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The Best And Most Appropriate Temperaments?


Guest spottedmetal

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Guest spottedmetal

Thanks for comment about oscillators . . . Modding an existing board could be easy with possibly only a capacitor necessary to jack-up the frequency by three octaves. What inspired me was getting a diode-matrix stop control board which clearly links notes through from octaves and quint intervals, if I can get to grips with understanding it, clearly crying out for super-high stop experimentation! Oh dear - another relay or transistor board to wire up to get dual outputs from the keyboards . . . or perhaps a midi interface would provide more versatility.

And which composers continued to use certain keys for certain moods, simply based on the legend that a certain key was associated with certain moods, despite not being able to hear them for the universal adopton of ET?
A nice example of this is the wonderful triumphant central section of Norman Cocker's Tuba Tune which goes into a lovely remote key. One wonders if he had any surprises in mind?

 

Could one dare play that piece on any instrument in any UT? An interesting example bearing in mind comments that Tubas weren't intended to be played in chords!

 

Best wishes

 

Spot

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Ask a toaster manufacturer how he feels about laser-perfect tuning. They actually go out of their way to build random mistuning into their instruments because perfection sounds too lifeless. At least, the better ones do - I can't speak for all.

 

You are quite right, and some also generate a certain amount of radomised unsteadiness in the note to simulate a less than rock steady sound. Most also inject a certain amount of wind 'slump' to stop the sound being to clinically 'perfect'. These parameters are completely random, even to the extent of varying each time the instrument is switched on.

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Guest Barry Williams
You are quite right, and some also generate a certain amount of radomised unsteadiness in the note to simulate a less than rock steady sound. Most also inject a certain amount of wind 'slump' to stop the sound being to clinically 'perfect'. These parameters are completely random, even to the extent of varying each time the instrument is switched on.

 

 

Yes, but they invariably and consistently over do it. The results are wobbly and make the instruments worse than they need be. These effects on a pipe organ are slight and subtle, which is more than can be said for the randomisation on, for example, a Bradford type system. These machines fail mainly because of the utter lack of aural skill in the voicing, and the tonal finishing (i.e. in the church).

 

Barry Williams

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  • 1 month later...
Guest spottedmetal

My youngest chorister son has pointed out

http://www.bbc.co.uk/radio3/bach/bachatozt.shtml

on which our kind host has commented

Subsequent letters in Early Music have cast considerable doubt on Bradley Lehman's conclusions and as a practical organbuilder with experience in unequal temperaments, I am doubtful as well. It may be a useful temperament (of which there are a significant number) but to suggest it is Bach's is far fetched and too complex. Indeed as a number of people have pointed out, a more simple interpretation of the squiggles can be made by *not* turning them upside down. But why would Bach "hide" his idea for a temperament at all if he had one?

 

It would be super to hear such further enlightenment here if he has time. . . Having tried the Lehman temperament, I ceased to be impressed by it after a short period and settled for Kellner which I understood to have been influenced by the cypher from Bach's signet ring and possibly the squiggle - and accords significantly with others who have analysed the squiggle.

 

Why would Bach hide his temperament? Perhaps he wasn't hiding it - the squiggle seems to be a perfectly rational mnemonic for expressing something as abstract as a temperament.

 

Best wishes

 

Spot

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  • 1 month later...
It would be super to hear such further enlightenment here if he has time. . . Having tried the Lehman temperament, I ceased to be impressed by it after a short period and settled for Kellner which I understood to have been influenced by the cypher from Bach's signet ring and possibly the squiggle - and accords significantly with others who have analysed the squiggle.

 

Why would Bach hide his temperament? Perhaps he wasn't hiding it - the squiggle seems to be a perfectly rational mnemonic for expressing something as abstract as a temperament.

 

Hello all,

 

I don't believe Bach "hid" anything there, but rather he drew a straightforward practical diagram: knock certain notes one or two little nudges off spot, or leave them at pure-5th position.

 

Bach wouldn't have even had to know any of the math about 1/6 or 1/12 comma, necessarily, or any speculative theory; only that one nudges the harpsichord tuning lever by these tasteful amounts from experience, or from trial-and-error. By 1722 Bach had probably already been tuning harpsichords by ear himself for over 20 years. (And his extant music from his early 20s, before 1710, shows that he already had a circulating system in hand, presumably good-sounding, by that time. See, for example, both the capriccii BWV 992 and 993, and all the toccatas BWV 910-916...especially 910 in F# minor with its wild modulations.)

