Yes: F# is sharper than Gb. It's a microtonal difference, but it exists (again, like the subtle differences between two identical twins). It's like those physics problems where you dismiss friction and only consider the most important factors, but it doesn't mean they don't exist. F# and Gb are enharmonically equivalent (i.e. they're so close to be the same that they're usually regarded as the same in order to ease things up), but they're not the same note, not the same pitch, not the same frequency, etc.
Equal temperament has a slight margin of error, which is shown in these things precisely.
Yara: There's nothing to 'forgive'. You expressed your opinion, and I expressed mine. I just want to add two things:
- Absolutely none of what I've written here in the past eight years is very 'technical' or 'complex'. They're barely past the first fifteen pages of a regular book on music theory. Just by reading my posts you can learn 99% of what I know.
- Sometimes maths are the only way to clear-up situations, because, indeed, some situations are indeed black or white. Compare:
** Roger sings better on Bohemian Rhapsody than on In the Lap of the Gods
** Roger sings better on In the Lap of the Gods than on Bohemian Rhapsody
Those are two statements that are entirely subjective, thus there's no way at all to demonstrate if either one is absolutely 'right' or 'wrong', and it doesn't matter if Roger did more ornaments in one or the other or if the range covered was larger or smaller... no theoretical concept, no physics, no maths, no psychology can 'prove' either answer: it's up to the person who listens and has an opinion.
But, compare:
** Roger's highest note on Bohemian Rhapsody is higher than his highest on Lap of the Gods
** Roger's highest note on Lap of the Gods is higher than his highest on Bohemian Rhapsody
** Roger's highest notes on Bohemian Rhapsody and Lap of the Gods are the same
There, there's no opinion involved: two of the three statements are absolutely wrong and one of them is absolutely right. Full stop. How do we know it?
Rog's highest note on ItLotG: Soprano A = 880 Hz
Rog's highest note on BoRhap: Soprano Bb = (880 * (2^(1/12))) Hz = 932.32752303618 Hz (and btw A# is a tiny bit sharper)
932 > 880 hence, Roger's highest note on Bohemian Rhapsody is higher than his highest on In the Lap of the Gods and there's absolutely nothing subjective about it.
Same for other topics: I can't possibly argue if someone tells me that, for instance, they prefer Brian's piano playing over Freddie's. I could (and would) disagree, but I can't tell them to think otherwise because it's a matter of opinion. But, if somebody tells me that Brian played as much piano on released Queen songs as Freddie did, I can prove them wrong by simply counting the number of songs each one played (actually, I could walk the extra mile and count the seconds, because the brief piano part on Now I'm Here isn't the same as a full epic song like March of the Black Queen). And for those cases, there is an absolute conclusion.
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I was taught in theory class that en-harmonically F# & Gb are the same but in theory and application they are very different. And that's theory being taught from a classical standpoint.