Bach's schematic, as it appears on the page
LaripS.com, © Bradley Lehman, 2005-13, all rights reserved.
All musical/historical analysis here on the LaripS.com web site is the personal opinion of the author,
as a researcher of historical temperaments and a performer of Bach's music.

Published articles about this tuning

My main scholarly article about this discovery is published in the February and May 2005 issues of Early Music: partly in print and partly on Oxford's web site. That article describes the historical context and provides musical and mathematical analysis. [Outline of all its portions]

  • 11 February 2005: Read the Early Music article "Bach's Extraordinary Temperament: Our Rosetta Stone" part 1, [Outline and free download] or purchase a subscription to the journal
  • 11 February 2005 - This "www.larips.com" web site released and announced as a resource to accompany the Oxford article, with clarifications and news. The initial pages in this release were the sections from the article's manuscript that Oxford University Press had chosen to eliminate from their edited version. I was therefore free to recycle these parts onto my own web site.
    Those first-release sections were:
    [The discovery story (crediting influences)]
    [Epigrams at the top of the article's manuscript]
    [Cube-puzzle layout (a concise model of the keyboard-tuning problems to be solved)].
    I also started three new resources in that release:
    [Usage roster]
    [FAQ (Frequently Asked Questions roster)]
    [Practical instructions to set the temperament by ear].
  • 18 February 2005: Supplementary materials at Oxford's site as noted on page 18 of the article [Outline]
  • March 2005 - Goshen IN: feature article "Bridging traditions: organ music connects generations of worship" by Anna Groff, for Goshen College Bulletin. Introduces the Taylor & Boody organ Opus 41 on campus.
  • March 2005 - Goshen IN: feature article in spring issue of Bethany Christian Schools' alumni Bulletin, page 7
  • 22 March 2005 - Elkhart IN: feature article about the Goshen College organ, by Marilyn Odendahl in The Elkhart Truth. The story has been picked up in Louisville and Indianapolis on March 22, and Fort Wayne on March 23 and March 25.
  • April 2005: news item in The Organ
  • ? April 2005 - Sydney Australia: Lehman/Bach in the Carey Beebe Harpsichords Technical Library
  • 20 April 2005 - Goshen IN: feature article about the organ and this discovery. A longer version of the article is printed in the spring issue of the alumni Bulletin. See also the article in the same issue, "Bridging traditions: organ music connects generations of worship".
  • 29 April 2005 - South Bend IN: Feature "Bach to basics: 'Opus 41' is attuned to composer" in South Bend Tribune
  • May 2005 - Diapason magazine, cover story featuring the Opus 41 organ by Taylor & Boody
  • May 2005 - review by Jan-Piet Knijff in De ORGELkrant 2005/5 of Het Orgel (review of part 1 of the Early Music article, February 2005)
  • 2 May 2005 - Elkhart IN: Elkhart Truth review of the organ dedication service
  • 2 May 2005: Mennonite Weekly Review article "Goshen alumnus solves Bach's musical puzzle", a light revision of Goshen's alumni Bulletin article (see April 20)
  • 25 May 2005: Newly public link! Early Music article "Bach's Extraordinary Temperament: Our Rosetta Stone" part 2, Oxford University Press [Outline and free download]
  • 26 May 2005: "Mission: Possible" - May 25, 2005 organ "rampage" by Dan Long, featuring this tuning at http://www.bachorgan.com
  • 10 June 2005 - Harrisonburg VA: Daily News-Record feature "Cracking A Musical Code" by Martin Cizmar. Also reproduced at Eastern Mennonite University's news pages as part of the Bach Festival promotions, and at Shenandoah.Com.
  • 12 June 2005 - Harrisonburg VA: Joan Griffing, Pedro Aponte, Bradley Lehman, Shenandoah Valley Bach Festival Orchestra. (Bach's triple concerto, BWV 1044)
  • 13 June 2005 - Staunton VA: Staunton News Leader feature "Tuning into Bach" by Alice Mannette.
  • August 2005: Goshen College feature about their Opus 41 pipe organ. The article is reproduced from the dedication-week booklet from May 2005.
  • August 2005: "Case Study Supplement" as noted in part 2 of the printed article. Analysis of BWV 622, 591, 802-5, and a single-page printout of a practical bearing plan for tuning by ear. [Outline]
  • August 2005: Updated! Errata and clarifications for "Bach's extraordinary temperament: Our Rosetta Stone"
  • August 2005 and May 2006: correspondence in Early Music by other writers, remarking on the February/May 2005 article.
  • 10 October 2005: The New Yorker magazine. Apparently the fiction piece "Early Music" by Jeffrey Eugenides is inspired by the present research...and it reproduces the temperament layout faithfully: "Rodney, who was capable of keeping straight the 1/6 comma fifths of Bach's keyboard bearing (F-C-G-D-A-E) from the pure fifths (E-B-F#-C#) and the devilish 1/12 comma fifths (C#-G#-D#-A#), had no trouble performing the following calculation in his head: Each one of the Mice 'n' Warm mice sold for $15."
