Notation in a fugue

[i_will_die_playing_schumann]

Hello,

I've been working on a prelude and fugue (des-dur, Shostakovich #15 Op. 87). The prelude is straightforward and buoyant, the fugue I love even more -- but I can't shake a feeling I am misunderstanding some of the notation. I spend most of my time -- conspicuously -- with Schumann and there's not a whole lot of polyphony of the kind you find in the fugue in question. And being in des-dur doesn't help with clarity in terms of accidentals.

I hope to have attached an image -- but in case not, this link https://drive.google.com/file/d/1qNHwInVWrP7u0L8jK_VA0DG3z09viC4r/view?usp=sharing should work; the relevant bars are, e.g., 21-22).

It seems fairly straightforward but somewhat counterintuitive that in bar 22, the natural for C6 is to make sure we don't continue on with the flat one from the previous measure. But since it's a different measure, it should ideally be in parentheses, as a courtesy accidental. Unless the tie across a measure boundary somehow annuls that convention. Notably, while the link and the .png are from a Soviet edition, I found a (seemingly) French edition which did have the parentheses. (Still, in bar 57 of the Soviet edition, there's an accidental with parens as well so it's not like they had a different convention.)

Similarly, for bar 24, I am wondering about the double flats. B5 which is being double-flattened is already pretty flat given des-dur. My understanding has been that the double-flat-on-B5 is played as A5, not A5 flat -- which also seems counterintuitive since there are 2 accidental flats not after a natural + 1 key flat which should theoretically bring it down to A5 flat. (The aforementioned understanding of mine received some justification from measure 56 of the prelude where tripling the flats made zero sense.)

I just wanted to double-check my intuitions. I am fairly confident about the first one, but not so much about the second one.

Regardless, thanks for looking at this! Also, interestingly, double flats in that fugue are swarming whereas double sharps are hardly any -- which makes sense in terms of consistency and is easier to play, but sort of strange to observe.

[lelle]

Hey! I'll try to clarify the things you asked about.

It seems fairly straightforward but somewhat counterintuitive that in bar 22, the natural for C6 is to make sure we don't continue on with the flat one from the previous measure. But since it's a different measure, it should ideally be in parentheses, as a courtesy accidental. Unless the tie across a measure boundary somehow annuls that convention. Notably, while the link and the .png are from a Soviet edition, I found a (seemingly) French edition which did have the parentheses. (Still, in bar 57 of the Soviet edition, there's an accidental with parens as well so it's not like they had a different convention.)

The older the sheet music, the more likely that it doesn't follow modern conventions or might be inconsistent according to modern standards. In this case, the natural sign in front of the c in bar 22 is just to remind you to not play a c flat again, since the first note of the bar is defacto a c flat. So basically a courtesy accidental.

Similarly, for bar 24, I am wondering about the double flats. B5 which is being double-flattened is already pretty flat given des-dur. My understanding has been that the double-flat-on-B5 is played as A5, not A5 flat -- which also seems counterintuitive since there are 2 accidental flats not after a natural + 1 key flat which should theoretically bring it down to A5 flat. (The aforementioned understanding of mine received some justification from measure 56 of the prelude where tripling the flats made zero sense.)

Double flats (and double sharps) are "absolute", so to speak. So if you have a B in the score with a double flat, it ALWAYS becomes an A, regardless of key signature (for example if the key signature contains a B flat and an A flat) or existing accidentals in the bar. The same goes for the E double flat in the left hand in the same bar. It becomes a D natural.

It's a bit like when you put a sharp sign in front of an E in a key signature that includes an F sharp. The E becomes an F natural in this case, and does not get further raised into an F sharp by the key signature. (That kind of defeats the point of writing an E sharp in the first place!)

In this case, the purpose of the double flat is to get a note that sounds like A natural without having to write a natural sign in front of the A to cancel out the A flat in the key signature. This is for music theory/harmony reasons. A short and incomplete answer is that he wants to show that the voices are moving chromatically towards the A flat major chord in bar 25 but haven't arrived at that harmony yet.

Regardless, thanks for looking at this! Also, interestingly, double flats in that fugue are swarming whereas double sharps are hardly any -- which makes sense in terms of consistency and is easier to play, but sort of strange to observe.

You'll most often find double flats in key signatures with many flats, and double sharps in key signatures with many sharps. As you might have guessed by now, this is for music theory/harmony reasons. Basically, the basic chords used to construct music are made from stacks of thirds (look at a C major chord in root position or write one out on a staff to see what I mean), and once you start getting into keys with many sharps or flats, you start needing double sharps or double flats to still be able to spell certain chords as stacks of thirds.

