Composing Phrase by Phrase, 2-4

Ending the First Prelude

Hello and welcome or welcome back to Composing Phrase by Phrase! The past couple weeks have been spent looking at basic approaches to using tone rows for composing. This week, I'm going to wrap up the piano prelude I've been working on. I'll be using the same set notation as last time, if you need a refresher. Otherwise, here's the last few measures.

1.1 mms. 12-15

The first thing to note here is the use of rhythm as a motive. Measures 10 and 11 set up the rhythmic idea used in 12 and 13: a syncopated half-note, a quarter tied to an eighth over the barline, an eighth, and an eighth-rest providing a slight hiccup before the last sustained chord. For clarity:

1.2 rhythmic motive

It's worth noting that this idea of offset syncopations isn't an entirely new idea within the work. Back at the beginning, the main melody rarely changed pitches on the beat. In fact, looking back at it, if we're strict with the time signature, the original melody never changes pitches on the beat. In the second half of the piece, the off-beat rhythms are slightly less off-kilter because of the slower tempo and longer sustain, but it's not coming completely out of nowhere.

Moving on to the chords. The previous two measures used the inverse row form, I(8). The little pizzicato-like figure at the end of measure 11 briefly brought the E-flat into the musical figure. This was done mostly because it sounded right, but partly so that I could stay in the I(8) form while also starting the same rhythmic motif on a new part of the row. I expect this approach is an extremely important idea for achieving both cohesive composition and variation within 12-tone composition. especially if we're maintaining strict row orders for the work.

Now that the row has been offset from the rhythmic motif's first statement, the new chords are I(8): [6,2,0,4] and I(8):[3,11,9,1].

1.3 m.12 chords

The accented chord in measure 13 requires a little more attention. Three of the notes (D,C, and F) round out I(8). One pitch, however, doesn't fit: the E. When looking at the upcoming chords, we will find this E is pulled from I(9). This recalls the "row form modulation" used in the first half of the composition, which also transposed the row up a single half step. See, the first time, I was being lazy. Now that I'm repeating the idea, I'm being clever. Eh? Eh?

1.4 m.13 common-tone row change

The process is different this tine. Previously, we moved from one form to the next by finding overlapping subsets and using those to pivot into the new form. In this case, I'm just sneaking part of the next transposition into a chord with pitches from the previous form. The notation of this chord might be something like... I(8):[10,5,7]+I(9):[9]. I'm curious how actual theorists would notate this. This will suffice for now. Moving on, we round out measure 13 with I(9):[7,3,1,5].

Looking at these chords as sets, the set analysis would be [0,2,4,6], [0,2,4,6] again, [0,2,4,5] at the pivot to I(9), then [0,2,4,6] again in the new transposition. It's worth mentioning how much the voicing and changing pitch content of each chord influences the sense of the chords. Even though three of the four chords use exactly the same set, they don't quite carry the same sound. Highly trained musicians will probably hear the underlying similarity, but I expect it would slip past most ears.

Also worth bringing up is the change in set shape at the introducion of I(9) - it is all the same as the chords surrounding it except for one pitch which is a half-step lower, [0,2,4,6] and [0,2,4,5]. This recalls a similar chord shift in measure 10 which contains [0,2,6,8] and [0,2,6,7]. This is one of those happy accidents I wish I could say I thought up myself. But you know what they say: every time you write a happy accident, an angel grows its afro.

Moving on to measure 14, the first chord is I(9):[4,0,10,2]. The second chord uses a similar approach as above, including a pitch from an upcoming row form in the chord - I(9):[11,6,8,9]+P(1):[1]. For the last bar, the chord P(1):[1,3,7,9,5] is used as a kind of "pre-dominant" chord setting up the final [0,2,4,6] set. The last four notes (G,A,F, and B) are not the next pitches of the P(1) row. As a composer, I simply brought that chord back from measure 13 because it sounded right. I personally think this is what a composer should value most - their sense of aural taste. Not everyone will agree and to them I'll say, fine, meet me in the parking lot. Er, I mean. Agree to disagree.

1.5 mms.14-15 chords

Rhythmically, the last two measures fragment the rhythmic motif used in the second half of the composition. Measure 13 uses only the consequent part of the motif and measure 14 does the same except adds a little more space to allow the cadence to feel more like a completion. The last chord and its voicing sound to me a bit like a musical question mark (in English). I will say that I had Robert Schumann's "Entreating Child" from his Kinderszenen in mind with this ending... although it might be more like Pierrot asking for another tipple, in this case.