  • 28 November 2005 - Bennebroek, The Netherlands: article "The 'Bach temperament' and the clavichord" by Bradley Lehman, in November 2005 issue of Clavichord International. It contains further discussion of practical issues: some specifically for clavichord, some more generally in analysis of Bach's keyboard music, scale structure, enharmonic considerations, and by-ear tuning instructions. The compositions presented include BWV 772-801, 802, 808, 849, 887, 988, 1079, and 1080. [Outline] [Complete text]
  • December 2005 (or earlier?) - Scala file for synthesizers, available from Huygens-Fokker Foundation, Centre for Microtonal Music. [File listing] [Zip file]
  • December 2005 - "300 Years Ago Today" feature in Keyboard magazine, about Richard Egarr's forthcoming recording of Bach's Goldberg Variations
  • December 2005 - Southeastern Historical Keyboard Society (SEHKS) Newsletter, Volume 26, #1. "Light Reading for the Winter" by George Lucktenberg, including a brief review of the two-part Early Music article. Lucktenberg includes his suggestion of a practical and easy new all-purpose temperament inspired by that article:
    C t G t D t A t E t B o F# o C# t G# o Eb t Bb o F t C (where t is 1/8 PC on average, and doing it by taste and feel rather than any rigid mathematical scheme).
  • 13 January 2006: Goshen College press release "Opus 41 organ CDs by alumnus Bradley Lehman now available through Music Center" about the recordings LaripS 1002 and LaripS 1003
  • 5 June 2006 - Musica Omnia. Bach: Well-Tempered Clavier, Book 1 played by harpsichordist Peter Watchorn. Booklet essays by Bradley Lehman (November 2005) and Peter Watchorn.
  • 1 August 2006 - BBC Music Magazine, August 2006 (Vol 14 #13). Feature article "In Good Temper" by Bradley Lehman, presenting this temperament from a practical angle as a blending of C major and B major scales.
  • 2 August 2006 - "Bach's Art of Temperament" web article by Bradley Lehman. The longer and more detailed draft: source of the BBC Music Magazine article.
  • 2 September 2006 - American Record Guide September/October 2006, pp 28-29. Feature article "Cracking the 'Bach' Code: Breakthrough WTC Recording" by Peter Catalano, reviewing Peter Watchorn's set of WTC book 1. This issue of ARG also includes Rob Haskins's reviews of LaripS 1002, LaripS 1003, and Richard Egarr's set of Goldberg Variations. Peter Catalano's collection of articles is here.
  • October 2006 - Keyboard magazine October 2006, p96. "Putting the pedal to the WTC" by Mahan Esfahani, reviewing Peter Watchorn's set of WTC book 1. [Online version of this article]
  • 3 October 2006 - "Bach-style keyboard tuning" by Mark Lindley and Ibo Ortgies. Early Music, Oxford University Press - web release of the article as PDF download, before the printing in an upcoming issue of the journal. [My remarks...]
  • November 2006 - Piano Technicians Journal, "The Bach Temperament?" by Fred Sturm. Additional comments and corrections by Bradley Lehman were posted in the Piano Technicians Guild discussion group in December.
  • 10 November 2006 - "Bach-style keyboard tuning" by Mark Lindley and Ibo Ortgies. Early Music, Oxford University Press - final version for print, November 2006 issue. [My remarks...]
  • 10 November 2006 - "Bach's temperament, Occam's razor, and the Neidhardt factor" by John O'Donnell. Early Music, Oxford University Press - November 2006 issue. [My remarks...]
  • 13 November 2006 - How Equal Temperament Ruined Harmony, And Why You Should Care by Ross W Duffin. W W Norton, ISBN 10: 0-393-06227-9, ISBN 13: 978-0-393-06227-4. See also his web letter to readers of the book offering listening examples: comparing this Bach temperament with equal temperament, in music by Wagner/Liszt, Brahms, Debussy, and Gershwin! Duffin book
  • 11 December 2006 - Mention in Dave Benson's book Music: A Mathematical Offering. Cambridge University Press, 2006. ISBN 0521853877. See also the free online version as PDF, maintained by the author as a post-print update.
  • December 2006 - article "Quinten mit Schlaufen: Zu Johann Sebastian Bachs 'Wohltemperirter' Stimmung" by Klaus Miehling, in Concerto - das Magazin für Alte Musik 23:211 (December 2006-January 2007) p.34-40. Miehling apparently agrees with my opinion that Bach's drawing is a diagram, but (like the earliest outspoken correspondents in Early Music) he tries to "improve" the solution by presenting different interpretations. He reads the diagram in either direction, with various transpositions, after dismissing the "small c" capitalization stroke that is a red herring for so many others as well (and not, in any case, essential to my argument!).

