The difference between 12-tone and serial music is that in 12-tone music only the pitch is given a row. In serial music all musical elements (rhythm, register, dynamics, etc.) can be, or will be govern by a row. That is, non-tonal approaches can be adapted to all aspects of a musical composition not just the pitch.
Rhythm and meter:
What is tonal rhythm?
Tonal meter implies downbeats and upbeats, strong and weak beats that are discernible, as well as metric regularity. Tonal rhythm dwells in this metric landscape. Tonal rhythm can be stretched, but not broken. Even if a down beat is only implied its still creates tonal rhythm. Composers can get around this by creating formal designs that never seem to arrive. For example, the down beat, or main point of arrival, can never reached (Sibelius, Debussy) or reached only once at an unexpected point.
Breaking down tonal rhythm:
Motor rhythm addresses this problem by creating constant accent—no weak beats. Parts of Stravinsky’s Rite Of Spring is all down beats. Everything an unnotated 1/8 measure. The move from constantly changing meter groups of changing 2’s and 3’s stretch tonal rhythm but rely on tonal rhythm for their effect. Or, if a work has no point of arrival it can have no strong beats.
Messiaen with his use of bird song and Indian ragas creates consecutive uneven subdivision which also obscures meter. Rather then motor rhythms Messiaen would create uneven durations. For example, changing groups of even quarters to uneven 16ths and back—this will also disrupt tonal rhythm as the changing accents would then fall in between the metric beats.
What next?
The move into rhythmic serialization comes from the above two directions; from motor rhythms (i.e. meter-or letting the rhythm define the meter), a prominent feature of modern music of the Neoclassical school. This is the constant reiterated groupings of steady pulse or a single note type eighth quarter etc. Examples would be found in the music of Babbitt in his “time point system”, and Carter in his “tempo modulations”, or from the direct manipulation of durations (i.e rhythm-rhythm disrupts or disintegrates the meter), as in the music of Messiaen and Boulez.
The constant reiteration of a single note (duration) also implies a tempo, Ives composed orchestral works where 2 or more different tempos(related or not) exist at once.
Carter, who worked for Ives, tends to assign a particular note type(duration) to each individual part. A composition can then have any number of different parts with different note types or tempos for each part. This creates an cumulative effect obscuring pulsation.
Babbitt, in his time point system uses 12 as a way to subdivide measures into equal units of time points(attacks-he does not define the durations). These equal units are related to motor rhythms as they are uniform just like motor rhythms are-but their effect is completely different. Time points push rhythm past the concept of tonal rhythm. Since Babbitt’s music unfolds at a constant- rate, the change in measures has a drastic effect on the surface density of his music. a 6/4 measure would feature eighth notes (Calm) a 2/4 measure 16 note triplets (intense) . (These audible changes in surface density was the subject of a paper of mine on Babbitt’s String Quartet No. 3).
If serial music is a refinement of 12-tone technique, where does rhythmic serial technique fit in?
Total serialization, of which rhythmic serialization is a part, was not necessarily a natural outgrowth of 12-tone music, but rather part of a accelerated nationalistic musical “arms race” after WW2. It was a matter of getting there first-and for art, first is not always best—Remember that Hauer came up the combinatorial row before Schoenberg. The most successful compositional techniques are those that mature over time.
Early attempts at rhythmic serialization are numerical groupings of motor rhythms, or durations–this causes strange musical effects in some works. Otherwise sophisticated works are saddled with a simplistic rhythmic element that seems foreign to the rest of the composition. This is not the case with the music of modernist pioneer Ruth Crawford-Seeger.
Other methods of rhythmic precomposition include; creating rhythmic relations; durations, meter, tempos, derived from the 12-tone interval set, or from a special interval series or chord (see Hemholtz), or from any rhythmic/metric design of the composers imagination.
Bartok, was fond of using the Fibonacci series to define rhythm and meter –see George Perle’s book.
What is an irrational measure?
Ok, folks lets stop making sense! In music there is usually more than one way to notate anything but if we focus on uneven durations it seems only likely that uneven measures will surely follow. “2 and 3/5 quarter” “3 and 3/32 eighths” etc. These measures by their very nature obscure tonal rhythm. Tonal points of arrival are constantly reset.
An irrational measure is a way to facilitate many of the techniques mentioned above. They can be a compositional element, they can also be used to notate precise tempo changes, or to graft different rhythmic elements together. For example a “7 triplet” or a “2 and 1/3” quarter measure might work better than a 4/4 plus 3/4 or a 7/8 measure with a different tempo than the proceeding music in a given situation. They can also be used as an ossia, an alternative notation to make some notational problem easier and more clear. True, they can also be more fussy and time consuming. I would suggest that irrational measures work best in smaller groups compositions,
Henry Weinberg in his Cantus Commemberabils 1, sets a single tempo then uses his row intervals to create durations and irrational measures into a varied and intricate surface.
What is a nested measure?
Unlike the irrational measure which is a a rhythmic (durational) innovation, the nested measure is a metric innovation. A nested measure is where say a 4/4 measure is divided and subdivided into triplets within triplets within triplets within triplets etc. In a sense it is placing measures within measures. This technique can, like the irrational measure, create very precise and rapid changes of tempo with in a measure. Nesting is also a way to precisely notate several different and contrasting tempos going on simultaneously with losing control of their relationships. Though Nesting does not necessarily obscure tonal rhythm as tonal meter is still the reference though that reference could be just that. Nesting is a feature of Ralph Shapey’s music.
Many serial and 12-tone works already have analyses available for study, why not consult these instead of copying these out by hand?
The irony of recent theoretical approaches is that they are not about theory at all but about certainty. The accurate retelling of a works precompositional material is a fine thing but it is not an analysis of a work any more than a blueprint is an analysis of a building. A blueprint does not describe the experience of a structure in time and space only its dimensions. Many works which use rows and or serial techniques have very similar blueprints, but their compositional effect is completely different. The question to ask is not how closely the composer follows their “system,” but what are the results and the musical effect?
Questions
Find the spot in the “Rite Of Spring” where everything is accented as a down beat.
Find the Symphony of Sibelius where there seems to be no down beat.
Read Messiaen’s “Technique De Mon Language Musical”
Create your own rhythmic “set”, then use it.
Think about how you would serialize “dynamics”, and what would be the effect.