Errata and Corrigenda to Lindley/Ortgies: "Bach-style keyboard tuning"
 

Mark Lindley's and my joint article has appeared in Early Music

Mark Lindley and Ibo Ortgies:
"Bach-style keyboard tuning."
Early Music 2006 vol. 34,
no. 4: 613-623.

Links to the article and abstract:
Full text
Full text (pdf)
Abstract

In it we discuss some of the historically wild and methodologically wrong speculations published last year (2005) by Bradley Lehman in his article in Early Music (Note 1), where he claimed to have discovered "Bach's temperament.”
The Lehman temperament is of modern design. It is, like the one designed by the late Herbert Anton Kellner on July 7th, 1977 (i.e. 7/7/77 – so Kellner said), based on an imaginative interpretation of a small image from the year 1722: for Kellner, Bach’s seal; for Lehman, the ornamental scroll at the top of the title-page of Part 1 of Das Wohltemperirte Clavier (“The Well-tempered Clavier”).
Lehman is following previous musings, especially by Andreas Sparschuh, who published the ornamental-scroll idea on September 9th, 1999 (9/9/99) as a kind of practical joke to make fun of Kellner.

Some difficulties in the Oxford-University-Press editorial process prevented certain corrections at proofreading stage from being implemented in our article:


IN THE MAIN TEXT:

Page 616, right-hand column,
the sentence reading:

Significant documentary support for the claim that Bach always tempered E–G♯ by as much as shown in fig. 3 is to be found in some remarks by Sorge implying that he considered the scheme represented here in fig. 4 to be the only form of unequal temperament that really works for tonal music.


is a quote or paraphrase of Bradley Lehman's argument and should therefore be accordingly completely in italics:

Significant documentary support for the claim that Bach always tempered E–G♯ by as much as shown in fig. 3 is to be found in some remarks by Sorge implying that he considered the scheme represented here in fig. 4 to be the only form of unequal temperament that really works for tonal music.

Page 616, last sentence,
should read:

(b) Neither Sorge nor Neidhardt countenanced tempering E-G# (for any reason whatever) in actual musical practice by as much as Dr Lehman says Bach always tempered it.

Neidhardt designed many mathematical schemes [in the interest of making an exhaustive set] of temperament, most of which he did not recommend for musical practice. He selected a handful as suitable for certain social contexts: village, small town, large town and court – with somewhat different versions in his publications of 1724 and 1732. In no scheme that he found musically viable for any context is the major third E-G# wider than Ab-C.


Page 617, first sentence
should therefore read:

(c) Nor indeed did Neidhardt ever countenance tempering E-G# more than Ab-C in any tuning that he recommended for use in any kind of social context whatever (i.e. at a court, in a large city, in a small town, or in a village).10


Note:
The editor of Early Music tried to have the revised versions of those two sentences put into the printed version of our article, but was unable to have it done because the article would then have exceeded slightly the space allotted to it and an advertisement might have had to be removed or altered.


IN THE FIGURES:

Figure 2 (“Equal temperament”)
must of course have the same ciphers throughout for each kind of pitch-class interval.
So, the “-1” between Bb and F is incorrect.
The correct number to have here is “1” ("plus one", as for all other fourths/fifths in equal temperament).

In Figure 6 (“Another alternative”),
between F# and C# there must be a zero ("0").


MINOR CORRIGENDA

IN THE ENDNOTES


In Endnote 8,
read "Messen und Rechnen" (i.e. with capital letters M and R)

In Endnotes 8, 11, 29, and 30,
the exact title of Dähnert's book is
"Der Orgel- und Instrumentenbauer Zacharias Hildebrandt"

In Endnote 18,
the link for HPSCHD-list should be given as
http://www.albany.edu/hpschd-l/

In Endnote 22,
read "Orgel-Probe" (instead of "Orgelprobe")

In Endnote 27,
read "Prätorischen" (instead of "Praetorischen")
and "Neidhardtischen" (instead of "Neidhardischen")

In Endnote 34,
read "Vielfalt" (instead of "Vielfach")


Notes

(1)
Bradley Lehman:
"Bach's extraordinary temperament: our Rosetta Stone"
Early Music 33, 2005, no. 1: 3-23, and no. 2: 211-231.