Piano World Home Page Forums Our Most Popular Forums Composer's Lounge Harmony Exercises - Post #1

Hello all,

A recent discussion got people interested in doing and sharing their work on some harmony exercises. Looking for material, I stumbled upon the San Francisco Conservatory's website. They have a variety of additional exercises online for their theory and musicianship courses. (They use Aldwell-Schachter)

So I propose a bit of a homework share. Let's start with the first worksheet - common chords.

Go here:

http://www.sfcmtheory.com/figured_harmony/figured_harmony.htm

And download "1.c Exercises"

Eventually, I'd like to get through the whole set. So...who will be the first to post?

(Do any of the exercises you want - I'd urge everyone interested to participate regardless of skill level. Give it a try. I'll do my best to provide my solutions with some commentary.)

Happy Harmonizing!

Good to have some common material, and I'm also interested to join you folks in going through the whole set over time.

Some stupid questions to begin with (I hope I don't get disqualified for them ):

1.) Is the task in ex. 1c to fill in two middle voices, obeying the rules of 4-part setting?

2.) Given that this is called 'common chords' does this mean we are allowed to use T, S, D and their parallels in ground form, but no inversions or other chords than these?

3.) What is the meaning of the '#' and 'natural' signs below the system? I'm just not familiar with the notation.

I've also been interested in joining. (But I may not have enough time to do all the exercises I want to until late this month.)

Here are my questions:
Based on the notes provided, I would guess that inversions are permitted.

Kreisler, is there a reason you have jumped to exercise 1c and skipped 1a Common Chords: Cadences and 1b Common Chords: Sequences? It seems to me that understanding and working through these exercises would help with understanding 1c.

Rich

I thought people might be more interested in the longer examples that are in a more musical context. I'm happy to entertain questions and comments on the foundational exercises in 1a and 1b.

Perhaps we should devote this post to anything in 1...

And yes, I believe the 1c examples are given to fill in inner voices.

Also, since the symbols below the staff are figured bass, and subsequent exercises deal with inversions, I think all of these chords are to be done in root position.

Kreisler, I'm interested in the one that has sequences, because my book has already touched on it and I think I can grow into that one. However, I am missing the approach that is used for sequences. Is there either a resource for that, or is it something that can be sketched out in a few words?

What I have in Horwood is a brief bit where the pattern in the soprano either ends up zigzagging its way down i.e E,F,D,E,C,D,B,C or descending in seconds like a scale. The pattern or approach he uses is "using a series of chords with roots raising a fourth and falling a fifth alternatively. This is sometimes known as the dominant sequence." [diagramatic examples follow]

Is that generally "it"? Is there more? Something I/we should know? [assessing whether to try it when I get the time]

Okay, here's the 2nd sequence from worksheet 1b.

The idea behind a sequence is that you have a pattern that is repeated at a higher or lower pitch level. Thus, whatever we use for the 1st measure we simply move down a step for the 2nd measure, and so on until the final cadence requires a break in the pattern.

My inner monologue went something like this:

"Okay, so we have roots in the bass and begin with a 3rd in the soprano. Usually, we like to double the root, so let's double the root in the alto and add the 5th in the tenor. The second measure has the 5th in the soprano, so the tenor and alto get the doubled root and the 3rd. Tenor can't go down to the third because it's a huge awkward jump. Tenor can't really go down to the fifth because it creates direct fifths with the bass (approaching a perfect consonant by similar motion is ethically questionable in counterpoint land.) So tenor has to go up to the 3rd, and the alto part gets to sit on the C:



I was unhappy with this for two reasons. First, I used to sing tenor (long ago), and that high A, while common in virtuoso operatic arias, is just a bit too high for my tastes.

So I thought I'd try the other option - begin by doubling the root in the tenor and put the 5th in the alto. This actually works out pretty well, the only problem being the direct fifths from beat 3 to beat 1, but that's not too bad because it's between the inner voices and one of them is stepwise.

Here's the finished result with the cadence added at the end:

Oh, and somebody proofread me. I actually make a lot of mistakes, and while I'll do my best to edit this stuff before I post it, I can guarantee some mistakes will creep in.

