Lesson with Mark

First of all, I would like to alert you that I edited my second secondary dominant example, keeping the harmonies in an attempt to make the III+6 more convincing. But I think the problem is that it is a very new chord for you. Either way, I will be teaching about it eventually.

First, however, I will discuss corrections. I liked the sound of all of them, especially your V/ii and V/vi exercises. I was, however, bothered to find upon closer inspection a dangerous amount of parallels. My criteria for parallels is much more liberal than some composers of the Classical period: in the Renaissance and Baroque many parallels were easily accepted as long as they were hidden with arpeggiation or other intervening material.

There were not, however, outright parallels unless the composer was sure no other solution would respect the musical vision. For beginners like you and me, this means we must train well now in exercises like these to avoid them, so that in real music we can focus on melody and expression. As someone who has battled with this extensively, I can say that with practice, avoiding parallels almost becomes subconscious. I found at least six parallel fifths and octaves; I think it might be a good idea for you to check those exercises and find and correct all of the parallels.

Also the dominant chord in bar three (after the V/V) really needs a 3rd and can easily get one in the tenor.

That said, it's nothing to worry about. Its not really what our lessons are about, and I think you are showing some true understanding with these progressions. I was extremely impressed to see the Bb Major chord before V/ii. Could you explain why you used it?



VOICE LEADING SECONDARY DOMINANTS

Even in dense four part harmony, all of the voices often have clear melodic trajectories. In a contrapuntal piece, all of the voices should have excellent and different curves to them. Whether approaching homophony or polyphony, Baroque composers often thought in terms of melody above all other aspects of music.

Thus to study secondary dominants, we must see how their extraordinary feature, their leading tone, their third, is used in melody.

Please open the attached file "Secondary Dominants - Voice Leading." The repeats divide the file into numbered examples I will refer to.

Example 1 shows the chromatic tone used in a stepwise pattern, somewhat like a passing tone. Border tone figures are also very common. Example 2 shows another stepwise pattern, this time composed exclusively of semitones. Both approaches are common whether the altered tone is in a florid melodic part or in an accompaniment.

Examples 5 and 6 illustrate how those approaches can be harmonized. Notice how the 7th can sometimes very conveniently be used. Example 5 is a sort of deceptive progression, and example 6 shows a root motion down by a third then up by a fifth, very common when a line rises by semitone.

Examples 3 and 4 have the leading tone approached by a leap. Note that in instrumental music, the melodic diminished fifth or fourth that may result is often acceptable. In example four, we see one leading tone deceptively resolving by a whole step to another leading tone. Notice carefully how I harmonize that in example 7, where V/ii makes an altered deceptive cadence to V/iii, a beautiful effect. Also notice how I retained the root of V/ii to become the 7th of V42/iii.

Some special sequences and voice leading patterns became almost traditional in the Baroque period. Example 8 shows the circle of fifths varied with secondary dominants. Notice the pattern where a leading tone resolves extraordinarily downwards, becoming the seventh of the next dominant. In a sequence like this the ear may loose track of the tonality; the music can continue indefinitely like this and jump off the sequence at any desired key.

A variation of that sequence can harmonize descending chromatic lines. Also, the circle of fifths can be varied in any way imaginable, using secondary dominants and leading tone chords as well as normal triads and sevenths.

Example 10 is a common embellishment to the deceptive cadence:
V V6/vi vi
Once again the bass moves upwards by semitone.

Finally, example 11 in E minor shows how a rising chromatic line in the bass can be harmonized by alternate 5 and 6 chords (you do know figured bass, right?), a favorite during the 17th century.



These are just the beginnings of the common ways secondary dominants were voice-led. All of these should be tools available for you to use, so they should ALL be carefully studied and mastered. Pay attention to how I managed every note, and, just as important, pay attention to their sound, their harmonic effect. Study other formulas in your favorite music. Use some of these in your remaining exercises . Above all make sure they are used appropriately; don't unnaturally force them in, and you will find that they will write themselves into the music.

