Bach's keyboard pieces that "fit meantone"

Continuing the discussion from Organ music suitable for harpsichord?:

Andrew asked:
“Bach and meantone tuned organs - is there a chronology available of the Bach organ works? I’d be interested to see if the keys he used for pieces were all playable using meantone, around 1720’s say.”

There is no need to guess from a chronology. Look at the notes required in the pieces…which is not merely making estimations from key signatures or from names of the home key. And then, tune in meantone and try the pieces. Does he require (say) G# and Ab in the same piece? How about D# and Eb? How about the more exotic notes farther around the spiral of fifths in both directions?

As the data set for my 2021-22 article, I tabulated all the Bach keyboard pieces, showing which enharmonic notes are used in the score. Look them up by BWV number in this list:

And then, armed with that knowledge, make your conclusions whether they “fit meantone” or not.

The article explaining all of that is here, as a PDF offprint from the BACH journal:

Bradley Lehman

Indeed. It is my strong impression that there are no Bach keyboard works, or keyboard collections (such as the Inventions), which can be played in meantone (unless the instrument has split keys).

A friend of mine once programmed a number of the ‘Neumeister Chorales’ for a recital on a historic organ which is tuned in meantone, without split keys. As I sat there listening, it seemed obvious to me that these pieces were not by Bach, as their limited melodic and harmonic content fits perfectly into meantone. (There are other reasons why I believe this collection is not by Bach - the biggest one being that there is no real evidence that it IS by Bach.)

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So @DouglasA my question still stands. Does this mean all the organs Bach had at his disposal were not meantone? That’s what I was trying to ask.

Surely not, as shown by Ibo Ortgies. What is apparent is that Bach only composed for organs tuned in circular temperaments. Decades earlier, while also composing for circular temperaments, Pachelbel composed most of his works playable in meantone.

Organs ‘at his disposal’ would, I suppose, refer to all the instruments he played from the 1690s to 1750. That would have been an awful lot of instruments and I’m sure that some of them were in meantone.

We do know that most of Bach’s organ playing (and that of his contemporaries) was improvisation. Unfortunately we can only know the notated pieces. Some of these he collected (ie Orgelbüchlein), and some of them he published (Clavierübung III) - and from these pieces we can conclude that they are not intended for meantone instruments.

When JSB had the opportunity to improvise at a meantone instrument, no doubt he would have played it in the way it sounded best. We can never know what MS have been lost, but from what has survived, we cannot find much if any evidence that Bach was happy to compose for meantone instruments.

You’re right about there not being any evidence that the collection is
by Bach, but the meantone arguments isn’t very persuasive because if the
pieces were by Bach, they would be very early, maybe the first things we
have by him (14 or 15 years old? I don’t remember), when he presumably
would have been mostly likely to have had to put up with meantone


With respect I must disagree with Douglas’s statement as it stands. There’s a possibility that he meant “intended for meantone”, but the subject here is ""Bach’s keyboard pieces that “fit meantone” “”.

I can think of 2 examples off the top of my head that “fit meantone” w/o split keys:

  • the Fuga sopra Magnificat BWV 733 - not an early work;
  • the prelude in d BWV539, which has been prefixed to the organ version of Bach’s ‘violin fugue’.

Neither of these pieces exceeds the limits of a ‘standard’ meantone tuning, i.e. e-flat, b-flat, f, c, g, d, a, e, b, f#, c#, g#.

I’m sure that there must be so many others that I find it difficult to believe that Douglas meant precisely what he wrote.


Thanks, Dale, for the correction. When I wrote that I ‘had the strong impression’ I had a niggling thought of ‘well, there might be SOMETHING’ and I thought perhaps there were individual movements or a variation within a partita . . . So yes, the prelude of 539, and a chorale setting, and there may be more short pieces.

What I am trying to say is: Bach’s musical language, looked at as a whole, is not one that can be expressed in meantone (unless there are split keys).

Stuart, we may speculate that Bach’s compositional language was different when he was a teenager and had more exposure to meantone organs. But that is speculation - we don’t KNOW that, because, if I recall correctly, we have no keyboard work which we are certain was written before 1705. We cannot say what Bach’s musical development was like in his childhood and teenage years. Looking at the New Grove, there is speculation that 766 could date to Lüneburg (around 1700) - it is in f minor. Also 767 - c minor, with its extremely chromatic 8th variation (arguably problematic in any tuning). BWV 566, it has been suggested, could date to 1706 with its Buxtehude-like qualities; it is in E major and has B sharps. So, if there were early composed works which make good use of meantone, we don’t have evidence for them.

Dear Dale. I also though at first sight that Bach’s Fuga sopra Magnificat was fit for meantone. Until two things happened:

  1. It has been shown that, almost certainly, this piece was composed by Krebs. The evidence is a dated manuscript by the latter and the fact that all the surviving handwritten copies derive from this one, not from any lost Bach manuscript. The other piece of evidence is that Bach never entitled “Fuga” a piece that, on many counts, is not a fugue at all.