Also, I tend to write based on experience, my ear, and my own version of "the rules." In my annotations, I'm giving you the way I think about things, and they may or may not line up with how the material is presented in textbooks or by real theorists. (For example, I'm pretty sure there's something fishy about what I said about direct fifths earlier, but it seems to work for me.)

YMMV!

HAHAHA! Found my first error already. The B in the tenor on m. 1 beat 3 and the A on m. 2 beat 3 in the first example should be down a step. The tenor should stay on the same note for beats 2 and 3 in both measures.

Ugh..this is why theory teachers always tell you to play your examples. Unfortunately, I'm sitting in the coffee shop and too lazy to get the headphones out. :P

And there I was thinking those were some interesting-sounding chords.

It means that that particular chord will have that kind of accidental in it.

I had to look that one up. A "common chord" simply means one of the chords that in root position has three notes a third apart, i.e. occupying 3 adjacent lines or space in closed position: major, minor, aug or dim.

Yes, the # is figured bass shorthand for #3 and means a sharp third above the bass. You'll see things like b6, natural-3, etc...

They all relate to an interval above the bass NOTE. (Not necessarily the root of the chord.)

Here's my take on the 1st sequence in exercise 1b. Is this correct or are there any mistakes?



In that website, every topic seems to have some sequences associated with it. I have never seen sequences used so prominently. In my (German) books on harmony, sequences are just mentioned on one or two pages. In particular, one of them mentions "The functional analysis of sequences..." (like indicated by me below the notes) "...is usually not very helpful." This makes sense to me since after one atomic part the entire sequence is essentially predetermined, isn't it? The book recommends just to label the first atomic part (in this case bar 1: T D) and for the repetitions just mention their anchor points (here: bar 2=Tp, bar 3=S, bar 4=Sp).

So in a nutshell I'm currently a bit confused what is the learning goal from filling out the sequences? Oddly I also did not find anything on it in the Aldwell/Schachter book (3rd ed) which seems to be the basis for these exercises.

In any case, this is going to be fun. I hope we will have enough motivation to do this for some time!

PS. In my post, the image appears downscaled as compared to the original and therefore the lines look a bit strange. Does anyone know how I can adjust the scaling?
PPS. Thanks keystring & Kreisler for the notation explanation.

Is this the right idea? It's another exercise in 1b

(Sorry about the smudgy appearance)

Do accidental always refer to the 3 (middle note of chord in root position)?

AFAIK, in basso continuo notation, an accidental without a number always refers to the third of a chord. In contrast, e.g. an augmented 4th would be denoted as 4#.

Edit: As often, Wiki seems to have some good summary:
http://en.wikipedia.org/wiki/Figured_bass

Thank you.

Ex. 1c, part 1 -- any comments/hints would be welcome (tomorrow, I plan also to look at others' "homework", e.g. keystring, Kreisler). I just played it and it sounds quite strange!! (something wrong?)



I have tried to consider the following rules for harmonization (but I'm tired and have little experience so I guess there are quite some errors):

Doubling of notes:
--Never double the leading tone when it is part of V or VII
--Double more stable parts, often the root. The final chord almost always contains the root doubled.
--Never double the 7; in 7th chords sometimes the root is doubled and the 5th omitted

Forbidden parallel motions:
--Parallel unisons, octaves, and fifths WITHIN THE SAME PAIR OF VOICES
--Consecutive octaves or 5ths resulting from contrary motion
--Hidden 5ths or octaves (i.e. a 5th or octave is approached by similar motion): far less dramatic than real parallels, but at least avoid hidden octaves in the outer voices unless soprano moves by step

Btw, a more comprehensive summary of the "rules" is given on p. 78 of Aldwell/Schachter.

Good night from Switzerland for now

I'd love to participate. Can someone tell me how to post images of the exercises as everyone has been doing?

Also, I've always wondered, what's the big deal with all these parallels? I just don't hear anything strange. I'm studying theory on my own, and came across "implied parallels." This is frustrating! If I don't hear normal parallels, how can I catch implied ones?

What do the symbols "T, D, Tp, etc." mean?