I will assign analysis exercises after we finish the tiny four part harmony assignments.



And I have links here to scores of some of the pieces we discussed:

Domenico Zipoli - Canzona e Minor
http://icking-music-archive.org/scor...Canzona_Em.pdf

J. H. Rameau - Suite in a Minor - Sarabande
http://icking-music-archive.org/scor..._Sarabande.pdf

J. H. Rameau - Suite in a Minor - Gavotte and Doubles
http://icking-music-archive.org/scor...Gavotte_Am.pdf
It turns out that the progression I thought this featured is actually not here. But if you want, it might be a good exercise for you to analyze the harmonies of the gavotte itself. The doubles are all variations on the gavotte and thus share the exact same progression.

I see what you mean about the parallels, I wasn't paying too much attention to them, was concentrating on the secondary dominants. I shall be much more attentive on the next ones, to ensure none slip in

Yes, I do know figured bass, and use it regularly, I find it much easier to write melody and bassline, figuring the bassline, if I'm in a hurry to get something notated than to write out the harmony in any other way.

The Bb major in my V/ii exercise was there to lead smoothly into the A major chord, it could be analysed as VI in D minor, or a borrowed VII from the tonic minor. I personally would call it both

I shall make a start on the Minor ones, and should have them done relatively soon. I shall make an effort to be slightly more creative with them, trying out some of your formulae, and looking for others of my own.

Originally Posted by Mark

The Bb major in my V/ii exercise was there to lead smoothly into the A major chord, it could be analysed as VI in D minor, or a borrowed VII from the tonic minor. I personally would call it both

Very wise; and of course the fact that it is VI in d keeps the following V/d from sounding too unexpected. That's also the sort of thinking that may help you write a more convincing V/iii .

I have finished three progressions in c-minor.
They aren't too spectacular, but you still might want to take a quick look at them, especially the V/III, which as I used it could almost be called a modulation.

Here are three minor phrases I'm fairly happy with. I'm aware of one hidden parallel fifth in the third phrase, between the bass and the alto, bars one to two, but as far as I know the rest is clear. I've tried to be a bit more creative with these than the last ones, which were mainly just tonicizing the predominant.

I've tried to vary the exercises slightly, by using different meters and registers, just to keep things interesting, and give myself practice in more situations.

Thought I'd provide a brief analysis, to give you an idea of my intentions in each exercise:

In the first exercise I used a V/iv to precede an imperfect cadence. It seems more like an 8 bar sentence in structure than a 4 bar phrase, as the second bar ends with an imperfect cadence - though with a minor v - and the fourth bar ends with a perfect cadence after a bit of repetition, so I suppose it could be barred in 2/4 and called an 8 bar sentence. I was in a happy mood, and so ended with a tierce de picardie.

The second I was slightly more adventurous and decided to end the phrase with a perfect cadence on the relative major. This is definitely a four bar phrase, and leaves a definite feel of a need of a consequent phrase to balence it, with a perfect cadence on the tonic. I might write one actually, next time I have some time to kill

The third phrase I tried using one of your formulae, example ten in your finale file: V - V/VI - VI. This was a slight problem for me as your example was in the major mode, and I am in the minor, but eventually I worked out what I think to be a pleseant sounding and theortically sound progression.

I look forward to your comments/corrections

Originally Posted by Mark

Here are three minor phrases I'm fairly happy with. I'm aware of one hidden parallel fifth in the third phrase, between the bass and the alto, bars one to two, but as far as I know the rest is clear. I've tried to be a bit more creative with these than the last ones, which were mainly just tonicizing the predominant.

I've tried to vary the exercises slightly, by using different meters and registers, just to keep things interesting, and give myself practice in more situations.

