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I'm self-learning 18th-century music theory because I like the music from that era. I'm obscure about the concepts of counterpoint and harmony. I'm aware that rules are not absolute within the 18th-century music. I heard the music adorned with augmented seconds. So I have a few questions.

Aldwell

In 18-century harmony, there are two distinctions: structural chords and prolonging chords. In this case, it appears that such dissonant leap usage is permitted as a prolonging chord.

  1. In the case mentioned earlier, the prolonging chord dominant inversion is singular, but, it seems possible to prolong the chord even further than this. So, I'm unsure about the condition for allowing melodic dissonance in the strict composition. Is melodic dissonance only permissible when it's singular, and is the concept of prolonging chords broader?

I'm also struggling to grasp the concept of 'seventh.' It seems there are situations where the concept of 'seventh' is necessary. When looking at this phrase, explaining F# as a suspension resolved to E doesn't seem to fit:

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In such cases, there are several cases where it's not inappropriate to refer to a note as a suspension without invoking the notion of 'seventh':

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  1. I've also learned that seventh should resolve after preparation like any NCTs, so I'm not sure how to distinguish between them.

I have these questions, leading me to the following inquiry.

So, it may sound peculiar, but when listening to fugues, it seems that both non-chord tones and chord tones can coexist within a single chord. In other words, it appears that there are instances where the melodic dissonance and chordal dissonance do not align. Here are a few observations I can make in this case:

  • The chord of first beat of measure 109 is a structural chord.
  • If the answer of 1. is restricted to only 'singular,' then either B# or E of measure 108 must be a prolonging chord. In other words, either B# or E is contrapuntal phenomenon. (in a broader perspective, it is currently within the dominant domain)
  • To explain the chordal dissonance between Fx and E, either G or E on beat 2 of measure 108 is a chord tone.

then, possible explanations could be E is a suspension and Fx is not contrapuntal, or Fx is a neighbor tone and E is not contrapuntal. However, if E is indeed not contrapuntal, it raises questions regarding the conditions for B# to be contrapuntal in the context of melodic dissonance, or whether melodic dissonance and chordal dissonance should be considered separately.

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I have these questions, and therefore, I'm unsure how to perceive dissonance.

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    "doesn't seem to fit": why not? It is a suspension, so we can only help you understand where your analysis has gone wrong if we know what your analysis is. One thing that might help is to keep in mind that Roman numeral analysis was developed after Bach and does not describe how early to mid 17th century composers thought about their compositions. That is, it is a theory that describes 17th-century music, but it is not 17th-century music theory.
    – phoog
    Feb 24 at 13:14
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    Also "it seems that both non-chord tones and chord tones can coexist within a single chord": of course. Chord tones define the chord; if they were absent then there would be no chord, or the chord would be different. Consider: if you analyze a measure as C major but there are no Cs, Es, or Gs, then how do you justify analyzing it as C major?
    – phoog
    Feb 24 at 13:18
  • Oops, my first comment should say "18th century" -- I've never managed to keep it straight. But also "there are several cases where it's not inappropriate to refer to a note as a suspension without invoking the notion of 'seventh'": this seems to imply that suspensions necessarily involve sevenths, at least normally, but that's not at all the case. They can also involve the inversion of the seventh, which is the second. One of the most common is the "4-3" suspension (though this also typically has a second between the fourth and fifth of the chord). Sequences of 5-6 or 6-5 are also common.
    – phoog
    Feb 24 at 17:35
  • If that's a suspension, then from my perspective, it seems reasonable to view it as "decorated resolve" at measure 105, beat 2. / I've checked some unexplained points in the Bach chorale.
    – schwarz
    Feb 24 at 21:39
  • So, I started to separate the terms "non-chord tone" and "contrapuntal." If we think completely contrapuntally, whenever there's dissonance between two voices, one of them should be contrapuntal. In such discussions, explicit cases like sevenths or six-four chords, or examples such as viio6, where there's a tritone with another voice, suggest that one of them is contrapuntal. However, when I delve deeper into this, it becomes a bit tricky to analyze.
    – schwarz
    Feb 24 at 21:53

2 Answers 2

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The first example: There is nothing special about the example you show, certainly not in the soprano. The leap by a tritonus is very common and just standard 3rd-7th-1st progression in minor tonality by the rule of the octave in the soprano. In the bass, it's even more standard 1st-2nd-3rd.

The only unusual thing is the fact that the F is not resolved to Eb, which would be the proper thing -- while it is by a full tone, the role of the F as a leading note should not be ignored. This can be explained by fauxbourdon (parallel 6th chords), but it is slightly non-standard, in particular if the Eb isn't in the same position in another voice.

Now a bit more general: You can't really separate the "harmonic" and "ornamental" function. It helps when you start, but I have a feeling from your first call of the B natural as "ornamental" that you already confuse things a bit. So I'll offer another way of thinking: Each note has "a" function, and the note can be where it is if you have a way of explaining it by "a" function, regarless of what function it is. The confusing thing could be that both "appoggiatura" and "leading note" have a similar function -- they create a tension, and we have a good feeling of how that tension shall resolve. (Note that this means that if you don't resolve it the expected way, it's fine, as long as that lack of resolution plays a function, maybe to surprise the listener -- see how it complicates?)

