A Clear and Practical Introduction to Temperament History Part 1: Introduction By (original) (raw)
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Tuning and temperament: practice vs science 1450-2020, Roma, Gangemi, 2023
Tuning and temperament: practice vs science 1450-2020, 2023
Until now, the problem of tuning instruments has been mainly viewed as an aspect of a phylologically correct performance practice. Besides several chapters dealing with this important latter aspect, the volume also devotes ample space also to the evolution of the tuning problem from a purely scientific point of view, starting ftom the Scientific Revolution and more particularly during the Enlightenment, with the decisive development of a new science: "Acoustics". It consists of a series of articles, most already published in Italian, presented here in English translation − revised, restructured, partly rewritten, expanded (in some cases radically) − and distributed over 21 chapters.
Approaches to tuning and temperament
The Journal of the Acoustical Society of America
Chairman's Introduction-9:00 Invited Papers 9:05 R1. Spanning the two cultures 1550-1750: Scientists and humanists seeking a quantitative account of contemporary musical scales.
Tuning the témpérament ordinaire, 2002
“Tuning the témpérament ordinaire" in Harpsichord & fortepiano, Volume 10, no. 1, pp. 22-29. UK 2002, 2002
The evolution from meantone into the 18th century French circular "tempérament ordinaire" is described. The latter is accurately reconstructed, based on the analysis of sources by Rameau, d'Alembert and Rousseau. More recently this work has been thoroughly updated, with a fully revised Rameau temperament, a detailed assessment of the differences between d’Alembert and Rousseau, and an analysis of the diverging tuning trends between pipe organs and other instruments in 18th century France. See the sections 8.3 pp. 108-112 and 21.3 pp. 418-429 of the eBook "Unequal Temperaments: Theory, History and Practice", 3rd. ed., 2013. See http://temper.braybaroque.ie/
Equal Temperament Tuning: The Nature, Cause and Effect
Equal Temperament is a tuning system that divides a pitch of a note by two to establish its octave, or the nearest same relative pitch distance; and then equally partitions the values of the notes within the octave by a factor. The most common factor used in Equal Temperament [ET] is twelve thus giving us the infamous western twelve equal semitones within an octave. By halving or dividing a fundamental tone by two, the vibrations or cycles creating the tone are an exact 2:1 ratio, the first natural harmonic overtone inherent within a fundamental tone. Aside from establishing the first octave, the ET system disregards all other natural overtones to enable equal partitioning for attaining consistent octaves. ET is the most popular of many tempered tuning development from the Pythagorean system of tuning based on the ratios of 3 (fifth intervals strongly apparent within natural overtones), discovered about 2500BC though documented by Pythagoras of Samos in the sixth century BC. The different methods in attaining a twelve-note octave are both audible and practical where ET compromises harmonic richness and sustain occurring from natural overtones for technical versatility and broader functional purposes. To assist in comprehending the contradiction between ET and the Pythagorean tuning systems, we should examine the natural overtones within a monophonic fundamental tone and the Pythagorean method of attaining a twelve-note octave.
Proposal for a Comprehensive Evaluation of Well–Temperaments and so called “Bach–Temperaments”, based on a calculation of the beating rates spread, of C-major diatonic fifths and major thirds., 2022
A musical temperament impurity measure formula is worked out, based on the calculation of the spread of diatonic fifths and major thirds beating rates. It enables to determine which temperaments hold a low spread of the beating rate of the C-major diatonic fifths and thirds. The very top of a well temperament ranking based on this calculation contains the temperaments mentioned in the breakthrough historical and musicological research of professor H. Kelletat on musical temperaments, especially concerning well temperaments and so called "Bach-Temperaments", enlightening their typical and essential characteristics. The proposed comprehensive evaluation therefor appears to lead to meaningful results regarding well-or circulating temperament evaluations.
Zarlino's Harpsichord: A Contribution to the (Pre)History of Equal Temperament
Muzikološki zbornik/Musicological Annual, 2018
This paper deals with the tuning question as it is discussed in Gioseffo Zarlino’s principal musical-theoretical treatise, Istitutioni harmoniche (1558). First, Zarlino’s tuning system in vocal music (the syntonic diatonic) is presented; then, its shortcomings are discussed; and finally, its adjustment (temperament) for the use in instrumental music is explained. Prispevek obravnava vprašanje o uglasitvi, kot se kaže v osrednjem glasbenoteoretskem spisu Gioseffa Zarlina Istitutioni harmoniche (1558). Predstavljen je sistem uglasitve, ki ga Zarlino utemeljuje v vokalni glasbi (sintonični diatonični sistem), prikazane so njegove omejitve in slednjič njegova prilagoditev (temperacija) za rabo v instrumentalni glasbi.