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What is the point of the notation of say a whole note in the lowest voice with the alto voice using that same note in piano music? The piano can't double the note.

Basically in almost any piece of music by the masters, you find melodic lines that notationally use the same note which can't be played by the instrument.

e.g., C in the alto voice and C in the bass voice at the same time. Sometimes I see them do this melodically: first note is in C in bass and second note, starting later but overlapping with the first, in the alto.

Of course, it makes sense when each voice is is from a different instrument.

Basically, for piano, the composer could have notated it using one voice and a rest in the other in the case of a harmonic unison and it would still sound exact the same(or is there some interpretation for this?)?

So did Bach in his Well-Tempered Clavier do this because he wanted to make the individuals lines clear and not obscure what was going on? Did he do it in hopes that it would be played by other things than the piano(a quartet for the fugues)? or what?

E.g., you can find examples in in bar 9, 21, 24 in the fugue 1 in C. Each case is different.

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    This only makes sense when the voices are from different instruments (and/or human voices). – Shevliaskovic Mar 13 '16 at 0:15
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    Yup, BWV 846, WTC I-1, @MatthewRead. The unisons are definitely there in the Bach-Gesellschaft Ausgabe. OP is calling them doublings when he means unisons. We've actually covered this before. Check here: music.stackexchange.com/questions/32898/…? – user16935 Mar 13 '16 at 3:33
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    Bach also wrote a lot of organ music, and it is possible to play the same note at the same time on two separate manuals on the organ, so he might have been prone to having lines that went to unisons and he felt that it still made musical sense on keyboards that can't play unisons. – Todd Wilcox Mar 13 '16 at 4:02
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    Harpsichords als exist in two-manual versions, where it is actually possible to play the same note more than once. – guidot Mar 13 '16 at 11:27
  • @Todd Wilcox, yes, but, in some of these cases, look at which hands have to take the middle voices - the alto and tenor pass between the hands, and that makes it very hard at times to find a place to cleanly separate the voices between manuals. If the descant and alto are in the right hand on one manual, and the tenor and bass are on another, and the tenor needs to be taken by the right hand for a stretch, you are going to have trouble. If the shift coincides with a phrase, well and good. Most of the time it doesn't, though, and the change of registration for a few notes will be noticeable. – user16935 Mar 13 '16 at 15:13
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So did Bach in his Well-Tempered Clavier do this because he wanted to make the individuals lines clear and not obscure what was going on?``

The one-word answer is "yes." For example in bar 9, the bass part ends on the C on beat 3, not on the G before. Also the C in the bass is an 8th-note, while the C in the tenor is only a 16th-note. Writing a 16th-rest in the tenor part instead of the C would give the wrong idea that the tenor part ended one phrase on the D before, and started another phrase on the B after.

In bar 24, you play both the C's in the left hand, and hold the second one (the written 8th-note) for the rest of the bar to represent the remainder of the first one (the written whole-note).

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On any instrument, notes are articulated. On a piano, this includes timing and strength of the attack, and of the release. When playing multiple voices, a common note has to be articulated in a manner consistent with the performance of either voice.

If the voices enter arpeggiated, a common note will enter with the timing of the earlier voice. Its strength will be at least as strong as the louder of both voices. Its release will be in line with the articulation of the voice having the longer release.

As much character from both voice lines that can be accommodated into that single note will be present, and as little as possible contradicting the idea of both voices sounding simultaneously.

To give the player the possibility to play in the best manner consistent with the idea of the piece, the idea needs to be written down.

A score does not have the performance-level precision of a piano roll: that kind of fine-level detail needs to be articulated by the player.

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Basically, for piano, the composer could have notated it using one voice and a rest in the other in the case of a harmonic unison and it would still sound exact the same(or is there some interpretation for this?)?

Possibly he could have, but it's entirely possible that the line receiving the rest would be interpreted differently: perhaps the performer would perform the note before the rest shorter so as to create the impression that the particular line has a break in it, and isn't moving into a unison. A rest implies that the line isn't continuous. That's definitely not the case for any of the lines moving into a unison in WTC I-1.

So did Bach in his Well-Tempered Clavier do this because he wanted to make the individuals lines clear and not obscure what was going on?

As alephzero states, yes. In Bach's case in particular, it was a point of pride that the lines of his fugues made sense individually, to the point where he wrote the Ricercar a 6 of the Musical Offering in score (even though it's eminently playable on a single keyboard).

Did he do it in hopes that it would be played by other things than the piano (a quartet for the fugues)?

Other keyboards than a piano, to be sure (fortepiano still being somewhat uncommon in his time), but the collection is called, after all, Das wohltemperierte Klavier, that is, the well-tempered keyboard. The music had a didactic purpose, and was meant to be studied and played at home using whatever keyboard instrument was at hand, be it harpsichord, spinet, unfretted clavichord, positive organ or fortepiano. The music is idiomatic to keyboards.

By the same token, WTC I & II are really written for single manual keyboards. Fugues that comprise more than 2 voices are normally very difficult to separate between two manuals, because the inner voices tend to wander between the left and right hands at need - for instance, the alto might drop while the descant rises, and thus need to be taken by the left hand briefly.

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