The time – fixation - diagram


If improvisation and composition form a continuum, a piece of music (whether improvised, composed or both) can be placed  upon an axis with the degree of fixation as a variable. In this way a specific situation of creating (inventing) music can be given a place on this axis, according to the degree of fixation: a very free form of improvisation (like the ‘Freye Phantasie’ described by C.Ph.E. Bach) will be at the lower side of the axis, and a composition which is notated in an extremely precise score will get a high value. Of course, the differences are qualitative: there is no way of measuring the degree of fixation, or of comparing different ways of fixating music.

If the degree of fixation is one parameter, another one, much easier to determine, is the point in history when this specific situation of creating music occurred. For a free improvisation this will be the year when it happened, for a composition the year of composing. If this parameter is represented by a second axis, we are able to make a diagram with situations of creating music, as reported in historical sources. For published scores the amount of examples is obviously so enormous, that only a few instances can be included. For historical reports of improvisations the situation is very different.

This ‘time-fixation-diagram’ makes it possible to attribute to a historical musical event (e.g. Brahms improvising Hungarian Dances together with Reményi) a set of coordinates, the first of them being  rather arbitrary (because qualitative), the second one usually precise (except for a phenomenon that lasted for a longer period, like basso continuo). The diagram shows clearly that in one particular time segment several levels of fixation occurred simultaneously. A striking general tendency appears in the 'Western Art Music' composed during the 19th century and the modernism during the 20th - a more or less closed repertoire area that featured an increasing amount of notational fixation, shown in the diagram as a movement in the bottom - right direction. Interestingly, the period at issue (the 19th century) shows a larger variety than the reputation of that century would suggest. Of course, the diagram only can show reported situations, a fact that might influence the general picture. 

Freye Phantasie

(C.Ph.E. Bach)

Improvised opera fantasy à la Liszt, Thalberg

Fantasie à la Czerny (chapter xxx), Beethoven (op. 77, introduction Chorfantasie)

Franck, Dupré: improvised sonata (organ)

Franck, Dupré: improvised fugue (organ)

Elgar improvising

Improvised variations à la Czerny, Beethoven

Free improvisation

Cadenza à la Czerny, Hummel

Prelude à la Clara Schumann

More developed prelude à la Czerny (chapter 2), Kalkbrenner

Albéniz improvising 

Variations à la Mozart

Improvisation on a ground

Cadenza à la Mozart (instrumental)

Simple prelude à la Czerny (chapter 1)

Fixated composition

Improvised Hungarian Dances (Brahms, Reményi)

Improvised chorale prelude (organ)

Basso continuo

Improvised ornamentation in baroque slow movement (Corelli, Telemann)

Vocal solo cadenza (Händel, Mozart, belcanto)

Prélude non mésuré

Morton Feldman Chamber music

Ornamentations in Chopin, Field

Improvised ornamentation in Mozart sonata slow movement

Bach English Suite

Classical sonata fast movement

Bach Kunst der Fuge

Beethoven sonata

Brahms piano pieces

Brahms chamber music

Beethoven orchestral music

Brahms Symphony

Mahler symphony

Ravel orchestral piece

Strawinsky Symphony in 3 movements

Messiaen organ music

Steve Reich Music for 18 musicians

Boulez Structures