 Proportion Sequences of Babylonian MedietiesKarlheinz Schüffler
Chapter 4 in Proportions and Their Music, 2024, pp 153-194 from Springer Abstract: Abstract In this chapter (Proportion Series of Babylonian Medieties) we consider the process of perpetual averaging – formations and in this way obtain whole families of babylonian medieties chains as nested iterations. This can be done both in the interior of the interval [a, b] and in its exterior. It leads us to the following three types of iterated mean-value-proportion chains: the families of iterated babylonian medieties as nested iterations of babylonian proportion chains in the interior of the interval [a, b], the families of ‘contra-medieties’ as a bipartite series of iterated proportion chains belonging to the exponential division parameter series (a/b)n the families of the third and higher proportions as interpolation of progressing mean proportions into the exterior of the interval [a, b]. Hence, chains of proportions of arbitrarily great length are created. For these, too, a harmonia perfecta maxima infinita can be developed, which describes the symmetries running to infinity and thus provides an inner order for the processes of boundless – and partly microtonal – interval generations. Date: 2024 There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-65336-4_4 Ordering information: This item can be ordered from DOI: 10.1007/978-3-662-65336-4_4 Access Statistics for this chapter More chapters in Springer Books from Springer |
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