Second example: That's a nice and a bit complex one. If it were a four-fold cadence into C#, I would say it's simply G# with figures 7 5 (3) -- 6 4 -- 5 4 -- 5 3, which is a common variant. But here it seems modified as (8) 7 5 -- (8) 6 4 -- (9) 6 4 -- (3)=(10) 7 5 and who knows where it goes. (I actually love this idea of 8 6 4 -- 9 6 4 and I shall implement it at some time as it's so cool!)

Thinking about it in terms of "7th chords" (in the modern way of chord naming) is so limiting that I would recommend avoiding that and just thinking about it as a very nice cadential progression over the penultimate!

Third example: Offers two explanations. You seem to explain the Bb as a 7th over the C that resolved to a 3rd of the F. This is probably more plausible given there is already a C major chord before that Bb, but you could also explain it as a suspension of the C in the 16th, so as ornamentation. (See how it gets complicated?) The rest is funnily simple: F 7, F# 7b as a sharpening, leaping to Bb major -- that's quite courageous, but why not :)

Fourth example: First, I would avoid using marks such as viio7/V, that's so limiting compared to the contrapunctual richness of the music! But if you insisted, then I would say it's F##7 (yeah, diminished etc., but that's not that important) -- G#7 -- c# progression, basically just subdominant -- dominant -- tonic, with the subdominant being enriched with a 7th instead of the usual 6th, the rest is just ornamentation. Bar 110 is then again a 7 5 -- 6 4 cadence. If you asked what role does bar 108 play, then it's just a dominant that's not resolved to a tonic but rather prolonged by sidestepping to the subdominant, basically making one very long penultimate step. (The function of this sidestep is to enforce the dominant nature of the G# bass note.)

If you wanted to be precise, then I'd say that structurally it is[108] G# 9 7 - 6 4 | [109] F## 7b 5(b) -- 6 -- 6 5(b) | G# 7 3#, but maybe some of the numbers in bar 109 can be taken as ornamentations. (I would be reluctant to call the E as an ornament though, as it's doubled by the end of bar 108, suggesting that one of them is a prepared note, really belonging to the first chord of bar 109, where it then probably should be considered as structural. But who knows.)

Conclusion: I'm not sure I helped, but I hope I at least managed to show the complexity and maybe a (non-unique) way of thinking about the music. TBH, if you are new to the topic, you didn't choose some simple music to start with.

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  • I intended to watch it like you, so I intentionally brought those examples, as I find musical interest in those parts. It seems like you know how music works.
    – schwarz
    Feb 26 at 2:04
  • I didn't mean to say that appoggiaturas and leading tones have upward functions at that moment. What I meant is viewing harmony in a broader context. For example, when considering the penultimate dominant section of a c# minor fugue, from the perspective of the soprano line in a broader context, B# would be structural, and the rest would be ornamental phenomena. Therefore, I think that, for "musical reasons", the E in measure 109 is structural, and beat 2 of measure 108 is an anticipation.
    – schwarz
    Feb 26 at 2:05
  • In the case of that ornamental dominant seventh, in some instances I know, as you said, consecutive three parallel tenth motion allowed the ascent of F. However, according to Aldwell, it seems that such dissonant leaps and parallel motions are also permitted, I don't feel particularly convincing.
    – schwarz
    Feb 26 at 2:09
  • So, what I meant to say is that melodic dissonance seems to be justified within the larger context of harmony, similar to what I mentioned earlier. The question was whether you know the exact conditions for this justification.
    – schwarz
    Feb 26 at 2:12
  • Any dissonance (or consonance for that matter) is justified as long as it has a function. At least that's how we seem to understand e.g. JSB's music nowaydays. As for consonance -- dissonance: in the dorian tocatta by him, there are moments where you so much expect a 7th that the 8th Bach placed there functions as a dissonance. (And now excuse me, but I don't have the time to get into what seems like an endless discussion -- that's not even the point of a question-and-answer site like this one; it's not a discussion forum.)
    – yo'
    Feb 27 at 8:09
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For Roman numeral analysis, the second half of that measure is V7/V. The F double sharp is definitely not a non-chord tone. Bach would have thought of it as a 7-6 suspension between the soprano and bass.

From the comments:

If that's a suspension, then from my perspective, it seems reasonable to view it as "decorated resolve" at measure 105, beat 2.

I'm not familiar with the term "decorated resolve," but it is certainly a resolution, and it certainly is decorated, so I suppose so.

I started to separate the terms "non-chord tone" and "contrapuntal." If we think completely contrapuntally, whenever there's dissonance between two voices, one of them should be contrapuntal.

If we think completely contrapuntally, how can anything be not contrapuntal? What would it mean for a note or a voice to be not contrapuntal?

Thomas Benjamin 'The Craft of Tonal Counterpoint' suggests that Fx of measure 109, beat 1 is a neighbouring tone.

Well yes. But it's not a non-chord neighboring tone (as is the D♯ in the "decorated resolution" discussed above) because the harmony changes.

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