The list of frequencies in pitches.h and the agreed (western, named) pitches seem to differ. Is this because electronics need the "pitches.h" frequencies to sound like the natural pitches? Harmonics of "A" seem to be the only note that is constant at multiples of 440.
If the frequencies are timer-generated, it is not necessarily possible to produce the "agreed upon" frequency. You are stuck with whatever results from integer divisions of the CPU clock frequency.
Thank you. This makes sense (the math error causing the product difference).
The "natural" frequencies seem to differ from pitches.h more than a quotient of 2^x (and quite different source to source). I wonder if there is an ISO like the length of a meter is some wavelength of kryptonite. I know nothing of music, other than it is a waveform or multiple waveforms.
Just international agreed-upon conventions. Very, very few people have "perfect pitch" and as a result, if an instrument or group of instruments are tuned so that they are all consistent with each other, most people can't tell the difference.
Concert A is 440 Hz exactly, by ISO standards, but optional, and many orchestras and groups deviate from that standard. Background reading: Concert pitch - Wikipedia
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I totally skipped that column (except for the A harmonics), I was looking for D6 and higher... which are probably due to the division issue mentioned.
If you use DDS methods to generate pitches you are not limited to integer multiples though, often you get millihertz resolution or better in such a system.
Direct Digital Synthesis Direct digital synthesis - Wikipedia
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