{"id":4026,"date":"2011-02-26T06:15:36","date_gmt":"2011-02-26T04:15:36","guid":{"rendered":"http:\/\/www.kulturtechno.de\/?p=4026"},"modified":"2011-02-25T13:29:17","modified_gmt":"2011-02-25T11:29:17","slug":"narayanas-cows-von-tom-johnson","status":"publish","type":"post","link":"http:\/\/www.kulturtechno.de\/?p=4026","title":{"rendered":"„Narayana’s Cows“ von Tom Johnson"},"content":{"rendered":"

Ein sch\u00f6nes Beispiel f\u00fcr die gehalts\u00e4sthetische Wende<\/a> ist Tom Johnson’s „Narayana’s Cows“. Johnson hat ein mathematisches Problem in Musik umgesetzt. Ultraalgorithmisch, zugleich ganz aus der Lebenswelt!<\/p>\n

Six or eight years ago one of us (T.J.) found a German edition of a little book on the history of mathematics by a Ukranian scholar named Andrej Grigorewitsch Konforowitsch. The book was full of curious information, but I was particularly struck by the following, which Konforowitsch attributed to Narayana, an Indian mathematician in the 14th century:<\/p>\n

A cow produces one calf every year. Beginning in its fourth year, each calf produces one calf at the beginning of each year. How many cows and calves are there altogether after 20 years?<\/p>\n

In working this out, T.J. came to know a unique numerical sequence, and a year or so later I found a way to translate this into a composition called Narayana’s Cows. It begins with the original cow and her first calf: long-short. The second year she has another calf: long-short-short. The third year: long-short-short-short. Then in the fourth year, the first calf also becomes a mother and the herd grows from four to six: long-short-short-short-long-short. The music continues like this, though it doesn’t go all the way to the 20th year, because by the 17th year there are already 872 cows and calves and 15 minutes of music.<\/p><\/blockquote>\n

Noch mehr dazu hier<\/a>.<\/p>\n

Johnson hat das in ein zweistimmiges Musikst\u00fcck gesetzt. Ein Moderator erkl\u00e4rt jeden Zwischenschritt. Mit der Zeit erzeugt diese Melodik, oktavierend gespielt, einen ziemlichen Sog, ja, man mag fast mitpfeifen! Und dennoch, so man diese Unterscheidung machen will: Das kann nur Neue Musik sein, kein Popmusiker w\u00fcrde so etwas ersinnen. <\/p>\n

Witzig ist auch, dass Johnson, in alter Kunst-der-Fuge-Tradition, keine Instrumentation vorgegeben hat. Hier verschiedene Interpretationen:<\/p>\n