The concept of statistics is taken from mathematics and is used in a sense analogous to the statistical surveys that give the average values present in any given complex. In musical terms this means that from the listener's point of view there will be elements, partial forms and individual groups which fuse into a whole from which they can no longer be disentangled. The composer establishes such statistical criteria beforehand and proceeds to work with them; thus he does not regard the form as a mere aggregation of the individual elements with all their properties, but rather he proceeds from the organising principle itself-from statistical criteria. In a kind of music in which the individual note plays a subordinate part in a conglomeration or pile-up of notes, something which in itself may be very complicated becomes a matter of simplicity. The criteria of statistical composition are determined by the boundaries of the clouds of density and by their proportional frequency of occurrence. One cannot account for the whole on the basis of the individual part, for the whole is conceived as the probable result of many components. (Source - Reduced from Karl H. Wörner (1973). Stockhausen: Life and Work. (Hopkins, B. ed., trans.) Faber and Faber.)

Le concept de statistique est emprunté aux mathématiques et utilisé en analogie avec les enquêtes statistiques qui donnent une valeur moyenne de n'importe quelles données complexes. Dans le domaine de la musique, l'écoute statistique signifie qu'il y a, du point de vu de l'auditeur, des éléments, des fragments de formes ou des groupes d'éléments qui se fondent en une seule entité et qui ne peuvent être démêlés. Le compositeur choisit les critères statistiques et travaille ensuite à partir d'eux, ainsi, il ne considère pas la forme comme une agrégation d'éléments individuels possédant des propriétés mais plutôt comme un principe d'organisation interne fondé sur des critères statistiques. Par exemple, une musique dans laquelle les notes individuelles jouent un rôle subalterne dans un congloméra ou un ensemble de notes peut être quelque chose en soi de très compliquée et devenir alors, grâce aux techniques statistiques, une question de simplicité. Les caractéristiques d'une composition statistique sont déterminées par les limites des nuages de densité et par leur fréquence de répétition. On ne peut expliquer le tout à partir des parties individuelles car le tout est conçu comme le résultat probable de nombreux composants. (Source - résumé de Karl H. Wörner (1973). Stockhausen: Life and Work. (Hopkins, B. ed., trans.) Faber and Faber.)

Il concetto di statistica è mutuato dalla matematica e utilizzato in analogia con le indagini statistiche che danno un valore medio a qualsivoglia serie di dati complessi. In musica, l'ascolto statistico sta a significare che, dal punto di vista dell'ascoltatore, si hanno degli elementi, dei frammenti di forme o gruppi di elementi che si fondono in una sola uni e che non possono essere separati. Il compositore sceglie i criteri statistici e lavora a partire da questi, non considera la forma come un'aggregazione di elementi individuali con proprietà specifiche, ma piuttosto un principio di organizzazione interna fondato su criteri statistici. Ad esempio, in un brano, un conglomerato molto complesso di note che a loro volta giocano ruoli subalterni complessi, può diventare semplice se considerato statisticamente. I criteri di una composizione statistica sono determinati dai limiti delle nuvole di densità a dalla loro frequenza di ripetizione. Non si può spiegare il tutto a partire dalle parti individuali perché il tutto è concepito come il risultato probabile di numerose componenti (Fonte - - ridotto da Karl H. Wörner (1973). Stockhausen: Life and Work. (Hopkins, B. ed., trans.) Faber and Faber.).

The concept of statistics is taken from mathematics and is used in a sense analogous to the statistical surveys that give the average values present in any given complex. In musical terms this means that from the listener's point of view there will be elements, partial forms and individual groups which fuse into a whole from which they can no longer be disentangled. The composer establishes such statistical criteria beforehand and proceeds to work with them; thus he does not regard the form as a mere aggregation of the individual elements with all their properties, but rather he proceeds from the organising principle itself-from statistical criteria. In a kind of music in which the individual note plays a subordinate part in a conglomeration or pile-up of notes, something which in itself may be very complicated becomes a matter of simplicity. The criteria of statistical composition are determined by the boundaries of the clouds of density and by their proportional frequency of occurrence. One cannot account for the whole on the basis of the individual part, for the whole is conceived as the probable result of many components. (Source - Reduced from Karl H. Wörner (1973). Stockhausen: Life and Work. (Hopkins, B. ed., trans.) Faber and Faber.)

El concepto de estadística es tomado de las matemáticas y es usado en un sentido análogo al de las encuestas estadísticas que dan los valores promedio presentes en cualquier complejo. En términos musicales esto significa que desde el punto de vista de quien escucha habrá elementos, formas parciales y grupos individuales que se fusionen en un todo del cual ya no podrán distinguirse. El compositor establece los criterios estadísticos de antemano y procede a trabajar con ellos; por lo tanto él no ve a la forma como una simple suma de elementos individuales con todas sus propiedades, sino que trabaja desde el principio organizador en sí -desde los criterios estadísticos. En un tipo de música en la que la nota individual juega un rol subordinado dentro de un conglomerado o apilamiento de notas, algo que en sí puede ser muy complicado, se transforma en un asunto muy simple. Los criterios de composición estadística son determinados por los límites de las "nubes de densidad" y su frecuencia de ocurrencia proporcional. Uno no puede explicar al todo basándose en lo individual, porque el todo se concibe como el resultado probable de muchos componentes.

(Fuente: extractado de Karl H. Wörner (1973). Stockhausen: Life and Work. (Hopkins, B. editor, traductor) Faber and Faber)