"Bach is when Western Music's harmonic complexity peaked."

Cafe Society
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http://onbeing.org/program/bernard-chazelle-discovering-the-cosmology-of-bach/7026

On Being is an NPR show hosted by Krista Tippett. This week, in conjunction with one of the NPR stations here who is having Bachstock, playing his work all November, she interviewed a computer scientist who is a huge Bach fan.

I am not sure this fellow, Bernard Chazelle, is formally educated in music, but he seems to know more than a bit. But I really enjoyed how he frames Bach’s place in music - exploring harmony, focused on the craft of music and the uplifting power of music.

One thing he said was interesting that I want to put out there on the SDMB and hear from formally trained musicians and everyone. He said that Bach’s work is the acme of harmonic complexity. Basically, when Bach explored harmony with, say, the Goldberg Variations, there are 6 equal melodic voices working togehter - harmony emerges from how these equal melodies interact. Because that was incredibly hard to do and also complex, the “rules” evolved to favor a main melodic line with complementary, supporting harmony lines above and below it.

I hadn’t thought of Bach that way - is it a fair way to describe how harmony evolved?

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If you restrict yourself to the major and minor scales and their variants – all derived in some way, more or less, from medieval European modes – then, yes, Bach certainly explored counterpoint to its mathematical limits. But counterpoint is about intervals and motion when you juxtapose melodies.

Bach also explored more straightforwardly harmonic ideas, in concertos and the like, but he didn’t push the boundaries much. That would come about 150-200 years later, with late Romantics, Impressionists, and especially 1890-1960 composers from Bartok to Stravinsky to Pierre Boulez.

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Once the Florentine Camerata defined what music was going to be and how it was going to be judged, Bach was definitely composing some pretty complex stuff. Unfortunately, I’d have to say that they ruled out as acceptable some of the dissonances and atonal music that are more common today, and that a more modern composer may have produced more complex music, if the yardstick is “how many different sound combinations are there”: if you’re not going to allow some combinations, you’re not going to be as complex as possible.

That said, the most complex Bach harmonies are going to be a great deal more enjoyable to the casual listener than a more modern piece would be.

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To follow up on the OP’s final long paragraph, I can see a case being made that Stravinsky, Boulez, etc. were finally creating a harmonic vocabulary that accommodated the harmonies implied by the radical counterpoint explorations of Bach.

That’s why music from about 1750 to 1880 – in other words, true Classical up through high Romantic – generally sounds “easy on the ears” compared to what came just before (Bach’s solo keyboard works) and just after (Schöenberg and the like). It’s “easy” because there’s a relatively clear division of melody and harmony, and because the harmony often proceeds as easy-to-identify chord progressions, like most mainstream rock, pop, and folk music of the past 70 years or whatever.

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Interesting and insightful - and well articulated to this non-Theory guy. There was some discussion in that linked podcast about how tight the harmonic structures were that Bach used, and that he didn’t shy away from dissonance. But I think you and Ethilrist point out that Bach did what he did within a recently defined, but tightly circumscribed set of harmonic rules.

It’s funny - when I think of Why Music Works on Humans, I think I have concluded that music basically “Tickles our Instincts” - we have evolved sensitivities to certain types of sounds, to pattern recognition, and to focus on new/changing sound fields - all in the name of survival. And certain sounds/combos evoke certain emotions as a byproduct of that nature and nuture.

Music takes those instincts and reactions and exploits them for…fun, for entertainment, for communication. I think that is very cool. So when I hear a particularly cool piece of Bach’s, with all of his lines meshing and knitting and sounding like a beautiful math explosion unfolding in front of me - I feel like Bach is there thinking to himself “*This *oughta fire off all of your neurons ;)”

…but that’s probably just me. :stuck_out_tongue:

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I haven’t listened to the episode yet, (looking forward to it later), but yeah, that is very much how harmony and the tonal system evolved. Polyphonic music before Bach’s time was much more haphazard harmonically speaking. Multiple melodies were set against each other as carrying equal weight, but there was no robust system of functional harmony in place that pushed the music through time, though there were certainly hints of it.

With Bach, (and I presume Handel and other composers of the time, but I know Bach’s music the best) you get this incredible, sophisticated counterpoint where the separate voices operate horizontally as melodies while at the same time function vertically as chords which create or resolve tension, each leading you to the next.

When you study music formally, you start out analyzing the shit out of his Chorales (and composing your own) since these are such clear and perfect examples. 3 or 4 voices, each acting as a melody (which makes sense since they were composed to be sung by ordinary people, so each voice needed to be singable and easy to follow), often all together in a straight quarter note rhythm, where every beat forms a harmony in the progression which resolves at the end of the phrase with a cadence.