But, we've got to cut ol' Pierrot off. That's the end of this little composition for piano! I have more dodecaphonic music coming down the line, though. This was a really good learning experience for me in terms of what kind of things to look out for in composing with tonerows both in terms of what ideas are possible and in how to connect those ideas fluidly. The main thing seems to be finding clever ways of cycling through the row to access different harmonic and melodic possibilities while also looking for interesting ways of overlapping different row forms.

Anyways, I hope you found this as instructive as I did! Hope you drop in again next week as I start a new prelude!

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Composing with Tone Rows 2

Hello and welcome or welcome back to Composing Phrase by Phrase! I've started a series of mini-projects this time around, looking at how you might use tone rows to compose music. Last week, I set up the very basic basics - what a tone row is, making a melody from the row, creating simple harmony from the row. From that, I composed a phrase of music for piano using a row as a melody and using adjacent dyads to create a harmony for that melody.

There's a few directions we could go from here. The most simple step is to recognize that simply moving from dyad to dyad (or triad or tetrad or whatever) can feel a little jarring. It's like writing a tonal song with harmony built entirely from root position triads. It's fine, nothing's stopping you from doing that, but if you try to write anything longer than a 3 minute pop tune with that approach, it's all going to feel very... samey.

We can take a page from tonal harmony to help expand on the simple approach used last week - the idea of common tones. If you go to music school, chances are you're going to write voice leading exercises. This practice is largely about making harmonies sound as rich as possible, with as smooth a connection between each chord as possible for the sake of a choir's intonation (particularly if you have amateur singers).

A tonal progression with decent voice leading might look like this:

1.1 Tonal Voice Leading

Below is an example of using common tones in a tone row. Dyads are used for the sake of clarity.

1.2 Tone Row Common Tones

At this point, a huge number of possibilities opens up to the composer. One could maintain a single tone as a drone while a subset of the row plays out. One has great freedom in deciding which pitch is held in common between each chord. On top of this, a composer needn't stick to dyads or triads, but could use a mixture of chord densities for dramatic effect.

It's all a bit much, really. Figuring out a means of whittling down the massive possibilities is the primary concern of a composer using tone rows. I mean, that's honestly true of any music, it just seems much more obvious when working with dodecaphonic music.

With that in mind, I'm going to continue with the prelude introduced last week. Here's a short fragment of the next phrase. To review, pitches in rows are counted from 0-11 (you might also see the letters e and t used, but this is a different approach where each chromatic pitch is assigned its own number, regardless of row form, rather than assigning a number to the order pitches appear in a particular row form).

1.3 Prelude 1, mms. 6-7

In this case, the use of a "common tone" in these dyads creates something analogous to a suspension in modal or tonal music. That's not something that will happen with every tone row. It's an outgrowth of this tone row containing a sequence of seconds and thirds within it. You may also notice one of the pitches from the row enters a little earlier than is strictly should. Oops. Oh well.

Now. Eventually, you're going to go through a row and think to yourself, "Man, I wish I could do something slightly different." Which is crazy, because there's already a billion things you can do with a row, but it will come up faster than you might expect. What do?

Well, good news! You can perform some simple transformations to the row to give you access to a bunch of new possibilities. The easiest is to transpose the row. Just keep the intervals but begin from a different pitch. Here's the row used in this prelude along with a transposition, for demonstrations.

1.4 Row and transposition

To me, the question of "when" to use a different row form is a little less important than the "how." At least, it is now, since I'm not writing long form works yet. Again, I'm going to take a page from tonal harmony, this time looking at the process of modulation. In tonal music, if a composer wants to modulate from one key to another, the next most obvious thing to do after just plopping the music into the new key is to use a pivot chord. This is a chord which is shared by both the starting and target keys, but takes a different function in each.

So, if a composer wants to get from C major to G major, they might use an Amin chord as a pivot point. In C major, the Amin chord (vi) would typically set up Dmin (ii) as a predominant for Gmaj (V). In G major, the Amin is the ii, acting as a predominant for Dmaj (V) which would lead towards Gmaj (I). Here's what it looks like stripped of anything musically interesting.

1.5 Modulation from C to G major

In dodecaphonic music, you will find similar opportunities to pitvot from one row form to another. It will frequently occur that two row forms will share the same subset of pitches in the same order. These pitches can be taken as a pivot point connecting one row form to the next. Looking at 1.4 above, the prime 0 row shares B-flat, A-flat, and D with prime 1. Here's what I ended up coming up with.

1.6 Prelude, mms. 8-9

Had I been a little more careful, the order could have matched, as well, but I think it's probably ok to consider small groups of pitches as their own harmonic set (which doesn't care about order, just the interval relationships).

