Keyboard temperament from the title page of Bach's "Das wohltemperirte Clavier" (1722).
The step-by-step explanation here shows how it is derived. Two full-length performances on harpsichord ar...
Keyboard temperament from the title page of Bach's "Das wohltemperirte Clavier" (1722).
The step-by-step explanation here shows how it is derived. Two full-length performances on harpsichord are included: Bach's C major and B major preludes from this book.
Research by Bradley Lehman, 2004, continuing a doctoral project from 1993-4 in "modified meantone" tuning as applied to Bach's music. The interpretation is based on analysis of Bach's extant keyboard music, plus a historical study of tuning methods, plus (in 2004) the suspiciously irregular drawing on Bach's title page.
This research was first published in an _Early Music_ (Oxford University Press journal) article, February-May 2005. Two printed portions and five web files comprise that article.
See http://www-personal.umich.edu/~bpl/la... for an article similar to this video demonstration: explaining how the C major and B major scales are blended together to derive all 12 notes of the chromatic scale, and tuned in this manner.
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Have you also guessed explanations of why the two "t" are autographically different, or the significance of the form of "D" with squiggles and two dots that make it look like a face, and "W"?
Did you read John Charles Francis' 2005 thesis "Das Wohltemperirte Clavier Pitch, Tuning and Temperament Design" where he attributes to the decorative curve an indication of temperament?
What about the sqiggle underneath "per" which is missing from your drawing?
I have read the authoritative Early Music articles. Quite a lot of researchers will go to great lengths to prove a theory. In this case, one can hardly disprove your speculation. Bach did not leave us letters concerning his ideas about tuning. Or recordings.
But was Bach so original. What about the John Bull Ut Re Mi Fa Sol La of the Fitzwilliam Virginal Book (page 183 of the Dover Edition)?
What's the point of applying your theory to an A=440 Hz keyboard?
What about that marvelous Bull fantasia? I've been playing it for 25 years, most recently in a concert on the Goshen organ (playing it on the viola da gamba 8, making it sound like viol-consort music). I also discussed that piece quite a bit on TUNING-L, with regard to its enharmonic swaps and the way it drops a comma.
On your question about an A=440 keyboard, the pitch level is irrelevant: the temperament's shape is exactly the same, irrespective of anything in Hz. And, this video is at 440!
Regardless -- the squiggle story may be entertaining but -- your tuning is logical and is a better, more moderate, mousetrap. I love it. I had tried various compromises and yours is very usable. Frankly I do it using my Korg OT-12 - set all white keys and Eb to Vallotti, but not B, then do the remaining +2, -2 and +4s. I haven't had a chance to make one yet, so a recipe for A=440 using the Korg's other presets for the non-Vallotti notes would be welcome.
"I iz sitting on your harpzikords listening to your Bachs"
But seriously, if you're supposed to turn the diagram upside down, shouldn't the "C" in the drawing come out right side up? Is there an explanation for the right 5 loops (viewing the squiggle right-side up as it is is in the document) having 3 turns and the left three having 2? A more honest interpretation would be that each 5th gets between 1 and 3 "nudges".
Perhaps the drawing at the bottom of the page is a lost cantata?
Autoshare makes certain YouTube activities public on the services you choose. Select only the services you are comfortable with - like Facebook, Twitter, or Google Reader - to let your friends know what you like on YouTube. You can turn Autoshare off at any time.
Did you read John Charles Francis' 2005 thesis "Das Wohltemperirte Clavier
Pitch, Tuning and Temperament Design" where he attributes to the decorative curve an indication of temperament?
What about the sqiggle underneath "per" which is missing from your drawing?
Quite a lot of researchers will go to great lengths to prove a theory. In this case, one can hardly disprove your speculation.
Bach did not leave us letters concerning his ideas about tuning. Or recordings.
But was Bach so original.
What about the John Bull Ut Re Mi Fa Sol La of the Fitzwilliam Virginal Book (page 183 of the Dover Edition)?
What's the point of applying your theory to an A=440 Hz keyboard?
On your question about an A=440 keyboard, the pitch level is irrelevant: the temperament's shape is exactly the same, irrespective of anything in Hz. And, this video is at 440!
- How much is a "nudge"?
- Is a nudge higher or lower?
Regardless -- the squiggle story may be entertaining but -- your tuning is logical and is a better, more moderate, mousetrap. I love it. I had tried various compromises and yours is very usable.
Frankly I do it using my Korg OT-12 - set all white keys and Eb to Vallotti, but not B, then do the remaining +2, -2 and +4s. I haven't had a chance to make one yet, so a recipe for A=440 using the Korg's other presets for the non-Vallotti notes would be welcome.
But seriously, if you're supposed to turn the diagram upside down, shouldn't the "C" in the drawing come out right side up? Is there an explanation for the right 5 loops (viewing the squiggle right-side up as it is is in the document) having 3 turns and the left three having 2? A more honest interpretation would be that each 5th gets between 1 and 3 "nudges".
Perhaps the drawing at the bottom of the page is a lost cantata?