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When discussing modulation my book describes the 5-6 technique and here it gives an example when discussing pivot chords. I dont get why the C to Am progression is labelled C 5-6? Ok if the bass remained on C I'd get it but here the bass goes to A. What gives?

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The book example is illustrating a musical process derived from 5-6 technique. The RNA is not intended in this case to be literal; it's just there to show the points in the music that are under consideration and their functional purpose.

The basic element of 5-6 technique is that it shifts a major chord to its relative minor chord: C major to A minor in this case. This technique can be used, for example, to break up parallel fifths, to destabilize the major chord, or to modulate.

What the example is demonstrating is that even though Haydn's chords are not literally I5-6, they function in the same way as would the literal progression. That the skip down to the root of the A minor chord can still be interpreted within the larger 5-6 technique context is explained in the earlier chapter referenced.

Aaron
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  • Why would IV ii be "not permitted?" Assuming the voice leading isn't bad. – Michael Curtis Oct 29 '21 at 19:15
  • Aaron, the 5 - 6 technique referenced in the chapter mentioned speaks about the movement from I to vi6... that is a I chord moving ^5 up to ^6. This is not happening here. Do you actually have the book because you said that the answer is there when I can tell you that I read that part several times. In this case he says that the bass also skips down to the root but doesnt that mean that it is an A minor chord and that the progression is simply I to vi? –  Oct 29 '21 at 19:16
  • @MichaelCurtis I don't understand the question. There's nothing wrong with IV ii. – Aaron Oct 29 '21 at 19:18
  • @armani The Haydn example is not a literal 5-6. It is a harmonic motion derived from 5-6 technique. In the Haydn, the move from C major to A minor in a generalized example of 5-6 technique. It includes the bass motion explained in the earlier chapter, which explains that the bass movement — also not a literal 5-6 use — can also be a part of the overall 5-6 technique purpose. (Yes, I have the book. Different edition, but the text is identical in this section.) – Aaron Oct 29 '21 at 19:21
  • @Aaron, you wrote: That the skip down to the root of the A minor chord is "permitted". In RNA I read that to mean G: IV ii is "permitted", as if skipping to ii would otherwise be not permitted. – Michael Curtis Oct 29 '21 at 19:38
  • @MichaelCurtis Okay, I understand. What I meant was that the IV ii progression is still considered an example (a generalized example) of 5-6 technique — in the view of Aldwell and Schachter. It's the interpretation as "5-6 technique" that's "permitted", not the chord progression itself, which is, of course, fine, regardless the interpretation. – Aaron Oct 29 '21 at 19:42
  • @MichaelCurtis Would appreciate your thoughts on whether my edit sufficiently clarifies the point. – Aaron Oct 29 '21 at 19:44
  • @Aaron. Yeah, that looks good. Although I have to say "clarify" and "understand" in relation to this textbook's example really push the limit of sensibility! So strange to make an analogy to IV ii6 (apparently for it's simple voice leading) instead of just saying root position IV ii will involve some skips and avoid parallel motion, or something like that. – Michael Curtis Oct 29 '21 at 19:50
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The 5-6 notation makes me think that is supposed to mean either scale tones ^5 ^6 or something like the counterpoint suspension 6-5 in reverse order. Broadly, 5 usually conveys the sense of "root position", at least for figured bass.

But the bass moving from C to A and the author clearly saying the chords change from C major to A minor don't seem to match the Roman numerals given. It seems like the textual description would match this...

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If it weren't for the text clearly saying "A minor chord" I would think the analysis is saying the A minor chord is just a kind of elaboration of the C major chord that shouldn't be analyzed with a Roman numeral.

That would be similar to how the V Roman numeral is used instead of I6/4 V7.

Two chords labeled I (or IV in G major) and two chords labeled V seem to show how the function is just two events - subdominant to dominant - for four chords.

Again, the confusing thing about that is the bass changes on the I (IV) but the bass stays the same for the V.

Does the book actual explain its use of Roman numerals? I learned them as indicating chord roots. But I also understand they can denote scale degrees. This...

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...treats V as a scale degree indicator and is very much like figured bass.

EDIT

This was my first thought, but it was so preposterous I didn't post it, but after writing it out is sort of makes sense. Works better in notation that words...

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...the first bar is what I though of as a "5-6 motion", the second bar is what you get after moving a bunch of notes around changing all the intervals so that the 5-6 motion is obliterated, and the resulting root position A minor chord is ignored for no apparent reason.

Michael Curtis
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  • Michael. Why would the A min chord be an elaboration of the C major chord when it is in fact an A min chord? –  Oct 29 '21 at 17:36
  • @armani, I just ask confused as you on that question. I'm just trying to make sense of how the Roman numerals were applied. The elaboration would be something like C major triad becomes Cadd6 - or if you did it with sensible Roman numerals - C: I vi6/5. But that doesn't make sense to me when the second chord is so clearly an root position A minor chord with no seventh. In other words, if the second chord were Am7, you could view it as just a rearranging of voices from a Cadd6, and elaboration. But, In my crazy world I would analyze G: IV ii I6/4 V7 | I. – Michael Curtis Oct 29 '21 at 18:52
  • The numeric figure 5-6 is especially confusing. On the one hand it indicates some kind of ascending step of which there is none. And as a figured bass number, under a root position A minor chord, it corresponds to no interval in the chord. Again, one might think a possible misprint, but it's all repeated in the textual part. Maybe I'm missing something that someone will reveal in another answer. – Michael Curtis Oct 29 '21 at 18:52
  • @armani, I added an edit, FWIW. – Michael Curtis Oct 29 '21 at 19:04