JS Bach's Tunings

Early Music, 2005

Early Music, 2005

Keyboard tuning for Johann Sebastian Bach's music, derived from the evidence of enharmonic requirements in his music plus the line drawing in his autograph copy of "Das Wohltemperirte Clavier". This file is only the first section, approximately 1/7th of the article. See also the printed part 2 and the web files and musical examples, all parts of the argument. (Download them from the "outline" web page.) https://doi.org/10.1093/em/cah037 https://doi.org/10.1093/em/cah067 There is a follow-up article from 2022, as well: "The Notes Tell Us How to Tune".

"Did Bach indeed leave a record of how he tuned his keyboard instruments as Bradley Lehman's 2005 article, 'Bach's extraordinary temperament: our Rosetta Stone' would have us believe? With a bit of cloak and dagger work, can we get to the bottom of this Da Vinci Code of tuning secrets? Has a Bach temperament solution miraculously appeared by way of a tantalising hint Bach may have left for us at the top of the title page of The Well-Tempered Clavier in the form of a cursive calligraphic flourish, a secret codified message, a memory jogging reminder; or was it even just a doodle?  Sadly, Lehman's "Bach temperament" is not only incomplete, but misleading, suggesting something which is neither probable, nor representative of the tuning traditions of Bach's time and likely vastly different from that which Bach knew, or used, or would have found acceptable. That the calligraphic scrolling glyph on the title page of The Well-Tempered Clavier is indeed a diagram of a temperament can be supported in that it can be broken down into structural elements which compare in structure and placement with intrinsic values of temperament intervals found elsewhere in the literature of the period. So how did he really tune his harpsichord? This paper seeks to provide an overview of the Bach temperament issues raised by Bradley Lehman and attempts to provide an actual working historical temperament possibility as a Bach temperament. This paper is an abridged version and under review pending its full publication. In writing this paper I have carefully and intentionally avoided modern scholastic writings as much as possible and chosen to keep focus on historical work in order that subjective modern ideas not cloud the issues discussed. "

2016

The New Baroque Organ at the Orgelpark (= Hans Fidom (ed.), vol. 5/1, Orgelpark Research Reports), 2014

During Bach’s lifetime, the history of temperament in Western music took new turns, but his relationship to this development is far from well understood. The article explores a number of relevant questions to help define what we actually can know about this matter: • Which sources about musical temperament are relevant in regard to Bach’s practice and what can be learned from them? • How detailed, plausible or credible is the relevant information? • Do we know whether Bach had any influence on the choice of temperament in organ projects? If so, to what extent and what was his advice? • To what degree do extant contemporary reports, expert opinions and historical instruments allow us to reconstruct temperaments in the organ building of Bach’s age? • What role did the temperament of instruments with fixed pitches (like keyboards) play in interaction with free-intonating instruments and singers? It appears that conclusive evidence for answering these question does not exist, which might be liberating: In the end, it remains a matter for the individual to decide which temperament seems to be musically apt for the performance of any of Bach’s compositions.

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.""

There is currently no direct source linked to J.S. Bach (1685-1750) himself that indicates his temperament preference. Thus for the tuning of keyboard compositions by J.S. Bach, the modern-day opinions have been and remain still divided. The first part of the article gives original quotations (with translations) on musical temperaments from then well-known writers (from antiquity up to the 18th century), as well as those temperaments that were in use during J.S. Bach’s lifetime. This part of the article summarizes the main writers (and practitioners) from 1. Classical Antiquity; 2. The Middle Ages to 16th Century; 3. 17th century Netherlands; 4. 17th century France; 5. Early 17th century Germany 6. 17th and 18th century England 7. Late 17th century and 18th century Germany 8. The introduction of the equal temperament (gleich-schwebende Temperatur) in Germany in the 18th century by writers such as Neidhardt, Sinn, Fux, Mattheson, Meckenheuser, Mizler, Sorge, Adlung, Silbermann, Fritz, Kirnberger, Marpurg and C.P.E Bach. The second part of the article is a compilation of quotations (with translations) from the 18th-century that relate to J.S. Bach’s musical temperament as can be found in the Bach Documents. It is important to read the first part of the article so as to obtain an understanding of what was considered “common knowledge” regarding temperaments during the first half of the 18th century. With this background (and common) knowledge it then becomes possible to contextualize the quotations in the second part of the article that relate to Bach's temperament. The second version of this article has extended the information regarding Mersenne and the 17th century German writers. In addition, the second section now contains an added 18th century quotation which connects Bach with equal temperament and which is not included in the Bach-Dokumente, Comments most welcome - please send an email to: bachstemperament@hotmail.nl

2017

Performance Practice Review, 1996