Baroque "chord progressions"

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Originally Posted by Larkenfield

‘The "diminished seventh" chord itself, supposedly built on the vii degree, is not really that at all: it's to be considered an incomplete G7 dominant (B-D-F), and should be resolved as that by assuming a G root, according to two respected sources: Walter Piston's Harmony and Schoenberg's Harmonielehre.’
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Add the A of the C-major scale to the B-D-F and you have the half-diminished chord that naturally resolves to the E minor chord of the scale. Mahler started off his Seventh Symphony with a half-diminished chord but did not resolve it to the tonic. B-D-F is part of the half-diminished and is much more than an incomplete dominant seventh because it has a different root than a dominant G chord. ;)

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That makes perfect sense to me. I'd never thought of it that way.

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Originally Posted by BabyGiraffe

12 equal is not just a simplified representation of 5 or 3-limit (generated by perfect fitths) diatonic. Hexatonic, octatonic, various "blues/oriental/gypsy/ethnic" or symmetrical 9, 10, 11 (this one is the chromatic, skipping the tritone) notes scales exist in it and are better represented in bigger divisions of the octave (and lead to bigger "tonalities" that are not generated by stacking perfect fifths).

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I understand this, but it's the stacking of fifths that is the most important point. This has harmonic consequences. If you stack fifths C-G-D-A-E, stopping at five, you get the pentatonic scale C-D-E-G-A, which you will notice has no tritone and no fourth degree. This scale is therefore more consonant than the diatonic major scale, since it has no tritones.

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Originally Posted by millionrainbows

I understand this, but it's the stacking of fifths that is the most important point. This has harmonic consequences. If you stack fifths C-G-D-A-E, stopping at five, you get the pentatonic scale C-D-E-G-A, which you will notice has no tritone and no fourth degree. This scale is therefore more consonant than the diatonic major scale, since it has no tritones.

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Pentatonic scale has only 5 degrees. You are trying to shove it into some heptatonic models. Many of your favourite atonal theorists and composers explored 5, 6 etc note scales as their own thing. It also sounds like its own unique tonality (after listening to just traditional Chinese/Japanese music for a few days, Western diatonic may sound "chromatic" for a short period of time).
We have a "wolf" interval similar to the tritone in the black note pentatonic, it's 400 or its inversion - 800 cents, instead of 500/700 (when we stack fourths or fifths).

I think hexatonics are the most important in 12 ET, because of the symmetry and complementarity in it.


Of course, it's more consonant, the more intervals in the chord, more dissonance we get. Still, I don't listen to music that uses the whole diatonic as a chord...
I'm not sure, if there is a objective measure about how consonant are the intervals in a melody.
In general, smaller intervals around semitones are probably considered the most dissonant (way more dissonant than intervals around tritones ) and hard to distinguish or even play by amateurs (give a chromatic piece to a school brass band and just listen to the end result).
Sometimes, small intervals can even sound wrong (like alterations, instead of new musical objects) when you play the chromatic scale - I guess it's something related to our pitch perception (some cognition "experts" have suggested melodies and scales with no more than 9 different notes) and psychological expectations; these two factors ruin many of theoretical musical resources like polytonality/non-octave divisions etc.
Tritones can sound pretty "cool" and are staple in all the spy-thrillers and blues/jazz. The simplest consonant ratio is 7/5, I don't think it's that great, but it doesn't sound wrong.

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Originally Posted by BabyGiraffe

Pentatonic scale has only 5 degrees. You are trying to shove it into some heptatonic models. Many of your favourite atonal theorists and composers explored 5, 6 etc note scales as their own thing. It also sounds like its own unique tonality (after listening to just traditional Chinese/Japanese music for a few days, Western diatonic may sound "chromatic" for a short period of time).
We have a "wolf" interval similar to the tritone in the black note pentatonic, it's 400 or its inversion - 800 cents, instead of 500/700 (when we stack fourths or fifths).

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With six-note scales, we get the most variety of intervals (Hanson) before redundancy sets in (i.e. repeats of intervals with no new interval introduced). The pentatonic doesn't have all six intervals; it is missing the tritone, so harmonically speaking, it is a very "consonant" i.e. tonic-reinforcing scale. 400 cents refers to the major third, and when you generate a scale from fifths, the thirds will suffer, but it is a less-important interval than the fifth, as far as harmonic stability over the entire range. That seems to be the difference in our thinking, I consider scales harmonically first and foremost.

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Of course, it's more consonant, the more intervals in the chord, more dissonance we get. Still, I don't listen to music that uses the whole diatonic as a chord...

