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Baroque "chord progressions"

54K views 239 replies 18 participants last post by  millionrainbows 
#1 ·
I know the concept of chord progression is not applicable in the period of the Baroque. However, I cannot help but hear certain progressions as I listen to Bach orchestral suites or concertos, or Vivaldi for that matter. They seems to rise or fall on the diatonic scale by a step, repeating the same motif. Does that make sense? For example, Bach seems to like repeating downward scales on successively incrementing steps; building tension upward with the key, while descending melodically.
 
#165 ·
Literally no one will ever tell you "chords did not exist in Baroque music," as that would be wrong and insane.

Some notable major seventh chords in Bach are in WTC book 1 C major prelude. Since the piece a series of broken chords each lasting one measure, it would be very hard to argue that Bach wasn't thinking in terms of chords or that he considered the major sevenths to be less "real" than the other chords in the piece.

Another major seventh occurs in the ritornello of "Sheep may safely graze."

I'm sure there are many others, those two come to mind because they're very famous.
 
#166 · (Edited)
Literally no one will ever tell you "chords did not exist in Baroque music," as that would be wrong and insane.
I don't believe that. In fact, this entire thread starts with these words:

I know the concept of chord progression is not applicable in the period of the Baroque. However, I cannot help but hear certain progressions as I listen to Bach orchestral suites or concertos, or Vivaldi for that matter. They seems to rise or fall on the diatonic scale by a step, repeating the same motif. Does that make sense? For example, Bach seems to like repeating downward scales on successively incrementing steps; building tension upward with the key, while descending melodically.
Some notable major seventh chords in Bach are in WTC book 1 C major prelude. Since the piece a series of broken chords each lasting one measure, it would be very hard to argue that Bach wasn't thinking in terms of chords or that he considered the major sevenths to be less "real" than the other chords in the piece.

Another major seventh occurs in the ritornello of "Sheep may safely graze."

I'm sure there are many others, those two come to mind because they're very famous.
I agree that it sounds as if those are major seventh chords. But CP theory (and this includes Baroque) doesn't recognize these as chords. And I think Bach thought contrapuntally (not harmonically except in a very general sense).

This shows us that Bach and contrapuntal music in general is not based on how things sound harmonically, but is based on strictly-defined voice-leading procedures and concepts of "non-harmonic tones."
 
#178 ·
If you want to get an idea of how he thought, you have to study his music. That's all there is to it.
Okay, I get it. It's okay to tell a modern harmonic thinker like myself that "major seventh chords on the I (tonic) degree do not really exist in Baroque music because they contain non-harmonic tones," but if this is used to demonstrate that, in this instance "Bach did not think harmonically" it's wrong?

It sounds like to me "non-harmonic tones" are being used as a bludgeon in invalidating the idea of a major seventh chord on the I (tonic) degree, because that's a jazz concept.

Why did the academic thinker who asserted that "chords were not recognized as such in the Baroque" even bring this up, then?

And beyond that, I still see problems with writing or analyzing music without using the idea of chords.

I think these defenders of Bach want it both ways, but they can't explain any of it.
 
#169 ·
Music has nothing to do with morality and feelings!!! You can associate certain sounds with some kind of cultural norms, it doesn't mean anything.
And using stock motives/phrases/whole sequences has little to do with order or balance in composition, more with craftsmanship and commercial productivity + lack of creativity (or else Telemann wouldn't write 3000 compositions). And this remark can be applied to other musical periods and famous composers.
 
#195 · (Edited)
MR just try writing Bachian counterpoint without an awareness of harmonic function and progression. The concept of writing contrapuntally and harmonically at the same time is clear to any composer who has studied and practised it. The two disciplines are intertwined and feed off each other.

I quote from Oldroyd's Technique and Spirit of Fugue...

A great hindrance to contrapuntal work is poor harmonic basis. The power to choose chord progressions well - in a word, clear harmonic thinking - is the first essential. Weakness in this respect is too often an unsuspected cause of trouble....

That's back-up of something I know anyway as does any composer worth their salt.
 
#196 · (Edited)
Oh, I completely agree with this.
The aspect of this which I disagree with is the characterization of "composing by ear" as "harmonic thinking," which is misleading and not explicit enough. Not so much the term itself, but the way it is being used.
What is called "harmonic thinking" is just "using your ear" to hear the "harmonic truth."
It has less to do with harmonic rules or regulations. It is derived from the act of hearing, not rules.
https://www.talkclassical.com/blogs/millionrainbows/1174-function-harmonic-model-part.html
 
#197 ·
What MR has pointed out through a number of sources here, is that the CP harmony is contained within the rules for part-writing and figured bass, with the chord nomenclature a later codification began by Rameau and not fully accepted until the later 18th century. Bach thought in figured bass, not roman numerals (which according to Wiki, began in 1774 with the work of JS Bach's student Johann Kirnberger's Die Kunst des reinen Satzes (wonder if there are any references to him in the work?). But, figured bass is a system for representing chords and harmony, not counterpoint, which began in the early 17th century
 
#199 · (Edited)
What I'd rather point out is that "harmonic thinking" is possible without any rules; it operates more on the level of the ear, as a directly perceived "logic" of the senses.

