Kurzweil K150 - APPENDIX 1 Appendix page 6

For relative partials, frequency multiples are expressed using the same 1/2048th octave units. A perfect 4th harmonic, for
example, would be expressed as +4096. General conversion formulas are:
Note that while frequencies can be specified very precisely with these formulas, the final result produced by the hardware is
quantized to 0.298Hz. This means that even sounds in which perfect harmonic intervals have been specified will generally
not "sit still" on an oscilloscope because the frequency quantization error alters the exact ratios slightly.
For noise partials, the "frequency" field specifies an integer playback rate through the noise table. The two tables are in fact
interleaved in the synthesizer memory and the noise type specification (high/low) simply affects the initial setting of the
noise table pointer to either zero or 4. The spectrum of the noise is defined for a playback rate of 8. Other playback rates
will create different but unpredictable spectra. Note that if the playback rate is not a multiple of 8, samples from the two
tables will be intermixed creating yet another effect. The hardware noise table pointer wraps-a round at 32768 so a playback
rate of 32760 is equivalent to 8 except that the noise table is scanned backward. The relatively short length of the noise table
(4096 samples) limits noise usage to relatively short bursts; otherwise repetition is readily apparent.
1.5.3 Amplitude Units
Where absolute amplitudes are specified, they are represented by an unsigned 8-bit integer in units of 3/8 of a decibel. This
gives a range of 0dB to 95.625dB. In most cases the dB value is an amplitude which means that 0 is silence and 255 is
maximum loudness. In other cases, the value is an attenuation, so 0 is loud and 255 is silence. The .S.M.P.'s user interface
generally uses 0dB to represent maximum amplitude and -95.6dB to represent silence.
1.5.4 Slope Units
As described above, contours are represented in the hardware as delta time (sample period counts) and slope. Slopes are
represented by signed 16-bit integers using the following conversion formulas:
Fast Slope
Note that the relatively large slope unit size restricts usage to fairly rapid slopes. By setting bit 14 of the slope value to one
(after the two's complement for negative slopes), the slope may be reduced by a factor of 16 and thus slower slopes may be
represented accurately. The conversion formulas are now:
Slow Slope
Slow slopes are accomplished in the hardware by updating the partial amplitude every 16 samples rather than every sample.
This can lead to audible modulation noise if the slow slope flag is on but the slope is relatively fast. Thus judgment in
trading off the greater precision offered by slow slopes with the absence of noise offered by fast slopes must be exercised. In
any case, a routine for converting absolute breakpoints to relative ones for the K150FS should keep track of the errors
incurred and "feed back" a correction to prevent the errors from accumulating. The Apple II .S.M.P. does this and it is
completely effective. The basis of this error feedback process is shown below:
Value = 2954.6394 * ln Multiple
Multiple = exp Value 2954.6394
Value = 0.034953 * (dB/sec)
dB/sec = 28.6098 * Value
Value = 0.559248 * (dB/sec)
dB/sec = 1.788116 * Value