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Would an orchestral string player use an open E string to play any note in a major scale of F♭?

Is it possible to play a scale of F♭ major on a modern pianoforte accurately?

Which is highest in pitch; the middle E♭ in a C minor chord, or the middle D♯ of the penultimate chord of a perfect cadence in E major, played by the same player in a string quartet?

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    There's nothing particularly exotic about an Fb major chord as the Neapolitan chord in Eb major or minor. J S Bach wrote a nice "symmetrical" example in the "48", where a D# minor prelude uses a prominent E# major chord in a cadence, and the following Eb minor fugue uses Fb major in the same way. But of course that was not written for string quartet. – user19146 Jul 3 '18 at 19:01
  • There is no scale called Fb Major, there is E Major though. – Neil Meyer Jul 4 '18 at 10:19
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One of my composition teachers explained that string players will play in the direction of the notes. Heading toward higher pitches, they will play slightly sharper. Heading toward lower pitches, they will play slightly flatter. He made it sound like a function of the physical aspects of playing. The hand naturally pulls in the direction of which ever end of the fingerboard the player is heading enough to make just a little difference in the pitch.

He used this while giving advice about writing, especially in heavily chromatic or non-tonal music, where the notes do not necessarily have a strict function in the key. He said to write sharps when heading upwards in the music and flats when heading down, instead of using standard key signatures.

So, in short, in answer to the OP's last question, the Eb in C minor would probably be played slightly flatter than the D# in E major. For singers, I'm not sure, but I would guess that since sharps communicate raising a pitch, singers will subconsciously sing slightly sharper when seeing a sharp, especially if unaccompanied. I would wonder if the same is true for any instrument that can make slight changes to pitch using embouchure.

When it comes to pitch, the question of "what is the music doing?" is just as important as "what note is written?"

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    Although it's true that rising leading-notes may be played a bit on the high edge, this does not mean E♭ < D♯ etc. is a good rule of thumb. This only applies for dissonant notes prior to resolution. For consonant notes of tonic chord, it's usually the other way around, because a sharp note is more likely a major third and JI major thirds are narrower than in 12edo. I'd say a better rule of thumb is “sharps are a bit flatter than the next note flattened, unless they anticipate a resolution upwards”. – leftaroundabout Jul 4 '18 at 13:15
  • @leftaroundabout, can you address what my teacher said about non-tonal music? I understand what you are saying in regards to tonal music, but how would that apply to notes that are not consonant or not leading to resolution? – Heather S. Jul 4 '18 at 14:38
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    for most non-tonal music, 12edo is the “gold standard”. Of course string players will still deviate from it a bit in practice, but I don't think there is one “correct way” of doing that. It may be true that they tend to play rising passages sharp out of habit with high leading tones, but that about it being a “function of the physical aspects of playing” is questionable IMO. If there is such an effect, then it should be practice-purged out lest it come in in places where the sharpening is musically inappropriate. – leftaroundabout Jul 4 '18 at 14:58
  • @leftaroundabout, it is possible that I misunderstood my teacher as to the reason string players might raise or lower a pitch just slightly. – Heather S. Jul 4 '18 at 16:03
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An orchestral string player probably wouldn't be playing open strings anywhere, unless directed to.

Whilst Fb and E are enharmonically the same, on 12edo properly tuned instruments, and here we'll assume the piano is tuned thus - which is a slight fallacy - an E note in one key will most likely not be played at exactly the same frequency/pitch as Fb in a different key. And you're hardly going to find a piece with both notes featuring in different places.

EDIT: comparing 12edo with just temperament (which often sounds more 'musical', Eb, as a minor third of C minor, is higher in JI, whereas D#, as major third of B major, is lower in JI than in 12edo. So, yes there will be a significant difference in the pitch, depending which key one is playing in. Obviously only for instruments which can (and do) play in JI. Which I think is the nub of your question.

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    Yes, Tim. I agree. I cannot speak for an orchestral string player, but if I were making an equivalent choral contribution, I would generally expect to sing a sharp note fractionally higher than its enharmonic equivalent, particularly if it happens to be the major 3rd, 6th or 7th degree. – Douglas Jones Jul 3 '18 at 17:45
  • Although teorethically correct, most performers will not be thinking about this, and unless they have the gift/curse of absolute pitch, they will not even notice the difference. – awe Jul 4 '18 at 11:36
  • @awe - true, most players won't even think about it, but it'll happen, to keep the music 'in tune'. They maybe haven't even been aware of it, but it still happens. Choirs are (in)famous for this too. – Tim Jul 4 '18 at 13:53
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As the other answers said already, string players generally avoid playing open strings at all, except for old music in historically informed performance. That's not a hard rule though. If a fast passage can be made easier by playing some of the less emphasized notes on open strings, then I don't think many players would have qualms doing so (those notes just need to be bowed a bit extra carefully not to stick out). In fast passages, especially played by a whole string section, pitch isn't so clearly discernible anyway. And for a passage in something as far out as F♭, the players would probably not have much motivation thinking too much about the mess of flat-signs and fine-intonation details. Most would probably just mentally translate “F♭ = E” at that point, and might, again, use the open string if that makes sense.

