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```From: Patent Tactics, George Brock-Nannestad

Hello,

the following is the kind of calculation you want to do when you have a
frequency counter for measuring a pitch rather than an electronic tuner for
measuring a note or a predominant chord.

The principle is that the tempered octave is divided into 12 equal parts,
i.e. the proportion 1:2 is split into 12 parts so that the proportion between
the parts is the same. This is obtained, if we see to it that you multiply by
the 12th root of 2 going from one note to the one above. The 12th root of 2
is equal to 1.05946309436 (and then some). So, you multiply 33.333333.... by
this number and count the number of times you have to do that to get to 78.
There is a saving, because 66.666666.... is an octave, which already accounts
for 12 semitones. Doing the calculation you get

74.830802 for 14, and
79.280473 for 15 multiplications.

Now, fortunately, a semitone as defined above is divided into 100 cents, each
representing the 1200th root of 2, and the calculation may be continued from
14, using that figure instead. Precision increases! Looking at a table that I
use for these things it seems to be 28 cents short of 15 multiplications,
i.e. 14 semitones and 72 cents. This is the 78.00 rpm case.

However, are we talking 78.00 rpm here, or is it 77.92 rpm (a European speed
for electrical records recorded by means of a synchronous motor drive,
equivalent to a 77 bar stroboscope) or 78.26 rpm (a US speed for electrical
records recorded by means of a synchronous motor drive, equivalent to a 92
bar stroboscope). Or is it Victor's acoustic recording speed of 76 rpm (at a
time when they positively recommended 78 rpm for reproduction)??

Another way of approaching the problem would be to use the small calibration
record SC-1 that I made in 1982-83. This record has a tone track on each side
(one side Berliner, the second side H&D) that represented 10 Hz per rpm. So
when put on a 78.26 rpm turntable a frequency meter would read 782.6 and when
put on a 33.33 turntable it would read 333.3 rpm. It was meant to be put on
top of the record on the turntable and the sound from it recorded on the tape
while both turntable and tape were moving. The record would then elegantly be
lifted off (a small wire already projecting from the label would ease that)
and the music recorded. Thereby a signal directly indicating the rpm would be
on the tape, and any discussion about the correct speed of the original
record could easily be determined by the tape user: by whatever criteria you
want, find out the speed by varying the tape recorder speed, and then go back
to the beginning where the tone track would instantly tell you by means of a
frequency counter what the speed of the original record should be (in your
humble opinion). Here, the number semitones could be bumped up until 78.26
featured as a strong spectral line when analyzing the signal.

Kind regards,

George

Steven Smolian wrote:
> I'm having a problem dubing a bunch of 78s which skip a lot at that speed.
>
> They seem to play through at 33.
>
> Eq aside, if I record at 33, how many half-tones do I need to bump up the
> sound file in the computer to get to 78.26 or thereabouts?
>
> Steve Smolian
>
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