 

I'm curious: those of you who disagree with my work, have you actually read my papers and watched the videos, or is your reaction mainly to other people's remarks about things they didn't like? (Source vs hearsay....) It's all available for free download from http://www.larips.com

 

A vital part of the process, I maintain, is to play through all the music I mentioned in the academic papers, and also at

http://www-personal.umich.edu/~bpl/larips/testpieces.html

to hear the issues involved. Other temperaments (Kellner's, Werckmeister's, Barnes's, et al) fall on their noses whenever the music gets out too far beyond the usual two or three flats, or four or more sharps.

 

It's not just about looking at key signatures. It's about playing the whole piece, and observing what notes actually turn up in use. The set of inventions and sinfonias, for example, uses 25 different enharmonic notes. Many of those individual two-page pieces use 13, 14, or even 15 different notes...not only 12. Even if one sets out to retune the harpsichord a little bit between pieces, favoring the correctly-spelled notes for the piece to be played, it falls down whenever we get past 12 notes. And on fretted clavichords, retuning is right out: one needs to bend and reposition tangents. On organs we're even more locked in with a hardware commitment than on fretted clavichords.

 

Take a quick trip through WTC book 1. Try the first prelude and fugue. Obviously the prelude needs an Ab...but the fugue needs a G# instead of the Ab. What's going on here? Surely one isn't supposed to tweak notes on the harpsichord between playing the prelude and the fugue? No, there has to be an intermediate G#/Ab of some sort that sounds decently good as both.

 

Flip on to the next piece that looks relatively easy to play (yes, we'll come back to some of the others) and alight on the D major prelude with its formulaic and etude-like texture. Ah yes, we need a D# instead of the Eb, so that's easy...but we need both an A# and Bb in this little prelude, and we need both an E# and an F! 14 different notes in just one piece of a couple of pages!

 

What's going on here? And surely we're not supposed to move the common note F around whenever we need an E#, are we? What is this Bach guy up to? Maybe some tuning scheme where one is supposed to set up notes once for the whole book (egads!) and not move them? [There's also a report that Bach did play the whole WTC 1 straight through at lessons for a student named Gerber.]

 

Try the two-voiced fugue in E minor. What notes shall we set up? Ah, it needs 15 different notes! D#/Eb, A#/Bb, E#/F, plus all the usual suspects in the regular cycle between them.

 

Try the book's first piece that is in a totally funky key signature, seven sharps (!). What notes should be set up to play it? Well, once again the prelude by itself uses 14: A-E-B-F#-C#-G#-D#-A#-E#-B#-Fx-Cx-Gx-Dx. If the tuner favors A and E, the Gx and Dx are going to sound way too high for their contexts. And conversely, if he favors the Gx and Dx (why would he ever do that?), the A and E will be too low. We're supposed to compromise A and E somehow, the downtown notes on violins? Intrepidly we continue into the fugue and notice that it uses a 15th note, Ax.

 

These are the types of issues to deal with. Again, I emphasize: the evidence is right there in the music, before even bothering to look at the Bach title page drawing or argue about its interpretation. The interpretation of the drawing only puts the final 5% of clarity on top of the layout that is already constrained by the music, within narrow limits.

 

At my web site there are also CDs with organ (Taylor & Boody #41, Goshen College, Goshen IN) and harpsichord. There's also the newer Taylor & Boody #46 here in Virginia, in the church right across the street from the factory, tuned in this way from my papers.

 

Other organ builders have been using it, too: I try to keep up a current list at

http://www-personal.umich.edu/~bpl/larips/usage.html

 

=====

 

As for Kellner? Kellner's scheme has nothing to do with that Bach drawing on the WTC title page. I've read most of his papers. They are mostly based on numerology. Yes, he also did a little thing with Bach's signet ring toward the end, but Kellner mainly based his "reasoning" on a couple of odd notions: (1) that Werckmeister somehow had a private 1/5 comma scheme that he chose not to publish, and (2) Bach somehow knew about it and championed it. Kellner's temperament from the mid-1970s is a shaved-down version of Werckmeister III, plain and simple; and everything else by him is after-the-fact rationalization looking for patterns in Bach's work that can be forced to point in that direction.

 

I have a handy survey of such other "Bach" temperaments here:

http://www-personal.umich.edu/~bpl/larips/bachtemps.html

 

 

Cheers,

Bradley Lehman

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I'm curious: those of you who disagree with my work, have you actually read my papers and watched the videos, or is your reaction mainly to other people's remarks about things they didn't like? (Source vs hearsay....) It's all available for free download from http://www.larips.com

 

When I mentioned (below) your amazing research earlier on the Message Board there were very few replies! I'm not sure why?