For example, look at a G flat major chord in it's basic form. It contains G flat, B flat, D flat. It looks like a stack of thirds if you write it on a staff. Now, if you want to write a G flat minor chord, you spell it as G flat, B double flat, D flat - still looks like a stack of thirds. If you write it as G flat, A natural, D flat, it no longer looks like a stack of thirds, and could be confused as some other, incomplete chord.

Hope that helps, and feel free to ask more in depth if you want. I love explaining this sh*t

[i_will_die_playing_schumann]

[...] Hope that helps, and feel free to ask more in depth if you want. I love explaining this sh*t

Thanks a lot! All of this makes sense and is helpful -- and I am sure I've been told that at some point while being taught -- but it's definitely been some time since I encountered a piece this dense. Perhaps it wasn't the best idea to start this p&f alone in the summer -- it was all too tempting, though.

With that in mind -- making active use of your invitation to ask more coupled with absence of a teacher until October --, I do have a couple of questions about this fugue. Mainly related to structure. Here they are, and if any of them spark an interest to answer, I'll be glad:

• The fugue has some things from the prelude, which is nice. On the other hand, if one looks to response to countersubject in bars 7-14, I wonder where that shape came from. Why does the response take that particular shape other than Shostakovich's fancy? Now same applies for bars 14-19 until the subject comes back.
  
• In bars 64-65, there's a bit that goes g-f♯-g-g♯-a. Am I imagining things, or is it a version of a fragment of the aforementioned response in bars 7-14?
• Now, about the augmented bits -- particularly the ones on 102 forth, but this applies to the ones from 90 too -- how are they executed? That is, there are these chords going on, and they get pretty low starting at 102 which means they'll devour the countersubject that is going on above (slightly reinforced as it comes with D). There's no instructions left apart from ff and marcatissimo at the onset -- but I do need to distinguish those things. If one just goes equal ff and equal marcatissimo on those octaves and the line in the right hand, the countersubject would be barely heard if at all (no?).
• So in bars 116-117 is a straightforward quote from the prelude, that's all neat. The quote in 225-6 is not so straightforward. No doubt, there are least three occasions on which the a-d octaves appear in the prelude. At the same time, there are these double thirds shaped d-f above. Now, these never appeared in the prelude, not with d flat anyway. And when they did appear with d natural, the context was different, they didn't repeat and so on. So what are they doing there, those double thirds which are neither a straightforward quote from the prelude nor a thing of the fugue (the fugue isn't big on repeating double thirds)?
  
• Now, in terms of that a-d octave thing in 225-6. There were indeed three cases in the prelude where they appeared, two are instances of the same, just repetition of the closure of the first part. However, there is only one occasion on which a-d octaves appear with a rest in front of them, and it's in the very last measures of the prelude. Is it significant, then, that the quote from the prelude consisting of a-d octaves is preceded by a rather significant rest in the fugue? (The entirety of 224 and most of 225.) It is also odd that a rest precedes this quote, but does not precede the quote from the same place in the prelude in fugue's 233-34.
• From 230s on, there is more and more prelude stuff, various (why various?) cadences, so why is it that there is more and more of it? There's a general pattern of ramping things up and augmenting everything more and more until the end -- which serves what harmonic purpose, if any? Perhaps it's just DSCH's style.
• In 272-275, he starts the subject and breaks it with a cadence -- and is it to create this sense of interruption that he doesn't continue the unaugmented subject after the first interruption, but starts anew and breaks it off again? And is it unaugmented to reinforce that interruption? On the other hand, it would seem a more naturally-interruptive environment to have the slower (so "weaker"?) augmented opening of the subject interrupted by sfz-like cadences.
• Lastly, he oscillates a lot in the fugue between Gb and Bb, this is particularly clear I guess in the 263-270's line above the subject being brought back and down. Does this have much to do with Gb and Bb being submediant and subdominant for Db? And in 266 and 277 we see Aa and F which just accidentally happen to be dominant and mediant, I reckon. [\li]
  

I listened, I think, to all of the existing recordings of this prelude/fugue -- too bad DSCH didn't record it, but perhaps Mark Mazullo's right in his book on these preludes that it was too difficult for him to play given his rapidly deteriorating hand. Everyone has different interpretations of the fugue, it seems -- some separate cadences at the end dynamically, shifting the fugue to f while cadences are at ff; some don't. It's ad lib pretty much. The best version I heard I think was, oddly enough, not by Nikolayeva in the 1960s but by Keigo Mukawa at last year's Queen Elizabeth competition. I think there are some inconsistencies in terms of rhythm in his prelude -- some things go faster and some go slower, but I was really taken by his commitment and attention to detail there. Such a wonderful rendition. Nikolayeva's 1980s recordings are not very good in terms of hearing elements of the fugue distinctly.

Regardless, thanks again for the last reply on accidentals, that was helpful!