    Miehling presents a table of major 3rds in the home keys in Bach's compositions, as if the frequency of use proves anything. Music is more complex than the use of isolated tonic, dominant, and subdominant triads, duly measured in cent offsets from purity. Miehling's focus is on static triads, not the scale membership requirements of any of the named notes used in Bach's compositions. (Which compositions require D# and A#? Which compositions need flats and sharps all to work smoothly, both melodically and harmonically, through enharmonic swaps? How does any transposed solution compare with any other known temperaments in Bach's milieu?) Miehling's superficial analysis doesn't approach such questions, or much else that I covered in my printed part 2.

  • February 2007 - article "Better Than the Da Vinci Code" by John Marks, in Stereophile magazine, pp 47-53. Part of the regular bimonthly "Fifth Element" series.
  • 5 March 2007 - Cambridge University Press. J S Bach: A Life in Music by Peter Williams. ISBN-13: 9780521870740. Pages 336-7 discuss the first printed half (only!) of the "Rosetta Stone" article; cited also in the References section on page 389, but only that first half. Most of Williams's objections here -- about the Bach drawing, and the reasoning in Lehman's presentation -- were already answered in the second half of Lehman's article! My response is on the Bach temperaments page.
  • May 2007 - Clavichord International. Article by Miklos Spanyi, "Kirnberger's Temperament and its Use in Today's Musical Praxis" (dated 2006 at the end of the article). My response is on the Bach temperaments page.
  • March 2008 - Bernhard Billeter's article "Zur 'Wohltemperirten' Stimmung von Johann Sebastian Bach: Wie hat Bach seine Cembali gestimmt?" appears in the March 2008 issue of Ars Organi, pp 18-21. It addresses some of the argument in the printed portions (only!) of my main 2005 article. My response is on the Bach temperaments page.
  • June 2008 - Peter Bavington's review of books by Ross Duffin and Alexander Mackenzie is in the British Clavichord Society Newsletter, June 2008. On the references to my work inside Duffin's book, Bavington complains: "Readers will be left with the impression that the question of Bach's keyboard tuning has been settled without doubt, which is very far from being the case."
  • October 2008 - James Madison University, Visiting Scholar public lecture about this temperament; masterclass for harpsichord students. Bradley Lehman. [Slides in that PowerPoint presentation]
  • December 2008 and March 2009 - First and second editions of Unequal Temperaments: Theory, History and Practice by Claudio di Veroli, self-published on the Internet through Lulu.com. The author presents this temperament briefly, but dismisses it as it does not suit his expectations (especially with regard to the size of the interval E-G#). Is Bach not allowed to have brought a paradigm shift away from the classic problems of meantone, modified meantone, and the Werckmeister temperaments? And why should we prefer the methodology of John Barnes, from his flawed article that studied "prominent" major 3rds, but ignored major 10ths and 17ths altogether (even though they make more acute effect than 3rds do)? Barnes omitted all the minor-key music and all the fugues, too. With a hopelessly small and biased data set like that, omitting more than 3/4 of the available evidence for the experiment, the results are meaningless! [My response]
  • March 2009 - Juilliard school newspaper, "The Ongoing Quest for Bach's Temperament" by Tamar Halperin.
