In Quantz, Versuch einer Anweisung die Flöte traversiere zu spielen several harmonic/melodic skeletons are presented as the basis of melodic embellishment. Here are four which cover significant portions of a full scale (embellishment examples not included.)


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It occurred to me there is almost enough there to make a sort of "rule of the octave" for a treble part. With some overlapping and transposing of Quantz' examples I got this...

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...the ossia staff is my bass to end with a authentic cadence.

For some reason Quantz didn't show examples descending by step to/from the tonic. Figure 5 was the only descending scale to work from...

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...the small notes and ossia staff are my additions to complete a descending scale harmonization.

Do these two scale harmonizations seem ok? Obviously, I want them to fit with Quantz' early classical style.

Please share any alternatives or concerns.

2 Answers 2


A few thoughts:

  • I don't understand your use of 6/4 figures. I'm assuming the penultimate bar in your first example is a simple error and is meant to be 6/4/2? As for the second example, 6/4 chords wouldn't be idiomatic in 18th-century style in either of the places they are written in the first few bars.
  • The use of viio to harmonize ascending scale degree 4 is unusual. I'm not saying it never occurs (it does!), but harmonizing 4 with any sort of dominant function tends to accent its role as seventh of that chord and push toward a downward resolution in the melody. It's interesting that Quantz chooses that option here. It likely has to do with the specific melodic fragment he's quoting, where F is a passing tone from E to G on a weak beat, and therefore the larger harmonic rhythm of the bar revolves around tonic. The default intermediate option when connecting two tonic chords on strong beats (if one is trying to harmonize the weak beat) is generally viio or V(7) in this style, though that works better on 1-2-3, 3-2-1, or 5-4-3 than the ascending 3-4-5.
  • Also, pace Quantz, it's generally a better and more common option in this style when creating a tonic-dominant-tonic stepwise progression to use a dominant function with local scale degree 4, either vii7 or V7 in whatever inversion. Not that I-V-I doesn't occur, but if you look at rule of the octave examples, you'll frequently see what I mean. Take note of that for some of the other uses of V in your harmonizations, e.g., 1-2-3 or 3-2-1 with a V in the middle is very likely to have a 6/5.
  • One point I do take away from Zoe Sparks's answer is that I don't think Quantz was attempting to generalize to universal chord progressions for scale harmonization in the way you're doing here. And I don't think he intended them to be chained together in this fashion. Hence my previous issue with how to deal with ascending 4, which may depend on the particular context of a particular melody. There are obviously other ways to harmonize ascending scale degree 4 using IV or other chords that avoid the "fa wanting to go to mi" problem. Also, in most actual ascending melodies, the 4 would simply be treated as a passing tone, rather than assigned its own harmony.
  • That last point gets at the issue with harmonizing 8-7-6-5 that you bring up in the question. It's a known problem, because just like 4 in the melody wants to go down to 3, 7 wants to go up to 8. And the 7-8 tendency is a lot stronger with that leading tone than with 4. Unlike descending bass patterns (which obviously are quite common idioms in 18th-century style), descending harmonized scales are much less common. Usually, these notes are treated as passing tones.
  • In order to treat them as chord tones, one needs to significantly undermine the need for the leading tone to resolve upward in the melody. Two common idiomatic methods for 18th-century style: (1) Create a series of dominant sevenths, i.e., I-V7-V7/IV-IV. Unfortunately, that requires interpolation of a ♭7 into your scale, but it's more idiomatic. (2) Change the function of scale degree 7 to something other than a potential leading tone. E.g., I-V/vi-vi (though then you need a good progression for 6-5, and it's tough to create something strong there).
  • The difficulty we're encountering here with 8-7-6-5 is perhaps why it's pretty rare to see it occur melodically with each note harmonized in 18th-century style. It's also perhaps one of the reason why "rule of the octave" type patterns never emerged for descending scalar melodies. One thing you pretty much can't do in 18th-century style is have V-IV with either of them in root position (as you attempt in the second example). The 6/4 options don't help; as I already noted, they're unidiomatic. With the descending 8-7-6-5 in the bass, one can fall back on first inversion chords to create a V6-IV6 which is acceptable (particularly in sequential 18th-century patterns). Obviously that can't be done with 8-7-6-5 in the melody, and iii6-ii6 is just not going to be able to create a strong progression (though it might occur as part of a long sequence). viio6-vi6 also does occur as part of sequences, but at that point are we just going to harmonize the whole descending scale as descending sixth chords? (That's actually a better option than most others.)

