Here is a small correction in the documentation which does not affect the use of Lilypond,
just for the sake of correctness of the formulas...
On this page <https://lilypond.org/doc/v2.23/Documentation/music-glossary/syntonic-comma>
about the syntonic comma,the arithmetic expressionscontains a mistake and some
inconsistency. Addition and subtraction of intervals should be represented in the
arithmetic expression by multiplication and division operators.
So the first expression should be written “(9:8)^2 / (5:4) = 81:80” rather than “(9:8)^2 -
5:4 = 81:80”.
For the second one, there is also a missing pair of parenthesis (or a sign
error):
It is written as “(3:2)^4 - (2:1)^2 + (5:4)”, but should rather be written “(3:2)^4 -
((2:1)^2 + (5:4))”. Then, replacing the addition/subtraction signs, one gets “(3:2)^4 /
((2:1)^2 * (5:4))” as the correct arithmetic expression corresponding to the textual
definition — which is equal to “(3:2)^4 / (2:1)^2 / (5:4)”, if we write it without the
additional pair of parenthesis.
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