PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2014 | 42 | 1 |
Tytuł artykułu

Mathematical aspects of musical scales and series

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Musical scales may be interpreted as specific increasing sequences of real numbers. Periodic scales, i.e. musical scales whose pattern is periodic, feature in this article. Of special interest are regular scales of which are given seven properties in four theorems which are new results, engaging the concepts of: the period of scale, the length of period of scale, the pattern, being homomorphous, a transposition and having the same key. This paper considers the idea of musical scales in general, hence it is possible to consider more complex musical scales not only in the twelve-tone equal temperament, and also proposes tools to investigate traditional musical scales as Messiaen’s Modes of limited transposition [4, p.58], the major and the minor scales as well as ancient Greek scales inherited by medieval Western music. The paper also goes beyond the notion of musical scale and contains new interesting result which gives way to determine when one can form a series from a shorter sequence of sounds by transposing the sequence.
Rocznik
Tom
42
Numer
1
Opis fizyczny
Daty
wydano
2014
online
2014-08-20
Twórcy
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_14708_ma_v42i1_393
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.