At low sampling rates and/or high fundamental frequencies, the string simulation can sound ``out of tune'' because the main delay-line length is an integer, which means that the fundamental frequency is quantized to values of the form where is the sampling rate and is the delay (in samples) of any filters in the feedback loop. For example, in Fig.4, equals the combined delay of filters , , and . In Eq.(1), we had the digitar tuning formula because is the phase delay of the two-point average used in the KS digitar algorithm.
In this section, we look at designing a tuning filter so as to fine-tune the fundamental frequency as desired (even at low sampling rates). Keep in mind, however, that such a filter is not needed when the sampling rate is sufficiently high compared with the desired fundamental frequency.
For simplicity, here we will use the two-zero damping filter described
in §3.4, so that its phase delay is always one sample.
The tuning formula becomes