Moinmoin,
sorry for the long post(s), but one of my most sensitive spots has been hit
I want to apologize if I seem a little bit eager, even sometimes react incensed regarding things
right in principal but
out of range in practice: Unfortunately I am not only musician, but also an engineer in signal transmission and processing...
The musician performs as a (fretless) bass player for 30 years. He is of course able to distinguish notes better than in 3Hz increments (
Although meanwhile at the age of 58, I definitely can tell and play the difference between unstopped E-string and 1st fret F ).
The engineer knows, that letting two frequencies beat against each other is a very common method of measuring slight frequency deviations otherwise not possible with enough resolution. And yes, the human reception also will be more sensitive. Every bass- or guitar player tunes his instrument this way, even if he is totally def and relies on electronic tuners exclusively, as these devices use the very same effect.
This method has a drawback however: You will have to measure (listen) long enough to be able to realize that beating:
Perfect match even needs
infinite time
(Attention: It's theory again...) So if the frequency-difference is let's say 0,2 Hz, You will have to hear 5 seconds for a full circle. If it is not about precision (tuning!), You will not have to wait for a full circle or even more to complete in order to hear an effect, but it will surely take a second or so.
We need not discuss at all, whether life above 20kHz in the sonic domain will have any impact on human beings, especially of the older-than-15-years-and-regularly-practicing-as-well-as-performing-musician-type: For the P'08, which I bet is controlled by MIDI internally as well as externally, there is a hard restriction. MIDI note numbers [0, 127], representing a key range of [C0, G8], will result in a range of [16,356Hz, 6,27192kHz].
As the designer may handle modulation of +/- one octave in a constant way for the entire range, we will generously enlarge this to finally [~8Hz, ~12,5kHz]. And as the control of DCOs has to be done for the
fundamentals, we need not care for harmonics or bat-ears.
Beating with ~0,1Hz (one full circle in 10 seconds) in this frequency range will result in deviations of ~1% and ~0,00001% at the low/high end respectively. As even those of us with bat-ears may not really enjoy listening to string sounds with fundamentals at 12kHz, we may restrict the higher end to practical values in the 1kHz region, resulting in minimal deviations of about 0,01%.
This would be possible with 20Bit resolution, gaining 2
-20 = 0,0095%.
The engineer having said all that, this is a very academic discussion: MIDI teaches us, that even 7Bit are enough as
control signal width. All the rest said here may be handled DCO-internally: As DCOs are digital, two or more of them would react exactly the same, if digital calculations are made before the very control of the analog part.
I do not know, where DSI generates this "real thing" controlling the analog part of the DCO, but there are so many ways to achieve this.
The musician also has to put his feew cents in: Tuning of wide frequency ranges has some psychoacoustic impacts, that every piano tuner knows of. Electronic oscillators should not need stretched tuning, as their harmonic content should be precise, but You never know how exact Your analog sine/saw/rectangle ist at which frequency...
All I want(ed) to tell is that brute force aproaches - and using 64Bit is exactly that - will neither help nor even lead to the right direction, they never do.
Martin