Baroque "chord progressions"

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Originally Posted by Bwv 1080

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

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Figured bass represents upper voicings against a bass note, not against a root note or a key note. In this sense, it is not harmonic as we know the term.
Figured bass classifies voicings, not chords.

Figured bass classifies chord voicings by groups: all seventh chord voicings, all 6/4 voicings, etc.

It does not distinguish or group "all C chords" because there is no reference to a root or the key. Roman numerals were used only later in figured bass.

Bach's system did not recognize chord inversions as being the same chord. It did not recognize chord function, or use chord progressions.

So "where's the beef?"

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Originally Posted by millionrainbows

This is just talking about figured bass. Yes, figured bass is a system for representing chords and harmony, [B]but only in relation to a bass note. It does not specify function per se, which had not been invented. So this is not truly "harmonic thinking" as we now know it.

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You are repeating the same mistakes with which you began in this thread, over, and over, and over again. Bach's use of figured bass has nothing to do with his functional understanding of harmony. It was just a system of notation. Bach was not trying to represent function.

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Originally Posted by millionrainbows

"Harmonic thinking" is possible without any rules; it operates more on the level of the ear, as a directly perceived "logic" of the senses.

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But there were rules to harmonic thinking. As I demonstrated, they were set down in famous treatises on harmony and counterpoint generations before figured bass existed. Everyone including Bach knew them. The only one who doesn't know them is you, because you haven't made an effort to study the theory of classical music and its history.

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Originally Posted by millionrainbows

Yes, Bach was thinking harmonically" but without any specified rules or principles such as "chord function" and "chord progression." He was doing this intuitively, by ear.

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This is an unsupported and incorrect assertion. Of course Bach understood the chords he was using in a functional sense. It's obvious to anyone who has studied his music and learned to write progressions in his style — oh wait, you haven't done that so of course you don't understand this.


Oh, as a footnote, I love how whenever your assertions have been disproved you throw in the same irrelevant charts about intervals and scales, regardless of how little it has to do with the subject under discussion. No one is distracted or impressed by this attempt to appear learned.

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Originally Posted by EdwardBast

You are repeating the same mistakes with which you began this thread, over, and over, and over again. Bach's use of figured bass has nothing to do with his functional understanding of harmony. It was just a system of notation. Bach was not trying to represent function.

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Then it is not a "mistake" to say over, and over, and over again that Bach's figured bass system is not harmonic, and does not represent function or key.

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But there were rules to harmonic thinking. As I demonstrated, they were set down in famous treatises on harmony and counterpoint generations before figured bass existed. Everyone including Bach knew them. The only one who doesn't know them is you, because you haven't made an effort to study the theory of classical music and its history.

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Of course Bach understood the chords he was using in a functional sense.

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I agree. Bach was thinking harmonically" but without any specified rules or principles such as "chord function" and "chord progression." He was doing this intuitively, by ear.

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It's obvious to anyone who has studied his music and learned to write progressions in his style

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Yes, I agree. Bach was thinking harmonically" but without any specified rules or principles such as "chord function" and "chord progression." He was doing this intuitively, by ear.

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It's obvious to anyone who has studied his music and learned to write progressions in his style.

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Yes, it's obvious, but no one here has attempted to explain how this was done except me.

I question whether the notion of "functionality" should be the exclusive domain of CP tonality.

The underlying principle of function in CP tonality is an hierarchy derived from harmonic factors of dissonance, in relation to a root chord, now known as "I."

Thus, the others followed, and were named: ii, iii, IV, V, vi, and viiº. It simply makes the harmonic factors into horizontal functions.

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Oh, as a footnote, I love how whenever your assertions have been disproved you throw in the same irrelevant charts about intervals and scales, regardless of how little it has to do with the subject under discussion. No one is distracted or impressed by this attempt to appear learned.

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Footnote duly noted.

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Originally Posted by EdwardBast

But there were rules to harmonic thinking. As I demonstrated, they were set down in famous treatises on harmony and counterpoint generations before figured bass existed. Everyone including Bach knew them.

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What you posted earlier as your "historical evidence" did not go into function or chord progression; it only talked about general harmonic principles like "triads."

