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Author Topic: Bach's E-minor Gigue  (Read 1060 times)
increpatio
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« Reply #30 on: 15:41:47, 23-11-2007 »

This is what good old Bach wrote with his own hand...
To confuse the issue yet further*, am I right in seeing 'triplet' numeric indicators under the three beamed groups in the bar 2 LH, Baz? Wink

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(although admittedly the issue in question is only 'how many quavers fit into a minim?', to which there can only be one answer, whatever the notation; the deeper question of what to do with the pairs of crotchets remains unaddressed)


For sure t_i_n. But since when have 2 crotchets subdivided into 3 triplet quavers?

Baz

Well I've always thought that crotchet triplets, when the intended effect is something flowing ("quavery") always look a bit queer to my eye.
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time_is_now
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« Reply #31 on: 15:47:05, 23-11-2007 »

This is what good old Bach wrote with his own hand...
To confuse the issue yet further*, am I right in seeing 'triplet' numeric indicators under the three beamed groups in the bar 2 LH, Baz? Wink

_______________________
(although admittedly the issue in question is only 'how many quavers fit into a minim?', to which there can only be one answer, whatever the notation; the deeper question of what to do with the pairs of crotchets remains unaddressed)


For sure t_i_n. But since when have 2 crotchets subdivided into 3 triplet quavers?
Exactly: that's what I meant about 'remain[ing] unaddressed'!

So, I'm dying to know: how has this question been addressed by scholars performers and exegetes down the generations? Or did a number of intermediary generations pass in blithe ignorance of Bach's peculiar original notation?
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The city is a process which always veers away from the form envisaged and desired, ... whose revenge upon its architects and planners undoes every dream of mastery. It is [also] one of the sites where Dasein is assigned the impossible task of putting right what can never be put right. - Rob Lapsley
Baz
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« Reply #32 on: 15:57:28, 23-11-2007 »

This is what good old Bach wrote with his own hand...
To confuse the issue yet further*, am I right in seeing 'triplet' numeric indicators under the three beamed groups in the bar 2 LH, Baz? Wink

_______________________
(although admittedly the issue in question is only 'how many quavers fit into a minim?', to which there can only be one answer, whatever the notation; the deeper question of what to do with the pairs of crotchets remains unaddressed)


For sure t_i_n. But since when have 2 crotchets subdivided into 3 triplet quavers?
Exactly: that's what I meant about 'remain[ing] unaddressed'!

So, I'm dying to know: how has this question been addressed by scholars performers and exegetes down the generations? Or did a number of intermediary generations pass in blithe ignorance of Bach's peculiar original notation?

Well there are two schools of thought: a) some play the crotchet pairs as "crotchet-quaver" (to fit the surrounding triplet quavers), while b) others (e.g. Peter Hurford inter alia) play them as equal notes (giving a 2-against-3 rhythm).

The problem with a) is this: if Bach intended the crotchet pairs to be unequal, why did he not just write them as crotchet-quavers?

There seems to be an attempt here (in my view) for clarification of a 2-against-3 intent. Even though the result is "incorrect" notation, perhaps this clarification of intent is a case of achievement by fair means or foul.

Baz
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increpatio
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« Reply #33 on: 16:06:35, 23-11-2007 »

The problem with a) is this: if Bach intended the crotchet pairs to be unequal, why did he not just write them as crotchet-quavers?
There's a similar problem with the other argument as well, though.

*cough* feeling a little bit talked-over here...
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Baz
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« Reply #34 on: 16:16:37, 23-11-2007 »

The problem with a) is this: if Bach intended the crotchet pairs to be unequal, why did he not just write them as crotchet-quavers?
There's a similar problem with the other argument as well, though.

*cough* feeling a little bit talked-over here...

? <baited-breath emoticon>

Baz  Shocked
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time_is_now
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« Reply #35 on: 16:22:14, 23-11-2007 »

Well there are two schools of thought: a) some play the crotchet pairs as "crotchet-quaver" (to fit the surrounding triplet quavers), while b) others (e.g. Peter Hurford inter alia) play them as equal notes (giving a 2-against-3 rhythm).
And what did editors do with it in the dark days of the 19th and earlier 20th centuries? Did they convey to their readers the fascinating nature of the original notation? If not (as I suppose they may not have done), were they unanimous in the solution they adopted?

