It's funny (fascinating actually!) because it reads just like your typical highly opinionated software engineering blog post, only applied to music. Yet most of it, particularly the first three points, has no basis in reality. (E.g. point 3 - any music theorist will tell you there is a VERY valid reason for choosing a double-sharp over a natural in particular contexts.)
To me, that mostly reads like a UX report. This person admits he has no musical education, and just wants to play - the issue seems to be that reading a score maybe shouldn’t require a degree in musical theory, the same way that using a piece of software doesn’t require a CS degree.
As another amateur musician, I was nodding at most of these points. I fully believe it’s all very complex and double sharps exist for some reason, but how much of that do you really need the reader to understand?
It is like a UX report, and the author has every right to make one! But I'm afraid that if this were a pull request into the western-music-notation repository then I would find it hard to resist closing it quickly.
Yes, it is true that using a piece of software shouldn't require a CS degree. But you still expect the source code to follow "CS principles". Similarly, you expect scores to follow "music theory principles". Now, it takes time and effort to understand these principles, just like with CS. However, whereas almost everybody understands that the subject of computer science is vast and is not to be underestimated, the same doesn't seem to be the case for music theory. And I can sort of understand why - computer science is math (1 + 1 = 2), but music theory is just hand-wavy rules made up by dead people, no? Well, yes, but that does not make it any less "true". Music theory as a tradition is very real, and you can't expect people to take your music-theory "PEPs" seriously unless you have been deeply embedded in that tradition.
Of course, this is not me knocking the author in any way. Sometimes the best innovations come to those with fresh eyes. But I just hope to convey the idea that music theory (or maybe more accurate to say "music tradition") is not something to be easily dismissed and, just like in computer science, a good solution requires a good understanding of the problem.
The problem is you don't want to make the score harder to read for someone who does know some theory. Say you're in G# minor, then F double sharp is going to be pretty common. If you notate that as G natural, it will confuse me. Raised 7th degree in a minor key is easy to understand. Flat first degree is...well, I can only assume we've entirely changed keys. And this is going to happen automatically in my mind, but figuring out it was supposed to be a raised 7th but was notated wrong will not be automatic and therefore slow things down.
The only really solid rule I've seen stated for accidentals is that you want to use sharps when you're going up (as in, playing a rising sequence of notes) and flats when you're going down.[1] There are also many, many people out there who will tell you that you use sharps when the key signature has sharps and flats when the key signature has flats, which (1) is really easy to implement, but also (2) makes no sense.
Anyway, my first guess for a double sharp would be that you're e.g. notating an F# which is itself sharp for whatever reason, and you can't just notate it as a G because Gs are also sharped. (As will be true in any key signature with three or more sharps.) Then the reason for marking F𝄪 rather than G♮ is exactly the same as the reason you'd mark F# rather than G♭ in a key that didn't sharp either note. And even from a pure usability perspective, if you're in a key with three sharps and you're doing a lot of alternating between F𝄪 and G#, it's kind of nice having the two notes at the positions of F and G so that you can give them the appropriate accidentals once per measure instead of every time you play either note, the way you'd need to do if they were both on a G.
The first half of the vibraphone part looks like you're mainly doing downward variations, so I wrote it with flats. But the second half obviously suggests that it wants F#s rather than G♭s, and it felt really weird to use F# sometimes and G♭ other times.
Since I know virtually no music theory, my approach was to ask people for help on the internet. I found someone who had majored in music theory and his response was "hmm, interesting", followed by asking a bunch of his friends. Consensus eventually worked out as something like "Hmm, interesting! Could go either way, but maybe F# is a little better than G♭. Whatever you choose, be consistent."
It was all fairly unsatisfying and I'd be interested in other comments on how the accidentals in the piece should be marked. Following the general theme of "F# looks a little better, but be consistent" I interpreted every accidental anywhere in the piece as a departure upward rather than downward. :/
[1] I've also seen sharps used while going down, but it was pretty obvious what was going on there - the music had changed keys, but the score hadn't changed key signatures. Those sharps just reflected the new key rather than being departures from it.
Your engraving looks good to me - the only change I'd make is measures 7 and 8, changing the C# to a Db. Basically, that harmony there is V - i (G major to C minor, a.k.a. perfect cadence), but with a tritone substitution of the V. So what would normally be the bass is replaced by a note a tritone away. Normal bass = G, so a tritone away would be C#/Db, i.e. I# or IIb. But I# -> i is not a resolution whereas IIb -> i is. This is because, generally speaking, you can't resolve a note to another note if they have the same note name. So C# -> C doesn't resolve, but Db -> C does.
Similarly, regarding the F#/Gb question in the vibraphone part, F# is better than Gb because you are resolving UP to G, so you want to use a different note name. The only questionable part is measures 11-12...I won't go into detail but I would say it can go either F# or Gb - both are perfectly fine ("depends on the person" kind of thing!)
The rule "you want to use sharps when you're going up and flats when you're going down" is maybe only really true for chromatic scales, and even then it's tenuous. In general, you pick accidentals based on the key or harmony that you're in.
Unfortunately music theory commentary does not translate well into English at all, so apologies if this comes across as gobbledygook. And make no mistake, I don't think in these terms when playing/composing music. It's more like a deep intuition you get after a while.
I beat you to it, but your writing is much better than mine, and you are more comfortable with the ideas than me! It's good that between the two of us we hit both of the "depends on the person" options.
So, I might just be way off, but even in measure 7 I'd use a D flat instead of C sharp. It feels like a diatonic run in the violin with the D flat borrowed from the key of F minor to me (which is only one flat away from the key you're already in). I know the "rule" about using sharps going up and all, but that really just feels like a diatonic run to me.
The B natural (raised 7th in C minor) helps keep you grounded by pulling very hard back to C minor. Also, the B natural is the raised 4th of F minor, and raised 4th is being used a lot when you're on the tonic as well which helps keep the feel. Very much double harmonic minor in feel all taken together.
Your actual question... Honestly I don't know and feel the same as others you've asked. I guess the violin in measure 12 feels like it's hitting a flat 5, so personally I'd choose G flat throughout that section for consistency. But I dunno, it's kind of a toss up to me.
Even without a music theorist telling you that point 3 is wrong, it just makes the music harder to read. Of course, the reason is what the theorist would give, but it highlights that he isn't really reading music. He's reading notes. He hasn't learned what those notes mean in context. It's like he's learned how to sound out written words in a foreign language but doesn't actually know what any of the words mean.
It's funny (fascinating actually!) because it reads just like your typical highly opinionated software engineering blog post, only applied to music. Yet most of it, particularly the first three points, has no basis in reality. (E.g. point 3 - any music theorist will tell you there is a VERY valid reason for choosing a double-sharp over a natural in particular contexts.)