"half note = quarter note" and "quarter note = half note" have the same effect
They both slow down tempo instead of one of them speeding it up. EDIT: I was wrong, they both speed up, but by a factor of maybe 10% instead of 100%.
Unchecking and re-checking "follow written tempo" makes them slow down by half.
FURTHER EDIT: it seems that the actual problem is twofold:
1. They don't activate until "follow written tempo" is unchecked and rechecked, and they probably default to 120 bpm instead (which is indeed slightly under 10% of increase from my piece's previous 110 bpm)
2. I was reading them backwards, inverting the meaning of the left and right half of the equation
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" I was reading them backwards, inverting the meaning of the left and right half of the equation "
It's complicated! The tempo indication "half note = quarter note" or "quarter note = half note" used to be interpreted as:
new value = preceding value
But in contemporary notation the tempo indication "half note = quarter note" or "quarter note = half note" is now interpreted more logically as:
preceding value = new value
See Elaine Gould's music notation handbook "Behind Bars" in the section Tempo equations on pp.185-187. Here are the opening paragraphs on p.185:
In reply to " I was reading them… by DanielR
Oh, I see. I still think iit's probably a bug if Musescore's default behaviour is for them to be turned off but appear turned on.