Why I write fugues (Part II)

This is part II of Why I write fugues. Part I is a discussion on compositional techniques and methods, which you may find interesting if you are into composing fugues.

Its potential for cross-genre innovation

Fugue has its roots in improvisation. The notion of contrapuntal writing developed from polyphonic exercises in the Renaissance Era (ca. 1400 – 1600) that helped plan out a basis for improvisation. Eventually, the fugue became recognized as a distinct texture on its own and rose to its prominence in the Baroque Era (ca. 1600 – 1760) notably with the music of Bach. Fugues were often based on pre-existing material or musical cryptograms using a variety of encodings.

Vid. 1. Video recording of the fugue from Variations and Fugue on a Theme by Handel (Op. 24) by Brahms. Pf. Andre-Michel Schub.

Contrapuntal writing based on pre-existing material allowed composers to give their music an additional dimension. Typically, the pre-existing material would be a melody or a fragment of a melody from another source, such as a hymn, a folk song, or a piece of music. The fugue from Brahms’s Variations and Fugue on a Theme by Handel is an example of such a work from the Romantic Era (ca. 1815 – 1910).

Musical cryptograms are a way of correlating written language to musical pitch classes. Notable examples are:

• the BACH motif (from J.S. Bach): B flat, A, C, B natural; and
• the DSCH motif (from D. Shostakovitch): D, E flat, C, B natural.

(In German music conventions, B-flat is represented as B and B natural is represented as H.)

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Fast forward to modern day, a world dominated by computers, mass media, and popular culture. While “classical music” (art music) still has a prominent presence in art and culture, it is less accessible to the public, and therefore not as well understood, compared to popular music.

The fugue is now a thing of the past, but I feel that shouldn’t be the way it is. In Part I of Why I write fugues, I had talked about how I appreciate the art of fugue writing as a fascinating puzzle. It is an engaging challenge that leads to the revelation of things that were once not obvious to the composer. And in turn, the composer learns more about himself through this process. That is why I believe that the fugue form is important and should be brought back to some degree of prominence. That is what I hope to achieve through my work on YouTube.

I didn’t start posting score videos until some time in 2008. (“Score video” is a term I made up to describe a slideshow of sheet music synchronized with music playing in the background.) My first upload of this kind was my piano solo arrangement of Lilium, the opening theme song from the anime Elfen Lied. I composed the arrangement in response to all the positive feedback I was receiving from my Lilium improvisation video. Soon after, my first score video received lots of comments and views, which gave me an idea.

Vid. 2. Score video for Nokia Fugue (Op. 31), an original composition.

Seeing that people liked the idea of score videos, I thought I’d make some more to see where it would lead me. But anime music, while popular with selected audiences, still does not compare to the popularity of pop culture. Then I thought of cell phones and started sketching out the beginnings of what would later become the the Nokia Fugue (Op. 31).

From that point on, I realized that the fugue form (and canons) was a link between art music and pop culture. By writing fugues that incorporated elements from pop culture, I could speak to a broader audience and raise awareness of this art form to audiences that otherwise would not have been aware. Later on, My YouTube subscriber count rose quickly after the user smalin, who is known for his visually appealing music animation videos, animated the Nokia Fugue.

Vid. 3. Score video for Fugue for Sycra (Op. 35), an original composition.

In November 2009, I composed Fugue for Sycra (Op. 35). Extending the idea of musical cryptogram into the 21st century, I came upon the idea of writing a fugue loosely based on the letters of a friend’s YouTube username. As mentioned previously, there are many methods of encoding letters to pitch classes. Being the case that I do not speak fluent German, I decided to go with the “French” method of the musical cryptogram, which basically encodes the first seven letters of the alphabet as expected, and then the rest of the letters are encoded to their corresponding pitch class given in the top row of the following table:

A	B	C	D	E	F	G
H	I	J	K	L	M	N
O	P	Q	R	S	T	U
V	W	X	Y	Z

Tbl. 1. French musical cryptogram encoding scheme.

I say this is an extension of the traditional cryptogram-based fugue because it is based on a username as opposed to an actual name. It is essentially an adaptation of traditional methods to the modern world of technology.

By writing fugues using pre-existing melodies and motifs from pop culture, I can combine my appreciation for the fugue with something to which the general public can relate. With time, I hope that more and more people can appreciate the beauty of the fugue along with its complex compositional techniques.

Why I write fugues (Part I)

Introduction

For those visitors of my website, Audiomuse, you may have noticed that the last blog post was written nearly half a year ago all the way back in August of 2009. I had mentioned that I was going to blog more often, and write interesting articles on certain music-related topics, but yet again, I have not kept my word. For that, I apologize. “Why,” you ask, “am I posting now all of a sudden?” Well, due to some interesting circumstances, I now have an incentive to blog; one of my university courses requires me to keep a regular blog, so I thought: What better opportunity to write articles on topics of personal interest without feeling guilty of procrastinating than this one?

