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?

Originally Posted by Majesty

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.

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?

[I just realized I forgot to say G# in the final inversion (last bar), to avoid the augmented second in the theme, which is not really an interval that belongs to it]

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

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.