It’s actually not that difficult once you learn and understand the system and the “rules” of counterpoint.

I’d add though that, with much of Bach’s music, I don’t agree that the individual melodies are necessarily equal (unlike most music written before this time). With these chorales for example, the highest voice is clearly heard as the melody that stands out to your ear and it’s the one that takes the big interval leaps, while the inner voices tend to move as little as possible. The voices rarely cross. And aside from this type of homorhythmic counterpoint he wrote plenty of music that has a clear single melody which is harmonized by the other parts. (Jesu, Joy of Man’s Desiring e.g.).

On the other hand, his fugues and 2 and 3-part inventions clearly do exemplify the former idea.

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Not just you! (and thanks for the compliment). I know just that feeling, which I get from Bach’s works for solo instruments (keyboard, cello, violin…), and from almost-free jazz when in the most capable hands, e.g. John Coltrane’s “Impressions.”

It’s rare for an artistic work to stimulate both the “right” and “left” hemispheres so well – math and beauty – but these do it. In Bach’s solo works, Glenn Gould is known for emphasizing the “math,” and Yo-Yo Ma the “beauty,” but they both do both in equal measures, for me anyway.

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In a word: yes.

However, the genius of Bach was not the harmonic complexity, but rather that he used such complexity to create genuine, affecting music. You could spend a lifetime studying the counterpoint of his Prelude & Fugues, but to evoke the very hand of God…cannot be learned.

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Bach is when Western Music’s harmonic complexity peaked

Not sure I agree.

Like others have said, Bach brought a particular way of writing and structuring musical thought to its peak namely, the counterpoint. Of course, he didn’t invent it: it had been around for centuries and there were already some great masters during the Renaissance, more than 200 years before Bach. However, one can argue that his work represents a pinnacle of the form.

As a result, it is perhaps not a surprise that the sonata form, which is a completely different way of structuring musical discourse, took precedence over the counterpoint after Bach. Younger composers could still write in that form (Beethoven was a master of it as his Große Fuge shows) but the sonata form became the main way of expressing deep musical ideas. Now, is it less harmonically complex than the counterpoint? I really don’t know. They’re so different that it’s difficult to assess: counterpoint is about stacking different voices, the sonata form is about developing an idea. If the sonata form was good enough for Mozart, Beethoven and Brahms, then it’s good enough for me…

With the 20th century, you encounter a new problem: the end of tonality. Gone are the rules about using certain notes and avoiding others: now all the notes are at your disposal. Schoenberg thought (probably correctly) that total freedom would lead to chaos so he felt it necessary to come up with new rules to structure his works. That’s why he invented the twelve-tone technique. Interestingly he used several processes that were similar to those found in counterpoint (inversion, retrograde and retrograde-inversion) but applied to all 12 notes of the chromatic scale instead of just the ones in a given tonality. Later in the century, composers like Boulez extended the concept to all parameters of musical discourse: pitch, duration, intensity, timbre. In Le Marteau sans Maître every single aspect of the score is most rigorously determined. Are twelve-tone technique and total serialism less complex than Baroque counterpoint? I’m not sure at all.

So Bach’s music is undeniably one of the most harmonically complex music ever written. But the harmonical peak of Western music? Not sure.

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To add to what has been said already - I’m no music theory expert, but it seems to me that some of Beethoven’s chord progressions could never have been used by Bach, so from that perspective I disagree with the thread title. Of course, you could argue that interesting chord progressions are not in themselves evidence of harmonic complexity, but I think my point still stands. When I was playing (for the umpteenth time) the first movement of the moonlight sonata the other day, it just struck me how Beethoven manages to make the next chord sound unexpected and yet so perfect at the same time. I think his ability to do that consistently is unrivalled by any other composer and it is why he remains my favourite.

I’m not going to threadshit by arguing that anything written after 1900 isn’t really music any more, but it is interesting to wonder whether a piece written to include all possible audible frequencies (i.e. microtones) in random combinations would qualify as more harmonically complex than even Schoenberg. However, when does it become noise rather than music? Many people (myself included) don’t find even atonal music particularly pleasant to listen to.

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As good a place as any to share one of my favorite quotes:

*‘I don’t think a greater genius has walked the earth. Of the 3 great composers Mozart tells us what it’s like to be human, Beethoven tells us what it’s like to be Beethoven and Bach tells us what it’s like to be the universe.’ * - Douglas Adams

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That’s not a threadshit, Dead Cat, MHO, though we are going off on a bit of a tangent. I agree with you – for me, the breaking point is right around Bartok. It took me several listenings before I could appreciate Bartok’s string quartets, for example – but now that I am used to them and love them, they almost sound “tame,” not all that removed from (say) Brahms.

