Please excuse the intermission in posting, but I have been suffering with some computer-realted issues: My trusty Cube has been suffering relatively frequent kernel panics since I upgraded it's OS to 10.3 and my old AirPort Base Station's internal modem has pooped out. As a result, I have had to post from my PowerBook, and am crippled by not having the luxury of my 23" Cinema HD Display. So, I had to get the following nine screen shots on the Cube, transfer them to the PowerBook, and then upload them to my Smugmug account. To call this process tedious or time consuming would be an understatement. But, I did finally get it done, so here we go.
As I was working on the harmonic canons
, I came up with a nice theme that will work well for a sonata-form movement, and so I will be pursuing that subject in today's post. The toughest nut to crack for an aspiring composer who is trying to learn to write fugues or sonata-form movements is the question of subject or theme choice. What makes a good fugue theme? What makes a good sonata theme? I bring these up together because they share some common traits, and yet they are different enough that what works for a fugue theme may not work for a sonata theme and vice versa
Both fugue themes and sonata themes should be flexible. By that I mean first of all that they should lend themselves to quadrant rotation
- the primary theme should work in it's original rectus
form, in inversus
, and in the retrogrades of these two forms also, if at all possible. Not only that, but they should also work in either the major or minor genders, and be amenable to frangibility
, or fragmentation into smaller portions. Fugue themes usually have an increasing frequency of attacks, and a decreasing frequency of rests: in other words they have longer notes at the beginning, and shorter ones at the end. These type of subjects are called head and tail
subjects, and the Royal Theme
that C.P.E. Bach and Frederick the Great created in a vain attempt to befuddle J.S. Bach that is found in the transcendental Musical Offering
, and the Motto Theme
that works with the BACH musical anagram that Bach used in his other towering monument, The Art of Fugue
are the best exemplars of this species of subject. There are a bewilderingly vast variety of fugue subject types in Bach's two Well Tempered Clavier
volumes, but if you look at what he was using at the end of his career, he chose the head and tail
types almost exclusively for their obvious superiority. Fugue themes also usually lend themselves to canonic interactions for stretto
sections, and writing fugue themes as canons is in fact the best of all possible proceedures, which I will cover at some point.
Sonata themes, on the other hand, may have the shorter notes at the beginning and are often followed by a broader figure that lends itself to powerful cadential interpretations. The most startlingly brief of these would be the Fate
theme from Beethoven's Fifth Symphony, followed by his overpoweringly strong first theme from the opening movement of the Ninth. Again, Beethoven used a wide variety of sonata theme types, but his most powerful and memorable movements were created with these short and sweet cadential types that lend themselves to frangibility
and quadrant rotation
: I believe if you are trying to follow the legacy of great composers like Bach and Beethoven, it is most instructive to analyze what they were writing at the end
of their careers - when they were at the height of their powers - rather than their earlier more formative works.
It is with that idea in mind that I have been seaching for a sonata theme that has elements in common with that first theme from the Allegro ma non troppo, un poco maestoso
of Beethoven's Ninth Symphony. As I was working on ornamenting one of the recent harmonic canons I developed, I stumbled upon a figure that worked with one of the nota cambiata
quadrant rotations that was "perfect". The following pages from my sketch book will demonstrate some of the techniques used to develop this theme.
Sketching and sketchbook creation and useage is something that I was never taught in all my years as an undergraduate, nor did I encounter any professors who taught the subject right through my years as a doctoral candidate. This is ridiculous on it's face, since virtually every great composer in history had well developed sketching proceedures that they employed on a constant basis, and since with modern music notation programs with built in sequencers, today's composer has the technology to create sketching proceedures and sketchbooks that a Bach, Mozart, or Beethoven would have died for (Though Beethoven's deafness would have made the sequencer sort-of limited in it's value to him personally). I had the oportunity to look at some facsimilies of the surviving notebooks of Mozart and Beethoven, and the progress of the themes, especially those of Beethoven, from relatively mundane basic figures to well polished utterances of musical magnificence is startling. The theme of the slow movement of Beethoven's Fifth Symphony, which is one of sublime beauty, started out sounding like something a neophite would have written. Noticing this proceedure, which often spanned years, was a seminal moment for me, and so I thought it worthy to share a little of my own sketching techniques.
Above is page one of my sketchbook for this theme, showing first the theme in the major mode harmonized as simply as possible in four voices. Even if the theme is going to be used for a movement in the minor mode, as this one will, I find it advantageous to start out in the major, as translations to the other gender are more readily made than from the minor, which has a lot more gender-specific elements to it. The second stave has the theme with a constant half note bass line, and introduces a vi(m7)
on the second half of the first measure, while the third staff has a constant quarter note bass line. Note that the second and third examples also have the traditional deceptive resolutions
with the deceptive movement native to the current mode first, and the one from the parallel minor second. It is usefull to not only hear these effects, but also to work out where they are available and where they are not, as we shall see. The bottom three staves show the theme translated to the minor gender with the corresponding natural reversal of the deceptive resolutions' target chords.
