- Jeff