Things look differently for notes that are long enough for fine-intonation though. Orchestral players do intonate notes differently depending on context, even if they would be the same on piano. General statements as to whether a flattened note is higher or lower than the sharpened enharmonic are problematic though, because the factors needed to decide are also dependent on the environment. The crucial decision is whether you construct a note from Pythagorean or Ptolemaic tuning. I discussed it somewhat extensively in this answer.

To adress the concrete question

Which is highest in pitch; the middle E♭ in a C minor chord, or the middle D♯ of the penultimate chord of a perfect cadence in E major, played by the same player in a string quartet?

This depends on the interpretation. For both of these notes there are reasons to play them higher than the E♭ on a 12edo piano:

  • E♭ in a C-minor chord has the JI ratio of 6:5 to the fundamental, which is about 16ct higher than three 12edo half-steps above C.
  • D♯ in the 7 of E-major is a leading tone that wants to resolve up. The player may emphasise this effect by intonating the note higher than it would be if the chord were meant as a stable consonance. How much higher isn't really defined, this depends on how much “pain” the player wants to put in the note.

I suspect a first violinist or cellist might play the D♯ a bit higher that the E♭, a 2nd violinist or violist would rather do it the other way around. But more likely, it would just be different for every performance.

  • I like this answer. It includes some unfamiliar terminology which I will have to research. For now I am siding with the 1st violinist and 'cellist! – Douglas Jones Jul 4 '18 at 14:07
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Fb is the same note as E. Although there may be reasons to notate one or the other from a music theory perspective, the notes sound identical. A pianist playing an Fb major scale plays the same notes as one playing an E major scale.

Likewise, Eb and D# are the same note and have the same pitch.

  • Of course! But would any of the notes reproduced by the piano be correct when compared with the equivalent pitches performed by a string orchestra or an unaccompanied choir? – Douglas Jones Jul 3 '18 at 17:34
  • This is half an answer. Let's have the rest! – Tim Jul 3 '18 at 17:35
  • I thought of this question after trying to accompany John Rutter's setting of 'Afton Water' from A Sprig of Thyme during a rehearsal yesterday. I wondered whether the choir would have sung it differently if Rutter had set it in F sharp rather than G flat. The piano part ought to sound the same either way, though I am not sure which would have been easier to sight read. I think Rutter chose his keys carefully for good reasons. – Douglas Jones Jul 3 '18 at 18:00
  • @DouglasJones I think what makes it easier to sight read has more to do with which keys the musicians are most familiar with. Orchestra compositions are often written in flat keys, so they are generally more familiar with seing flats. Althoug in the wind orchestra I play in, our director has arranged a lot of pieces that are rock/pop songs, which are often in sharp keys (and he often do not transpose it because we will perform with a vocal artist that would often like to sing in original key). In the beginning it was quite challenging, but now we are more used to seeing a lot of sharps. – awe Jul 4 '18 at 11:49
  • Very true. A few years ago I founded a children's training orchestra aimed at beginners. All the parts need to be written for each individual player. Nearly every piece ended up in C or F major! It seems nobody publishes really good arrangements for very inexperienced players good enough to enable, inspire and develop such a group of musicians. – Douglas Jones Jul 4 '18 at 13:51
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Question 1: Yes, with the giant caveat that string players rarely play open notes.

Question 2: The short answer to this question is yes. The long answer to this question is that it depends very much on what you mean by "accurately".

Question 3: By modern performance conventions they absolutely should be the same pitch. Perhaps in practice this will not always be the case because of the more distinct consequences of confusing a minor third with a major third, but as far as I know no definitive answer exists to the question "do string players play leading tones with more accurate intonation than they do thirds".

  • Thank you for taking the time to answer, Fugu. I only chose string players because, like singers, they have infinite variation of pitch due to being fretless. It is possible to add brilliance to the overall effect of the sound by sharpening some intervals. I wasn't implying that string players play certain intervals more accurately than others. – Douglas Jones Jul 3 '18 at 18:21
  • @DouglasJones But that is effectively the question that you're asking, given the knowledge that Eb and D# are enharmonic and the only distinction you drive between them is that in one case, it's the minor third and in the other it's the leading tone. – Fugu Jul 3 '18 at 18:36

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