  2. A few years ago I was invited by the distinguished organist Armando Carideo to try a “new antique” relatively small Renaissance organ in Rome, in Santa Barbara dei Librai. Somehow pipes and action survived for an instrument that had the case ruined. A simple new case was built, pipes and action restored, and I tried the Fuga sopra Magnificat, playable on a small Italian pedalboard. The score is misleading: not a single major third outside the meantone range. What is easy to forget is that the 4 meantone wolves and the wolf fifth are NOT the only wolves in meantone! Let me digress with an explanation for the less-temperati.

TRITONE. In ET we are used to dissonant tritones. However, as is well known, the natural tritone spans three tones (for example C-F#) and is quite consonant with its frequency ratio 7:5. It is also quite consonant in 1/4 S.c. meantone, with just 3 Cents of deviation.

DIMINISHED FIFTH. The number of semitones is the same, but they are organised differently, for example F#-c. Of course, in ET the size and dissonance is the same as for the tritone, but in natural or meantone scales the difference is huge. The natural ratio is 10:7, quite dissonant. In meantone things get much worse, with 38+ Cents of deviation: we have an unplayable wolf.

While I was playing the fugue, I had to stop at some diminished fifths that sounded really impossible, and realised that this piece was obviously not meant for meantone.

Claudio, the attribution of 733 to Krebs is very weak. Yes, it survives in an MS in the hand of Krebs. But he copied lots of music by his teacher. True, it is not a fugue, but we don’t know that JSB called it a fugue, only that Krebs did. And the complexity and style of the piece points much more strongly to JSB than to Krebs. I think most people have abandoned the Krebs theory.

Your comments on playing the piece on a meantone organ are of course very interesting.

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Dear Claudio,

Thanks for your reply. I am not sure why you object to diminished 5ths if

  • they are tuned correctly in meantone;
  • they are spelled correctly;
  • they are treated correctly according to the the rules of counterpoint and harmony.

If they sound ‘dissonant’, that’s fine, because they are dissonant. The diminished 5th occurs naturally between the 2nd and the 6th degree of the minor scale - between e and b-flat in this fuga - so there’s nothing outrageous about them, with the above conditions. I haven’t made a list, but I assume that they are frequent, both melodically and harmonically, in music ‘intended’ for meantone.

What am I missing?


Douglas: you have certainly a point, thanks for your comments.

Dale: please find a church organ tuned in meantone, go and play the piece and you will realise that diminished fifths in meantone are not just dissonant, they are wolves almost 1/2 semitone far away from any consonant interval, and sounding as bad as a wolf major third.

And no, I cannot recollect any diminished fifth in meantone music. Surely there must be some for example for the harpsichord in short notes, where they will hardly be noticed, but not for the organ. If you find one, please tell me.

My observation about wolf diminished fifths that afternoon in Rome, by the way, was witnessed by both Carideo, a great specialist in Renaissance organ music, editor of a complete Frescobaldi edition reviewed as among the best, and Prof. P. Barbieri, the great temperament scholar.

Edit 1: an account of this matter is included on p.399 of my recent Unequal Temperaments edition. Barbieri read it and had no objection.

Edit 2: Just sit at any pipe organ tuned in 1/4 s.c. meantone, play first c-f#, certainly not a really consonant interval, and it is used in baroque music for tension, then play f#-c’ and you will hardly recognise the notes at all, because the size of the interval is very, very different.
Now if you find a meantone organ with split sharps for g#-ab (there are quite a few nowadays but are still a rarity), you can test the difference between the wolf g#-d’ and the nice sounding tritone ab-d’.

Thanks again, Claudio, for your reply, to which I hasten to reply.

I have already found a church organ tuned in meantone and played Bach’s or Krebs’s Magnificat fuga on it. It has split keys but I didn’t use them. I found nothing objectionable then, nor do I now. Can you please refer to specific measures or passages in this piece that you find ‘impossible’?

Here’s another example for your consideration: Frescobaldi’s Capriccio sopra begins {of course} with a descending hexachord, but surprisingly with the ‘ut’ raised a ½-step. This gives a melodic diminished 5th between the 2nd and the 6th tone of the subject each time that it appears unaltered. In m.21, moreover, there’s a harmonic diminished 5th between the alto g and the bass c#, which is resolved correctly: g moves to f, c# moves to d. These are not simply passing-tone dissonances but fully harmonic tones in Very Polyphonic music. There’s another harmonic diminished 5th in m.125.

Louis Couperin: Allemande in d, the 2nd bar after the internal cadence {double bar} also has g against c#, ergo harmonically. The Pièce de trois sortes de Mouvemens has the same on the downbeat of m.3, as well as at the beginning of the 3rd section. One of the Sarabandes has the same on the downbeat of m.2.


