Help with Double Stop Intonation in Andante from Bach A minor Sonata

Edited: June 20, 2019, 7:58 AM · Hi everyone,

I have been encountering some difficulties in double stop intonation while practicing the Andante from Bach's Solo Sonata No. 2 in A minor. For instance, for the opening double stop, I understand that there is a need to narrow the interval since C and E form a major 3rd. However, the question is whether to lower the E or raise the C.

Also, there are subsequent double stops where there is a conflict between maintaining the integrity of 2 independent voices (horizontal-wise) and keeping the purity of the intervals (vertical-wise). One example would be in bar 2, where the B in the accompaniment has to be flat in order to make the 6th interval with the G pure -- yet, since B is the leading note in C major, it should be sharpened.

Any advice would be greatly appreciated!

Replies (37)

June 20, 2019, 6:49 AM · It is mathematically impossible to maintain pure intervals throughout the first line without running into pitch drifts. You just have to fudge things so that things sound both melodically and harmonically convincing. In other words, you just need to make decisions as to which notes you want to play slightly out of tune (with respect to pureness).
Edited: June 20, 2019, 7:17 AM · In the opening double stop, keep the E in its natural position for the most resonance. Give slight priority to the upper voice throughout the piece, the lower voice is just an accompaniment; and Kevin is right about trying to keep pure intervals.
June 20, 2019, 8:15 PM · Thanks Kevin and Theirno for the helpful advice! In other words, the key is to make compromises right?
June 20, 2019, 8:47 PM · 2 words: analysis paralysis.
June 20, 2019, 11:56 PM · @Rocky ?
Edited: June 21, 2019, 1:20 AM · Joel, isn't it salient that the Andante is in C major?
Just play C and E for a few seconds until they sound like a good C major third. Then let the melody lines sing. Don't analyse.
June 21, 2019, 2:15 AM · @Gordon yes I have considered that, but like Thierno pointed out, playing C in tune and E slightly flat could compromise the resonance of the E with the open E string
Edited: June 21, 2019, 6:42 AM · With a two-voice Bach sonata and a double-stopped major third, with the E the main melody note, I'd wonder if resonance was gilding the lily.

Also, since it is preceded by the A minor sarabande (? from memory), the audience might already have had enough resonance on the E string!

Anyway, on a practical note, if you can play the C and the E without touching the E string, you've got longer fingers than I have!

June 21, 2019, 6:50 AM · @Gordon hmm perhaps you have a point.

By the way, do you mean the Grave? There isn't a Sarabande in the A minor sonata

June 21, 2019, 7:15 AM · Yes, whatever comes before - the music is shut away in a box, and my memory is not that good.
June 21, 2019, 8:05 AM · Against C, pure E and F will seem well-separated. Accept!
(Unless we consider the F as a mere appogiatura.)

Pure 5ths and 4ths are vital; we "indulge" in pure 3rds and 6ths whenever we can..

And don't listen to those who don't care!

June 21, 2019, 8:23 AM · @Adrian when you say "Against C", do you mean an in-tune C or a raised one?
June 21, 2019, 10:52 AM · Also, are you referring to the F in bar 2?
Edited: June 21, 2019, 4:35 PM · In-tune C!
And yes!

The open (higher) E must be in tune with an A that is in tune with open D that is in tune with open G..

On my violin, the syntonic comma (a bit over 20 cents) is about 2mm in 1st position: wider than my usual vibrato.

June 21, 2019, 8:23 PM · If it's possible to discern on recordings what the pros do, then what is that? And if it's not possible then maybe it's not all that critical as long as it sounds good.
June 22, 2019, 8:24 AM · Pros vary. But I won't actively split hairs (except in my own practice..)
June 22, 2019, 9:01 PM · @Adrian agreed, professional violinists seem to have different ways of making the compromise between the purity of the interval and keeping the linear integrity of the melodic/bass line
June 22, 2019, 9:03 PM · @Paul, you're right that it's quite difficult to discern through recordings of professionals, but perhaps that is because they're doing it so skilfully that melodic impurities are disguised and alnost indiscernable to the human ear?
June 22, 2019, 10:13 PM · You can do anything you want, as long as it sounds in tune. In theory, since the movement is in C major, we need the tonic and the dominant to be in tune with each other, so raising the C would be problematic because you would have a very wide 4th with the open G. However, if you start with the higher C and then gradually lower the center until bar 4 when you have the open G, you can enjoy the best of both worlds. But this is VERY hard.
Edited: June 27, 2019, 4:03 AM · Suziki's own recordings of his method has sweeter thirds and wider semitones than David Nadien's, who seems to prefer a "Pythagorean" sound.

I prefer Suzuki's, (although Nadien was a much better player..)

June 27, 2019, 4:06 AM · Bruno, I think the in-tune C is more important the the resonance of the open E.
Edited: June 27, 2019, 12:15 PM · If you want to make the deep dive into intonation, here's a great place to start -- Kurt Sassmannshaus explains the different intonation systems and when to use them.

That Bach movement is a superb example of how you have to make compromises. Every violinist will handle the compromises a little differently.

You're right that you have a choice right away with the major third -- IMHO it has to be tuned based on the upper note because that is the melodic line that you have to establish. So you squeeze the third and play the upper line on the low side for the next two measures. Musically this makes sense because it helps give a sotto voce quality which is nice for opening the movement.

However by the third measure you have to transition upward because you are starting to involve open D and G strings and the melody turns from sotto voce to something more brilliant.

By upward obviously I am talking about very subtle difference in intonation, but it is audible.

You can hear it in Hilary Hahn's recording of this movement -- when you listen to the first 4-5 bars closely purely for intonation, the top line seems almost flat. But it sounds beautiful to the listener.