Regardless, I did what I did and used those three pitches to move from Prime 0 to Prime 1. I chose Prime 1 for two reasons. First, by pivoting with these particular pitches, it sets up a repetition of the C/E dyad but follows it with a different dyad (D-flat/F instead of D/F-sharp). Second, it was the row right below the first row in the matrix, so... Yeah. Here's the same two bars with the row and row counting for clarity.

1.7 mms. 7-8 with P(1)

And here's a link to the video again. It's short enough I don't think I need to do timestamps for this. Thanks for reading!

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Composing Phrase by Phrase the 2nd

Get Set...

Hello and welcome back to Composing Phrase by Phrase! This past couple weeks it's been more like "Composing Measure by Measure," but I've been using tone rows to compose and those get involved pretty quickly. I've been focusing, as much as possible, on the basics of what's possible with this approach. Making a melody from the row, making dyads for harmonization, different voices performing the row offset from each other... Today, I'm going more into harmony again.

There's an important distinction between writing melodies from tone rows and writing harmony from them. With melody, the order is fixed by default. With harmony, all that really matters is that the pitches of whichever subset are present all at the same-ish time or so. So, a composer has a great deal of flexibility along a couple of axes - the voicing (the notes' order from top to bottom, the spacing between them, and which ones are doubled by another voice) and the register (how high or low the pitches are placed).

Analyzing this stuff can get complicated in a hurry. I'll be using two approaches at the same time. One will be the tone row analysis to locate the pitches in whichever row form is being used. The other will be set notation, which is a way to generalize collections of pitches that aren't just tonal triads. I'm sure there's an established way of doing both in academic settings, but it's been a while since I've been in a classroom, so I'm going to use my own.

For rows, I'll write the first letter of the row form next to the transposition in parentheses followed by the particular pitches in brackets. I'm also going to switch from just numbering the ordering (which, while simple for demonstration, is also imprecise) to numbering the actual pitches from 0-11 separated by commas. I think 0 is supposed to be C, but since I calculated my row matrix from G, that's what it's going to be 0 here. Sorry for any confusion, I'll look it up later.

For sets, they will simply be bracketed. Just like tonal triads have a closed root position, sets have a default ordering in which the pitches are stacked with the smallest intervals between them possible. For my purposes, the bottom note is then labelled 0 and the intervals are given a number based on the number of half-steps that pitch is from the bottom note. I know this is not typical, but I have reasons for doing it this way. Mostly, it's to clearly see how closely related any two sets are.

Oooooookaaaaaay. Let's look at the next couple of measures in question.

mms. 10-11

The new section kicks off with two sustained chords. Their pitches are drawn from the inverse row at the 8th transposition (in this case, Eb, a minor sixth above G). Their row analysis will give the pitches from bottom up. They are I(8):[6,0,2,8] and I(8):[3,9,11,4]. These are not, however, the chords' "root" position.

normalized chords

Now that they are condensed, their set notation would be [0,2,6,8] and [0,2,6,7]. From this notation, it's easier to see that the two chords are fairly closely related. Their basic "shape" is only off by a half-step. The ear can certainly hear that distinction. The first has an open, spacey kind of sound while the second has a tighter, sharper quality to it.

Speaking of ears, the voicing has an impact on how we hear the chords in question. The first chord is voiced as two tritones separated by a major second. The second places a tritone at the bottom and a perfect fourth at the top, separated again by a major second. These open voicings give both of them a broader quality and (I think) actually help emphasize their similarity compared to the two normalized chords. If you agree, it's likely because dissonances are softened by distance. A minor second has a more pungent sound to my ears compared to a major seventh, even though they are both technically the same pitches.

Moving on! After that, it gets more simple again. Two dyads in the right hand, I(8):[1,10];[5,7], carry the melody forward. At the end of measure 11, the left hand echoes the I(8):[5,7] dyad with a quick, pizzicato-like figure which wraps the music back around to E-flat (8).

Ok, that was kind of a lot for very little. This was mostly to help set things up for future analysis. Next week's post will wrap up the first prelude and then we're on to another written from a different tone row! Thanks for reading and I hope you learned a little to aid your own compositions down the line!

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Composing with Tone Rows

Row, row, row your boat...

Hello and welcome or welcome back to Composing Phrase by Phr... No, wait. That's not quite right. I want the next Composing Phrase by Phrase composition to be 12-tone. That's a couple steps more complicated than the last composition (which was already pretty complicated, mind) and I'm not as familiar with using tone rows for composition as I am with triadic, quasi-tonal harmony. So, instead, I'm going to do a number of little piano preludes to help demonstrate different ways of using tone rows for composition, both to prep the readers and to prep myself.

