Warning: I know very little music theory, or even proper notation names.
Let’s take Rachmaninoff’s prelude in C sharp minor as an example. As the name implies, the piece is in C sharp minor, so the key signature has F sharp. What happens if there is an F sharp accidental in a measure? For example, in the third measure has an F double sharp on the third chord, followed by an F sharp later. Does the double sharp apply to the ‘base’ F without considering the key signature, in which case the note would be a G? Or does the double sharp mean that the note is two semitones higher than F sharp, in which case it would be a G sharp?
Similarly, the fifth chord has an F sharp accidental. Does the F sharp accidental operate (I like mathematics) on the F sharp due to the key signature, or does it operate on the base F? Also, does this F sharp accidental apply to the F on the last chord of this measure?
The sharp accidental never “adds a sharp” to one already indicated by the key signature - it sounds like from what you’re talking about it’s being used to “cancel out” something like a natural sign or double sharp applied to that note earlier in the measure, and letting you know that it and all subsequent F’s will be sharped as per the key signature.
It would still be read as an F double-sharp, i.e., a “G”.
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Similarly, the fifth chord has an F sharp accidental. Does the F sharp accidental operate (I like mathematics) on the F sharp due to the key signature, or does it operate on the base F? Also, does this F sharp accidental apply to the F on the last chord of this measure?
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That F# should be played as an F#. Yes, that F# carries over to the next chord. Accidentals “reset” at the bar.
It might be worth pointing out that a great many conventions are designed not only to conform to music-theoretic ideals, but simply for readability. All looks right above, so the question’s answered, but it’s an interesting dialectic at play between the needs of the performer and the theoretically correct spelling of certain chromatic tones.
There are also courtesy accidentals, where the sharp (or flat) is shown just because people might be inclined to play the wrong note. Sometimes these are in parentheses, other times they are not.
As stated. an extra sharp sign never sharps an already sharp note. The sharp sign does not mean “raise the note a half step” but merely “play the sharp version of this note.”
Readability would be my guess. The chord in question also contains an A with a sharp accidental and the key signature calls for G-sharp, so marking the note as a G would require a natural accidental and would really cram up the first line and space.
I think it’s because the G in C#m is sharped. I guess they could have used the natural symbol on the G, but the other notes in the line may make that unworkable.
Consider the key of G# minor. It has five sharps, and is the relative minor of B Major. In order to have a Major Dominant chord, the chord would have to be written as D#, Fx (double sharp) and A#. If you spelled that chord as D#, G natural and A#, you would not have a major third, you would have a diminished fourth. In sight reading, this is confusing, as it looks like a sus4 chord built on D# (and, in fact, it would not be at all uncommon to have a chord of D#, G# and A# that then resolves to D#, Fx and A#).
Yes, enharmonically, Fx and G natural are the same pitch, just as ‘F’, ‘GH’ and ‘PH’ are graphemes used to represent the unvoiced labio-dental fricative in speech. If you go around writing the word ‘fish’ as ‘*phish’ or ‘*ghish’ or ‘*ghoti’, it wouldn’t be clear to the person reading it.
I recently finished performing a piece where the composer had written long passages in Eb minor by using the key signature for Eb Major, and using F# instead of Gb, and using B natural instead of Cb. It was horrible to sight read, and I had to re-write most of the part before I could trust myself to get it right in performance.
I truly don’t know. All I can say is that she’s a composer who doesn’t think harmonically so much as she thinks of monodic lines that collide and create harmony in a rather co-incidental way. Her music was nowhere near as complex as she thought it was, and it drove her nuts to have me sit with her and reduce all the harmonies to simple chord descriptions. (“Oh, that’s a Bb minor 9. Oh, that’s a DMaj7#5 over a G pedal. (F*ck me, that was one ugly son of a bitch of a chord.) Oh, that’s gm/Ab.”) She seemed to think that she had been discovering harmonies that no-one else would ever have thought of.
I jokingly said to her that she had obviously bought the cheap version of Sib7, and that we should all chip in and buy her the Gb and Cb that she seemed to be missing. By the end, I don’t think she had much of a sense of humour left about her writing, but then, she hadn’t been the poor bastard fishing for notes and trying to memorize this stuff.
To build on Le Ministre’s post #10, the reason for double sharps and other oddities is to make the pitch names match harmonic theory.
A triad with the root of C must be spelled C-E-G no matter what flavor it is, but the E-G part might be modified with sharps or flats. Therefore, a minor triad must be C E-flat G, not C D-sharp G, since there is no “D” of any kind in a C triad.
As a side note, I wrote a music notation computer program display ages ago. I stored each pitch as an absolute number, then decided what to display depending on the key sig. Pitch #34 might be D sharp in one key and E flat in another. The computer didn’t care what you called it, and would play the same pitch thru the speakers either way, of course.