Thought I'd provide a brief analysis, to give you an idea of my intentions in each exercise:

In the first exercise I used a V/iv to precede an imperfect cadence. It seems more like an 8 bar sentence in structure than a 4 bar phrase, as the second bar ends with an imperfect cadence - though with a minor v - and the fourth bar ends with a perfect cadence after a bit of repetition, so I suppose it could be barred in 2/4 and called an 8 bar sentence. I was in a happy mood, and so ended with a tierce de picardie.

The second I was slightly more adventurous and decided to end the phrase with a perfect cadence on the relative major. This is definitely a four bar phrase, and leaves a definite feel of a need of a consequent phrase to balence it, with a perfect cadence on the tonic. I might write one actually, next time I have some time to kill

The third phrase I tried using one of your formulae, example ten in your finale file: V - V/VI - VI. This was a slight problem for me as your example was in the major mode, and I am in the minor, but eventually I worked out what I think to be a pleseant sounding and theortically sound progression.

I look forward to your comments/corrections

I like how all of your exercises sound; I see you are improving and these are all harmonies that would fit in nicely in any music you might write.

And I have many comments and concerns .

NOTE: I actually had comments about your exercises, but they turned into a historical and philosophical commentary on parallels. So feel free to not read the rest of this post. I will post real comments and criticism tomorrow.

First, about those hidden parallels: I personally would advise you be more careful and avoid them. As for the truth, however, I doubt it matters at all. Parallels between an inner voice and the bass, especially fifths, are hardly noticeable.

Historically composers have been far less consistent with managing parallels than modern textbooks admit. Vocal composers of the Renaissance often religiously avoided parallels like the ones you used... That said, certain parallels textbooks now prohibit were common in many Renaissance situations! Parallels were often hidden with ornamentation in one of the voices so that the perfect interval would ultimately be approached by contrary motion despite the underlying parallel structure. The reverse was also common: when consorts would play vocal music on instruments, improvised ornaments and scale elaborations ("divisions") would often introduce hidden parallels. Renaissance treatises explicitly permitted such hidden fifths in fast music on the grounds that the ear barely hears fast notes!

Furthermore, as composers ventured further into the realms of accompanied melody and homophony, many theorists questioned whether or not parallels were an issue in chordal passages where the voices were not meant to sound independent. Keyboard treatises of the Renaissance often asserted that parallels were perfectly fine as "filler" in keyboard music. So in Frescobaldi's correntes and toccatas and in Byrd's excellent pavans, we can easily find parallels... everywhere! And of course the music was skillfully composed; the composers knew what they were doing.

That said, all Renaissance composers were quite skilled at avoiding parallels in contrapuntal and sacred music. And this trend eventually affected keyboard music and figured bass too, so that by the Baroque period parallels were once again taboo.

As an example of how I personally view parallels, I will present a small excerpt from Pachelbel. Pachelbel's music (and his Canon is neither representative of his style nor his skill) is always smooth and careful; every note is always clear and singable, each one carefully chosen. Pachelbel, perhaps more than Bach or Buxtehude or others, guarded a conservative ethic and almost never broke the rules he set for himself.

Now open the attachment "Parallel Fifths."

So imagine how surprised I was to find a perfectly obvious parallel fifth in the left hand of this variation from his Hexachordum Apollinis... a passage both virtuosic and flowing and intense... I admire his daring here. A composer who was so disciplined, yet here he simply decides the fifths are necessary. And having made his wise decision, he leaves the fifths plain to the eye, makes no pretense to hide them. A true master .



Well, I am sorry to bother you with that little unrelated rant, but I think it is important to have a deep understanding of the place of rules in music... which is something of course you will see with time, and probably already begin to realize.

As for me, I will refuse to purposely write certain parallels until I feel as wise as Pachelbel . Not that I haven't found accidental ones in my own music afterwards.. I just leave them there.
As for you; do whatever you want as long as you have thought through it.

Have read through and understood all that you've said, and think I've come to the decision that I'll try and avoid as many parallels as possible, as long as I can do so without screwing too much with the music, and avoid parallels between the bass and soprano, of course, and in contrapunctal textures - where the individual line is much more important that in homophonic textures.

