To continue our discussion of the twelve tone scheme and the Second Viennese School, we’re going to talk today about the method itself. I’m going to be up front with you, though. I’m not a professional musician, I am not a historian, a musicologist, an acoustician, or anything of the sort. I am a reader and a listener. For purposes of this article, I’m going to be as simple and non-pedantic as possible while still explaining the idea constructively. Again, in my mind, it’s better to go from knowing 0% about something to 80% about it, even at the risk of containing a few sweeping generalizations or factual errors in the process. For all amateur purposes, that’s enough to get an informative and satisfying grasp of the concept. I think the best way to view this is to contrast it with “traditional” Western classical (“diatonic”) harmony. Perhaps all of that should have been capitalized. Before I explain the ideas, though, let’s identify two major components of music: melody and harmony. These words are so familiar as to seem not to need definition, but you may find them hard to pin down technically. Melody is made up of notes played in succession, one after the other. Sing the lyrics or hum the tune of any song you know, and that’s a melody: one note after the other, horizontally. Harmony is made up of notes played at the same time (vertically) to create chords. The twelve-tone system affects both.
Let’s take the C major scale, for example
. On a piano, playing that scale, we don’t use any black keys. We have eliminated them because they’re not part of that scale. You could think of the scale as a color scheme. Each scale has seven notes that all work together a certain way, so a C major scale is C-D-EF-G-A-BC. If you look at a piano, you’ll notice that there are no black keys between EF or BC, which is why I’ve typed them like that. From C to D on a piano is one whole step, made up of two half steps. The same is true for D-E, F-G, and so on. So the pattern of a major scale is
two whole steps, a half step, three whole steps, and another half step. That is true of ANY major scale you play, the difference being WHERE you begin, and then as a result WHERE those whole and half steps fall. A scale (in one octave) will have eight notes, the first and last are “the same.” An octave is just a jump from, for example, one C to the next C above or below it. For our purposes, we can say that all Cs are “the same” just in different octaves. There are scientific reasons for this, as well as for the other things we’ll talk about, but I’m going to avoid discussions of frequencies and waves and overtones; a study of the basics of that is fascinating. In short, as you know, sounds are waves, and whether notes (pitches) sound “good” or “bad” together is determined by their individual frequencies and how they interact. It’s just math. (“good” or “bad” here is subjective, but one should say “consonant” or “dissonant.”) In any case, as a result of this, the notes in the scale have certain properties. You could say that some notes are stronger than others, or more important. Since the first note is repeated as the eighth, we could eliminate its repetition (refer to it as 1) and just say that there are seven notes to a scale, 1 2 3 4 5 6 and 7. 1 is obviously the strongest, since it’s what everything else is based on. It’s home, it’s the tonal center, it’s what the ear focuses on. The next most important is 5 (in the key of C, that would be a G). These two are super important! The next most important is 3 (an E in C major), and you’ll notice that these three notes make up a C major chord, C-E-G
. They sound very good together. It’s stable and clean and pretty. The weaker ones are 2 and 4 and 6, but 7 (in this case, B) is pretty important too because it wants to lead back to 1. It points us (leads the ear) in that direction. So that’s a sort of system, and different types of chords built on these “scale degrees” (1-7) have certain properties. That, fundamentally, is what the whole tonal system is based on. This phenomenal variety of sounds, individually or in chords, in certain orders, creates a palate that a composer can use to create tension and release and build a narrative with contrasts and beauty. It in itself is a structure, a technique, a method, but one built on the inherent properties of the frequencies themselves, and using them in different orders or sequences, that, along with variations in rhythm and instrumentation, create the melodies and harmonies and all the music that Mozart and Beethoven and all the music that the traditional diatonic school of thought has brought us. That was easy enough, right? It in itself is a method, based on the inherent qualities of each individual frequency. There are ideas of voice leading and chord progressions that kind of dictate, in a general sense, what chords could or should come after others to create tension or resolve, and which ones sound “good” together. So that’s one system. Now let’s talk about dodecaphony
(the 12-tone-system). A piano, from one C to the next above it, had not just those seven notes that play well together, but 12. That includes ALL the black and white notes, with no regard for the “strong” or “weak” notes of a major or minor scale or how they work with or against one another. Herein lies the issue that so many people have with dodecaphonic music. It gives equal weight to ALL the possible notes on a piano, with (theoretically) no specific focus given to any tonal center. More about that shortly. For now, let’s talk about the actual method, in its most basic conception. Like I said, twelve notes. Everything in one octave from C all the way to B, all notes included. We said earlier that it doesn’t matter which octave (section of the piano) we’re in, a C is a C. Because we treat all Cs as Cs, all F#s as F#s, we can disregard octave and treat them all the same. You’ll see the “pitch” or “name” of the notes referred to as a “pitch class.” There are twelve “pitch classes” (different notes) on a piano, repeated every octave. That make sense? Cool. Now instead of using note names like C or D or do, re, mi, we’ll replace them with numbers, and you’ll see why in a bit. So C = 0 C#/Db = 1 D = 2 D#/Eb = 3 E = 4 All the way up to B = 11