Yes, figured bass is a system for representing chords and harmony, but only in relation to a bass note. It does not specify function per se, which had not been invented.
 
#198 · (Edited)
MR, when writing counterpoint, considerations of spacing are present. Spacing is a vertical dimension and has a considerable influence on how a part might proceed and what its possible subordinate role is to be at a particular vertical point. That is harmonic thinking whilst thinking in a linear fashion.
I give you a page from Cherubini, admittedly just after Bach...from his Treatise on Counterpoint and Fugue. . Perhaps not the sort of thing you'd expect.

Font Parallel Rectangle Pattern Document
 
#208 · (Edited)
Just remembered an ideal illustration of what we're talking about, starting at 6:30 in the video below. Unfortunately a mis-timed ad comes in a couple seconds into the movement, at least for me - click past it and keep going.



The violin and keyboard right hand in this movement are playing a strict canon, while the keyboard left hand is outlining the chords. A perfect marriage of counterpoint and harmony. This kind of thing is why people think Bach was such a genius!
 
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#209 · (Edited)
Just remembered an ideal illustration of what we're talking about, starting at 6:30 in the video below. Unfortunately a mis-timed ad comes in a couple seconds into the movement, at least for me - click past it and keep going.


The violin and keyboard right hand in this movement are playing a strict canon, while the keyboard left hand is outlining the chords. A perfect marriage of counterpoint and harmony. This kind of thing is why people think Bach was such a genius!
Nice. The 'cello part is not exactly the same as the left hand part in the scrolling score but very well played.
 
#218 ·
Riemannian functional harmony is derived from heptatonic model of music, tuned to meantone (while heptatonic 5-limit music can be tuned to other temperaments where other chord progressions, not possible in meantone without enharmonics, can be realized). And it's not even capable of explaining like 1/5 of the progressions in romantic and modern period (which on top of that require enharmonic modulations in meantone (that's one of the main motivations of Neo-riemannian theory - to explain chromatic harmony in 12 equal.))

Imo, figured bass as an idea is more useful model for pure intonation music - over a bass note you can build a major or minor chord, or any of its inversions, and harmonize to your musical taste.

I doubt Bach was understanding his music in "functional sense" - this makes no sense, considering when this theory was invented and popularized, but certainly there are chromatic passages where he was using his "well-temperament tuning" in chromatic (12-tone fashion), not heptatonically.

Even, if this is slightly off-topic, since Million likes scale models, let's do one -
Regardless of tuning, here is quantization of some of the most useful for harmony and melody 5-limit limit ratios, reduced to heptatonic model:

I. 1/1 -unison, 25/24 - chromatic semitone (this means that this semitone is tempered in 7 equal and, in accurate systems, you use it for modulation to other keys; obviously, diatonic and chromatic semitones are equated in 12 equal, potentially giving us the option to play confusing for the listeners tonicizations, not knowing, if you modulated or not)
II 16/15 - diatonic semitone (inverse of 15th octave reduced harmonic), 10/9 - minor whole tone, 9/8 - major whole tone (octave reduced 9th harmonic)
III 6/5 - minor third, 5/4 - major third (octave reduced 5th harmonic)
IV 32/25 - diminished fourth (inverse of 25th harmonic), 4/3 (inverse 3rd harmonic, reduced to octave), 25/18 (augmented fourth).
And that's it - you can get fifth, sixth and seventh degrees by inverting these modulo octave.

So, we get a heptatonic scale with variable scale degrees that can be useful for creation of most ethnic and non-ethnic modes in 12 equal (useful technique is using these as melodic tetrachordal blocks, giving us Arabic/Hindu/Greek take on scale construction, obviously playing alterations of the same scale degrees can sound potentially bad ).
Tempering 81/80 gives us a regular temperament and the ability to play meantone progressions (like the infamous in jazz 2-5-1 chains)...