Page two of my sketchbook shows how the inversus
of the theme works with exactly the same basic harmonization variants, in both the major and minor modes, that the rectus
does, so long as the inverted form is diatonically mirrored at the normal fifth degree's tonic level. Note though, that with the doubled fourth degrees in the penultimate dominant seventh harmony the traditional deceptive resolutions are no longer available.
Since both the rectus
forms work with the same harmonizations individually, they obviously will work in simultanaity. This is a very cool effect, if I do say so myself.
Focusing on the minor mode that the sonata-form movement will actually end up being in, we find that the minor gender of the theme will work with an idiomatic descending chromatic bass line, as I have shown in the top example. The A-flat descending to G in the bass presents the oportunity to employ a V(4/2/b)/V
at that point, and in the traditional arrangement found with the so-called French Sixth
. On the third line I created more minor-idiomatic chromaticism in the interior voices, and developed that into an echo of the theme's rhythmic head figure intervallically contracted penultimate to the resolution. This is a powerful unifying force here. The bottom two staves present this variant reduced to a three voice contrapuntal texture, which will be used in the actual composition, above yet another variant that can be used in a complete simultaneous diatonic mirror
, as we will shortly see.
On page five of my digital notebook, I used the same chromaticised minor mode variants with the theme in the major gender. Interesting and seldom-heard sonic effects can be achieved with this technique. Note that I have again been alternately employing deceptive resolutions in these examples, but the only one available is the version native to the major mode because the note B must descend to A instead of G moving to A or A-flat: A melodic augmented second in the bass could be used, but in these sketches I want only the most normal and natural deceptive movements at this point for reasons based purely on personal prefferences.
On page six I have developed these chromaticised interior voices in the minor and major genders over diatonic bass lines. Here, both the native and parallel mode deceptive resolutions are available again.
For page seven I returned to the three voice contrapuntal chromatic variant I developed earlier to create a complete diatonic mirror
, which you can see on the second stave. The process for creating a diatonic mirror involves using the third degree of the tonic triad as the point of axial rotation and answering the first degree with the fifth degree. In the seemingly amazing arrangement found on the third stave, these two mirrors work in simultanaity to create a six-voice complete diatonic mirror
without any contrapuntal laws being broken. I repeated this process with the major/minor gender hybrid form of the theme on the three lower staves. I had to change the chromatic figure that previously implied a V/V
-type harmony in the secong half of the second measure of the theme to get this to work out. These two six-voice mirrors sound quite magnificent, with the pure minor version sounding particularly bizarre
, or even macabre
, while this effect is slightly attenuated in the hybrid form. Obviously, these will be saved for climactic moments in the final symphonic movement.
I wanted a less severe sounding version of these simultaneous mirror climaxes, so I developed one in the major mode over a diatonic bass line on page eight. Notice I left out the chromatic inner voice as well, but maintained the constant eight note surface rhyhtm by continuing back the alternating C motion of the final figure. This ended up being highly effective and the resulting pure major diatonic mirror sounds quite grand, but there is one parallel fifth. Since this parallel fifth is at the octave double of a twelfth, and since the twelfth is the location of the lower note's harmonic anyway, this neither noticable, nor is it distracting in any way. Having completed initial development of the basic theme, I extracted it's most obvious frangibility-based sequential version on the bottom two staves. The repeat of the sequence has secondary dominant leading tones and the V/V
's lowered seventh. This particular episode sounds more than a little Haydn-esque.
This is as far as I have gotten: The final page of the sketchbook so far has two more variants of the sequential elaboration. In the first example on page nine, I have added the inversus
of the head figure to the interior voice, which creates a nice dialog between the top two voices, and in the second version I started out in the minor mode. The minor mode version is unusual in that the flatted sixth degree of that scale creates a secondary dominant that tonicises the major chord found on the flatted second degree of the scale. This is the region associated with the so-called Neapolitan Sixth
chord - which has nothing to do with the various augmented sixth sonorities - and is quite a remote tonicisation to make so quickly (I will cover the so-called Neapolitan Sixth
chord when I address secondary subdominant
harmonies). It's a quite interesting effect, and the second phrase's return to the major mode offsets the unusual nature of the first phrase quite effectively. Note that I continue to look for the available deceptive resolutions of the dominant seventh.
So, this is an example of the technique I use to set up a digital sketchbook to develop both fugue subjects and sonata themes. During the process of coming to know a theme on this level of intimacy, elements sugest themselves that will lead to related themes, as well to the archetectural blueprint for the entire resulting piece of music.