[Ike]

Hi. At 71, I'm hoping to try my hand at composing, even without any formal training. To do so, I've purchased several books on music theory, and I just finished reading (studying?) my first, Piston's textbook on Harmony (I have the 4th edition).

It's a pretty dense book, and I often found parts where I either thought there was a typo, or I just couldn't understand what Piston was saying. So I thought I'd ask about those passages here, if anyone would be willing to help me understand. I include 'apparent' typos, because I fear rather than there actually being a typo, I may just not understand. So I'll start off with the first few questions I have, going through the book from start to finish. If folks are kind enough to reply, then I'll keep going... there must be dozens of questions I have altogether.

1. p. 16 Example 2-7. the text gives two examples of overtones on a grand staff. The second 'overtones from E', is clear enough: a whole note chord of E below low C, G below middle C, middle C, and G above middle C. Then to the right, consecutively, are quarter notes showing the overtones: E below low C, E below middle C, B below middle C, E above middle C, G#, and B. Pretty straightforward, although I don't know why the three top notes on the chord are shown, nor do I know why the first overtone is the E below low C... I would have thought the first overtone would be the E above that.

But it's the first example that seems to have the typo. It is labeled 'overtones from G', and its chord is C 2 below middle C, middle C, E, G. The overtones are C 2 below middle C, C below middle C, G below middle C, middle C, E, and G. Aren't these the overtones of C, not G?


2. p. 118 Example 8-22 (also 8-25 on the next page). These are short passages from Handel and Bach, both with a signature of D major. In each of the analyses below the music, they begin with "B:". Shouldn't that be "b?", since both are in b minor? It seems that later in the text, Piston consistently uses lower case for the minor keys, but early on he isn't as careful (though there is a "b:" in example 8-16, page 115).


3. This is from the chapter on Secondary Dominants, which gave me fits, lol. It would be much too long to describe in full, so I guess only those who have access to the 4th edition of Piston may be able to help. In any case, it is on p. 248, Example 16-4. It shows all the the triads that have a secondary dominant function in the key of C (9 chords are shown). The text says "Four dominant sevenths, dreived from the major triads, are included in parentheses because their parent triads cannot readily be understood as having a secondary dominant function unless the seventh is present." However, only two of the chords are in parentheses. In addition, there are three labels under the chords that are in parentheses (none of them of chords in parentheses). But that makes 5 parentheses. So, is the 'four' in the text a typo? Are parentheses missing that should be around two more chords? Something else? I can't figure that out at all.

Well, that's certainly enough for a start. If folks are kind enough to help me out, I will continue my list of questions thereafter.

 

[EdwardBast]

1. p. 16 Example 2-7. the text gives two examples of overtones on a grand staff. The second 'overtones from E', is clear enough: a whole note chord of E below low C, G below middle C, middle C, and G above middle C. Then to the right, consecutively, are quarter notes showing the overtones: E below low C, E below middle C, B below middle C, E above middle C, G#, and B. Pretty straightforward, although I don't know why the three top notes on the chord are shown, nor do I know why the first overtone is the E below low C... I would have thought the first overtone would be the E above that.

But it's the first example that seems to have the typo. It is labeled 'overtones from G', and its chord is C 2 below middle C, middle C, E, G. The overtones are C 2 below middle C, C below middle C, G below middle C, middle C, E, and G. Aren't these the overtones of C, not G?

I have the 3rd edition. In it, only the examples pertaining to your first question seem to be present, so I can only answer that one:

In the 3rd edition the example is in a short section under the heading "Spacing." The overriding point is that a sense of "clarity and balance" results from placing the larger intervals at the bottom and smaller ones at top. Both of the whole note chords in the example you cite illustrate this point. In both cases, the largest interval is on the bottom and each successive interval above is smaller. This -- the ideal vertical spacing for chords -- is the only thing you need to get from the example.

The rest of the example and discussion is there to illustrate an extraneous point, to wit: Some people point out that the ideal vertical spacing resembles the spacing of overtones in the overtone series, wherein one can also see larger intervals below and progressively smaller ones above, and from this observation they conclude that the ideal spacing is ideal because it is like the "chord of nature" (the overtone series). The second part of the example, an ideally spaced C major chord with the 3rd, the note E, on the bottom, is meant to refute this conclusion; The ideal nature of the spacing in this case can't derive from the chord of nature, since the overtones of the bass note E don't even agree with the notes above (B and G# instead of C and G). Bottom line: The point is as relevant as how many angels can dance on the head of a pin. It isn't something he should have included in the beginning of a basic theory text. Once again, the only thing you need to get from the example is that the ideal spacing of chords, to be used when possible, is large intervals on the bottom, smaller ones on top.

In future, if it is possible to scan and post Piston's examples, we can answer your questions whether or not we have the same edition.

 

[Vasks]

I have the 4th edition. It indeed looks like there's a typo on p.16 and indeed pp.118-119 are b minor. Typos in a big book are not uncommon. I can recall the first edition of a theory book my mentor made. It was riddled with errors. His second edition corrected most but still some were retained.

As for 4 parenthesis, the example goes from bottom of p.248 to top of p.249!!

 

[Ike]

Thank you both! As for the parentheses, I totally missed the continuation at the top of the next page! What a dummy. Now it makes sense.

 

[Ike]

I replied to the two above posts yesterday, basically thanking you both, but since I'm a new member, it hasn't posted yet. I won't repeat it (hopefully it will be posted soon), but thanks to your kind and very helpful answers, I'll continue on to another question. I'd love to scan and upload the relevant pages of Piston 4th ed, but I don't have access to a scanner, much less a flat bed one, and until I have 10 posts and 12 additional hours, I can't upload anyway. Instead, I'll just try to describe the text as carefully as possible.