And was that solution the one later adopted by Hurford or does his (Baz-approved, I take it) solution represent a break with previous thought on the matter?
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The city is a process which always veers away from the form envisaged and desired, ... whose revenge upon its architects and planners undoes every dream of mastery. It is [also] one of the sites where Dasein is assigned the impossible task of putting right what can never be put right. - Rob Lapsley
martle
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« Reply #36 on: 16:25:19, 23-11-2007 »

It's obvious to me that the groups of 4 semiquavers are played as straight semis, often against the notated triplet quavers.

Great discussion!

Baz, the groups of 4 semis never actually do appear 'against' the triplet quavers. Although the dotted quaver/semi rhythm does further on.
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Baz
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« Reply #37 on: 16:33:19, 23-11-2007 »

It's obvious to me that the groups of 4 semiquavers are played as straight semis, often against the notated triplet quavers.

Great discussion!

Baz, the groups of 4 semis never actually do appear 'against' the triplet quavers. Although the dotted quaver/semi rhythm does further on.

Your clinical correctness is admirable (I've just checked!) and I had in mind the dotted-quaver/semi patterns (which, in each case, can become triplets). Thanks martle.

Baz
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C Dish
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« Reply #38 on: 16:39:18, 23-11-2007 »

oy -- so is it possible that a notated 6/16 is meant to sound like a real 6/8, thus making one fourth of the notated bar equivalent to the basic metric unit of a gigue?

Then the usual lilting, swing-like gigue rhythm of crotchet-quaver crotchet-quaver (here quaver-semi, quaver-semi) doesn't appear in the subject. It is only when the countersubject appears that ye typical gigue rhythm unfolds (ie antiphonally btw voices). Is there a precedent in Bach for such a maneuver?

I am now disregarding the truly odd stuff in bar 9 and 10 until this question has been addressed.
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inert fig here
rauschwerk
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« Reply #39 on: 16:45:04, 23-11-2007 »

I quote from the article on Rhythm in the Oxford Bach Companion:-

Alignment or resolution of notated duplets with simultaneously notated triplets is another recurring situation in Bach's music which is sometimes heatedly discussed by scholars (see Fuller, Helling, and Schwandt). Lacking definitive rules, each situation must be dealt with individually for an appropriate musical result. Often the short note of a dotted duple figure sounds best when it coincides with the last note of a triplet, as in the Corrente of the keyboard Partita in B flat major, or the Sarabande of the keyboard Partita in D major. In pieces such as In dulci jubilo BWV608, however, a duplet figure against a triplet enlivens the overall rhythm and sounds well played exactly as written. According to  J F Agricola (Allgemeine deutsche Bibliotek 1769, i. 242-3), Bach taught his pupils to align duplets and triplets only in fast tempos.
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Baz
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« Reply #40 on: 17:04:35, 23-11-2007 »

...In pieces such as In dulci jubilo BWV608, however, a duplet figure against a triplet enlivens the overall rhythm and sounds well played exactly as written. According to  J F Agricola (Allgemeine deutsche Bibliotek 1769, i. 242-3), Bach taught his pupils to align duplets and triplets only in fast tempos.

Interesting info rauschwerk - thanks. However, 3/2 (as in BWV 608) is a fast tempo!

Baz
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Sydney Grew
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« Reply #41 on: 10:31:08, 24-11-2007 »

Some further observations by way of context will perhaps not be go or come amiss.