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I was trying to say earlier that scales do have "harmonic content" because of the intervals which are generated by cross-relations, called "interval vectors." This is the way I've learned to think about unordered scales, so it might as well be a "chord".

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I'm not sure, if there is a objective measure about how consonant are the intervals in a melody.

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You could do a vector analysis of any melody, as I've demonstrated in my blog, with 12-tone rows. A tone row is an ordered set, like a melody, so its interval vector is much smaller than a scale. But any melody which is scale-derived (not a fixed ordered tone sequence) is better paired with the interval vector of the entire scale, since melodies are derived from an unordered set, called a scale.

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In general, smaller intervals around semitones are probably considered the most dissonant (way more dissonant than intervals around tritones ) and hard to distinguish or even play by amateurs (give a chromatic piece to a school brass band and just listen to the end result).

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Again, I don't look at notes individually; I put them in harmonic context, so a tritone is dissonant as an interval when we compare it to a fifth, and when one of those tritone's notes is the tonic, it destabilizes the tonic, which is a harmonic consequence. On the other hand, tritones sound more stable when they are the b7 and major third of a chord, but this also has to be put in harmonic context with a tonic on "1".

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Tritones can sound pretty "cool" and are staple in all the spy-thrillers and blues/jazz. The simplest consonant ratio is 7/5, I don't think it's that great, but it doesn't sound wrong.

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Again, this works in jazz as a tempered interval. to me, it's not necessary that it be a "just" ratio.

Even in the introduction of the book "Essay on the True Art of Keyboard Playing" by C.P.E. Bach, the authors admit that Bach's thorough bass practice would become unwieldy as more chords were added to the harmonic collection. Rameau's 'root system' was far smaller and easier to work with.

During the early eighteenth century, Jean-Phillipe Rameau articulated the modern notion of a chord, classifying basic musical objects based on their pitch-class content rather than their order or registral arrangement. Rameau implicitly suggested that three basic operations preserve the "chordal" or "harmonic" identity of a musical object: octave shifts, permutation (or reordering), and cardinality change (or note duplication). For instance, one can transform (C4, E4 G4) by reordering its notes to produce (E4, G4, C4), transposing the second note up an octave to produce (C4, E5, G4), or duplicating the third note to produce (C4, E4, G4,G4) - all without changing its right to be called a "C major chord." Furthermore, these transformations can be combined to produce an endless collection of objects, all representing the same chord: (E4, G4, C5), (G3, G4, C5, E4), (E2, G3, C4, E4, E5), and so on. To be a C major chord is simply to belong to this equivalency class - or in other words, to contain all and only the three pitch-classes C, E, and G. We can therefore represent the C major chord as the unordered set of pitch classes {C, E, G}. -Tymoczko, p. 36

I think figured bass is rather archaic unless one has an overview, and I think it's limited to that older style of music, and is really more of a "technique" which was used in lieu of harmonic/root thinking, which was not developed or accepted or used, whatever.

This figured-bass thinking was perhaps a method which worked its way into the stylistic arsenal of composers, and yes, they had to be handled in specific ways, but the abstracted convenience of thinking harmonically is still in evidence to modern analysts. Figured-bass tends to get bogged-down in voice-leading details which ignore a purer, freer abstract distillation of harmonic considerations. And as harmony got more complex, what happened to figured bass thinking? It failed, or rejected more complex harmony. Figured bass is an ideological artifact of a bygone way of thinking. We have bigger, more complex fish to fry.

A chord in all its inversions has the same root function (not bass note), and the same quality (major/minor).

Maybe in earlier times, it is treated differently...

In some convoluted sense, it could be said that since figured bass notation recognizes each inversion separately from a bass note (not a root function), that they are not "equivalent" in that sense.

WIK: Figured-bass numerals express distinct intervals in a chord only as they relate to the bass note (not a root function). They make no reference to the key of the progression (unlike Roman-numeral harmonic analysis).

Because that would be "harmonic thinking."

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Originally Posted by tdc

Well it has all the notes of a maj7, it sounds like a maj7, it has all the harmonic flavor of a maj7. Call it what you want.

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I was reminded of this thread the other day while listening to this piece,
Attachment 135514
which contains this passage with
C-----
---B--Bb--
C----------
the "contrapuntal motion" of the top voice and bottom pedal creating an interval of what seems like a 'major seventh' (held down for the duration of a half note), "resolving" to a minor seventh (with the inner voices making it a dominant seventh?). I think it's interesting.

[ 4:37 ]

https://www.youtube.com/watch?v=nnqKAuCPmr8

Still, that "major seventh" is part of a passing movement of the voice down to the flat-seven. This is not harmonic thinking, this is not chord thinking, this is contrapuntal thinking.