But anyway, the big point here is that unaccompanied Bach always has this tug of war between double stops and chords on the one hand, and these gorgeous melodic lines on the other.

The intonation has to be fluid in order to make it work. This is why violinists get paid the big bucks -- we have this wonderful fretless fingerboard and we can use intonation expressively in ways that many other instruments cannot.

Edited: June 27, 2019, 12:46 PM · Agree with most of the above comments. The "Leading-tone" concept should be left in the harmony text-book. It causes a lot of trouble when applied to intonation. The Bach Unaccompanied book is where advanced players collide with the problem of fine tuning; Pythagorian (aka Melodic, Expressive) vs. Just (aka Chordal, Tartini) tuning. Because of the difference tones (beats= interference tones), The brain is much more sensitive to errors on the double-stops than on a single-note melodic line. C is the tonic, home base for the piece. Don't raise it for that opening chord. Play it a perfect fourth above open G. 1st finger E will then be pulled back a little (1-2 mm?) to get the clean major third (5/4 frequency ratio). Then the 2nd finger F will be a perfect fourth (4/3) with C. The difference between E and F will be the "long" half-step, not the tight half-step you would use if you were playing it as an unaccompanied melodic line. With my fingers, there is a small gap between that E & F. One of the reasons the string instruments do Not have frets (=equal-tempered tuning) is so we can play in tune! Do we have time to think about that math while playing?-No. So let your ear be your guide, and just be aware that some notes will need to be bent sharp or flat.
June 27, 2019, 2:41 PM · Keep in mind some double stops give you more wiggle room than others. Sixths are more forgiving.

Fourths are murderously unforgiving. I'm sure there's a mathematical reason. They have to be perfect or they really sound awful. Sometimes you want to plan your fingerings around the fourths because the fourths have the least flexibility. I always am conscious of them as they approach and try to think about good left hand preparation.

June 28, 2019, 12:11 AM · continued; --Thomas B.-- Yes, the perfect fourths are " murderously unforgiving." The math, the frequency ratios for the perfect intervals, are octave (2/1), P5 (3/2), and P4 (4/3). That is also the inverse of the ratio of the string lengths. Any deviation from that is heard, by the player, as "beats".
June 28, 2019, 7:36 AM · Thanks everyone for the helpful advice!
June 28, 2019, 7:39 AM · "IMHO it has to be tuned based on the upper note because that is the melodic line that you have to establish. So you squeeze the third and play the upper line on the low side for the next two measures."

@Thomas I'm quite confused by this because there seems to be a contradiction. So do you suggest tuning based on the upper note (i.e. an in-tune E) or lowering the upper note (a flattened E)?

June 28, 2019, 8:53 AM · I would recommend trying out the tuning system that Stanley Ritchie lays out in his book "Before the Chinrest" (p.86). He starts by playing a C chord with open G and E, and making sure that these outer strings form a perfect sixth. Then he tunes the A from the fingered E on the D string. Then, using a fingered B on the A string, he tunes the D string to produce a perfect sixth. This results in slightly narrow open string fifths (as they generally are in keyboard temperaments). Well-tempered Bach on the violin!
Edited: June 28, 2019, 9:28 AM · Just dug out my copy. My thoughts:

I don't find any need to raise C's, except in A minor passages in the second half, where intonation is centered round open A & E.

Elsewhere the same E will be played with the fourth finger, lower than the open E.

In bar 8, the open E is at the top of a quick arpeggiated chord.

Edited: June 28, 2019, 10:26 AM · @Guglielmus wow thanks for that! It was really insightful -- never thought of tuning the A and D strings narrower. This is for all Baroque music in general?
June 28, 2019, 10:30 AM · @Adrian that's true...except perhaps on beat 3 of bar 8 the C-E-A chord should be played with the C raised since the E should be in tune with open A?
June 28, 2019, 11:51 AM · Joel, what I meant was you shade the E on the low side to make the third sound right with the c, and continue to shade low for the melody until the third measure when you have to match the open strings. Yes the lower line Cs and Bs have to conform to the upper line in that case.
June 28, 2019, 12:12 PM · Joel, I bar 8 I would not disturb the pedal C; the E & open A in beat 3 will be very brief, maybe arpeggiated, so we won't dwell on that horrid Pythagorean C-E, (nor on a grostequely widened fourth!)

Guglielmus, that willsound near to (very) mean-tone tuning.

June 28, 2019, 6:52 PM · Joel wrote: "This is for all Baroque music in general? ". Ritchie's book is about "Pre-Chinrest" music, so make of that what you will. He does say that when playing with a keyboard he will tune his open strings to match the keyboard's notes (so, almost certainly mostly narrow fifths). Notice how his system immediately solves a lot of the problems that are brought up in numerous comments above. For example, the situation that Adrian brings up here: "the E & open A in beat 3 will be very brief, maybe arpeggiated, so we won't dwell on that horrid Pythagorean C-E (nor on a grostequely widened fourth!)".

Adrian wrote: "that willsound near to (very) mean-tone tuning." Maybe this is a bit of a stretch-- we are only talking about 4 fixed pitch strings here--but yes, pure fifths are sacrificed for the sake of better sixths and thirds. And since we are violinists, we don't have to put up with any wolfs!

June 28, 2019, 8:56 PM · @Thomas ah I see, thanks for the clarification!
June 28, 2019, 8:57 PM · @Adrian that's true, most renditions I hear have this chord (and the previous) arpeggiated and I was wondering why
June 30, 2019, 10:13 AM · In fact Meantone (1/4 comma version) tuning implies tuning E to C, tuning D halfway by ear (hence the name) and distributing the "error" equally amongst the other fifths. Of course the keyboard can start the process on any note....

Guglielmus' suggestion of losing the whole comma on D-A I met in a workshop on a C major Haydn quartet.

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