Zarlino's Harpsichord: A Contribution to the (Pre)History of Equal Temperament (original) (raw)

The Harpsichord: Its Timbre, Its Tuning Process, and Their Interrelations

2013

At the Edinburgh University Collection of Historical Instruments (EUCHMI) there are two virginals where the strings are plucked extremely close to 1/4 of their length over a substantial part of the compass. Principles of Acoustics dictate that in such cases the fourth partial of the resulting sound is unlikely to be produced with any appreciable magnitude. Similar situations affecting different partials also occur when the plucking point is located at other fractional parts of the string length, such as 1/3 or 1/5. A database of plucking points, based on museum catalogues, was created and analysed, so that pitch regions are identified where such phenomena are likely to occur for different categories of instruments. The main cue used in harpsichord tuning is related to beat phenomena produced by partials of two simultaneously played notes, whenever there is a small difference between their frequencies. Partial four being relevant for major thirds and perfect fourths, these intervals may result less accurate, or less reliably tuned, in instruments like the above virginals. Historical sources were surveyed for expressions which describe the cues that tuners were supposed to use in identifying the ideal of an interval. Although expressions such as Schwebungen are mostly related with beats, broader meanings are discussed. Hints of the use of alternative, not beat-related cues, are identified. A series of practical tuning experiments was performed in which selected intervals were tuned, the accuracy of the tuning process being assessed from recordings, which were subjected to spectral analysis. Only cues that could be related to historical sources were used. The effects of factors such as pitch, pitch region, instrument, interval type, and particularly the potential absence of relevant partials were investigated, statistical methods playing a substantial role in the research. A logbook was created, where the experimenter detailed the cues used for each tuned interval in one of the experiments. The recorded information provided some insight into a number of strategies a tuner may use for coping with difficulties in cases of absent or weak partials. The impact of inharmonicity on the exact size of just intervals was also examined, both on theoretical grounds and based on data from the experiments. A number of case studies were included, where a comparison was made between missing partial notes predicted from plucking points and the degree of absence of those partials in the actual spectra for some historical instruments.""

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.

Innovations in temperament and harmony in French harpsichord music

1. The additional information about documentary evidence is derived from certain parts of Chapters 5 and 6 of my essay, "Stimmung und Temperatur," in F. Zaminer, ed., Hören, Messen und Rechnen in der frühen Neuzeit (= Geschichte der Musikhheorie, Bd. 6; Wissenschaftliche Buchgesellschaft, Darmstadt 1987), pp. 109-331. The relevant bibliographical information is provided there (and is, for the most part, not duplicated here); the French texts are given in footnotes there with the original spellings (which are here modernized).

CHAPTER NINE THE TUNING OF THE LITHUANIAN SKUDUČIAI 1 RYTIS AMBRAZEVIČIUS 2 AND RŪTA ŽARSKIENĖ 3

The Skudučiai, the traditional Lithuanian multi-pipe whistles or pan-pipes, usually contain from 5 to 8 pipes of different lengths with one end closed; made of umbellate plants, wood or bark. The Skudučiai differ from other pan-pipes: they are unbound and blown by several performers. The instruments were used to play specific polyphonic compositions. The pipes of the Skudučiai were tuned “by eye” (i.e. by selecting pipes of different length) and “by ear” (i. e. by playing the parts of the most popular musical composition of the village) successively from the lowest to the highest pitch or vice versa. We aim to measure and generalize the interval sizes in the tunings of archived Skudučiai, and to reveal their possible psychoacoustical origins. To complement the earlier findings of Skudučiai tunings, a comprehensive overview of the principles of the tunings based on ethnographical data is presented. Isolated pitches of three sets of Skudučiai preserved in the Lithuanian National Museum as well as several rhythmic patterns were recorded. Each recording was repeated twice (by the two authors). The acoustical measurements revealed the irregularities in the three pitch scales: no correspondence in their intervallic structures was found. The only generalization that can be made is that the scales are designed quite loosely; the intervals range from wide minor seconds to narrow minor thirds. Together with the samples studied earlier, the mode of the distribution of the intervallic steps equals 184 cents and the interquartile range is from 141 to 231 cents. Moreover, the pitches in the recordings by the two authors differ, as do the pitches produced by a single player in isolation and in a rhythmic pattern (presumably because of the differences in blowing force). Often these differences exceed 10-20 cents. It can therefore be concluded that Skudučiai makers were not concerned with precise tuning, in the contemporary sense. In addition, precision better than ~20 cents was hardly possible. Nevertheless, the maintenance of roughly 180-190 cents, on average, suggests that the psychoacoustical phenomenon of roughness was at work: probably the makers intended to achieve considerable roughness in the simultaneous sounding of two neighboring pipes (refer to the abovementioned case of vocal Sutartinės). The tunings of Skudučiai are loose; they share no resemblance with 12ET and present a peculiar pitch categorization: roughly equal intervals with the tolerance of mistuning considerably higher than that in the usual usage of 12ET. The tunings are centered on the phenomenon of maximum roughness as ideal. The insights of the present study, possibly, could be extended to the studies of different musical cultures featuring examples of Schwebungsdiaphonie.

The tuning of Trasuntino's "Clavemusicum Omnitonum" and Zarlino's enharmonic system

2024

The monochord made in Vito Trasuntino's workshop for his 1606 "Clavemusicum Omnitonum" with 31 keys per octave was designed with Zarlino's 2/7 comma tuning. Zarlino's diagram (Le Istitutioni Harmoniche, 1558) was the basis, but the whole tones were reproduced without tempering. Zarlino's 24-note/octave harpsichord (built in 1548) had a harmonic range G♭-A♯♯, although Zarlino's design required a further eight notes. This range avoided 30 cent mistunings of tetrachords resulting from Zarlino's 2/7 comma tuning. Trasuntino's 1601 enharmonic harpsichord exceeded the G♭-A♯♯ range, but the monochord reveals that Trasuntino changed the tuning system to avoid Zarlino's problem. The discrepant ♭♭ notes in the monochord were constructed with a 16:15 interval from the ♯♯ ones, leading to ♭♭ notes which were too flat in 2/7 comma. They would have been nearly correct for Trasuntino's new tuning: 31-note equal temperament [ETS 31], which was required for correctly-tuned tetrachords, and is close to 1/4 comma meantone. The Clavemusicum Omnitonum's monochord could not set the tuning because of the conflict of two tuning systems, but also from inaccurate manufacture. Nevertheless, the monochord documents Trasuntino's enharmonic instruments, which initially followed Zarlino's tradition, and differed from Vicentino's enharmonic system and his Archicembalo.

A concise account of historical harpsichord ranges, 2017

A concise account of historical harpsichord ranges, 2017

The historical evolution of the extension of the harpsichord's 12-note-per-octave keyboard, through the Middle Ages, Renaissance and Baroque eras, in the main local traditions. (For a discussion of ""enharmonic keyboards"" or ""split sharps"", see the author's book ""Unequal Temperaments: Theory, History and Practice"", 3nd ed. 2013, Section 5.4. http://temper.braybaroque.ie/. For a full discussion of multiple-division keyboards see the same book, Chapter 19.) This paper was published in NEMA Newsletter, i/1. This is an online publication by the National Early Music Association UK. The whole issue is freely available to the general public from the URL: http://www.earlymusic.info/NEMA\_Newsletter\_i1\_2017.pdf