(Before I begin, note that this article assumes of the reader some general knowledge in music terminology and fugue. However, I will try my best to express my ideas in a way that the material will make an interesting read for any audience.)

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The fugue form has always been a great interest to me, ever since encountering my first Bach fugue in my teen years. Two things I find interesting about the fugue form are:

1. the systematic approach and recursive nature of fugue writing
2. its potential for cross-genre innovation.

(I will talk about the first point in this post and save the second point for a later time.)

The systematic approach and recursive nature of fugue writing

While I have studied counterpoint (adj. contrapuntal) several years ago, I admit that I have forgotten many of the rules. (Counterpoint is a technique of polyphonic writing, in which two or more voices maintain interdependence in harmonic structure and independence in rhythm and melodic contour.) While I still adhere to things such as proper voice leading, priority in note doubling, and the avoidance of parallel fifths and octaves (those are the main ones that I can recall off the top of my head), much of what I write is based on what I think “sounds good.” In some ways, this can be a good thing, because it allows me to focus more on the actual composition than to be bogged down by rules. I guess what I’m trying to say is that while I am conscious of the rules of strict counterpoint, I am also conscious about musicality. Having said all that, I think it’s time to delve into the composition process.

Fugue writing is definitely a systematic process. In most cases, fugues are based on a single melodic idea, known as the subject, that is complete on its own. The subject serves as a starting point for the rest of the composition.

In addition to the subject, one may choose to also incorporate a countersubject. (A countersubject is another subject that is regularly, but not necessarily always, heard with the main subject. If the countersubject is featured prominently enough and treated like the main subject, it can be considered as a second subject, and the fugue is then referred to as a double fugue.) The countersubject is often tested for invertibility, that is, its ability to be contrapuntally logical when heard above the subject and heard below the subject (Fig. 1). I generally try to work in a good invertible countersubject, but sometimes it is not possible because of the intervallic constraints with the main subject. In this situation, I will either choose to modify it or to keep the main subject as it is because it just “sounds good.”

Fig. 1. Excerpt from Fugue for Sycra (Op. 35), an original piano solo, showing various elements in the exposition of a fugue. The fugue subject makes its first appearance in mm. 1 – 2. Then the countersubject appears in the middle voice (mm. 3 – 4) and again in the top voice (mm. 6 – 8) demonstrating invertibility when heard together with the fugue subject.

If one wishes to compose a “stretto fugue” he or she may choose to plan the subject such that it is possible to be heard in canon with itself in one or more ways. (Canon refers to a style of polyphonic composition where one or more voices strictly imitate the first voice at some interval, usually diatonic, and at some delayed duration, while still maintaining harmonic sense. Stretto, then, refers to the canon texture within a fugue composition.)

Fig. 2. Excerpt from Fugue for Sycra (Op. 35), showing an example of stretto in mm. 12 – 13 between the upper voice (leader) and the middle voice (follower).

This can be a frustrating experience, but once a stretto is established, it can be used over and over again to one’s heart’s content. The stretto may appear later on in various configurations. Either the leader or the follower may be above the other, and additional voices may be oriented to be above or below a voice. (Some configurations may not be possible due to excessive voice overlapping and other contrapuntal constraints.) I find the notion of stretto to be very fascinating because of its property of being strictly self-referential.

So far, I have briefly talked about two fugal features: the countersubject and the stretto. As you can see, both are closely related to the composition as a whole. I typically choose to focus on one feature more than the other, simply because it would be too time consuming to consciously integrate several features simultaneously. Because of this, my fugues usually have either a highly-developed stretto basis and a less-developed countersubject or vice versa.

From these observations, I perceive the process of fugue writing as a puzzle, where the composer discovers more and more as he progresses. It is like a puzzle in many regards:

• Contrapuntal devices are closely and firmly integrated, and so, there is a great deal of recursive dependency.
• Contrapuntal devices develop simultaneously as the composer writes the fugue, which makes fugue-writing suspensful and full of surprises.
• Harmonic relationships are not always apparent at first glance, so there is much trial and error involved.

The idea of a puzzle is even more apparent when the fugue subject is based on pre-existing material (such as references to popular culture) which I will be discussing in depth in my next segment.

I will leave it at that for today. In my next post, I will be discussing the notion of cross-genre innovation and how I relate this to the fugue.

It's been a while

It has been a long while since my last post. I am still around arranging music and making score-videos. A lot is going on in my life right now and I just need time to deal with some problems. ... But anyway, I have been getting a lot more traffic from YouTube ever since I started posting those score videos. Before I knew it, my subscribers count reached 100 and now it's nearing the 150 mark. So want to thank my subscribers and viewers for all the support you have given. I have been meaning to make a video blog about this, but I just can't seem to be satisfied with the way I look and sound on video. I suppose all bloggers go through this when they make their first video blogs. I have been working on a couple more Fray piano arrangements. I also have Kiss Me Goodbye, the theme song from Final Fantasy XII, well on the way. It's just a matter of not being lazy.

