Musical logarithms in the seventeenth century: Descartes, Mercator, Newton

Wardhaugh, Benjamin

doi:10.1016/j.hm.2007.05.002

Cited by 3 publications

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References 3 publications

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“…Descartes's manuscript is lost. [16] One of the four circular pitch diagrams contained in the Compendium Descartes gives a system of three structurally identical hexachords "ut-re-mi-fa-so-la" (mollis, naturalis and duris), whose references are Pythagorean fifths apart as in Guido's system, but whose symmetric interval configuration t-T-S-T-t is composed of superparticular limit-5 ratios with major tones T (9 : 8), minor tones t (10 : 9) and diatonic semitones S (16 : 15) in place of Guido's limit-3 intervals. Descartes's syntonic hexachord and its completions to octachords are shown in Table 2.…”

Section: Interval Structure T-t-s-t-t T-t-s-t-t-s-t T-t-s-t-t-t-smentioning

confidence: 99%

Isaac Newton's Microtonal Approach to Just Intonation

Muzzulini

2021

EMR

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In 1665 Isaac Newton wrote a notebook in which he collected materials for a musical treatise which was never completed. He investigated ways of approximately representing just intonation scales by dividing the octave into many equally sized intervals. Strictly speaking, equal divisions of the octave are incompatible with just intonation, and just intonation intervals are audibly different from the intervals played on a modern equally tempered modern piano. By increasing the number of parts of an equal division, just intonation can be approximated arbitrarily well. Scales with more than 60 microtonal steps per octave, however, never gained wide acceptance in music theory or practice. Newton divided the octave into 612 equal parts so that he could represent the syntonic chromatic scale very accurately and he studied several equal divisions of the octave with fewer parts. His approximation problem is looked at in three ways: (1) A reconstruction of how he determined the many EDO-representations listed in the notebook is given. (2) Using computer programs Newton's tuning problem is solved "empirically" through calculating and evaluating the related approximations comprehensively. (3) The findings from the computer-assisted analysis are used to develop a more general geometric approach to the approximation problem.

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Section: Interval Structure T-t-s-t-t T-t-s-t-t-s-t T-t-s-t-t-t-smentioning

confidence: 99%

Isaac Newton's Microtonal Approach to Just Intonation

Muzzulini

2021

EMR

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Influence of Philosophical and Aesthetic Concepts on the Description of the Acoustic Characteristics of Vowels (Late 17th – Early 20th Centuries)

Kochetkova

2020

Vestn. Volgogr. gos. univ. Ser. 2 Jazykozn.

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The article deals with the potential explicit or implicit impact of the cultural and scientific tradition on the way of thinking of the researchers in different epochs. The hypothesis is that aesthetic and philosophical thoughts may influence in some way the results of the scientific experiments. The paper follows the order of the research. It starts from the results of vowel acoustics measurements in 19th century and ends by finding their conceptual basis in works of the 17th century. Measuring vowel acoustic characteristics, researchers of the late 19th and early 20th centuries in most of cases used various sets of tuning forks. The brightest, i.e. characteristic tone of a vowel was defined by ear. The results of such experiments showed that there were intervals of one or more octaves between characteristic tones of various vowels. Among different factors that may lead to such results, beside the circumstances of the experiment itself, we suppose cultural, scientific and philosophical tradition. The analysis of the works of the authors who first explored acoustic characteristics of vowels, showed that the philosophy and aesthetics of the 17th century may have influenced directly or indirectly the descriptions of vowels during the following centuries. The idea of the main vowels of the Adam Alphabet may have had an impact on the acoustic instruments, while the idea of harmony and proportion, essential in time of the Scientific Revolution, may be found in vowel system descriptions up to the beginning of the 20th century.

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Światło a muzyka

Naliwajek¹

2022

Światło. Przyczynek Do Badań Interdyscyplinarnych

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Musical logarithms in the seventeenth century: Descartes, Mercator, Newton

Cited by 3 publications

References 3 publications

Isaac Newton's Microtonal Approach to Just Intonation

Isaac Newton's Microtonal Approach to Just Intonation

Influence of Philosophical and Aesthetic Concepts on the Description of the Acoustic Characteristics of Vowels (Late 17th – Early 20th Centuries)

Światło a muzyka

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