12-Tone Serial Compositions
Serialism is an Avant Garde composition technique that was invented in the 1920s by a composer called Schoenberg.
In a serial or “12-tone” composition, the composer begins by taking each one of the twelve different semitones (between two notes one octave apart) and then decides on an order to play those notes in. This is called a “tone row”. Each note can only occur once. The composer then constructs a rhythm to fit the notes to, always keeping the pre-decided order of pitches the same.
Here is an example of a tone row:
Once all twelve notes have been used up, the row is reused to create more music. It could be used in the same order, or it could be played backwards. This is known as “retrograde”, or “R” for short. “P” stands for “prime”, which means “first” or original row. (Sometimes “O” is used).
Here is the tone row I invented above, plus its retrograde version:
The tone row can also be transposed, to create a new set of pitches with the same interval relationship.
Serialism – How to Sound Atonal
Serial music is “atonal” which means that there is no obvious tonic or keynote: each of the twelve semitones is of equal importance. There are no rules about harmonic progressions, voice-leading conventions or forbidden melodic intervals. However, the notes need to be selected carefully, so that the music sounds properly atonal (rather than “wrongly tonal”!)
Look at the following tone rows. Notice how the first sounds as though it is in a diatonic key for three or four notes, then seems to shift to another tonal centre. Compare the second row, which never seems to rest in any particular key, even for a moment.
Let’s examine why they sound so different. (NB we need to consider both enharmonic spellings of the notes, not just those written on the stave.
Melodic Intervals
The first row is built from consonant melodic intervals – all the melodic intervals are major, minor or perfect. (Notice that Ab-B may look like an augmented 2nd, but it is just an enharmonic equivalent of G#-B, which is a minor 3rd. Similarly, B-Eb is the same as B-D#, which is a minor 6th). Consonant intervals create tonal music.
The second row completely avoids perfect intervals. Because the perfect 4th/5th is the interval between a tonic and its dominant, avoiding perfect intervals helps to move away from the diatonic system. It also uses some tritones and 7ths, for example G-C# and A-Eb (tritones), and B-C and C-Bb (7ths). One third of the intervals used in this row are dissonant, which gives the melody an atonal sound.
Triads
When notes move in leaps of thirds, we tend to hear three notes together as an implied chord. If you play the notes C-E-G in succession for example, your ear will assume a triad of C major. The same is true even if the notes are played “out of order” to make an inversion, such as G-C-E, or E-C-G.
If there are three successive notes in the tone row which could be stacked to make a triad, the ear will interpret them as such. If that triad is major or minor, then the three notes will sound tonal. If the triad is augmented, it will sound atonal. If the triad is diminished it might sound dissonant enough, but if the implied chords are vii°-I, it will sound tonal.
In the first row, the notes F-Db-Bb (a) combine into a chord of Bb minor (i.e. tonal). Ab-B-Eb (b) can be respelled as G#-B-D# to make a chord of G# minor. And B-Eb-F# (c) are enharmonically the same as B-D#-F#, which is B major. This row therefore contains three implied tonal chords.
In the second row there are no major or minor triads implied by any three successive notes. However, we do find augmented triads outlined, such as C#-F-A (a) (F augmented), and Bb-F#-D (b) (Bb augmented).
Key Groups
When a stretch of notes could belong to one single key, the ear will hear that section as tonal, especially if that group includes the tonic of the same key.
In the first row there are relatively large groups of notes which can be said to belong to the same key. We can bracket them to show the groups – there are just three. The groups overlap by one or more notes.
Rewriting the groups with their appropriate enharmonic equivalents will make the keys clearer:
Each of these groups also contains the tonic or keynote (for example, there is an Ab in the Ab major group). The E minor group uses both D# and D natural, which of course both exist in the melodic minor scale, but you could, instead, group the last five notes as G major.
Although we do not “feel” these keys in the same way we would if we were modulating through them in a tonal piece of music, the ear (being more accustomed to tonal music than any other type) will cling on to these vestiges of key.
Compare the second row:
Here are the notes spelled enharmonically according to possible key:
Not only are there twice as many groups overall, but none of the key groups contains its own tonic (e.g. there is no D in the D minor group). None of them contains more than four notes. Using smaller groups and avoiding the implied tonic of the likely diatonic key, will help to ensure atonality in the row.
Writing a 12-Tone Composition
To build a tone row from scratch, write out the twelve available semitones either in letters or notes, then cross each one off your list as you add it to your prime row.
Start on any note you like. Choose your second note (and so on), then calculate the melodic interval it forms with the previous note. If you used an accidental, consider the interval from the enharmonic spelling as well. Remember, generally you need to:
- Avoid outlining major/minor triads
- Aim for outlined augmented triads
- Avoid perfect 4ths and 5ths
- Aim to include tritones
By intentionally aiming to use tritones and augmented triads and avoiding perfect intervals, you will automatically avoid being centred for too long within any particular key.
NB In fact, Berg did write the following tone row in his Lyric Suite, which consists of a series of perfect 4ths and 5ths! The absolute equality between the notes makes it atonal.
Writing the Music
You may use each note in any octave. (The tone row is a collection of pitch classes[3] rather than specific pitches). Using larger intervals offers more possibilities for dissonance, because while a major or minor 2nd is a smooth step, a major or minor 9th is dissonant.
Thus, the following prime tone row:
could be written with the following pitches:
The composition is then created by using prime row in its entirety. (You will, of course, need to decide on a rhythm). The order of pitches must be strictly maintained, although you may use two or more of the same note in succession, or two consecutive notes can be combined into a trill or tremolo.
The prime row can be played backwards. This is known as “retrograde”, or “R”.
Here is a tone row, plus its retrograde version:
The retrograde row can be used to make a new section of music.
The composition can end on any note – it does not have to the be the first (or last) note from the row.
Form & Structure
Twelve-tone music works with an AB or ABA compositional form quite easily. You should also think about creating a good musical shape for your piece by building up to a single point of climax. A climax can be achieved by an increase in all elements of music: pitch, rhythmic complexity, dynamics, attack and tempo, or any combination of these. Because serial music doesn’t produce easily-remembered melodies, you could consider making rhythm the most important unifying element in your piece.
Here is an example composition, for flute, based on the shown tone row and retrograde:
