NOTATIO

The following example was pointed out by Heinrich Schenker in his Beethoven’s Last Piano Sonatas vol. 1: op. 109 translated by John Rothgeb (Oxford University Press 2015). Pages 50-51

The example comes from the second movement. The following explanation is based on my understanding of Schenker’s more succinct comments.

Note the strange downward direction of the stems in the tenor voice starting at X. At Y, the tenor voice stems resume normal direction: Beethoven is pointing out the path of the bass line C-D-E-F#-G#-A-B-C-D-D#-E-F#-G-F# shown by the red arrows in the example above.
This was necessary because the tenor voice crosses under the bass line as shown by the arrows in the following example: Beethoven uses voice crossing to mitigate the upcoming downward leap of a seventh A-B at Y in the first example. All of this was forced by the very long upward rising bass line and the outer voices drawing too close together at m. 87 to allow for middle voices to move freely.

Beethoven may have been particularly concerned about the stem direction in this case, because normal stem direction completely disguises the movement of the controlling bass line, yet the voice leading appears correct. Despite this, the first edition did not follow Beethoven’s notation and ironically, Schenker himself could not prevent the engraver from engraving this in the normal way in his own edition! At Z in the first example, the bass line continues with down stems as was often Beethoven’s habit in situations where a tenor line is present in the upper staff, or even where it is tacitly understood. The latter became more frequent as he explored the new expanded outer reaches of the piano keyboard and the inner parts had to be left to the listener’s imagination. And the soprano voice was sometimes given similar upward stemming in cases where an alto or other voice is understood but not actually present. Unfortunately, this meaningful notation, which causes a player to expand their view of the texture to include understood voices, was not preserved in the first edition or Schenker’s edition.

Continuing from the previous post.

Here is an example of Beethoven’s use of stemming to show both present and absent voices:

Points of interest:

1 The middle voice enters normally with down stems.
2 But the middle voice stems remain down as we await the arrival of the upper voice. The stems remain down in the bass part until m. 47 for consistency.
3 Writing the lower notes of the octaves on the lower staff forces the stems up for a moment; a compromise.
4 But the stems immediately revert to down as soon as possible.
5 Finally the upper voice enters. Upward stems continue on to show that there is missing material below.
6 The lowest voice in a sense ends here and re-enters on the same pitch at 8.
7 The middle part continues on with down stems as before and because it must now also function to replace the missing bass part. The “bass voice” notes missing at the eighth rests in the middle part are found in the upper voice. (Shown by chord names and arrows.)
8 The bass part reenters now with up stems to distinguish itself from the middle voice.
9 Normal stem direction resumes.

Continuing from the previous post.

Here is the same passage shown above from the later manuscript of the first movement of op. 111.

In the earlier manuscript of this movement Beethoven had written the octaves with all the stems up; but, as Schenker points out in vol. 3 of Beethoven's Last Piano Sonatas, in the margin of this version Beethoven wrote "NB Stem the octaves down" which is what he does here in the later version:
Note that at X, Beethoven writes the first note with stems down, which creates a very awkward centered beam to both write and engrave (and which I therefore placed in a footnote in my edition.) But it shows the lengths he was willing to go to continue the downward stem direction as long as possible! Stem direction is clearly no small matter to Beethoven. Unfortunately, none of this made its way into the first editions, or into Schenker's edition.

Continuing from the previous post.

Beethoven's copyist took the composer's remark in the first manuscript about down-stemed octaves (see above) very seriously and wrote the following at X. Apparently he took the remark to pertain from X on; thus the up-stemmed octaves in the first measure of the example. Beethoven realized the engraving difficulties at X and chose the centered beam version shown above. Neither proved engraveable.

Continued from the previous post.

Schenker points out another wonderful case of meaningful stem direction in the Arietta theme from the second movement of Beethoven’s Sonata op. 111. At * the droning E in the ("second alto") voice drops out until it returns at the end of m. 12. Thus the soprano (and alto 1) stems are turned up to show the missing lower voice. This is unfortunately not the way it is engraved in most editions.
But Schenker doesn’t discuss the interesting cases at ** and ***.

In measure 8a the tenor voice continues from the previous measure and the harmony remains a V in root position with the bass voice (the low G in m. 7) held through conceptually. But in 8b the V harmony resolves to a I on the very last sixteen note as shown in the example. Thus, what was the tenor voice expressing a G chord over the low G suddenly becomes the bass voice under a C chord. To show that the next note, the E at ** is also the bass voice (and actually the root of an E major triad acting as a dominant) Beethoven stems it upward just like the C before it even though the bass voice will be stemmed downward in the next measure! He felt he no other choice.

But at *** the bass voice before the E is down-stemmed (to show the missing tenor voice above), so there is no issue and Beethoven could stem the E downward to match!

I'm now hopelessly into the rabbit hole!

I've copied your excerpt from Beethoven 109 into Dorico and played a bit with the voicing. Here are my notes/questions on this: b 87
if the B is the tenor voice, why is there a rest in the left-hand, below the bass note?
Wouldn't it make sense that the B was still the alto voice and the rest and lower B in beat 2 were tenor?

bb 87–88
LH: keeping B-A-C upstem allows this to be understood as tenor voice, no need to put it "wrongly" downstem.

b 91
what now? The D-F natural are bass line and the lowest note of the right-hand are tenor, correct?

bb 92–93
the Schenker doesn't have the cautionary F-sharp here, right?

bb 93–96
would anyone interpret this as anything but the bass line with the correct stem direction?
At this point, one could bring the B-A dotted halves of 93-4 cross-staff below to show that it is the tenor voice?

Would this make sense as a voicing reading, including the last omitted notes in the tenor? It seems I cannot attach the Dorico file here.

Great questions, Neera. Thanks so much!

NeeraWM wrote: ↑28 May 2025, 08:56 b 87
if the B is the tenor voice, why is there a rest in the left-hand, below the bass note?

Perhaps to keep the rest and the next note together. Also see below.

NeeraWM wrote: ↑28 May 2025, 08:56 Wouldn't it make sense that the B was still the alto voice and the rest and lower B in beat 2 were tenor?

Technically you are right. The B is definitely in the alto voice, but I hear the previous tenor A leading to the same B and doubling the alto despite the rest below, which might be thought of more as a place-holder to show where the tenor voice enters again. And again, the voices in a keyboard piece are not notated strictly etc. etc.

NeeraWM wrote: ↑28 May 2025, 08:56 bb 87–88
LH: keeping B-A-C upstem allows this to be understood as tenor voice, no need to put it "wrongly" downstem.

I agree, and had wondered the same. But perhaps Beethoven is thinking of the tenor part as a kind of "replacement" bass at this point. As I mentioned in the first post, the voice crossing mitigates the jump downward of a seventh that the bass is forced to make at this point.

NeeraWM wrote: ↑28 May 2025, 08:56 b 91
what now? The D-F natural are bass line and the lowest note of the right-hand are tenor, correct?

Correct.

NeeraWM wrote: ↑28 May 2025, 08:56bb 92–93
the Schenker doesn't have the cautionary F-sharp here, right?

Schenker has one and so has Beethoven, obviously. The upper version is mine. I am the guilty party who omitted the cautionary erroneously.

NeeraWM wrote: ↑28 May 2025, 08:56 bb 93–96
would anyone interpret this as anything but the bass line with the correct stem direction?
At this point, one could bring the B-A dotted halves of 93-4 cross-staff below to show that it is the tenor voice?

It's not that the bass needs identification, but that the notation is saying that there is something missing above.

NeeraWM wrote: ↑28 May 2025, 08:56 Would this make sense as a voicing reading, including the last omitted notes in the tenor?

If you mean: is this the movement of the voices?, I think you are correct except that in m. 92 the C-F# dotted quarters are the alto not tenor voice which eventually resolves to the E in m. 95 doubling the soprano. Then it evaporates (or is possibly understood as holding through the measure and moving next to an imaginary C# in m. 96.) So the lowest notes in the upper staff are all in the tenor voice.

If you mean: why didn't Beethoven write it split between the staves like this? then possibly because it doesn't use enough ledger line to justify splitting it.

I also wanted to respond to your comment regarding the op. 111 stemming from the thread on Debussy's Suite Bergamasque:

NeeraWM wrote: ↑27 May 2025, 19:32 I cannot say if it is only the rules, but to me having the stems up without something else causing it is highly disturbing and would not help my reading or understanding of the melody or of the voicing. But hey, plenty of composers wrote every stem to the left of the notehead until not so much ago, so ... at least when it comes to handwriting, it is very personal, like the stroke of a painter, and needs to be respected.
When it comes to final engraving, though, I would think it at least odd to see that stemming in Beethoven's 111.

The Schenker edition does in fact stem these measures exactly like Beethoven did in his manuscript:
One can think of the notation as showing that the alto E as not really missing, but only momentarily omitted to avoid an unnecessary thickening of the texture. The doubling of the droning E's an octave lower in the left hand creates the illusion that the alto E's are also still being played. Beethoven had a wonderful sense of piano sonority and omits any tones that can be implied. Brahms is supposed to have said that as far as he was concerned Beethoven was the greatest composer for the piano because he could imply what other composers had to actually write in. This makes his piano music sound full and orchestral, while asking pianists to play only a minimum number of notes.

*Much to learn still I have* would a wise master say!
In this last example it bothers somewhat less because the notes are still within the staff. When I saw Debussy’s Suite (or Ravel in several points) showing outward pointing notes from the 5th line up without neither rest not anything else below it I found it quite disturbing.
But again, there are certain quirks about cello notation that make no sense rule-wise, but look better. For example, when we have a single low note which would require up-stemming, we prefer down-stem. In this crude example, beats 1&3 are correct, beats 2&4 are what cello literature quite consistently uses. So, what we really miss, and your analytical work is of outstanding help in this, is a true idiomatic notation exception list.
Let’s not start on string harmonics, shall we! :-D

NeeraWM wrote: ↑29 May 2025, 07:12 *Much to learn still I have* would a wise master say!

Don't we all.

Regarding stem direction "rules" regarding stem direction for beamed groups, I have always followed the majority wins rule with the exceptions noted by Gould on p. 24. So in your example, the second and third (to avoid the three long stems) of your groups would be the way I would engrave them in a piano piece, all things being equal, which is often not the case. So, in fact, all four versions would have their place depending on the situation.

A book giving examples of exceptional cases would certainly be a great contribution, but not completely solve the real "problem", which is that rules can't take account of all the different situations that have and will arise. Engraving rules consider the music as a series of small slices, stuck together to form a whole, much like traditional harmony. But real music is not like that. It is a whole that can be viewed at different levels of structure much like viewing a complete specimen at different levels of magnification. All the parts interact in complex ways to form a whole and that has to be taken into account for rules to have real validity.