Perfect Pitch

 Here’s a strange piece of advice. Always tune your SS-30 from C#. It does not matter which octave, just use C# and you’ll get the most accurate tuning possible for the instrument. Choosing the wrong note, say D, and you will be compromising the tuning of some other notes more than necessary. Why?

Tuning

As noted in the post about how the top octave is generated, the frequency of each pitch generated by the TOG is within about 1 cent of perfect tuning, if the master clock is accurately tuned to 2,000,240 MHz or one of its divsions. That is a big IF though. That clock value assumes rock solid crystal accuracy. The tuning of the SS-30 is achieved by listening to the audio output at a particular note and adjusting the tuning control to match a reference, by ear, or with a tuning device of some kind. This means, in theory, you could select a note and adjust it in to be exactly in tune, with zero cents of error. That one note would be accurate at all pitches on all octaves. Meanwhile, the other notes will not only still be slightly out of tune due to the rounding inaccuracy of the divide-by-n method, but more 'out' than if the MCO is precision locked to the nominal frequency.

This raises the question: for any given note which one selects for tuning, how far out will the others be? Will any be noticeably out of tune?

Let's work an example using C4 as the tuning note. 

 The exact nominal clock frequency expected by the SS-30 TOG generating C4 (as the bottom C) is 125,015Hz. C4 is 261.63Hz when perfectly tuned, but the pitch generated by the TOG with this clock is 261.5377Hz. That is, -0.61115 cents detuned from perfect pitch.

Now let's say that the SS-30 is tuned, by ear or tuner, to perfect pitch based on C alone with no other notes used as reference. Again note that the octave won't matter - C will tune the same accuracy for all octaves. C4 will now be output from the TOG at 261.63Hz, with 0 cents of error. If you measure the MCO now it will be shifted to 125,059.14Hz - calculated by multiplying the C4 frequency by the divisor 239. All the other pitches from the TOG will now be +0.61115 cents shifted from their previous tuning.

My 2 Cents

As you can see from the table below, there are winners and losers. D4 is brought  more into tune whereas notes which were already out by over positive one cent are now even further out. It’s not terrible, but E and A# are edging towards 2 cents. 

It follows that this could be worse though. If either E or A# were selected for tuning then the other would be well over 2 cents out of tune. 

Conversely, tuning from C# guarantees less 0.1 cents deviation from the nominal tuning for all the other notes. F and G# are better too, but C# is the best option. 

 

So, that's why C# is the best tuning refermce for perfecting the pitch.

Note	Perfect pitch   (Hz)	Nominal clock   (Hz)	Series B 'n'   divisor	Nominal pitch   (Hz)	Nominal error   (cents)	Perfect C' clock   (Hz)	Perfect C' pitch   (Hz)	Perfect C' error   (cents)	Error delta   (cents)
C4	261.63	125015	478	261.5377	-0.61115	125059.14	261.63	0	0.61115213
C#4	277.18	125015	451	277.1951	0.094447	125059.14	277.29299	0.7055995	0.61115213
D4	293.66	125015	426	293.4624	-1.16507	125059.14	293.56606	-0.553921	0.61115213
D#4	311.13	125015	402	310.9826	-0.82045	125059.14	311.09239	-0.209298	0.61115213
E4	329.63	125015	379	329.8549	1.180686	125059.14	329.97135	1.7918376	0.61115213
F4	349.23	125015	358	349.2039	-0.12934	125059.14	349.32721	0.4818147	0.61115213
F#4	369.99	125015	338	369.8669	-0.57627	125059.14	369.99746	0.0348855	0.61115213
G4	392	125015	319	391.8966	-0.45693	125059.14	392.03492	0.1542215	0.61115213
G#4	415.3	125015	301	415.3322	0.134333	125059.14	415.47887	0.745485	0.61115213
A4	440	125015	284	440.1937	0.761819	125059.14	440.34908	1.3729713	0.61115213
A#4	466.16	125015	268	466.4739	1.165304	125059.14	466.63858	1.7764557	0.61115213
B4	493.88	125015	253	494.1304	0.877645	125059.14	494.3049	1.4887972	0.61115213
C5	523.25	125015	239	523.0753	-0.57807	125059.14	523.26	0.0330859	0.61115213