First let us convey the gist of something we found in the book Tonal Harmony, written for Northern American students by Stefan Kostka and a Lady. Dotted values, they tell us, present a problem where time-signatures are concerned. For example, if there are two beats per bar, and the beat note is a dotted crotchet, what would the time-signature be? 2/4½? 2/4+8? 2/8+8+8? There is no easy solution they say, and the method that survives to-day is the source of much confusion concerning compound beat. Simply stated, a compound time-signature informs the musician of the number of divisions of the beat contained in a bar and of what the division duration is. This means that the upper number of a compound time-signature will be 6, 9, or 12, because two beats times three divisions equals six, three beats times three divisions equals nine, and four beats times three divisions equals twelve. Here are some examples:


These compound time-signatures do not they continue follow the erroneous rule so often learned by the student-musician that "the upper number tells how many beats there are in a bar, and the lower number tells what note gets the beat." Of course there are some pieces in 6/8 for example that really do have six beats to the bar, but such a piece is not really in compound duple. A bar of 6/8 performed in six does not sound like compound duple; instead it sounds like two bars of simple triple, or 3/8. In compound duple the listener must hear two compound beats to the bar not six simple beats. In the same way a slow work notated in 2/4 might be conducted in four, which would seem to the listener to be simple quadruple. In both cases the usual division value has become the beat value.

Eaglefield Hull too is able to make an important contribution. The time he tells us seems at hand when the further requirements of the composer in the sub-divisions of the separate beats may well be deemed to require an improvement of the notation, or an altogether new system of signs, to indicate the various durations of sound. A distinct sign is certainly needed for the third part of a beat, since the use of compound time is often cumbersome, whilst the triplet is but a poor makeshift.

Half-beats against thirds, and quarters against sixths, are sufficiently commonplace he goes on to possess a less ambiguous notation than that at present in use. The composers' practice of marking irregular numbers over the beat hovers so indefinitely between the higher and lower powers that examiners are supplied with a never-failing source of confusing the candidate. The latter is asked to decide a question which the composers themselves have never solved - namely whether a quadruplet in compound time follows the rule of the quintuplet in simple time by being drawn from notes of higher power, as at (a), or lower power, as at (b), and how such practice is reconciled with the writing of the duplet, as at (c), and the Chopin values at (d):

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Baz
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« Reply #42 on: 16:41:59, 24-11-2007 »

...The composers' practice of marking irregular numbers over the beat hovers so indefinitely between the higher and lower powers that examiners are supplied with a never-failing source of confusing the candidate. The latter is asked to decide a question which the composers themselves have never solved - namely whether a quadruplet in compound time follows the rule of the quintuplet in simple time by being drawn from notes of higher power, as at (a), or lower power, as at (b), and how such practice is reconciled with the writing of the duplet, as at (c), and the Chopin values at (d):



All four of the above are correct, both technically and historically. They represent a hangover from Proportional Notation as practised throughout the 14th, 15th and 16th centuries (and simulated in the Baroque era through the continued use of Alla breve notation).

In the 14th and 15th centuries, where a composer wishes to write, say, 4 notes of one denomination instead of 3 notes of the same denomination (i.e. what we would term a "quadruplet") the symbol 4/3 would appear in front of the group. Similarly, if a 3-note group were to be replaced by a 2-note one (of the same denomination) the symbol 2/3 would be expressed in front of the group.

In other words, what we understand as "tuplets" are groups of notes that are to be performed in the time of the standard group of the same denomination that they are replacing. It is, therefore, irrelevant whether or not such groups exist in either compound or simple time.

Looking at the example provided by Mr Grew (above), it can be seen that a) and b) are both entirely correct! In a) it can be observed that 4 crotchets are to be performed in the time of 3 crotchets (that are replaced). In b) however, it can be seen that 4 quavers are to be performed in the time of 6 quavers (that are similarly replaced). In that way, both are entirely correct. The apparent confusion over note-denomination is merely an illusion - tuplets should always appear in the note-denomination that is being replaced.

In c) 2 crotchets are to be played in the time of 3 crotchets; while in d) 4 crotchets are played in the time of 3.

My interest earlier on in Bach's setting of In dulci jubilo was caused by his use of quaver triplets, in which 3 quavers were clearly intended to replace 2 crotchets. This caused me to wonder whether the consistent use of paired crotchets (instead of the equally-available crotchet-quaver pattern) was a notationally-licentious indication to play the crotchets as equal notes - thereby asserting (and clarifying?) an ongoing 3-against-2 rhythm. But then again the quaver triplets are not notationally incorrect either, since here 3 quavers (with a triplet sign) are made to stand in place of 4 quavers!

Baz
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