Then we just have to put these 12 numbers (0-11, but sometimes 1-12) in an order that will become the basis for the piece of music. Something you’ll see in many listings of tone rows is 10 and eleven being replaced with single-character replacements so as not to be confused with 1 or 0. Hence, 10 = t 11 = e So a tone row, for example, from one of my favorite pieces of music written with this method (Schoenberg’s piano concerto) is 07e21935t684 That one string of symbols determines everything in that 20-minute piece, and the composer MUST that pattern, in some way or other, and cannot (in the strictest of senses) deviate from it. From this, though, we can make up some other patterns, as long as the intervals (distance, or number of steps) between the notes is maintained. So you could play it back to front: 486t53912e70 This is called the retrograde. We could also flip it upside down or flip it upside down and backwards. These modifications, as well as transposition (moving the whole row up or down by a certain amount) gives us 48 potential options that all maintain a relationship to the original, or prime, row
. That link is to a fantastic calculator for creating a ‘matrix’ for all the potential rows based off of one prime. In performing these operations, it’s easier to deal with each pitch class by giving it a number and using addition and subtraction to get to the values you want rather than counting C-C#-D-D#-E and so on. It’s just become a standard way to represent it. Using this idea, and perhaps with a certain concept in mind, a composer creates a tone row and begins composing. I wrote a piece recently for clarinet and piano, and since the clarinet can (usually) only play one note at a time, my options for the clarinet’s melody as a solo instrument are quite limited. I can change that up, though, with rhythm, what notes are on what “strong” beats and how long they play, but they still have to play in that order. I could theoretically give a note to the piano and not to the clarinet
so that in one “cell” or measure, I still have all those notes showing up, but just not in the same voice. This is a more vertical approach to the idea and can allow for a broader interpretation and more options if you so desire. So what’s the result? Well, there are two main “side effects.” One is that a piece has more notes to it than a standard piece would contain, for example, we’ll have both F and F#, C and C#, B and Bb all playing in close proximity. The ear may at first pick out some of these to be “wrong”… They shouldn’t fit in the “scheme”, because they don’t in the traditional diatonic setting we mentioned above. C# and F# and Bb don’t belong in a C major piece, for example. But… Then again, there’s no context for the notes anymore. If there were only one F# in a piece in F, it would be easy to pick that one out as the “wrong note” just from context, but instead…. We have ALL the notes, so harmonic context goes out the window. Add to that the fact that not only do we have individual notes, but also chords and unique harmonies made of many of these “wrong notes.” The ear then, without the ability to find a tonal center or a focus point, has to accept them all equally, and this is the mental challenge for so many listeners. One can see how it would be so for two reasons. 1. The fundamental designs of diatonic (“standard” Western) music are based on the scientific properties of those sounds, so many would argue that it’s a natural result that music would focus on or exploit these inherent qualities. 2. It’s something that we in the West have used and been used to for centuries, so for most people, all the classical music they’ve ever heard is only in this system. Just as in diatonic (traditional) music, the method can be used to different effect. Diatonic harmonies can be used to write flowing beautiful nocturnes like Chopin’s
, but also to write dissonant crashing harmonies like those in Prokofiev’s war sonatas
(no. 7 there). In like manner, dodecaphonic methods can be used to write music as interesting and delicate as that of Dallapiccola
or as complex and challenging (for many) as this piece that I thought was unfinished
(just check out the comments for that video!). It is a method for writing, and not a style in and of itself. (As an extension of the twelve-tone technique is Serialism, a method of composition that brings the same formal structure of set patterns or values to other facets of composition, like note length, rhythm, instrumentation or texture. This is often called “total serialism” and is a different beast all together. As an example, compare Schoenberg’s fourth string quartet
with something like Babbitt’s sixth
, or a Webern work with one of Boulez’s. It’s another level of… Complexity and challenge. I’ve decided a section of this series will address that.) So that’s it. In summary:
The twelve-tone system does away with tonal centers or the idea of a “key” and gives a level playing field to all pitch classes (notes) and dictates that they all be given equal weight, one played just as often as another, by means of sticking to a “row” that dictates the order of notes within a section or passage of music. Dissonance is therefore created as a result of these notes all being equally present within the same piece. As a result of this non-reliance on (traditional) harmony, things like textures and rhythms and orchestration become increasingly important to emphasize melodic ideas and give structure to a piece.
In the next part, we’ll talk about how I came to tolerate, appreciate, and even love (some of the) music written in this modern compositional method.