Lesson with Ram

Ram is interested in working on his fugal techniques.

Lesson:

As you already know a fugue is a polyphonic piece were a number of voices enter/interact with one another using various contrapuntal means. Motifs are also extracted and are developed by contrapuntal means as well.

Before we begin writing fugues of any kind I'd like to first work on contrapuntal techniques.

So, in order to do so I would like for you to compose a fugue theme. Take special care in making the theme interesting in regards to interval leaps and rhythm as well. You can post it when you have done so. :)

OK, here is my subject proposal.

Do you use Finale?

Do you use Finale?

Ah no, sorry, I'm not using Windows at home: I have only Linux machines. Therefore, I'm using lilypond, which is free software. Why?

I use Finale and just wanted to know.:thumbsup:

Anyway,

First thing I want to talk about is a "Melodic Inversion".

A melodic inversion is what happens when a theme or motif appears but the direction of the intervals are moving in the opposite direction. The exact quality of the intervals may or may note be preserved in which case the inversion would be called a mirror inversion.

I will use your fugue theme as the example.

In your fugue theme you start on the note D and ascend a whole step to E and then another whole step up to F# then ascending a half step up to G then descending a half step back down to F#.

If you were to invert this part of the theme you would start on the note D and instead of ascending a whole step to E youwould descend down a whole step to C natural then descend another whole step to Bb then descend a half step down to A before ascending to a half step to Bb.

D-E-F#-G-A (Your original first two beats)

D-C-Bb-A-Bb (Inversion with quality of intervals preserved)

D-C#-B-A-B (Inversion with quality of intervals not preserved keeping the theme in the key of D Major)

Make sense? If so I would like for you to to give me 3 inversions of your entire fugue theme. The first inversion must preserve the quality of the intervals in the inversion. The second, should not preserve the quality and therefore the inversion would remain in the key of D Major. The third inversion should have moments where the quality of the intervals are sometime preserved and moments when they are not.

Makes perfect sense.

Here are the inversions you asked me to perform. During the exercice, I tried to think about the resulting key of the inversion (i.e. how I would harmonize the theme if it were in the soprano).

I'd say the mirror inversion could be harmonized in Bb major or G minor (since we don't have any F in the inversion, right?), the second is kept in D major whilst the last one is clearly in B minor.

However, I have a problem finding a proper harmonization at beat 3 of the first bar for the second inversion, without doing harmony syncopation (since the C# does not resolve in D major). The third inversion preserves the interesting tritone jump between the first and second bar, whilst giving little choice for harmonization -- in B minor, the only possibility I see is a cadential V (6:4) at the end of the first bar, which would be very surprising in the middle of an exposion, would not it be?

Going away and will return on Wednesday. We will resume lessons then. :D

Ok,

I see that the inversions were no ptoblem. One thing I would caution is that you should be careful about thinking only in keys. The inversions do naturally suggest keys that they may harmonized in, but remember a fugue is all about counterpoint and counteropint is about harmony being a product of melodic/intervalic occurances. The inversions may seem as if they can be harmonized in Bb Major, G minor, D Major and B minor, but when you begin to add lines of counterpoint you will not always have an entire phrase harmonized in one key at all times. Make sense?

Yes, I understand the mixing of different lines can pose constraints about which harmonies can be used / implied by a given passage, and that key changes can be more frequent due to those constraints.

Another note, these various techniques are valuable tools for development in your compositions.

Next, I would like for you to harmonize your various inversions with chords either above or below the inversions. This time, do so without a key signature and use accidentals as needed. I don't want you to feel forced to used harmonies that are diatonic to the suggested keys of the intervals.

Another note, these various techniques are valuable tools for development in your compositions.

Next, I would like for you to harmonize your various inversions with chords either above or below the inversions.

OK, here is a first attempt with the subject only, because I want to be sure I got the exercice right. I did not remove the key signature here for the subject, but I will do for the inversions.

