Lessons with Matthaeus

Hi Máté. Just to say sorry there hasn't been a lesson for so long. I'm working on it! In the mean time, you're welcome to do some very basic progressions (three or four chords max) and try a few suspensions with them.

OK Matt, I will do it soon!

Hello Matt! I'm attaching the progressions you asked. I had trouble with naming the dissonant chords (except 6/4), so I've added interval numbers only.
Some suspersions are resolved to 6/3 chord. I don't know if it's good, but sounds OK to me.

Máté

EDIT: In the C sharp minor progression, the last chord is v6/3 instead V6/3. Sorry for the typo!

Hi Máté

Thanks a lot for doing the homework. I now realise that there's a few things I should have told you before setting this h/w, and as well as doing corrections I've set another exercise in two part counterpoint that should help sort some of these problems out.

Just a few other things to remember when writing suspensions in four part harmony:

1) In 9-8 suspensions the root AND third must always be present in the other voices (the fifth is less important) - sorry I should have said this! - your f# minor suspension doesn't quite work because of this.
2) In 4-3 suspensions the root and the fifth must always be present in the other voices. No other notes can be present at the same time! (In your G minor suspension you have the third present with 6 and 4). Remember what I put in the lesson - the resolution note should not be present at the same time as the
suspension (except in the case of the 9-8 suspension, when it should always be sounding in the bass i.e. the root).
3) In 7-6 suspensions the root AND third must always be present in the other voices (again the fifth is less important).
4) Although your 6/4 chords are correctly prepared they aren't really used appropriately if you see what I mean. I will go over this in the next lesson so don't panic. However, there are only really THREE real acceptable uses of the 6/4. i) I6/4 as preparation for a perfect cadence before V ii) The progession I6/4 - V at an imperfect cadence iii) V6/4 used as a passing chord (like vii6/3) between I and I6/3. It's best used with the seventh (V6/4/3).

[The reason for this is that the 6/4 is almost like putting musical brakes on. It strongly implies that the bass note of the chord in the dominant note, because it has so much rhythmic/dissonant weight]

My advice for the moment is to avoid 6/4 chords altogether. They are not normal chords at all, and can't be used for much.

5) The melodic minor scale descending must never be used in the bass in the wrong direction (i.e. going up)! In your c# minor exercise, second bar, the bass moves up from a to b natural. This sounds really weak, and not really tonal... The best thing to do in the situation is move down to V, as that is what the descending bass motion that you (correctly!) had before. When going up, you should always use the melodic minor ascending, or at least the harmonic minor - I've attached some examples of these so don't worry if you don't get what I mean!

6) When you use chord vii6/3 after I, you must go to I6/3. In your G-flat major example you've substituted I6/3 with vi, which sounds very modal and weak, and not tonal at all. Although vi and I are closely related, they aren't exactly interchangeable. If you wanted to do this as part of a deliberate musical anti-climax, that would be fine, but again for now, I'd stick to using the progression I - vii6/3 - I6/3, or just I - vii6/3 - I.

Your voice-leading is still very good throughout the homework, which is really good to see. Keep it up, hopefully the above problems won't be difficult to sort out!

OK for the next homework, a few basic rules about writing two part counterpoint...

Always begin on a unison, fifth, or third. You can harmonise the other notes with a fifth, octave (but watch out for consecutives!), thirds or sixths. In general it's better to save the fifths and octaves for the very beginning and ending cadence.

You may also use suspensions wherever you wish, as long as the are prepared and resolve correctly (check out my examples in the last lesson).

Do not approach a fifth or octave by similar motion (e.g. G in the bass with B in the treble going to C in the bass with G in the treble). This is called hidden fifths/octaves, and sounds almost as bad as consecutive in two part counterpoint! Always use contrary motion instead (e.g. G in the bass with B in the treble goes to C in the bass with C in the treble - a perfect cadence in 2 part counterpoint).

You can also use passing notes, to connect notes that are a third apart, and you can leap to other notes if they are consonant with the bass note beneath.

Take your time, as this is actually quite tricky. Good luck!

Hi Matt, thanks a lot for correcting me!!! Sorry about the poor chord-progressions, I've concentrated on making suspensions first (extra sorry about my G minor 4-3 which is really a shame).