To begin with, what is a tone row? There are twelve pitches in Western music (more or less, I'm not going to debate that right now). A tone row takes those twelve pitches and arranges them into a collection where each pitch is repeated exactly once. The resulting construct is then used as the basis for generating melody and harmony in a composition. Here's what one looks like.

1.1 Tone Row Example

And here's another

1.2 Tone Row Example 2

As you can imagine, there are many, many ways to arrange twelve distinct pitches. 12! number of ways, in fact. That's some 479,000,000 and change. Luckily, many of these tone rows are actually "the same," so there are "only" 9,985,920 unique tone rows. This is, in part, a big reason why composing with tone rows can be so difficult - the number of possibilities to even start from is overwhelmingly large. Composers have found a variety of ways to combat that fact. Mine is to use a random number generator.

A quick note before proceeding. This approach to composition was invented by Arnold Schoenberg. When he invented it, he created a set of rules which were intended to avoid any semblance of tonality. The historical and personal reasons for doing so aren't what this post is about, but I bring it up only to say - I don't really care? Avoiding tonality isn't a particular goal of mine. Neither is the creation of aggregates (see: Babbitt). The only "rule" I'll hew closely to will be the "use the whole row" rule. That's kind of the point, after all.

Beyond that, there are a host of fairly complicated techniques developed by 12-tone forebears. I will, as much as possible, try not to reinvent the wheel. That I will inevitably develop idiosyncratic approaches to using tone rows is not only inevitable, it is (to me) desireable.

Now. To quote a famous British comedy troupe: Get on with it!

The very most basic thing one can do with a tone row is to take the notes of the row, slap some rhythm on it, and BAM! You've got yourself a theme. Here is a possible theme using the first of the tone rows above:

1.3 Using a tone row as a theme

Considering the "use the whole row" constraint, rhythmic motives and phrasing are among the primary means of composing with tone rows. This particular phrase is six measures and can be understood as four bars with a two bar "pickup" gesture, as follows:

1.4 Theme 1 phrase

Things get more difficult when creating harmony. Starting with the most basic thing I could think of, the easiest approach would be to create dyads, triads, and tetrads with consecutive pitches of the row.

1.5 Row dyads, triads, and tetrads starting from 0

There's nothing stopping a composer from using pentads or hexads or whatever. It just happens the 2, 3, and 4 divide the row neatly. Usings 5s or 7s would create some interesting possibilities where the harmonies would cycle through the row multiple times before returning to the first cluster. I'd say it would be tricky to make things sound unique, the more notes added to the harmonic stack, because you get closer and closer to sounding all twelve chromatic notes at once. These are chords which can really only be differentiated by voicing.

In any case, a composer is not limited to always starting the row from the first pitch of the row. By starting the harmonies from a different point, we get a new set of intervals and harmonic colors.

1.6 Row dyads, triads, and tetrads starting from 1

The approach I used to harmonize the above melody was to make dyads builts starting from pitch 1 of the row and place them underneath the melody. Because the harmonies are made from a row independent of the melody, I had a good deal more freedom in harmonizing the theme.

1.7 Theme with Harmonization

In this case, I chose to harmonize in a way that gave a sense of extended tonal harmony. It is true that the row also lent itself to that usage, though. Here are the triadic chords suggested by the harmony and melody acting together:

1.8 Chord Symbol analysis

As you can see, this isn't a particularly satisfying analysis of the harmony. A theorist approaching this phrase only with the tools of extended tonal analysis will quickly find themselves frustrated by the many elements that don't really fit and from the fact that there's not really a clear function to the progression. It's... planing thirds, I suppose. But the rest of the melody doesn't follow that plan. From a 12-tone perspective, however, the construction is relatively simple (ha! simple...).

1.9 Tone Row Analysis

There are two layers: the melody layer and the harmony layer. The melody, as stated above, is just the tone row with rhythm. The harmony is built from the exact same tone row, same transposition and all, except it's starting from the "second" note of the row rather than the first. In addition, there are three dyads at the end which are repeated: [7,8] ; [9,10] ; and [0,11]. This was to give the end of the phrase more of a sense of conclusion, which can be tricky to do when working with tone rows. Is this an unorthodox compositional choice? I suppose. Do I care? Not particularly.

So, that gets us started on a new composition with tone rows! These are going to be very short, probably four phrases, max. I'm also trying to figure out the best way to include audio. For now, I think I'll include a YouTube link of the full thing at the end of each, with time stamps for the example phrase. Thanks for reading!

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