Here is the interesting part - we can quantize pure ratios to different (and they are not unique and there may be several such options for creation of abstract temperaments - check 17 equal for example, 17 tone scale can be mapped in several ways to 5-limit) pentatonic, hexatonic, octatonic, nonatonic etc hierarchies (think of black keys pentatonic, found in Eastern and African music; or some of the synthetic scales, used by Scriabin, Liszt, Stravinsky etc), giving us different perspectives on the usage of abstract temperaments/scales. For example here is a pentatonic one -
I 1/1, 16/15 (diatonic semitone is a chroma!)
II 25/24, 10/9, 9/8, 6/5, 32/25 (!!!)
III 5/4, 4/3, 36/25 (!!!)
It doesn't look as pretty, giving options for improper and monotonically not ascending scales, but let's for examples check the intervals in the black keys pentatonic.


II 3 x 200.00000 cents
II 2 x 300.00000 cents

III 1 x 400.00000 cents
III 4 x 500.00000 cents

IV 4 x 700.00000 cents
IV 1 x 800.00000 cents

V 2 900.00000 cents
V 3 1000.00000 cents
Number of different intervals: 8 = 2.00000 / class

All this theory is backed by serious math (mainly linear and exterior algebra). (And can be useful for composing music/translating existing in/between different temperaments + just intonation)
 
#219 ·
It only takes one or two times to play or compose something by ear before you start to understand how it functions though. You don’t compose over four decades by ear. Most of the time, each thing you figure out, you figure out once. I mean, once you sat down and figured out C, E, and G go together and sounds good to the ear, you don’t need to figure it out again a second time. The same goes for a chord progression. You start to learn how they function. Also, you don’t live in a cave on Mars with your fingers in your ears. You hear and play and read other pieces by Vivaldi or whoever and see and discover how chords function. So even giving you the benefit of the doubt, no one of Bach’s genius would compose by ear for very long, certainly not almost 5 decades.
 
#220 · (Edited)
In the absence of musical examples and statements from the composer, it's tiresome to be told over and over what Bach did and didn't know and think while composing.

We start out being told that "Bach was not a harmonic thinker." Now we're told that "Bach's unaccompanied violin sonatas show that he was thinking harmonically," but that "no one has offered an explanation of how this is possible, except me." [emphasis in the original] Moreover, "Nobody else has presented any explanation of how Bach used 'function' when, at the time, it hadn't been codified yet."

I haven't seen any such explanation of Bach's ability to think harmonically. I do see what appears to be an assumption that there's something extraordinary about using compositional procedures that haven't been codified by theorists. That is a strange assumption, given that music theory is mainly just a way of thinking about the structure of existing music.

It was possible for Bach to "think harmonically" for the same reason it's possible for you, me, or anyone else to "think harmonically." Thinking in harmony is not an advanced compositional skill; knowledge of music theory is not required. All that's required is knowledge of music. I wrote an interesting and quite harmonically coherent little chromatic fugue at the age of 16 when I didn't know tonic from iced tea and had only things like Bach's organ works, Wagner's preludes, and years of singing hymns in church to guide my sense of where the harmony should go. There were a couple of instances of inelegant voice leading which a bit of theory knowledge would have had me on the lookout for, but in general I count it no disadvantage that I was enencumbered by such arcane concepts as inversional chord equivalence or hierarchies of dissonance. Whether or not Bach entertained these or other specific concepts, I'm sure that if a dilettante like me didn't need them to write convincing harmony, he didn't either.
 
#222 ·
It was possible for Bach to "think harmonically" for the same reason it's possible for you, me, or anyone else to "think harmonically." Thinking in harmony is not an advanced compositional skill; knowledge of music theory is not required. All that's required is knowledge of music. I wrote an interesting and quite harmonically coherent little chromatic fugue at the age of 16 when I didn't know tonic from iced tea and had only things like Bach's organ works, Wagner's preludes, and years of singing hymns in church to guide my sense of where the harmony should go. There were a couple of instances of inelegant voice leading which a bit of theory knowledge would have had me on the lookout for, but in general I count it no disadvantage that I was enencumbered by such arcane concepts as inversional chord equivalence or hierarchies of dissonance. Whether or not Bach entertained these or other specific concepts, I'm sure that if a dilettante like me didn't need them to write convincing harmony, he didn't either.
I agree with this. However, I DO think I've demonstrated how it was done, by ear, in the perception of intervals, i.e. scale degrees against a tonic note, as shown in the charts I posted.
 
#221 · (Edited)
Use your logic, please.

The concept of "chord function" cannot exist without knowing the root of a chord as related to a key or tonic note.
Bach was not interesting in identifying by analysis or in his figured-bass notation any chords except by the voicings above a bass note, and this does not identify roots of chords.

So he had to be doing it by ear. That's what I've been saying all along. That's not a form of "harmonic thinking" that is touted in the counterpoint textbooks. That's "using your ear" (both of them). That's "harmonic hearing."

In this way, Bach MUST have been hearing root relations to a key note, in order to hear any sort of "function" which he might have heard. It's inescapable.

This means my harmonic model (and all those charts I posted) are correct, because it is based on the perception of intervals, and not on codified theory.

No one else has offered any explanation except ME.
 
#225 ·
Sorry, but that reads like a medieval text on alchemy. Are you saying that the perception of degrees of dissonance between the notes of a scale and a tonic note is a sufficient guide to the procedures of common practice harmony and "explains" how Bach knew how to write a cadence with a Neopolitan sixth in it?
 
#227 · (Edited)
No one else has "explained" how Bach used harmonic function. You haven't. All you can do is invalidate other ideas. Why don't you do some work on this? You can't just narcissistically expect everyone to agree with your self-serving "rationality."

There may be some stylistic non-essential procedures like "a cadence with a Neopolitan sixth" which were followed, but, yes, I'm saying that the more basic perception of degrees of dissonance between the notes of a scale and a tonic note is done by ear, and the consonance/dissonance corresponds.

Here it is again.

What is the most closely-related chord to I? V, and so on. The correspondences follow with each chord function:

So a C major scale's horizontal functions correspond to these harmonic relations; and one can observe how these functions were derived:

I - 1:1
ii - 8:9
iii - 4:5
IV - 3:4
V - 2:3
vi - 3:5
vii - 8:15

Their importance in establishing the tonality is ranked by the order of consonance to dissonance, with smaller-number ratios being more consonant.

I - 1:1
V - 2:3
IV - 3:4
vi - 3:5
iii - 4:5
ii - 8:9
vii - 8:15


Using this model, a "function" hierarchy can be applied to any scale, after the degrees of dissonance are ranked.

Furthermore, I'm asserting that "chord function" is not exclusive to CP harmony, but is an innate feature of any scale which can be used in a tonality.
 
#228 ·
15/8 has higher complexity than 9/5, if you after consonant seventh degree. (And we get mixolydian mode, plus 9/5 is is close to seventh harmonic).And your given scale has wolf intervals, so some normal chords are ugly and modulate enharmonically, if you attempt typical progressions.
IF you actually read some of the functional harmony theorists, you will understand why major and minor are the structurally important ones, but it's not because of highest degree of consonance for sure...
 
#229 ·
That's weird...I thought that you, of all people, would believe in the primacy of the ear. I'm disappointed in you, Baby.
 
#238 · (Edited)
^^^ You're evading the elephant in the room, which I tried to place front and center: the variety of tonal systems, with their diverse conventions, throughout a long history of which common practice occupies only a portion. Your dismissal of this with "thanks for the examples anyway" tells me you're not capable of dealing with the problem they raise for your theory.

Your statement, "If a composer wants to move away from the tonic and create a chord progression, he does it on the basis of how closely-related the roots are to the tonic," is not true. Unless you have a special meaning in mind for the expression, "on the basis of," a composer does not have to concern himself with degrees of relationship to the tonic or be compelled by them in any way. There are certainly conventional relationships between chords, and it's true that the most commonly used chords and progressions use the chords closest to the tonic; the tonic-dominant relationship is basic to common practice, and the subdominant root is to the tonic root as the tonic root is to the dominant root. It isn't surprising that this "triumvirate" should have come to dominate common practice tonality (at least for a while), since the overtone of the fifth above the tonic is so audible and the harmony created between them so satisfying. But a composer who wants to move away from the tonic may do so in a number of directions - he can move to the supertonic or the mediant chord, for example - and he may proceed in any number of directions from there. Not even at a final cadence is there a necessity of sticking to the common V - I or IV - I formulas. In exactly what way do you feel composers are constrained by your hierarchy of dissonance?
 
#239 · (Edited)
the tonic-dominant relationship is basic to common practice, and the subdominant root is to the tonic root as the tonic root is to the dominant root.
Overtone relationships are one, voice leading relationships - another topic, that's why subdominant relationship has more validity as natural move of chords, related to a key (but it's not major/minor "key"). The only legal moves that don't imply modulation and don't introduce enharmonics are these found in the C-Eb-E-F-G-Ab-A scale. There is no dominant chord there. This is the 5-limit hexagonal lattice. Many-many scales can be derived, if we use selection polygons that go around pitches that are close on this lattice.
Here is the tempered version in 12 equal.

https://en.wikipedia.org/wiki/Neo-Riemannian_theory#/media/File:Neo-Riemannian_Tonnetz.svg

If you want dominant and typical classical music progression, you want hidden 80/81 (or inverse) and prooobably meantone temperament to get rid of them. If you want "romantic" chord progressions, you will deal with both 81/80 and 128/125 and their product - 648/625, so the whole basis of classical music is artificial construct.
 
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