 

May 22 2006, 07:39 PM Post #1

 

I don’t know if someone has already reported this information here and I missed it, but I have I’ve just come across these astonishing sites:

 

Larips

 

Bach tuning

 

They describe how the embellishment at the head of the title page of Bach’s Clavierubung is actually an explanation of how to tune the keyboard! Much more intriguing than da Vinci code puzzles!! It was in everyone’s face all the time….. There is much else of interest on both sites!

 

This seems to me such a wonderful breakthrough that it deserves more publicity.

 

However, harpsichords can be tuned relatively quickly; I wonder how useful it would be for organ tuning – organs are generally out of tune most of the time to some extent – would the effect of the fine adjustments be lost?[/i]

 

Since Christmas I've been playing the Well-Tempered Clavier Book 1 - Peter Watchorn CD, whose harpsichord is tuned according to the Bach scheme you have revealed, and what a beautiful refreshing sound it is. I recommend it to all Message Boarders. :rolleyes:

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When I mentioned (below) your amazing research earlier on the Message Board there were very few replies! I'm not sure why?

I've certainly mentioned it, and it's the temperament I use as for general purposes. It's available as an install for Hauptwerk, and I have it as the user temperament in my electronic piano.

 

I think that most people aren't much bothered with temperaments, leaving that to their tuners - unless they are harpsichord players, I guess - but they feel warm inside when they are told that a "historic" temperament has been used for some purpose, regardless of its appropriateness.

 

Paul

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I've been following the tuning debate with interest, and I've spent a happy few minutes listening to some of the excellent samples on Brad Lehman's website.

 

Just a couple of thoughts. Part of our fascination with Bach is that he successfully pursued two simultaneous goals -- musical and theoretical perfection. The 48 preludes are fugues are wonderful music, and also a masterful demonstration of technical skill, and I find the idea that Bach provided the clue to an appropriate tuning system on the title page perfectly plausible.

 

However, perhaps this tuning system was just the last piece in his *theoretical* jigsaw puzzle. A previous set of pieces, the 2 and 3 part inventions, also involved a clear key scheme: a rising scale, with major and minor pieces on the white notes from C to A, a minor piece on the white note B, and major pieces on the black notes Bb and Eb. This can be seen as summing up "normal" practice, pushing the unequal tuning system to its expressive boundaries (as far as F minor, for example), and enjoying the enharmonic surprises when they occur.

 

The "48" approach is completely different, presenting a piece in C sharp major not for its particular expressive qualities, but just as a piece. Perhaps this was Bach (not for the first time) looking "forward", compared to "backward" (or maybe sideways) for the inventions.

 

I could also raise a heretical point here. We are so used to the unfairness of the universe in depriving us of perfect thirds and fifths in all the keys that we ignore something that actually works in our favour: the more sharps or flats there are in the key signature, the easier it is to transpose a piece into a familiar key. A piece in C sharp major can be read quite easily in C major, for instance.

 

So, to sum up -- perhaps the temperament indicated is proposed as a satisfactory *theoretical* solution to playing the pieces as written, but at the same time as a departure from normal practice. Would practical musicians not simply have shifted the more difficult pieces into more accessible keys? Was Bach just in a theoretical mood that day?

 

Benjamin Waterhouse

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So, to sum up -- perhaps the temperament indicated is proposed as a satisfactory *theoretical* solution to playing the pieces as written, but at the same time as a departure from normal practice. Would practical musicians not simply have shifted the more difficult pieces into more accessible keys? Was Bach just in a theoretical mood that day?

 

 

Bach's organists for cantata accompaniment certainly had to improvise successfully through the hardest keys, especially on the flat side. They were given parts a whole step lower and two flats more (or two sharps fewer) than the rest of the band, to offset the fact that the organ was sounding at Chorton against the Cammerton of the ensemble.

 

In some sections of the St Matthew and St John passions the organist had to play as deep into the flats as six or seven, while developing correct voice-leading only from handwritten figured bass parts! There are also lots of cantatas in E-flat major or C minor where the organist was playing in D-flat major and B-flat minor. The temperament had to handle all those funky notes like Db, Gb, Cb, Fb, Bbb, and Ebb...and so did the player.

 

I have a recent pair of YouTube videos demonstrating that situation:

 

I think Bach really wanted his students to LEARN the outlandish keys, and not take shortcuts of half-step transpositions over to the natural keys. He challenged his students to know what they would really have to know, to go do their job after graduation: be able to play, improvise, and compose in any key, with sufficient fluency.