Dear Dale, with pleasure I respond to your interesting remarks.

“church organ … I played.” The dissonance depends greatly on the registration. If you used a very-poor-in-harmonics set of stopped pipes or flutes, you will not hear any dissonance. If you use a mixture you will.

“measures or passages”. Well you can find them on the score! There are quite a few “meantone wolf diminished fifths” in the piece. Just at a cursory glance I find an f#-c’ on bar 7 lasting for a crotchet, also a crotchet for an f#‘-c" on bar 72, then there is a g#’-d" on the last page.

Frescobaldi: why are you assuming he wrote for 12-note meantone? He did not. Please read my Unequal Temperaments book, section 11.9: demonstrably some of his works were meant for a 14-note split-sharps keyboard, if not for ET (in spite of demonstrably wrong contrary arguments I have read).

Louis Couperin. Another composer who wrote some harpsichord pieces that are not playable in meantone, no matter how you add a few split sharps or move the wolf fifth around. See again my UT book, section 11.8.


The registration I used, not knowing any better, was a full plenum with mixtures. Of course I heard the harmonic dissonances which are written, but they’re nothing I would call ‘impossible’ or even slightly objectionable or surprising in meantone.

But I disagree with your statement that “The dissonance depends greatly on the registration.” The dissonance was written by the composer and might be accented or diminished by registration; but it’s there in the notes. I think maybe you mean “The ugliness depends greatly on the registration.”

Just to make sure it’s understood: I do not suggest that Bach {or Krebs or whoever composed this piece} ‘intended’ or expected or desired it to be heard/played in meantone. I suggest simply that it fits in the category of “keyboard pieces that ‘fit meantone’”.

As to your f#-c interval in m.7 of the Magnificat fuga, I find here nothing extraordinary when heard or played in meantone.

As to your objections to my examples from Frescobaldi and Louis Couperin, it seems as though your argument is that the appearance of a diminished 5th is proof that meantone must be excluded - a circular argument at best.

Can you name any keyboard composer from whose works you’d accept examples?
Can you refer to early sources that disallow the diminished 5th, but allow the augmented 4th, in meantone in keyboard music?

Or is this just a matter of taste?


Dear Dale, I am surprised at how you perceive the same wolf-level dissonances so differently than myself (and Carideo and Barbieri who, by the way, became a temperament scholar after having been also an organist).

Whether it was composed by Krebs or by Bach, it appears to be a late-Baroque piece purposely composed in an archaic style (there are quite a few in WTC: see Ledbetter’s treatise). By the time of Bach’s death (see also Ledbetter and Rasch), meantone was been left aside in German lands.

Now I am puzzled. My objections to your examples from Frescobaldi and Louis Couperin has NOTHING to do with tritones or diminished fifths. I did not say that in my post and I did not in my book. Their works are not playable in 12-note meantone because they would imply playing very open and audible wolf major thirds. There are many more arguments. Frescobaldi in his proposal of ET had quite a few contemporary followers in Rome (there is an article by Barbieri on this matter, published decades ago). Louis Couperin has at least one harpsichord piece that defies anything but a truly circular temperament: the Pavane in f# minor.

The matter of what is suitable for meantone and what is not has been the subject of countless scholarly publications, and unlike other more thorny matters in early musicology, this particular one has most scholars in agreement. (Now please do not ask me to name again more scholars …).

Needless to say, you are free to disagree with me and with them.

Now I am even more puzzled: are you asking me for meantone music? Most of music composed before the 2nd part of the 17th century, of course, most of Pachelbel but not all, most of Louis Couperin but not all, and so on.

Guess this is everything I have to say on this matter!


Dear Claudio,

If you are unwilling to respond to my specific questions/objections on this forum, which I’ve repeated below, then it would seem that there is no point in trying to continue this discussion on this forum.

I specifically asked the following:
“”““As to your objections to my examples from Frescobaldi and Louis Couperin, it seems as though your argument is that the appearance of a diminished 5th is proof that meantone must be excluded - a circular argument at best.
Can you name any keyboard composer from whose works you’d accept examples?
Can you refer to early sources that disallow the diminished 5th, but allow the augmented 4th, in meantone in keyboard music?
Or is this just a matter of taste?””“”



Dear members of this forum.

I beg you to read carefully my latest posts in this exchange, and those of “draak”. I find my posts on meantone absolutely consistent, and also consistent with my UT book.

I fail to understand draak’s arguments, and especially his last two posts which I find bewildering and completely inconsistent.
Which is perhaps why my responses fail to convince him, and why he insists that I did not address questions I actually did.

But then, of course, I could suddenly have become so stupid that I can no longer argue about a matter of which I have been, so far, respected by the very best scholars.

One way or the other, it is pointless to continue.

Have a good evening everybody.