Is your C standard-conforming?

[Kaz Kylheku]

ISO 16:1975 establishes A4 at 440 Hz, which makes the middle C below A4
approximately 261.626 Hz (no relation to ISO 626). Conforming instruments must
implement C to within 0.5 Hz of this value. (Note that C# is 277.183, and thus
non-conforming and off topic).

In most implementations of C, additional frequencies are found, usually higher
than the fundamental but in some cases lower. Except in synthesized forms,
there is rarely a whole number ratio relationship between these and the
fundamental, and sometimes the fundamental doesn't contribute the majority of
the acoustic energy content.

The standard doesn't mention these real-world anomalies. It neither prohibits
them, nor requires them to be documented.

 

[luserXtrog]

ISO 16:1975 establishes A4 at 440 Hz, which makes the middle C below A4
approximately 261.626 Hz (no relation to ISO 626). Conforming instruments must
implement C to within 0.5 Hz of this value.  (Note that C# is 277.183, and thus
non-conforming and off topic).

In most implementations of C, additional frequencies are found, usually higher
than the fundamental but in some cases lower. Except in synthesized forms,
there is rarely a whole number ratio relationship between these and the
fundamental, and sometimes the fundamental doesn't contribute the majority of
the acoustic energy content.

The standard doesn't mention these real-world anomalies. It neither prohibits
them, nor requires them to be documented.

I deal with this problem every day, while trying to tune a guitar to
CFCFAC using an A440 tuning fork. One would wish to follow the
Helholtz ideal and tune the major third FA by harmonics, but of course
that throws the fifth sharp. I always end up just picking an F that's
close enough, fix the octave, and try to pull a tempered C off of
that. If the Cs have been adjusted beyond some invisible threshold the
overall pressures shift and the A has to be rechecked and the process
iterates.

Then the allure of the pythagorean third rears its head. It's a smidge
sharper than a tempered third (and quite a bit sharper than a
Helmholtz), but it seems to pull against the flattened fifths in a
pleasing way. But it's useful in that if you can find the Helmholtz
third and the Pythagorean, the tempered third is somewhere in the
middle.

Moral: decide upon the C that you want. the rest is just details of
implementation (including adherance to standards).