1. p. 309 Example 20-2. This is the difficult (for me anyway) chapter on the dominant seventh. The example is described as 'Dominant harmony consists, then, of the following group of chords:' The example then shows 7 chords. First, G B D, labelled V. Second, G B D F, labelled V7. Third (and this is the one I can't make sense of), B D F, labelled Vo9 (the 9 below the o), with another label below that, (VII). Fourth, G B D F A, labelled V9. Fifth, B D F A, labelled Vo9, with another label below that, (sometimes VII7). Sixth, G B D F Ab, labelled V9b. And seventh, B D F Ab, labelled Vo9b.

Ok.. all of these make fine sense except the 3rd. It has the same label as the 5th chord, which confuses me. In addition, how can it be a 9th chord without the A? The label in parentheses is fine... it is clearly the triad of of the 7th tone of C. The simplest explanation I can think of is that the label is a typo for Vo7. However, I don't remember Piston using the 'o' notation for the 7th chord, only the 9th. In any case, is that typo the explanation, or am I missing something else (as happens freequently!)?


2. I'll hold off on this one for now... it's about nondominant sevenths, and will be very complex to describe.

 

[Vasks]

Ok.. all of these make fine sense except the 3rd. It has the same label as the 5th chord, which confuses me. In addition, how can it be a 9th chord without the A?

Another typo. Which means you really know what the book is teaching you; enough to know when it's wrong.

As for the diminished symbol (small circle): It's being used correctly; however some text books make a distinction between half-diminished vs fully diminished (a half diminished has a slash through the circle. So the third and fifth chords are half-diminished (A natural on top) while the final two are fully (A-flat on top; the A-flat being "borrowed" from the parallel mode of C minor)

 

[Ike]

Thank you again! But just to clarify, the typo is that Vo9 in the third chord should be Vo7?

 

[Vasks]

Yes...............

 

[Ike]

Thank you! As noted previously, my next question covers a complicated passage in the text. However, I've thought of a way to post it without a scanner: I could take a picture of it with my simple smartphone, transfer it to my pc, then upload it. Before I do that, however, I want to be sure that it is legal to do so. The total shown would be about 1 page of the book. Might a moderator, or whoever an appropriate person might be for this, let me know if it's ok to upload a page of a copyrighted work? TIA.

 

[Taggart]

1 page out of 400 does seem like "fair usage".

 

[Ike]

Thank you, Taggart. Had to wait to get ability to post attachments... now to see if I can, lol.

OK, it seems to be working. Shown are the bottom half of page 348 of Piston (4th ed), and the top half of page 349, introducing nondominant seventh chords. (The pics aren't great, but hopefully they are readable when enlarged.) I think I understand the two examples (23-1 and -2), and the list of types of seventh chords seems straightforward as well. But when I come to the discussion after the list, I get totally lost.

Piston first mentions chords in the example which are in square brackets. He says these include the d. type, and 'the two forms of Vo9 (c, g)'. But while the d. and g. labelled chords are all bracketed in Example 23-2, none of the c. chords are. This is the first thing I don't understand.

The start of the next paragraph is worse. Piston refers to 'the other c forms'. What does he mean? The other c forms as opposed to what c forms? The c forms mentioned in the previous paragraph are 'Vo9 chords', but all of the chords labelled c are of this type (the three of them). So what can 'the other c forms' refer to?

Any enlightenment would be much appreciated!

 

[Vasks]

Piston first mentions chords in the example which are in square brackets. He says these include the d. type, and 'the two forms of Vo9 (c, g)'. But while the d. and g. labelled chords are all bracketed in Example 23-2, none of the c. chords are. This is the first thing I don't understand.

That's easy. The c chords are half-dimished. The d chords are dominant sevenths and g chords are fully diminished sevenths.

The start of the next paragraph is worse. Piston refers to 'the other c forms'. What does he mean? The other c forms as opposed to what c forms? The c forms mentioned in the previous paragraph are 'Vo9 chords', but all of the chords labelled c are of this type (the three of them). So what can 'the other c forms' refer to?

I'm not fully sure, but the answer seems to be in the paragraph when it says about "the other c forms" are an INCOMPLETE MAJOR NINTH. That would mean to me: b chords with a missing major third below them.

 

[Ike]

Thank you. However, I'm still confused, alas. Regarding my first question, I still don't see why the "c." chords are not bracketed. Piston certainly implies that they are, but there are brackets only on the d. and g. category chords.

Re my second question, there are only 3 'c.' chords total (4 if you include example 23-1). Which of those 3 (or 4) are "the other c forms"?

 

[Vasks]

OK, I've pieced together both of your concerns, Ike.

What Piston is saying is that the d & g chords are very strong in nature and need to resolve to their respective temporary tonics but that c chords are less strong in nature and therefore may not have to resolve.

If you need me to point out the voice leading implications regarding "resolution" please ask.

 

[millionrainbows]

That's easy. The c chords are half-dimished. The d chords are dominant sevenths and g chords are fully diminished sevenths.

I'm not fully sure, but the answer seems to be in the paragraph when it says about "the other c forms" are an INCOMPLETE MAJOR NINTH. That would mean to me: b chords with a missing major third below them.

I agree with that. Piston, elsewhere, considers the vii diminished triad (in C, that's B-D-F) as an incomplete G7 chord (G-B-D-F), and resolves it to I (C major). Beethoven would do this with dim7 triads, as in the late string quartet in F. He would simply put a new root below a dim 7, and change its function. This i somewhat advanced thinking; you need somebody like me to sit down with you at a piano, and you would understand it eventually. That's why it's so important to have a real flesh-and-blood theory teacher, instead of trying to learn it 'on line.'