I look forward to your comments

I like the sound of all of your exercises. You use all the secondary dominants well.

However I think the way you are using the minor v chord is affecting your sense of tonality. As I know you understand, the v chord is a modal phenomenon. It hardly tonicizes the i chord at all; in other words it does not at all fulfill the dominant function or any other tonal function for that matter.

This is an excellent example of the more general approach to harmony described in our first lesson.

Modal music in the minor modes from the Renaissance and early Baroque frequently utilizes the lowered seventh degree in sonorities like VII and v and III. These sounds, however, do not reaffirm the minor tonic. If anything, from time to time they will imply the relative major mode. More often a totally different "modal flavor" is imparted since even those dominant tendencies might not be followed to resolution... until the very end of the phrase, where a leading tone is artificially created in V or vii* to cadence onto i.

My favorite music is based on the old modes and I consciously adopt modal progressions in my music, so I applaud any use of modality in music. Your VII and v chords, however, are sending some of your exercises to the relative major.

Your second exercise is a classic example of what I tried to explain in my first lesson. You begin on a c minor chord and have three flats in your signature, so this must be in c minor, right?

You already know the answer: No. You do begin on a c minor chord. But then you move to a VII chord, a chord that lacks a leading tone and challenges the c minor feel. In fact, any major chord can be a dominant, and this one follows that tendency, although deceptively. You labeled the first three chords i VII6 i, but much more likely they sound like vi V6 vi6 in Eb Major. The minor v chord that follows worsens things further, and finally we see V7/III... or simply put, V in Eb Major. In fact this second exercise is attracted from the very start to Eb Major, never to c minor.

Your first exercise is more typical of modal music in that although the relative major is at first hinted at with the minor v chord, eventually a true dominant V chord appears to keep things in c minor.

The third exercise is nice, but what I was showing you originally was a varied deceptive cadence, V V/VI VI. Your secondary dominant is used well, but there is no deceptive cadence anywhere because there is no dominant - you used v once again! And of course such a modal progression is just fine as long as you understand what you are doing.

I have attached a version of your third exercise showing how I would use a true dominant where you used the minor v chord.



Like with the parallel fifths, I am not bothered by this at all. I myself love using v and VII in minor music. But remember that v and VII do not serve any sort of dominant function. So especially if you go ahead and use a secondary dominant right away, the ear may never get a chance to feel the original minor key... which is fine if that's what you intended.

So overall I enjoyed these last exercises and am merely checking to make you understand the affect those v and VII chords produce. Keep using v and VII as well as V and vii* in minor, carefully noting what keys are implied and the overall color and sound.

Another small issue is the augmented second I see in the bass of the third measure of your third exercise: the line moves from Ab to B. If the lower parts are not melodic and only serve to paint a rich harmonic accompaniment, chances are the ear will not notice the awkward melodic interval. If, however, you are writing vocal music or mean the part with the augmented second to be a melody, be sure you realize what you are doing.

The augmented second is often found melodically when arpeggiating through a diminished seventh chord or in between statements of a short motive. Only rarely is it appropriate in the middle of a continuous melody, perhaps as a special device. Otherwise it acts like a large leap, splitting the line in two or even worse, just sounding awkward.

Thus in a harmonic texture like yours it is fine. Once again I was just not sure if you were fully aware of it here.



And I found a good quote!:

Kostka, Stefan and Dorothy Payne (2003). Tonal Harmony, p.289. "The line between modulation and tonicization... is not clearly defined in tonal music, nor is it meant to be."

Your comments about v and VII make a lot of sense to me, and I shall think about what you've said. I personally love the sound of harmony based on the natural minor (Aeolian) but I see what you mean about the possibility of the tonic being ambiguous if other keys are tonicized before a true dominant in the original key appears. I shall think about this in my next exercises.

Your point about the augmented second is a good one, Iit wasn't intentional, and now - when listening for it - I do detect a slight 'awkwardness' and shall avoid this interval in future