I don't know if this is helpful. As Sanguinetti notes in his book (p. 116):

When placed in the upper voice, the scale obviously needed a counterpoint in the bass; however, in contrast to the [Rule of the Octave], a standard model of accompaniment never established itself.

He goes on to note small segments of the scale that did have some standardization, like 1-2-3 with the 8-7-8 bass. But I would assume if any harmonization of the ascending/descending scale had been given in a partimento treatise as a "model," Sanguinetti would have noted it. I think that absence is probably telling. Even though partimento practice revolves much more around bass than melody, obviously there are plenty of melodic patterns involving suspensions, etc. that get incorporated in the tradition. The absence of standard harmonizations for melodic scales is therefore interesting. I would postulate it may in part be because of the issues I noted above. The ascending version can be done, but it's a bit awkward. The descending diatonic scale is quite difficult to create a strong progression (particularly for 8-7-6-5). And on the rare occasions where it does occur in actual literature, the different possible solutions depend on which "rule" is broken or what specific inelegant option is chosen.

EDIT: Oops, I forgot to mention one other sequential possibility for 8-7-6-5, which would use the "descending 3rds" progression commonly associated with the Pachelbel canon (I-V-vi-iii...). With sufficient figuration in a sequence this might work and shows up sometimes in late 18th-century music. But it's less desirable as a simple harmonic structure because of the accented parallel octaves created with melody and bass in every other measure.

  • That Sanguinetti quote is very helpful. I read the book several years ago, but don't own a copy. I appreciate you found a quote that sums up the problem. More or less I did come to the conclusion that the full scale harmonization just doesn't work, especially 8 7 6 5. I keep looking out for it when reading scores, but it just doesn't come up! Commented Jun 24, 2021 at 18:40
  • Yes, the best Sanguinetti can do is find an example from Nicola Sala that shows two-voice invertible counterpoint, effectively a two-voice skeleton of a rule of the octave that's modified so the two voices can be inverted and still make some sense. But this two-voice example is more like species counterpoint, not functional harmony. Effectively, the two problematic bits I noted (with 4 ascending and 7 descending) are just harmonized with a series of sixths below. So my "solution" of just using a long series of 1st inversion chords seems to be the best 18th-century option.
    – Athanasius
    Commented Jun 24, 2021 at 18:56
  • Among scores I already have this Solfege manual imslp.org/wiki/… gave a harmonized scale as the first lesson, and as you say, it's solution is mostly sixth chords. 8 7 6 5 was really nagging me. Your answer is very helpful. Thanks! Commented Jun 25, 2021 at 13:38
  • Another example of 8 7 6 5 as I V vi iii music.stackexchange.com/a/121125/23919 Commented Feb 4, 2022 at 15:32

EDIT: Okay, sorry, I did misunderstand what this was about. I never had any exposure to "scale harmonizations", the "rule of the octave", etc. when I was a student—I learned tonal harmony in terms of chord construction and voicing, voice leading, characteristic progressions, modulation techniques, and large-scale structure. We did use figured bass, but not in that fashion, and when we talked about harmonizing melodies it was in terms of the entire edifice of tonal harmony, not something you could distill down to a characteristic set of chords over a scale. I'm not sure that that "partimenti-style" teaching approach was all that common outside of the Neopolitan tradition in the 18th century (although if you have references to the contrary I'd be curious to see them). I'm having a hard time finding much rigorous information on it outside of Robert Gjerdigen's website, so that what I'm working from.