Please comment on that first, and then I'll complete the harmonizations for the 3 remaining inversions. Note that all I did was block-chord harmonization, with only marginal concern about voice-leading in the chords, my main goal being to clearly outline the harmony.

Yes, that is the idea. However, don't feel the need to harmonize every individual note. You may use the block chords in other ways to create susupensions, anticipations, etc.

Anyway, I it looks good. I will take a much closer look at it and add more comments if I have any.

Yes, that is the idea. However, don't feel the need to harmonize every individual note. You may use the block chords in other ways to create susupensions, anticipations, etc.

I understand. I did a "basic" harmonization for the subject, but that does not mean it is the sole harmonization of it. I will try to do something different with it (since playing with the subject is likely to be something that occurs often in the fugue) once I have completed the harmonizations of the inversions you asked me to do.

Anyway, I it looks good. I will take a much closer look at it and add more comments if I have any.

So, I guess there was not much to say about it then...

Here's the harmonizations of the true subject inversion (with intervals preserved). You asked me to remove the key signature, so I obeyed.

Please comment before I proceed further with the two remaining inversions.

What you have is good so far. In your harmonizations below and above the inversion in measure two, beat one, I was a little surprised. But I liked it. Do How do you feel about the harmonizations you did? Eventually, I will ask you do write a fugue project. My hope is that you might take use some of the exercises as sketches or ideas. You could use the harmonization exercises as a kind of harmonic outline when leading your voices in the fugue.

Also, although some don't make a big deal out of parallel or direct perfect 5ths in the inner voices, I like to have them avoided if you can.

You can continue with the others.

What you have is good so far. In your harmonizations below and above the inversion in measure two, beat one, I was a little surprised. But I liked it.

OK then, I will continue and complete the harmonization of the other 2 inversions.

What surprised you? The sudden change of tonality? I've kept a smooth voice leading in the bass in the first case (F -> Eb) and a common tone in the second case (the upper C) to keep that as musical as possible. To my ear it did not sound bad, although I agree it is not something the listener can expect at this point. It can spark interest though, and the subject transition at this place is a tritone, a remarkable interval.

How do you feel about the harmonizations you did? Eventually, I will ask you do write a fugue project. My hope is that you might take use some of the exercises as sketches or ideas. You could use the harmonization exercises as a kind of harmonic outline when leading your voices in the fugue.

Well, I understand the aim is to write a fugue with this material, and this is only preparation... Of course I intend to use the harmonization exercises to guide me when writing the voices as counterpoint, but like I said, I did not pay too much attention to parallels when placing the various voices of these exercises, other than making sure dissonances were prepared when possible and resolve properly, and that no invalid doubling took place, but I did not pay attention to faulty parallels (the intent was to find harmonies to use whilst counterpointing, not writing 3 voices on top of the subject, right?).

So naturally, when writing the counterpoint, I will be able to use any consonant note in the harmony, not necessarily the one I've written during the harmonization. Or I may have to add an accented passing tone for imitation purposes... I have not really prepared the architecture of the fugue yet, although based on the harmonization work I've been doing, I think writing a fugue with this subject should be possible. Do you agree with that?

Also, although some don't make a big deal out of parallel or direct perfect 5ths in the inner voices, I like to have them avoided if you can.

I've been taught in the Conservatory to avoid parallel fifths and octaves between any two pairs of voices. So no problem here. However, for direct 5ths and octaves, we were taught to only avoid them between outer voices. The rationale being that these are actually causing "hidden" parallel 5ths and that those are very difficult to spot if they occur between the inner voices. I can try to avoid them though, but since I'm not used to do so, I may not spot them whilst writing, and fixing that after the fact can be tough.

Anyway, I it looks good. I will take a much closer look at it and add more comments if I have any.

Ooops, I noticed a mistake (probably a typo of mine) in the harmonization of the subject, when it is in the bass. In measure 1 (second system), beat 5, the upper voices must be D A D, not D B D or that is outlining a VI chord in D in the 6:4 position... As it is preceded by a +4 chord in D, it must go to I6, not VI6:4...

Do you agree?

