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I notice in his BWV 565, more well known as Toccata and Fugue in D minor, what looks like a lot of parallel octaves in the fugue. I have studied counterpoint before and every counterpoint resource I find says "Absolutely no parallel 5ths or 8ves between any 2 voices. If you have an octave or a fifth, use stepwise motion that is either contrary or oblique to avoid parallels" or something along those lines.

Here is the video starting at the fugue:

As you can see, right away, the subject is stated in octaves. There are several other moments where the octaves are very obvious. And these, if I'm not mistaken are parallel octaves, the same thing that every counterpoint teacher tells you to absolutely not use. I have been told by several people that these parallel octaves are not the same as the ones you need to avoid because of the specific voices they are in. Um, how does voice arrangement make any difference? Why isn't Bach breaking the rules every time he uses parallel octaves in this fugue? I thought parallel octaves were to always be avoided in Baroque counterpoint and that it is only really once you get to classical era and romantic era counterpoint that you are free to use octaves as much as you would like as long as the whole piece isn't just a string of octaves.

So I can understand the octave theme here in Beethoven's Grosse Fuge:

But why is Bach not breaking the rules of Baroque counterpoint with the parallel octaves in his Toccata and Fugue in D minor?

The counterpoint rules for parallel octaves (and fifths) apply in cases where two or more voices are meant to be heard as independent. Similarly for covered fifths and octaves. (Also for long strings of parallel thirds or sixths, maybe six or more for that matter.) Voices moving in parallel sound like a single voice with doubling or harmonization. These are not wrong unless one needs the independence of these voices. For piano, a single voice is often doubled (usually the bass or soprano or both, rarely inner voices) for emphasis. No independence is implied, it's just a thicker sound.

The only rules about relative motion are in textbooks.

Those rules describe norms or ideals for voice leading in a specific style, but outside of pedagogy there aren't rules. The clearest evidence that these are norms rather than rules is the fact that you can find them in real music of the Baroque and Classical eras.

If you include cases of parallel and direct 5ths/octaves exhibited in harmonic reductions (reducing broken chords and other figuration to block chords) it's not too hard to find example.

It wasn't the norm so you don't find lots of examples. But if keep your eyes open for them (and other so-called rule breaking) you will find them.

You will hear this "there are not rules" but "you broke the rules" stuff all the time. The worst is when it's phrased as "composer X could break the rules, because he was a genius." No. Anyone can do anything they want anytime. You don't need to be a genius. This kind of teaching isn't helpful for explaining the reasons why rules were sometimes followed and sometimes not followed. A more insightful explanation is needed.

Personally, this is what I think is the critical factor: the voice leading rules - which most definitely were taught as a list of prohibitions - were part of the learned style which figured largely with church music. When a composer worked in the learned style - making sacred music or vocal music - their approach was more conservative and "followed the rules." But when the music was secular or insturmental - Galant style would be a contemporary label from that era - composers weren't so scrupulous about voice leading.

This might not apply to this specific Bach example. But my point is just to be aware that the voice leading norms applied to a particular style and musical styles were constantly evolving. Bach used many different styles.

The example you use from BWV565 is not voicing but registration. There are no independent voices having some parallel movement in octaves. Instead there is a melodic line reinforced by octaves. In notation, you'd never give the constituent notes separate stems like you would for separate voices.

Organs have registers that will add pure octaves, pure fifths, pure thirds. They are used for creating a particular sound, not harmony. They don't share the temperament of the organ's tuning and they are not diatonic (when actually playing parallel fifths, you come across B-F and thirds change between major and minor all the time). Adding a fifth is sometimes done in bass voices for sound but rarely elsewhere, and fifths are prone to temperament. But in basically all common temperaments, octaves are pure throughout (stretch tuning on pianos is a different phenomenon). You can actually play them on the organ keyboard for reinforcement with an effect rather similar to pulling them in via registration.

The parallel octaves at the start of BWV565 are in the available handwritten copy (there is no autograph to be found any more I think). I think that part of the rationale found for it these days is that the piece was written with the intent of accommodating comparatively small organs with few registers, possibly as a test piece: the abrupt changes between filigrane single-line high coloratura and full-bodied low chords with pedal bass pose hellish difficulties for the typical air supply systems of older baroque organs: basically you need the kind of equalizing bellows systems Silbermann came up with in order to stop Bach from making his organs look bad. The inertia of a single main bellows will not allow switching from heavy air flow to very little without disgraciously overblowing the small pipes.

But I digress: the main point is that these octaves are not separate voices. They just add to the sound quality of a single coherent voice.

No, Bach didn't break any rules, because there are no rules. What Bach did was write music that people still want to listen to, a few centuries after he wrote it.

When you read a list of "unbreakable rules* in a theory book, ask yourself one simple question: Did the author of that book ever write any music that is regularly performed today?

Of course in a few cases the answer is "yes," but you are probably not getting your information about "unbreakable rules" from the few "theory books" written by people who are well-known as composers - like Rameau, Schoenberg, or Hindemith, to give three examples.

Incidentally, you didn't mention the other gross "rule breaking" in BWV565: the answer in the fugue isn't even in the right key! It's in the subdominant, not the dominant!! Shock horror!!! Didn't Bach even know the dominant of D was A, not G????!!!!

But if you want to see Bach really mess around with the idea that fugues have "rules", look at Variation 10 of the Goldberg Variations. After a conventional start with subject / answer / subject, the rest is mayhem, so far as conventional theory is concerned - but it works fine, as music.

Bach didn't break the rule because this rule can't be applied for these 2 examples and especially not for the unisono passages.

"Absolutely no parallel 5ths or 8ves between any 2 voices. If you have an octave or a fifth, use stepwise motion that is either contrary or oblique to avoid parallels"

If you google this "rule" you get:

No results found for "Absolutely no parallel 5ths or 8ves between any 2 voices. If you have an octave or a fifth, use stepwise motion that is either contrary or oblique to avoid parallels".

Why:

This rule has been developed by theorists for the four part counteroint progression.

Now your examples as Bach's Toccata are either not pieces for a four voices (Bach) or have unison sections (Beethoven), so there are logically pallalels of 8vas.

You'll find more information here:

http://www.choraleguide.com/vl-parallels.php