I got Sibelius!

I got Sibelius about a month ago, actually. It’s such an awesome software. What impresses me the most is the high modularity of the score file. Each element has a parent element. E.g. a slur beginning is the child of a note head, which is the child of a staff, etc. Also the use of sample libraries is so intuitive. Here is a sample of a test piece that I did.

Issues in Arranging for the Piano

This post is half tutorial and half discussion, but the main focus is on discussion. It is about problems in expressing music effectively using music notation. Basically, I want to start an open discussion on these issues and hear what views people have.

As a piano composer and enthusiast of music notation, I am often faced with a struggle between these two extremes:

• Expressing music in the cleanest way possible.
• Showing as much detail as possible.

The first extreme involves the ease of reading of the notation. To express this in the form of a question: Which decisions can I make so that the notation is uncluttered and easy to read for the performer? Meaningful elements such as slurs, articulations, and pedal markings are often included in a score to guide the reader to more closely understand the composer's intentions, but in some cases this can possibly hinder the reading of the music. On the other hand, showing only notes may not be enough information for the performer.

In the second extreme, I refer to details such as slurs, articulations, and pedal markings, but more importantly the delineation of voices on a piano score. We usually denote different voices by stem direction. In the most general sense, we can usually show four voices on a grand staff without being too cluttered.

Q: The question I would like to ask here is: How much voicing is too much voicing? Here, I use "voicing" to refer to the delineation of music into voices.

Unfortunately, music notation can only communicate so much with the performer. There are constraints such as horizontal and vertical spacing on multiple levels, page turning, and economy of production, but in this post, I will focus on a smaller-scale scenario involving making decisions within a four-measure passage that fits on one line. To illustrate these issues, I will use the case of a composer arranging a piece of popular music for solo piano. I will be using a four-bar passage from the song Scarlet from the anime Ayashi no Ceres. (For those of you know the anime and/or song, this will be an extra treat.) Here is a MIDI excerpt that goes along with the article. If you want, you can probably find the full song on YouTube. Just search "Ayashi No Ceres Scarlet".

The first step I take in creating solo-piano arrangements of non-solo-piano music is to listen to the recording and to choose the best notes to include in the piano arrangement. Things that I need to keep in mind are:

• Maximum stretch of the hands
• Distribution of notes between hands
• Important notes that determine the harmonic progression

So here is what I came up with:

Example 1

The music doesn't show a lot of detail yet, but it serves as a basis as to how I can split up the notes into voices or parts. The directive "con pedale" allows the performer to use the pedal to his liking, but doesn't give details such as where to pedal and where to not pedal in order to evoke the correct harmonies and prevent any unwanted dissonances.

Here is my first attempt:

Example 2

In this version, the melodic line has been singled out and further indicated by slurs to guide the performer with voicing (as the singer would sing it). In the third measure, notice how the upper staff has only one melodic line, yet the first chord is implied as belonging to an accompanying part.

Q: In such cases, would you separate the voices, and use rests to show the silences, or keep it the way it is for sake of clarity?

In the next attempt, the accompaniment is split up into multiple voices.

Example 3

A few changes have been made. The accompaniment is now delineated to show the bass line and the middle harmonizing part, which is shared between the two hands. At some points, the middle voice shares a similar rhythm with the bottom voice.

Q: In such cases, would you use two voices throughout to show the delineation of voices, or use a second voice only where the rhythm is very different?

Q: Is it necessary to mark phrasing for accompaniment voices?

In the end, this is what I came up with:

Example 4

The only major change here is the addition of a bass line that emphasizes the harmonic progression. You will notice that the notes don't always extend to the next chord change: sometimes it's a half note; sometimes it's a whole note. The reason for this related to the pedaling and the abstract concept of where a note ends.

In the first bar, the left hand can only sustain the low G until the A, and then it has to change positions to play the rest of the measure. The harmony implied here is a G-minor chord with an added second. I lifted the pedal at the B-flat because the A would create too much dissonance if it is sustained till the end of the measure.

In the second bar, I thought it would make sense to use a whole note, since the pedal is pretty much held for the entire bar, since all of the notes in the measure belong to the D-minor chord. So in an abstract sense, the F does sustain till the end of the measure, except the performer doesn't physically hold it down with his pinkie.

In the fourth bar, the notes played by the left hand span no more than an octave, so the performer can hold down the D with his pinkie and keep a clear harmony and use the pedal to produce a legato effect in the right hand.

Q: So my question here is: Where do you stand in terms of expressing the abstract idea of an implied harmony versus expressing what the performer can physically do at the piano?

Q: Also, which of the above solutions would you favour and why?

In addition to these questions, I would like to hear what people have to say about music notation in general.