Actually, I don't agree.

If you'd like to change the upper chord to D A D then that's fine. But what you have on beat 5 works because the preceeding chord is a V4 chord and

2

chord resolves without issue. Your leading tone, C# resolves naturally leading up to the tonic, your Supertonic can resolve up to the 3rd scale degree or down to the 1st scale degree which in this case it has resolved down, and your Dominant (A) could have remained to create I6 as you mentioned but leading the A up to B gives the resolution/cadence a decpetive feeling which you continue to resolve onward.

Actually, I don't agree.

If you'd like to change the upper chord to D A D then that's fine. But what you have on beat 5 works because the preceeding chord is a V4:2 chord and chord resolves without issue.

(Funny how anglo-saxons use 4:2 to name the 3rd inversion of V7 and we use +4 in France -- we also use +6 instead of 4:3, and name V7 as 7:+, the '+' indicating the leading note, here the 3rd of the chord. I'm using ":" as the vertical separator, because formatting vertically is almost impossible here).

You're right that my voice leading was correct. Still, I'm forming a VI of D in the 6:4 position. Perhaps I'm too analytical here and I should just view this chord as a "passing" chord, since all voices move forward conjointly up to the V6:5/ of G.

OK, I'll keep the orginal version then and stick to the deceptive resolution.

Any comments on my previous post?

You can continue with the others.

Here are the remaining harmonizations. I have added an harmonization of the homonym subject in D minor as well.

I've changed the mixed interval inversion when it is in the bass, putting a natural A instead of A# at the end of bar 1. This allowed a different harmonic path to be used. This should be OK given the nature of the inversion...

I have a few open questions in previous posts, and a new one for you:

In the mixed inversion harmonization, when subject is in the soprano, I have possibly used harmony syncopation at the bar1 / bar2 crossing: I end on the I of F# major, which is really the V of B minor, and I immediately make it clear that it's a V and not a I at the next bar because the subject adds the 7th (E). Is this permissible in that context or must I rework that part?

Thanks for your guidance.

Sorry, I've been really busy. I'll take a look at these and post comments

Still a bit busy. Will post comments after this weekend. My apologies! :P

Ok, looks good.

Next I want you to think about composing your Answer to your subject. Do you have much practice in working with the differences between Tonal, and Real answers?

Ok, looks good.

Could you answer the questions from my previous posts? There are too many loose questions...

Next I want you to think about composing your Answer to your subject. Do you have much practice in working with the differences between Tonal, and Real answers?

I'm afraid not. Does "tonal" answer mean that the subject is mutated to modulate back to the tonic at the end of the answer? How would you call an answer which is simply transposed to the dominant with only one alteration at the end, because the subject naturally modulates to the dominant and not mutating it would modulate to the dominant of the dominant, etc...?

Here are the remaining harmonizations. I have added an harmonization of the homonym subject in D minor as well.

I've changed the mixed interval inversion when it is in the bass, putting a natural A instead of A# at the end of bar 1. This allowed a different harmonic path to be used. This should be OK given the nature of the inversion...

I have a few open questions in previous posts, and a new one for you:

In the mixed inversion harmonization, when subject is in the soprano, I have possibly used harmony syncopation at the bar1 / bar2 crossing: I end on the I of F# major, which is really the V of B minor, and I immediately make it clear that it's a V and not a I at the next bar because the subject adds the 7th (E). Is this permissible in that context or must I rework that part?

Thanks for your guidance.

The E in the soprano on beat 1 of bar 2 is permissible. Remember the harmonization is not a strict 4-part harmony exercise. A fugue is a countrapuntal piece. THe purpose of the harmonization exercises is to get you thinking and planning about harmonic movement that you might want to consider when creating your lines of counterpoint for the fugue. The E adds a touch of dissonant color that you relsolve without issue.

Before we go on with tonal and real answers, are there any other questions you have? ;)

OK thanks, can you clarify what a "tonal" versus "real" answer is, and how to know which variant to use in general, and which I should use in my particular case with this subject?