 

Even the shorter/simpler compositions in the set of two- and three-part inventions force the student to grapple with A#, E#, B#, several double-sharps, Db, Gb, Cb, Fb, and some double-flats. The student has to tune the instrument appropriately, and then be able to play all that hard-looking stuff in extreme accidentals without flinching, in a cantabile style, while correctly phrasing two or three melodies simultaneously. That's all part of Bach's lesson to develop musicianship. There are no shortcuts. (And the trio sonatas are even harder, bringing in the pedal....) Who had time to be in "just a theoretical mood" when there were practical examples to learn and teach?

 

 

Brad Lehman

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I think Bach really wanted his students to LEARN the outlandish keys, and not take shortcuts of half-step transpositions over to the natural keys. He challenged his students to know what they would really have to know, to go do their job after graduation: be able to play, improvise, and compose in any key, with sufficient fluency.

 

Someone asked me off-list last night what the simpler keys such as F and G sound like, in this Bach temperament.

 

Here are some examples in F played on organ:

 

The CD set has seven other pieces in G (by Walther, Zachow, Bach, Fischer, and Erbach), and examples in most of the other keys as well. Fischer's "Ariadne musica", that prototype of the Well-Tempered Clavier, covers nineteen of the keys itself.

http://www-personal.umich.edu/~bpl/larips/cd1002.html

 

Here is the C major prelude on harpsichord:

 

Recordings by some other people, as well:

http://www-personal.umich.edu/~bpl/larips/recordings.html

 

 

Enjoy,

Brad Lehman

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  • 5 months later...
In some sections of the St Matthew and St John passions the organist had to play as deep into the flats as six or seven, while developing correct voice-leading only from handwritten figured bass parts! There are also lots of cantatas in E-flat major or C minor where the organist was playing in D-flat major and B-flat minor. The temperament had to handle all those funky notes like Db, Gb, Cb, Fb, Bbb, and Ebb...and so did the player.

 

This is an interesting point which reminds me of the time we provided a Continuo organ for Andrew Parrot's excellent recording of the B minor Mass. He asked for 1/6th comma meantone as being the then accepted wisdom of the temperament he would have had to cope with. But the string players in particular were having problems. We discussed this at great length (I had one 3 hour telephone conversation about it with the late John Toll). The next day at the session I said in a throw away manner something like "A pity Bach didn't write it in A minor, to which Andrew's eyes lit up pointing out that as far as the organ was concerned, he had as the choir would have been singing a semitone down, but the organ was a semitone up. So we "transposed" the temperament to have the same effect, leading to happy string players. I think this may have started the vogue for transposing temperaments as it did become popular after that. One eminent conductor asked us to transpose Vallotti for his Bach recordings, deliberating at great length as to which cantatas required a transposed temperament and which did not. I got into a bit of a stand up row with him when I pointed out Bach would never have used Vallotti, to which he replied "If Bach had known about Vallotti's temperament, he would have used it" to which I replied "And if Bach had known about swell boxes, he would have used them" (obviously well aware of the fallacy of that argument myself). This man replied that was different. "No" I said "It is exactly the same". People were moving away at this point as nobody was ever permitted to argue with this particular conductor.

 

On a very general point, even if Kellner's temperament is not actually founded in historic evidence (did he claim it was?) it is a very good general purpose temperament in my experience. With all due respect to Bradley Lehman's temperament (and I have studied and listened to it) I am not sure it really works and even following his logic in reading the squiggles, I see other interpretations of them which could also work. I wonder if it is a bit complex as well. But I am only a dumb organbuilder.

 

John Pike Mander

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  • 2 weeks later...

My friend, Sandy MacKenzie (properly known as Alexander MacKenzie of Ord) has recently brought out a book that is quite interesting in light of this discussion:

 

A. C. N. Mackenzie of Ord: The Temperament of Keyboard Music: Its Character; its Musicality; and its History. ISBN 978-0-9556030-0-6. Price: £75; available from bookshops or direct from the author at 24 Kingsdown Parade, Bristol, BS6 5UF

 

If the cost seems steep, it's because the book comes with two CDs included, one of which features an experiment by the author, conducted in a church with suitably willing clergy, organist and organ tuner. Certain ranks of the instrument were tuned using one of Sandy's own temperaments, and a selection of music from Frescobaldi to Messiaen (yes, Messiaen!) recorded in it. The results are truly intriguing......

 

Critics seem to be divided by the book, which is conceived as a single narrative designed to sweep you along towards a single conclusion - that tuning and playing in equal temperament is rather like taking a black & white photo when you have a full colour digital camera at your disposal. It's quite a compelling argument, although I can see why people would take issue with it.

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