The Art of Arpeggiation

Niels Pfeffer

Student Number 3167720 Supervisor(s) Patrick van Deurzen Title The Art of Arpeggiation Research Question How many different ways of arpeggiation is it possible to think of and how is musical meaning created through them? Summary This research is about discovering the expressive possibilities of arpeggiation – may it be indicated by an arpeggio sign or added arbitrarily by a performer. For two reasons this question seems relevant: 1. In the past century, the idea that musical performance should be an exact reproduction of the score has become increasingly predominant and in consequence the idea of exact synchronity has evolved. Seeking for a more creative and less reproducing way to perform, breaking up this rigid synchronity provides us with an exciting "playground" yet to be explored. 2. Particularly on the classical guitar arpeggiation can frequently be heard – often for more technical than musical reasons. Especially on this instrument, a more reflected use is desirable. It was barely looked at the rules on what happens "inside" an arpeggiation. A reason for that might be, that everything inside an arpeggiation usually occurs very rapidly which makes it a lot harder to be analyzed. Besides that, often in arpeggiation the performer relies on "automatic" processes that are difficult to be modified consciously. I propose the idea, that arpeggiation consists of multiple layers of meaning that can be put together in any possible combination. The layers of arpeggiation span with increasing subtlety from habitual arpeggiation to a meticulously planned effect. In the presentation I will demonstrate this concept by showing different ways and meanings of arpeggiation in recordings and on my instrument. Short Bio Niels Pfeffer finished his harpsichord studies at the Stuttgart University of Music under Jörg Halubek and his guitar studies with Johannes Monno in 2017. He is studying in master with Robert Hill in Freiburg (harpsichord) and with Zoran Dukić in The Hague (guitar). With the guitar he won numerous prizes at renowned competitions. He is passionate about playing continuo on theorbo and harpsichord. With both instruments he took part in opera and orchestra performances. As member of different early music ensembles he has been regularly successful in competitions. At the University of Music Stuttgart he is teaching continuo and theorbo.

The "100 Versions" Experiment

Starting point is the simple task to write down 100 "beautiful" versions of a given arpeggio. Assuming a seven-note-arpeggio, it is possible to (automatically) generate no less than 7! = 5040 versions/permutations of the existing notes.¹ In a next step, all 5040 versions are being played through (preferably on a keyboard instrument). According to his subjective judgement the player chooses 100 versions out of them.

Mechanical Creativity and its Background

Commonly creativity is thought to be connected to some kind of highly subjective process and almost "mystified" – and therefore withdrawn from rational understanding. In contrast to that the mechanical aspect of creativity shall be lightened up here.

The permutational aspect of music was frequently discussed in 17th and 18th century. As a first to be mentioned is Marin Mersenne and his Harmonie universelle. Not only is he doing very detailed calculations on the number possible permutations under various circumstances. He also dared to print in the Harmonie universelle no less than all 720 possible permutations of a hexachord. Combinatorical considerations can regularly be found also in later sources.² Common to almost all of them, including Mersenne, is the mentioning of God in the context of the "almost infinite" amount of variations that permutation can generate.

"All the people of the earth couldn't sing all of the possible songs contained in the harmonic hand […] Even if they sang a thousand different songs every day from the creation of the world until the present."

[Mersenne, Harmonie universelle]

"With evident regret, Mersenne conceded that it would never be possible on this earth to compose a perfect melody, although he held out the happy prospect that the devout Christian might yet hear such perfect melodies sung by the angels in paradise if it so pleased God. Still, the exercise in permutation theory was a useful one, if only to remind us of the unfathomable riches God has made available to us on this earth. Music is thus a parable for the plentitude of His creation. In contemplating this science of sound, Mersenne continually reminds us, the pious listener is lead inexorably to greater devotion to God."

[Thomas Christensen, "The sound world of father Mersenne" in Susan McClary (ed.): Structures of Feeling in 17th Century Cultural Expression, p. 69]

Yet, most of the sources considered combinatorial arts to be an important help in both, composition as well as improvisation.

Structurizing Voice Leading

Having chosen a set of permutations, it seems that by just repeatedly playing them the body (or "subconscience") has a tendency to organize the inner accents. Since a permutation per se doesn't have any kind of organization in it, I propose to systematize all possible structurizations. Lets assume as a basic principle that two voices are standing with each other in a dialogue. Ideally this dialog can be represented in keyboard instruments by the right hand for one voice and the left hand for another voice. Very easily all distributions of 7 notes on two voices can be generated, since it's equivalent to counting in binary format. Imagine 0 to represent the left and 1 to represent the right hand.³

0 0 0 0 0 0 0

0 0 0 0 0 0 1

0 0 0 0 0 1 0

0 0 0 0 0 1 1

0 0 0 0 1 0 0

0 0 0 0 1 0 1

…

1 1 1 1 1 1 1

All versions should be practised. While versions like 0 0 0 0 0 0 0 are obviously less meaningful, a surprising amount a variants makes more sense that expected on a first sight.

The alternating distribution 1 0 1 0 1 0 1 applied to permutation number 4367 sounds e.g. like this:

³ Applied to a randomly chosen permutation from the given set of permutations, we get the following result (stem up means right hand, stem down left hand)

²"To learn how to create such variations, however and here improvised technique came very close to compositional technique – writers suggested practising varying different intervals (Niedt, Quantz, Riepel and Daube), or chords (Daube), sometimes applying the permutation technique of ars combinatoria", Elaine Rochelle Sisman, Haydn and the Classical Variation, Harvard 1993, p. 52. For further discussion of Mersenne and other combinatorical approaches in music cf. Sebastian Klotz, Kombinatorik und die Verbindungskünste der Zeichen in der Musik zwischen 1630 und 1780, Berlin 2006, S. 61ff.

¹ For demonstration the first page of those permutations is given here

Tip

Tip