For music later in the 20th century, I was surprised at how much I liked Pierre Boulez’ “Dialogue d’un Ombre Double,” serial music for solo clarinet relayed through a computer connected to speakers all around an auditorium, with the music swirling around the audience. But maybe that’s just because I heard it live, in 1990, and I was as baked as a pumpkin pie. :wink:

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That’s fantastic. Could have been Douglas Hofstadter’s as much as Douglas Adams’.

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If you like Bartók, there are several post-WWII composers that shouldn’t pose any problem. Dutilleux, early Ligeti as well as some works by Lutoslawski, **Kurtág **and Penderecki spring to mind. Challenging but not much more “advanced” than Bartók.

Well, that’s not surprising.

Bartók’s music isn’t easy and the string quartet is probably one of the less accessible genres (Beethoven’s late quartets are still very challenging after 200 years).

Interesting.

I agree that Dialogue de l’Ombre Double is surprisingly accessible (relatively speaking). He transcribed it for bassoon and electronics and this version is even more appealing IMHO.

By the way, not everything that he wrote is impossibly challenging. Notations (for orchestra), Messagesquisse (for cello ensemble) and Anthèmes 2 (for violin and electronics) are not that difficult. Just relax and let the weird sounds carry you (something that I’m unable to do with his hardcore serialist stuff from the 50s).

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Thank you, LEDS! I will explore each of your suggestions as soon as I get a chance to. (Like most of us, I’m familiar with some Ligeti mainly thanks to 2001).

I agree that late Beethoven string quartets sometimes sound like they were written a hundred years later than they were. Pretty astounding.

(BTW, I put “tame” in scare quotes when referring to Brahms because his music is harmonically and melodically relatively easy to follow – but in terms of emotional impact, he could be the very opposite of “tame.” Just check out, for starters, the first and last movements of his F minor Piano Quintet.)

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Well you could argue that post 1900 music isn’t ‘western music’ in the same way that Bach is.
Back wrote A LOT of music. Not all of it is even heard by most people. I’m sure it you really get into the ‘deep cuts’ you’re going to find some really unusual stuff.

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Bach’s catalogue is gigantic. I’ve listened to his music regularly for the past 20 years and I feel I’ve only scraped the surface. Take the cantatas. There are over 200 of them. If you were to listen to them all non-stop, it would take you more than a week.

There’s some weird stuff in his oeuvre, that’s for sure. And some weak stuff, too (blasphemy!).

LEDS? Hmmm, I like it ;).

2001 featured some mature Ligeti (the best part of his output IMHO) but his earlier stuff is much less weird, clearly bartokian. Musica Ricercata for solo piano is one of his very best work in that style. But I repeat that his later stuff, while difficult, is absolutely amazing (Lux Aeterna, Requiem, Lontano, Clocks and Clouds, Piano Concerto… I must stop or I’ll list almost everything :D)

For Dutilleux, try Tout un Monde Lointain (cello concerto, very poetic and already a standard in the instrument’s repertoire) or Ainsi la Nuit (string quartet, a bit more difficult). His Symphony n°1 is very accessible and quite good, too.

Lutoslawski => Concerto for Orchestra (early work, bartokian) or Symphony n°3 (more difficult but amazingly daring with its beethovenian opening motif)

Kurtág => any of his micro-pieces for various solo instruments or string trio (Signs, Games and Messages)

Penderecki => He’s very hit-or-miss. Symphony n°7 or Cello Concerto n°2 perhaps.

Yes, astounding. I have no idea what’s going on in these works. I find his late Piano Sonatas easier.

Oh yes, Brahms is a towering genius, one of my top 3 composers of all time (ahead of Beethoven, actually). What appeals to me in his music is the fact that it is filled to the brim with intense emotions but he doesn’t make a big show of it like Tchaïkovsky or Chopin (whom I also love).

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Then I’d like to hear that argument. Because that music is why I think that the statement in the OP is obviously false. As complex as Bach’s harmony got, it’s still based on the same ideas of consonance and dissonance that were finally broken in 20th century music. And that’s without considering the previously mentioned movement away from tonality.

Bach is like a great mathematician that worked his heart out with natural and rational numbers, creating the foundations on which everything is built. He’s great, but he didn’t work with the irrationals, the complex numbers, the infinities.

Yes, there is a lot of music out there today that is less complex than Bach, but there’s a lot that is more complicated. Consider the harmonies of jazz, even.

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I’d say Wagner’s harmonies are more complex than Bach. Then we get into some of the 20th-century composers mentioned earlier on in the thread.

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I am traveling for work, but am following this thread and enjoying it. Go Music Dopers!