Notably, Quantz doesn't seem to have thought in these terms either, at least not as far as he lets on in that book. I flipped through Edward Reilly's translation and read the chapter the examples you cite are from, and he doesn't seem to ever present material the way those Neopolitan theorists do. Of course, he's not writing a composition manual—those are tips for beginning flutists to start on devising melodic variations when improvising and the like:

Since...most musicians lack the necessary instruction...so many incorrect and awkward ideas appear that it would be better in many cases to play the melody as the composer has set it rather than spoil it repeatedly with such wretched variations.

To remedy this abuse somewhat, I shall give some instructions, for those who still lack the requisite knowledge, as to how variations may be made in diverse ways on plain notes in the majority of the most common intervals, without contravening the harmony of the bass. ...

I do not pretend to have created in these few examples all the variations it is possible to discover on these intervals; I present them only as an introduction for the novice.

So, if we want to tease out a Neopolitan-style rule of the octave from his examples, we're going to have to make some pretty subjective decisions. He's not trying to present harmony in a systematic fashion like that, so we have to try to read his mind a bit; as I said in my original answer, those examples don't necessarily present progressions you could extend to a general case that way. What's more, I'm not sure he even thought about music in the same fashion exactly—again, maybe, but if so he doesn't let on. So we're kind of translating between one musical language and another, even if they do have a lot in common. I'll do my best to indicate what I think is more-or-less an objective truth and what's more a matter of opinion so that you can work based on your own tastes.

Anyway, the biggest problem with lifting directly from Quantz's examples is that he elides the rules of good voice leading. This is understandable because he's just sketching out harmonic frameworks for flutists to devise variations in—the flutists are meant to work out details like that themselves (see e.g. the other part of his Tab. X). However, rules of the octave are meant to provide guidance for writing harmony, so they do worry about voice leading, as you can easily verify from the manuals Gjerdigen put up. So, despite my earlier confusion, much of what I said is still relevant, although I'll do my best this time to put it in the proper context.

A few points in particular: Quantz doesn't concern himself much with avoiding parallel 5ths and 8ves, keeping the motion of individual voices varied, or balancing parallel and contrary motion between voices. We will need to correct for all of this somehow (there are some exceptions for parallel 5ths and 8ves as far as the Neopolitan folks go, which I'll discuss). None of that is just my opinion: on top of examining the rules of the octave given in the books Gjerdigen put up, you can read Fux's Gradus ad Parnassum for a text that was popular at the time and that states them quite clearly.

Also, rules of the octave are designed around harmonizing a descending or ascending bassline, not a melody. The partimenti exercises that come after they've been learned are designed around harmonizing a melody, but rules of the octave are meant to help students make connections between basslines and the harmonies implied by them. So, instead of working from Quantz's melodies, we'll need to work from the appropriate basslines, and see if we can harmonize them in accordance with Quantz's methods.

One last point: all the Neopolitan theorists seem to give three rules of the octave per "mood", starting with the 8ve, 3rd, and 5th on top of the I chord respectively. Since you only set out to write one, I'm going to do the same, in the interest of saving myself time. More-or-less arbitrarily I'll do one starting with the 8ve on top.

Just to make sure we don't stray too far from the Neopolitan tradition, let's do a quick analysis of one of their rules of the octave—I went with one of Fenaroli's:

Fenaroli's 8ve-on-top major rule of the octave (listen)

I did this in a rush so if there are any careless mistakes I apologize. :P

From this (and the other Neopolitan rules of the octave you can read about on that website) we can glean the following:

  • Always start and end with a I chord in root position.
  • End with a V-I, but it's okay if it's quite weak in cadential terms—the stepwise bassline forces you to make some sacrifices (cadences are taught separately anyway in this tradition).
  • You can handle some of the awkwardness of the descending bassline through a brief tonicization of the dominant key starting from the third step (other Neopolitan theorists do this as well).
  • Occasional parallel 5ths/8ves are permitted between the bassline and the inner voices, but never sequentially. (Apparent parallel 5ths/8ves in the upper voices are generally due to the entrance of a 4th voice for the sake of 7th chords and such.)
  • The inner voices can be more restricted in their movement than they might be in a real piece, but they should still have pleasing contours.
  • The "melody" in the top voice does not need to follow the rules of good melodic writing; it can be thought of like another inner voice (all of this is meant as a study of accompaniment).
  • EDIT 2: In my haste, I neglected an important point, which is that the chords assigned to step 5 of the scale should be appropriate for cadential purposes. Of course, when composing an actual piece of music, you could always substitute in the appropriate harmonies when you wanted a cadence, but these "rules of the octave" seem to be meant as a starting point for teaching purposes, so it's better to keep things simple. The Neopolitan theorists seem to always put a V chord there, and furthermore a triad as opposed to a seventh chord.
  • Other than these guidelines, follow the rules of good voice leading and keep the harmony moving.

