I'm confused about the Midi Tuning Standard. The spec gives some examples of frequency data:

However,

to the best of my knowledge, 8.2104 Hz differs 7 cents from 8.1758 Hz. How do we arrive at 00 00 0**1** then?

I would expect a value of 7/0.0061 = 1147 which I think then would result in 00 08 7A instead?

Another way to reach the same confusion is to try the reverse calculation:

00 00 00 -> 8.1758 because 440*(2^((0 - 69)/12)) = 8.1758 (yay!)

00 00 01 should then be 440*(2^(0.0061 - 69)/12)) = 8.1787 (eh? standard example says "8.2104" ??)

Can anyone please clear this up?

Maybe I completely misunderstand the system?

Thanks!

0xxxxxxx 0abcdefg 0hijklmn

xxxxxxx = semitone

abcdefghijklmn = fraction of semitone, in .0061-cent units

Examples of frequency data:

00 00 00 = 8.1758 Hz (C – normal tuning of MIDI key no. 0)

00 00 01 = 8.2104 Hz

[...]

However,

to the best of my knowledge, 8.2104 Hz differs 7 cents from 8.1758 Hz. How do we arrive at 00 00 0

I would expect a value of 7/0.0061 = 1147 which I think then would result in 00 08 7A instead?

Another way to reach the same confusion is to try the reverse calculation:

00 00 00 -> 8.1758 because 440*(2^((0 - 69)/12)) = 8.1758 (yay!)

00 00 01 should then be 440*(2^(0.0061 - 69)/12)) = 8.1787 (eh? standard example says "8.2104" ??)

Can anyone please clear this up?

Maybe I completely misunderstand the system?

Thanks!

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