I Apologize for reading from these notes. But in saluting Hans I don't want unduly and inappropriately to fumble or stumble. I'm conscious as I speak of his unique ability to think aloud in perfectly articulated and continuous sentences, something I could not hope to match. And in saluting Hans, I am also saluting Milein, and remembering her fortitude during this last week and recent months.

Everyone who came to know Roger Huntington Sessions and to admire his music was always deeply impressed by his integrity as man and musician. For us his high moral stand revealed itself in every aspect of his mature life: in his music, in his teaching, in his essays, in his moments of light-hearted humour in social gatherings. This quality has been evident to me ever since I heard his First Symphony performed by the Boston Symphony in 1927.

The difficulties connected with the idea of synthesis do not originate with the fact that as soon as he starts to elucidate the laws that have been formulated in general terms, Schoenberg postulates a musical space that only has two dimensions, the horizontal and the vertical. The scientific origin of these concepts could tempt one to think of this space (strictly geometrically) as a plane surface, and then to imagine it as comprising the paper on which music is notated, the dimensions then comprising the directions of the notation itself or of reading. But this is not yet musical space, and only if one tries to imagine a synthesis on this plane surface does one tend towards the concept of a diagonal. The inadequacy of the ‘diagonal’ seems to have been sensed by those authors who directed attention to the temporal aspect of music and who (perhaps by a popularizing analogy with the idea of time as the fourth dimension) attempted to locate the synthesis within the domain of ‘time’—say, the rhythmic domain. Schoenberg—and Webern followed him in this—distinguishes with terminological exactitude: wherever vertical and horizontal appear as concepts on their own, the explanation is always added: ‘The elements of a musical idea are partly incorporated in the horizontal plane as successive sounds and partly in the vertical plane as simultaneous sounds’; or: ‘In accordance with this [law], harmony and melody, vertical and horizontal, form a musical unit, a space, in both of whose dimensions the musical substance is deposited’, and similarly in the draft for the Princeton lecture. The conception of the dimensions of musical space is therefore connected with ‘harmony and melody’—without ‘vertical’ and ‘harmony’, or ‘horizontal’ and ‘melody’, thereby being identical. But how do matters stand on this plane with the ‘unit(y)’ that primarily interested Schoenberg and with the ‘synthesis’ upon which Webern apparently directed his attention?

The most remarkable development in 20th-century music has been the gradual rise of transcultural music to status as the dominant activity of composers. Interaction between musics of various types within the same culture, and between cultures (including those separated from us in historical time), has been more important than the conventionally-recognized classifications of 20th-century musical activity such as expressionism, atonality, impressionism, neo-classicism (in its purist, Eurocentric stance), serialism, total serialism, chance, and minimalism (when it poses as an intellectual movement without cross-cultural referrents).

Plato discussed the term ‘heterophony’ in his Laws, Part VII, The technique was widely in use by the Notre Dame school of composers in 12th-century Paris. Much of the indigenous music of the Near East and Africa is rich with it. Indeed, there is an important example in the Credo of Beethoven's Missa Solemnis. The Israeli composer Mark Kopytman has in recent years transformed this ancient term into a vital 20th-century technique, and made it the language of some of his important compositions. One of these, Cantus II for violin, viola, and cello (1980), will be performed at the ISCM World Music Days during March in Budapest.