Veranstaltungen 

Veranstaltungen der Fakultät für Mathematik

Mathematik in der Musik. Teil II. Die Natur der Töne., als mathkol

Termin

28.11.2011, 17.15 Uhr -

Veranstaltungsort
Mathematik-Gebäude, Hörsaal M/E28
Abstract
Jeder Musiker kennt das Phänomen: Die Töne treten nie alleine auf, sondern immer zusammen mit den anderen Tönen der Naturtonreihe des jeweiligen Instruments. Das erst macht den ”Klang” und die ”Klangfarbe ” aus. Im Falle der schwingenden Saite, der schwingenden Luftsäule in einer Pfeife, oder einer schwingenden Membran einer Pauke können die Obertöne mit Grundlösungen der sogenannten Wellengleichung identifiziert werden. Dabei ergeben sich Besonderheiten in der jeweiligen Obertonreihe aus den Nebenbedingungen (mathematisch: Randbedingungen), wie zum Beispiel gedackt oder offen bei der Pfeife. Die Pauke zeichnet sich durch eine besonders eigenwillige Naturtonreihe aus, die von der harmonischen (der Saite oder der Flöte) stark abweicht. Aber erst die Mischung der Naturtöne macht die Klangfarbe aus. Sie wird ganz wesentlich durch den Künstler bestimmt.
Als Schwingungen haben die Töne eine Frequenz. Da diese proportional ist zur geometrisch definierten Tonhöhe, kann man sie zu deren Messung verwenden.
Beispielhaft rechnen wir die gezupfte Saite durch oder bestimmen wir die Länge eines Fagotts oder einer Querflöte aus der Frequenz des niedrigsten Tones. Die Obertöne der Pauke führen auf besonders schöne ”Klangfiguren”.
Hinweis
Der Vortrag richtet sich an alle, deren Interesse in kulturhistorischem Kontext auf die Mathematik wie auf die Musik gerichtet ist.
Ohne Formeln geht es in der Mathematik ebensowenig, wie es in der Musik ohne Noten geht. Notenkenntnisse sind hier allerdings nicht erforderlich.
Vortragende(r)
Prof. em. Dr. Manfred Reimer
Herkunft der/des Vortragenden
Fakultät für Mathematik, TU Dortmund
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