Indeterminate notation

After having worked with more traditional notation, I found myself interested in alternative approaches, partly to move away from the habitual ways of interpreting sheet music and to open up for improvisation that puts less emphasis on harmony. This led me to try out indeterminate notation. Here, we'll examine three types of notation; boxed notation, indeterminate pitches and indeterminate repetitions.

Boxed notation  

In Dutilleux’s Sonatine for Flute and Piano, I used boxed notation in several places where a melodic cell –  from the original – would change through processes like rhythmic and melodic permutation, intensification, modulation etc. For example, take bars 37-42 from the first movement, how the melodic cell goes through different transformations:

Figure 8.9. Sonatine for Flute and Piano (Dutilleux, 1943), mm. 37-42.

For the version I tried with en en en, I used boxed notation to recreate and potentially extend the same passage:

Figure 8.10. Adaptation of 8.9 with boxed notation, for soprano sax and rhythm section. Concert pitch.

Recording 8.4. Sonatine for Flute and Piano, Knudsen & en en en. From Studio Øra, Trondheim, September 28, 2023. 

This way of notating, thus, invited us to engage with melodic building blocks and find our own ways of developing them. This sort of passage did, however, require a certain mindset as a performer. One of the challenges was to make the transition from composition to improvisation, to gradually move away from the written figures and then eventually dissolve it together. At one point, we experimented with giving visual cues for when this, but soon realized that it would work better if we based the process on attentive listening. As we played the material more and more, we could decrease the feeling of having a ‘seam’ between the composed and the improvised material. One of the qualities we discussed afterwards was that it sounded as if the improvisation could have been composed that way: 

EH: But it's a very good way to go into free improv, this, because now it sounds like it's still written in some way.

PK: But the challenge is that – when you have a very strong established groove, it's also harder to break away from it. …

EH: Because... it's fun to do it for longer. Now we were probably a little bit occupied that we're going to dissolve it. If we just think that – let's see what happens? Then we could have gone on even longer. (Conversation with Hegdal, Duch & Haugerud 2023-05-08) 

PK: Men utfordringen är att - när man har ett väldigt starkt etablerat groove, så blir det också svårare att bryta sig loss från det. …

EH: Fordi... Det er kul å holde på lenger. Nå var vi sikkert litt opptatt av at vi skal løse det opp. Hvis vi bare tenker at - vi ser hva som skjer? Så hadde vi jo kunnet holde på enda lenger. ]

As I revised this kind of passages in the score, I paid a lot of attention to the type of constraints that were put it the score, if they were indeed musically justified. For instance; should it end on an A, or can it be simply a high note? Is there a point in indicating a certain direction, e.g. move upwards ad lib? In general, I ended up taking away a lot of the initial instructions and constraints that I had put in, as I realized that they locked us in too much.

Indeterminate pitches

The example above also includes the use of indeterminate pitch notation, i.e., having a given rhythm where the performer is free to choose the pitches:

Figure 8.11. Indeterminate pitch notation without stems.

Indeterminate pitches can also be notated using cross-shaped noteheads, as in the free interpretation of the ending of Crawford’s Leggiero. Here is the original version:

Figure 8.12. No. 8 Leggiero from Nine Preludes (Crawford Seeger, 1928), mm. 61-68.

In the passage above, the original has a strong emphasis on the rhythmic accents and the overall energy, while the exact pitches appear to be of a less priority; the feeling one can get from this passage is ‘random pitches harmonized in fifths’ in a general descending pattern. By employing indeterminate pitch notation, I could achieve a similar effect without being restricted to the exact pitches. 

Figure 8.13. Interpretation of 8.12 with indeterminate pitches.

Recording 8.5. Ending of Leggiero with Knudsen, en en en, Halse & Åse. From the Department of Music at NTNU, Trondheim, 2023-12-08.

Indeterminate repetitions

With Leggiero, I also took a passage from the original as a starting point for a musical crescendo section that would gradually morph into the ending of the piece (as seen in fig. 8.13 above). The starting point was the piano figure presented in the start of the piece:

Figure 8.14. No. 8, Leggiero from Nine Preludes (Crawford Seeger, 1928), mm. 1-2.

In the reimagined versions, the contents from this phrase – focusing on rhythmic accents and general shape – was used as a model for rhythmic cells with indeterminate repetitions. These cells then underwent transformational stages, with a general increase in rhythmic density:

Figure 8.15. Rhythmic cells based on piano figure from Leggiero (8.14).

From the perspective of improvisational frameworks, these cells imposed a high degree of constraints, leaving little space for improvisation. As a result, this approach could serve to rhythmically organize the performers, something that could – for instance – create a background for other musical events. However, as I tried this approach with several ensembles[1], it became clear that it worked best to interpret the contents of the cells – and how to move between them – in a rather open way. Over time, they were used more as a reference, to give an initial idea of how the first figure could be rhythmically intensified over time, leading up to the ending figure in 6/8 (on cue). Thus, how the cells was actually used was ultimately left open to the musicians. However, as a way of synchronizing the ensemble, it was helpful to let one instrument – e.g., the bass – indicate when to continue to the next cell, especially when moving between the first two cells (in 4/4) to the second cell (in 3/4).