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Originally Posted by millionrainbows

Then it is not a "mistake" to say over, and over, and over again that Bach's figured bass system is not harmonic, and does not represent function or key.





I agree. Bach was thinking harmonically" but without any specified rules or principles such as "chord function" and "chord progression." He was doing this intuitively, by ear.

It's obvious to anyone who has studied his music and learned to write progressions in his style

Yes, I agree. Bach was thinking harmonically" but without any specified rules or principles such as "chord function" and "chord progression." He was doing this intuitively, by ear.



Yes, it's obvious, but no one here has attempted to explain how this was done except me.

I question whether the notion of "functionality" should be the exclusive domain of CP tonality.

The underlying principle of function in CP tonality is an hierarchy derived from harmonic factors of dissonance, in relation to a root chord, now known as "I."

Thus, the others followed, and were named: ii, iii, IV, V, vi, and viiº. It simply makes the harmonic factors into horizontal functions.



Footnote duly noted.

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Clearly your strategy is to just continue repeating errors and confirming your lack of comprehension of the theory and history of music until people get tired of correcting you.

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Originally Posted by EdwardBast

Clearly your strategy is to just continue repeating errors and confirming your lack of comprehension of the theory and history of music until people get tired of correcting you.

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Nobody else has presented any explanation of how Bach used "function" when, at the time, it hadn't been codified yet.

It's not an "error" to present information in the form of charts and intervals which clearly show how this was done, by ear, based on degrees of consonance and dissonance in relation to a key note.

The fact is, you have failed in offering an explanation of chord function which is based on anything other than principles of hearing, which were later codified into prescribed functions.

Tonal music is harmonic; music is vertical. It is based on vertical, harmonic factors which are instantaneous, based on hearing degrees of consonance/dissonance to a key or tonic note.

Melodies in counterpoint have a harmonic basis; they suggest triads, and can outline triads. Bach's unaccompanied violin sonatas show that he was thinking harmonically. But no one has offered an explanation of how this is possible, except me.

It is done by ear, using intervals and their degrees of dissonance to a key note, and their other suggestions of triads.

The intervals have a dissonant/consonant quality determined by their ratio, all in relation to a "keynote" or unity of 1; our ears/brain experience this as an instantaneous visceral sensation.

The intervals have a scale degree and place in relation to "1" or the Tonic, and triads can be constructed on these steps/notes. The chords thus constructed can then be given a "function" which is modeled after this harmonic relation to the keynote. Function is dependent on forward progression in time, and context, and both rely on memory.

This harmonic model is where all "linear function" originates, and is still manifest as ratios (intervals) which were derived from physical harmonic phenomena, which existed first.

Got it - you absolutely refuse to do the one thing that could help you, study Bach's music. Nothing more to be said.

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)

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.

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.

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.

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Originally Posted by Woodduck

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.

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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.

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Originally Posted by millionrainbows

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.

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I don't see that a charting of intervals explains HOW anyone composes music, any more than identifying parts of speech explains HOW humans think coherently. Why do you think it does? You seem to be positing some powerful psychological forces at work that operate innately, regardless of the existing musical culture. Would Bach's "ear" have been guided to the same procedures if he'd not been the heir of Fux, Pachelbel and Buxtehude?

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Originally Posted by Woodduck

I don't see that a charting of intervals explains HOW anyone composes music, any more than identifying parts of speech explains HOW humans think coherently. Why do you think it does? You seem to be positing some powerful psychological forces at work that operate innately, regardless of the existing musical culture.

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The chart of intervals and their consonance/dissonance ratios are representations of the way we hear. It's not ideas or psychology, it's the truth of sound itself as it hits our ears. It's called "music."

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Would Bach's "ear" have been guided to the same procedures if he'd not been the heir of Fux, Pachelbel and Buxtehude?

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Bach's "ear" was his own, and that of a superior musical intelligence. This ability to hear music is innate in people, some more than others. Good musicians seem to have it.

Also, certain theoretical approaches recognize that if something sounds the same, or makes sense to the ear, theory & nomenclature are meaningless. This way of thinking favors the ear above all else.


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

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?