Okay, now let's check out Quantz:

  • Tab. IX Fig. 2 steps 1-2-3 is basically just a long I chord (the apparent ii in the middle is basically passing motion on the way to a first inversion I). We don't really have the space for that here so we might substitute a vii as Funaroli uses, which shares some notes with the ii but will create a greater sense of motion.
  • Tab. X Fig. 4 steps 3-4-5-6 is I-vii-I-ii7-V. This gives us some trouble, both because using a vii on steps 2 and 4 will get monotonous and because we should avoid returning to the I after step 3 for the same reason. The vii forces us to move to the I next for voice leading reasons, so we can solve both problems by substituting something else. V7-vi7-ii7-IV might be the closest we can get, since we need to follow this with a V-I.
  • Tab. XI Fig. 6 is either steps 3-4-5 or 6-7-8 depending on whether you view this as in C or in G. In C terms it's vi7-II-V; in G terms it's ii7-V-I. On the ascent it doesn't really make sense to tonicize G, but we are planning a vi7-ii7-IV-V progression which is fairly close. On the descent we will tonicize G, but we can't really use this progression, both because we'll need to already be in G by step 5 (downwards) and because we'll have a B in the bassline on step 7.
  • Tab. X Fig. 5 steps 6-5-4-3-2 is IV-I-vii-I-V. We would need to transpose this into G for the first two chords. Sadly we can't use a IV (in G) at this point because of the A in the bassline on step 6, and we kind of have to use a V (in G) there anyway in order to move to G. We'll also need to do something else for the vii-I-V part because we need to get back to G on step 2. We could do IV-I-V (in C terms) which isn't so far away.

Adding all this up, we get:

Rule of the octave by Quantzzioli, Quantz's Italian cousin (listen)

EDIT 2: I realize this has a significant issue if you were to actually use this to try to compose 18th-century-style music, which is that the chord given for the 5th scale step in the ascending rule is a vi7 chord, and thus would not perform the appropriate dominant function in perfect cadences and things. However, I'm reluctant to change it, because we live in the 21st century and I love the sound of that chord very much, so I would happily use it compose with anyway, broken tonal functionality or no. But I will revise this to be more suitable for 18th-century-style composition purposes if you like.

  • "I don't think it really reflects how composers thought about harmony at any point in the common practice period" ...then what did they use the rule of the octave for? Commented Dec 31, 2020 at 16:42
  • @MichaelCurtis Okay, I revised my answer after doing some research. Hopefully this is more useful to you. Commented Jan 1, 2021 at 9:16
  • I'm confused about what you are doing. You have a scale harmonization in the bass. The question really is how the treble line ^1 ^7 ^6 might best be "harmonized" long the lines of Quantz. I suppose the common patterns were ^1 ^7 ^1 as I V I or ^5 ^6 ^5 as I IV I and if the full decent ^1 ^7 ^6 ^5 was used it would have been I V V/V V like the rule of the octave. If that's the case, one "harmonization" of the descending scale just isn't enough. Commented Jan 2, 2021 at 20:29
  • In other words, what I'm thinking is if ^7 decended to ^6 the typical thing would be to continue to ^5 and the harmonization would be V V/V V. Commented Jan 2, 2021 at 20:38
  • So, are you not actually looking for a "rule of the octave", but rather for a harmonization of a treble line? My understanding is that a rule of the octave is always a harmonization of an ascending/descending bassline, as I explain in my post—it wouldn't serve its pedagogical function otherwise. What's your larger goal—like, what do you mean to use this for? Commented Jan 3, 2021 at 4:24

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