  • June 2009 - Harrisonburg VA: lecture by Bradley Lehman at the Shenandoah Valley Bach Festival. [lecture notes] [comparisons with other temperaments]
  • June 2009 - Music Theory Online, "Discrete Fourier Transform and Bach’s Good Temperament" by Emmanuel Amiot. The author presents a way to measure "Musical Sameness of Scales" as a single number, in assessing the way temperaments circulate smoothly (or not) through all 12 major scales, and by extension all minor scales as well. He shows -- no more and no less -- that my Bach temperament is a useful general solution for playing music of extensive chromatic requirements, i.e. that it addresses the problem presented by Bach's own music.
  • November 2009 - Early Music, Bradley Lehman: "Unequal temperaments circulate again" letter to the editor, Early Music. A call for reasonable and valid argumentation in the field of temperament research. In Early Music (Oxford University Press), February 2010, Vol 38 #1. [PDF] [HTML] (It was accepted and set for the November 2009 issue, but the entire "Correspondence" section of that issue has been pushed back to February.)
  • January 2010 - "Unequal Temperaments", Bradley Lehman, The Viola da Gamba Society Journal vol 3 part 2 (2009), 137-163. I review a 2009 book by Claudio di Veroli, address some recent argumentation about Bach keyboard temperament, and debunk the 1979 analytical methodology of John Barnes. [PDF]
  • October 2010 - Boulder CO: lecture by Bradley Lehman at the University of Colorado. "Recovering Bach's tuning from the Well-Tempered Clavier". [lecture notes]
  • January 2011 - "Unequal Temperaments: Revisited" (correspondence section of the journal), Claudio di Veroli, The Viola da Gamba Society Journal vol 4 (2010), 164-182. I reviewed di Veroli's book more than a year ago, at his invitation, assessing it at face value as a stand-alone resource in this field. I took five months to read the book closely, and in doing that, I found the book weak or misleading in all the ways that I described in my review. It was not a personal attack against di Veroli, in any way; I merely pointed out the serious problems that I found with the writing, the reasoning, and the way sources were used (or important ones omitted). My review was published in January 2010; see above. Di Veroli has evidently misunderstood both my review and my intent, profoundly.

    This new piece is di Veroli's 19-page rejection of my 27-page review. He puts up a defense of his book. He defends things he didn't put into his book, yet expects that reviewers ought to have known, somehow: about himself, his private library, his own earlier but out-of-print writing, and his personal abilities. He also launches variously fallacious and misleading criticism against me and my reviewing style, as if that somehow validates his book. (Since when is it appropriate, or meaningful, to attack a reviewer as personally unworthy, and then pass that off as a defense against the objective points that were made in the review?) [PDF of the whole issue] [PDF of di Veroli's correspondence alone]

    Some handy resources for seeing through di Veroli's fallacies of argumentation, both in the Unequal Temperaments book and in his rebuttal to my criticism: [Taxonomy of Logical Fallacies at fallacyfiles.org] [Michael Shermer's list of 25 frequently-encountered fallacies (originally from his book Why People Believe Weird Things, 1997)]

My responses to the major publications are summarized on the responses page.


Return... Bach's schematic, rotated for use