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Originally Posted by Larkenfield

‘The "diminished seventh" chord itself, supposedly built on the vii degree, is not really that at all: it's to be considered an incomplete G7 dominant (B-D-F), and should be resolved as that by assuming a G root, according to two respected sources: Walter Piston's Harmony and Schoenberg's Harmonielehre.’
——
Add the A of the C-major scale to the B-D-F and you have the half-diminished chord that naturally resolves to the E minor chord of the scale. Mahler started off his Seventh Symphony with a half-diminished chord but did not resolve it to the tonic. B-D-F is part of the half-diminished and is much more than an incomplete dominant seventh because it has a different root than a dominant G chord. ;)

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B half dim resolves to C, not em, it has the same dominant function as b dim. Its the top 4 notes of the dom 9th (which is recognized in CP harmony)

Theory codifies existing practice, which is what both Rameau and George Russell did and its value stems from how well it assists people in understanding the music, it does not really matter what nomenclature the music’s creators actually used. You cant understand baroque music without CP harmony. Maybe Bach thought in figured bass and counterpoint because had so internalized and mastered everything we understand as chord theory from that alone, but so what? CP harmony is in Bach and its a better model than figured bass and counterpoint alone

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Originally Posted by Bwv 1080

B half dim resolves to C, not em, it has the same dominant function as b dim. Its the top 4 notes of the dom 9th (which is recognized in CP harmony)

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Thinking freely, outside of CP rules, if B half dim is the ii degree of A minor, then it can resolve to some form of E (v or V7), then go to A (i). What's your point, to remind us of CP restrictions? Or is this a possibility you had never even considered?

Considering B-D-F-G# or B-D-F-A as being G or G 'dominant flat nine' chords with an unstated root is common procedure in jazz, and is even accepted as a way of conceiving the resolution of viiº to I by both Walter Piston and Arnold Schoenberg in their harmony textbooks. Is this theory forum supposed to be for CP theory only? It's best to know ALL of these things.

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Originally Posted by Bwv 1080

Theory codifies existing practice, which is what both Rameau and George Russell did and its value stems from how well it assists people in understanding the music, it does not really matter what nomenclature the music’s creators actually used. You cant understand baroque music without CP harmony.

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And that's another good reason you should know all of the different approaches, procedures, and names for things. Like 'super locrian,' 'diminished whole tone,' and 'altered dominant' all being names for the same scale, so you can communicate with people from different disciplines.

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Maybe Bach thought in figured bass and counterpoint because had so internalized and mastered everything we understand as chord theory from that alone, but so what?

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I agree, but when the question of "did Bach use major seventh chords" is asked, invariably a CP academician will tell you that "chords did not exist in Baroque music."

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CP harmony is in Bach and its a better model than figured bass and counterpoint alone.

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I agree, basically; but here's the friction I'm talking about:

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Originally Posted by millionrainbows

So really, the whole concept of chord progression in Baroque as well as CP tonality is riddled with exceptions like this, which are exceptions to a modern or jazz concept of what qualifies as a "chord," much less a "chord progression."

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Originally Posted by unidentified academic

Baroque harmonic practice is part of CP. Jazz and modern conceptions aren't relevant here.

Non-harmonic tones include passing tones, neighbor tones, appoggiaturas, suspensions, etc.—notes understood to be non-chord tones. Therefore what you wrote: "non-harmonic tones such as a major seventh chord" makes no sense.

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Is this nit-picking or what?
I made the 'mistake' of pointing out a CP/Baroque instance of a non-harmonic tone as sounding exactly like a major seventh chord, and I am chastised for 'calling it a chord' because 'chords didn't exist in the Baroque era.'

This is totally inflexible and argumentative, as well as confusing to many non-academics.

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Originally Posted by millionrainbows

Thinking freely, outside of CP rules, if B half dim is the ii degree of A minor, then it can resolve to some form of E (v or V7), then go to A (i). What's your point, to remind us of CP restrictions? Or is this a possibility you had never even considered?

Considering B-D-F-G# or B-D-F-A as being G or G 'dominant flat nine' chords with an unstated root is common procedure in jazz, and is even accepted as a way of conceiving the resolution of viiº to I by both Walter Piston and Arnold Schoenberg in their harmony textbooks. Is this theory forum supposed to be for CP theory only? It's best to know ALL of these things.

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Within CP rules ii half dim is a sub for the subdominant iv chord in minor, just as ii7 is in major

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Originally Posted by millionrainbows

I agree, but when the question of "did Bach use major seventh chords" is asked, invariably a CP academician will tell you that "chords did not exist in Baroque music."
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Yes asking whether Bach used maj7 chords is like asking whether Dunstable used major triads

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.