TAGUTCOW'S GUIDE TO LINE LISTENING: (Or... My chance to be pedantic, Latin nerds!) I suppose a few words about the distinction between motives, themes, and melodies are in order here. However, it must be stressed that the terms are nebulous even to music theorists. In order to learn how motives, themes, and melodies interact from firsthand experience, there is no substitute for rigorous listening. In the meantime, you'll have to take my definitions on faith. - A motive or a motto is a combination of about three to five notes in a fixed order, played in rhythmic proximity. An example of this is the ABC arpeggio or the germinal theme to Beethoven's 5th Symphony. A motive is an atom of musical information. - A theme is a string of notes that can be developed. What exactly "development" means is kind of complex, but it basically entails expanding or truncating a string of notes by joining or severing motives from eachother. One of the reasons Boulez cut himself off from the Schoenberg tradition was Schoenberg's insistence on using "themes" in rondo or sonataoid forms, which Boulez thought was a crutch for the listener. The real logic in Boulez' music comes into relief when we examine the third of this trinity of musical elements: - A melody is a string of notes whose form is determined by the classical dynamic of tension and repose, climax and denoument. Most of the time, melody is an essentially transparent musical feature, but in the music of eg. Webern and Boulez, the first and last notes of a melody, or the highest and lowest notes of a melody, often form "motives" themselves in one of their transformations. So what is a transformation of a motive, and how do we recognize it? Well, first we must understand how a motive retains its identity under various transpositions. Say we have a motive that goes like this: Ą Ą Ą Ą C Ab F# D If we keep all the intervals of the motive intact (minor sixth or 8 semitones for C-Ab, major second or two semitones for Ab-F#, major third or four semitones for F#-D) We can move the motive up or down the chromatic scale (the scale of twelve semitones which forms the basis for all Western Classical music), the motive retaining its identity with each transposition. Ą Ą Ą Ą C Ab F# D C# A G Eb D Bb Ab E Eb B A F ... ... ... ... I hope I'm not boring you if you already know this, but, if this is all new to you, try playing the given motive in all twelve of its transpositions to get a sense of how it retains its identity with each transposition. The pitch level changes, but the intervals between the notes remains unchanged. A transposition of a motive isn't a transformation of a motive, however. Let's say that we invert the motive;-- that is, every interval that goes up in the original motive goes down in the transformation, and every interval that goes down in the original melody goes up in the transformation. Ą Ą Ą Ą C E F# Bb So instead of going up-down-down, as our original motive did, our inverted motive goes down-up-up. As well, the inversion of the motive has twelve transposition levels, giving us, so far, a total of twenty-four forms in which our motive retains its identity. "But," you may justly counter, "this inversion of the motive sounds nothing like the original motive. Am I expected to be able to identify the inversion?" My response would be that the inversion is relatively easy to identify compared to the retrograde, which we will soon examine. Really, as long as you know that the original consists of one large interval up and two smaller intervals down, you will be able to identify the inversion as being one large interval down and two smaller intervals up. As well, the last note of the original motive is higher than the first note, and is lower in than the first in the inversion,-- vice-versa the second and third notes respectively. It helps to be able to identify intervals by ear, but this is not necessary for enjoying music that uses inversions and retrogrades of motives. If you hear the original motive in a piece of music, and later hear the second string of notes, as long as all the criteria for "melodic shape" are met, you can be reasonably sure that the second is an inversion of the first. If, however, you heard this string of notes: Ą Ą Ą Ą C E F# D You would be certain that this couldn't be the inversion of our original motive. For one thing, the first note was lower than the last in our original motive, so it should be higher in the inversion. As well, the original motive had the two higher notes and the two lower notes moving in "contrary motion" with eachother, whereas in this string of notes the higher and lower notes are moving in "parallel." More obviously, the original motive had two "outer notes" followed by two "inner notes"; this doesn't. I realize this all seems terribly simple-minded, but the human's ability to percieve sound is, amazing as it is, relatively undeveloped compared to our facilities for sight. As such, hearing "higher" and "lower" notes requires more attention than we are sometimes accostomed to giving music. The retrograde is relatively tricker to identify, although it's simpler in theory. Quite simply, we reverse the order of the notes. Ą Ą Ą Ą D F# Ab C In the case of the retrograde, instead of going up-down-down as our original motive did, the retrograde goes up-up-down. More easily noticed is the fact that, while our original motive had two "outer" notes followed by two "inner" notes, the retrograde has two "inner" notes followed by two "outer" notes. As with the inversion, the retrograde has twelve transpositions. And, who didn't see this coming, the last transformation we'll examine is... the inverse-retrograde. Ą Ą Ą Ą Bb F# E C The inverse retrograde is, naturally, the inverse of the retrograde,-- or the retrograde of the inverse,-- both are the same at different transposition levels. Like all of the transformations we've examined, the inverse retrograde has twelve transpositions. The inverse retrograde is actually, counter-intuitive as it may seem, sometimes more easily identified than the inverse or the retrograde themselves. Let us examine again the original motive ("WAAAHHH! IT WENT OFF THE TOP OF MY SCREEN!") Ą Ą Ą Ą C Ab F# D As we see, the first and last notes of the inverse retrograde bear the same relationship as they do in the original form of the row, the first is two semitones lower than the last, something that was not the case with the retrograde or inversion. As well, we have a sequence of three notes retaining their down-down shape, something that again does not hold true of the retrograde or inversion. While the inverse-retrograde is only occasionally easier to identify than the inversion, it's almost always easier to identify than the retrograde, precisely because of these "shape-retaining" qualities. Schoenberg's innovation was the invention of the tone row, an ordered sequence of the twelve notes of the chromatic scale that forms the basis of a work. That is, the tone row, in any of its forty-eight transformations or transpositions thereof, is the source of all the pitch material in the piece. Later composers went on to "serialize" rhythm and other non-pitch elements, as well as invented ways to "modulate" between different rows, but this is of no immediate interest to us. What *is* of interest to us is the fact that Schoenberg effectively eliminated the distinction between a motive and a theme; both motivic material and thematic material are realized in the row, and the tone row itself saturates the pitch material of a work. We needn't abandon our four-note motive just yet, as we find that, with some clever use of inversions and retrogrades and transpositions thereof, we come up with a tone row: E C Ab F# D Bb C# A F Eb B G \________^________/ \________^________/ P RI11 We see the original form of the four-note motive, here denoted as 'P', in notes 2-5. As well, we see the eleventh transposition of the retrograde of the inverse of P in notes 8-11. The remaining notes are "filler", consisting of what would be known in the parlance as a diminished seventh chord. The forty-eight forms of the row can be organized in a chart: I I8 I4 I2 I10 I6 I9 I5 I1 I11 I7 I3 P E C Ab F# D Bb C# A F Eb B G RP P4 Ab E C Bb F# D F C# A G Eb B RP4 P8 C Ab E D Bb F# A F C# B G Eb RP8 [...] P9 C# A F Eb B G Bb F# D C Ab E RP9 RI RI8 RI4 RI2 RI10 RI6 RI9 RI5 RI1 RI11 RI7 RI3 The rows left to right are transpositions of P, from right to left retrogrades of P. The columns top to bottom are inversions of P, from bottom to top retrogrades of the inversions of P. I think it is fair to say at this point that we have left the realm of what is reasonable for a person to determine from a piece, as it is a rare person indeed who would be able to mentally take note of the entire tone row used by a piece and follow it in all its transformations. What *is* reasonable to expect from a person is the ability to be able to identify the motive in its prime and retrograde-inverse form in RI if the composer has rhythmically accentuated the motive to be identifiable as such. That's what's great about the serial method,-- it's essentially transparent. The composer can subordinate the tone row to motivic or harmonic musical ideas; it is a poor composer indeed who writes a serial piece just to write a serial piece. I was going to explore combinatoriality for the sake of Kibo's cultural super-literacy, but I'm too tired tonight. Thus ends your lesson for today. DOONNNNNNNNNGGGGG!!!