So I should always write suspensions 9 and 7 as 9/3 and 7/3, and 4 as 5/4 (without the 3rd) and the root must always present. I will keep that it mind.
6/4 chords are bad so I will not use them except the 3 cases you've mentioned. By the way, in the B flat major excercise I'm using ii6/4 (the 4th is prepared) which is not corrected by you. That means it's good?

I'm attaching the 2-part counterpoint homework. The A minor one was very difficult, because the 2nd bar of the excercise (bar 7 really) seems to start with a V7 so the 2nd note (D) cannot act as a preparation since it is the 7th of the chord, which is dissonant: placing the root (E) in the bass forms a 7th, placing the 3rd (G#) in the bass forms a diminished 5th with it. So I failed to make a suspension in this excercise.

I've tried to write implied harmonies below the notes on strong beats (except at suspensions), but I'm not sure they are good.

Waiting for the next lesson, I hope it comes soon!

Máté

Hi Máté,

Thanks for doing the homework so quickly. You've done a really good job, I'm impressed! The only problem, as you mention is the second bar of the a minor exercise. I think to be honest, in this sort of exercise, the best thing would have been to move to C major briefly, but having a G natural in the bass under the B and D, and then move down to C, creating a circle of fifths progression. Or otherwise, you could have had G-sharp followed by A, and then just tied this A into the next one. This would have been ok (but not great), because the dissonant D comes on a weak beat. Don't worry, it was a tricky exercise!

As you say, the D you have is unprepared, which in two part counterpoint like this, isn't really appropriate - although in other situations it might be. Having the B is more of a problem actually, because the C on the fourth beat of the melody isn't harmonised properly, I really wanted the bass note to be an A or a C here.

In the last exercise I didn't notice that 6/4 - thanks for pointing it out! I still wouldn't have it; I would change the E flat in the top voice a D, and if you wanted you could have moved to E flat on the second beat.

Ok good work, lesson soon.

The implied harmonies were all fine. It's funny you know though, everyone on here (in these lesson forums) seems to focus on implied harmonies when they write counterpoint - but it's really not that important actually. Counterpoint is much more about intervals than harmonies when you're writing in two parts like this. Of course when you have to write a Bach invention harmonies become much more important (because he does do things like jumping to the seventh), and obviously once you get up to three parts it's really all about harmony. Although there are some things Bach does that aren't really harmonic in his contrapuntal works, they are only justified by the horizontal movement of individual lines.

Ok lesson soon I promise...

Hello Matt!

Sorry about the implied harmonies! The excercise started with "Harmonise this melody...", so I thought I need to think in harmonies/progressions and that's why the roman numerals are written. I try to keep in mind that counterpoint is not all about harmony. When listening to a renaissance piece I'm often wondering, how could composers of 16th century make such beautiful music without any advanced theory about harmonies and progressions.

Hi Máté. Finally another lesson! Homework to follow.

Hi Máté,

I'm aware that we've been moving very slowly (which is completely my fault!), so once you've read that lesson I want to move on asap whilst I've got the chance to do some stuff with you. Have a look at this incomplete piano sonata by Mozart. If you can give it play through.

Now whenever you look at any piece of tonal music, as I'm sure you are, you should always ask yourself what key it's in. I think the title gives this one away a bit... C major.

Ok so now ask yourself: does it always stay in C major?
What happens bar 21? Where do those f sharp come from? Why are they there (i.e. what purpose do they serve)?

Hi Matt! I've read your lesson and managed to do some cadencial 6/4. I think we can go on, too.

In the bar 18 of the sonata there is an imperfect cadence (ends with G major). After that the next phrase(?) starts with a G major chord, too, and in bar 19-20, note F is not used. Bar 20 has a C major chord in 2nd inversion perhaps to avoid a cadencial "feeling" (V-I6/4 is not a perfect cadence), however I'm not 100% sure about it.

Bar 21: There's a D major chord in 1st inversion (F sharp in the bass) with an added 7th (C) at the end of the bar which suggests a modulation to G major (bar 22). At bar 23 a 7th (F natural) is added to the G major chord, and it modulates back to C major (bar 24).

Hope I've answered correctly. It's a pity I cannot play it on the piano :
I like anything in 3/4 time; this piece of the sonata can be very happy