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HPSCHD-L  June 2008

HPSCHD-L June 2008

Subject:

an experimental temperament for Buxtehude and Böhm

From:

Brad Lehman <[log in to unmask]>

Reply-To:

Harpsichords and Related Topics <[log in to unmask]>

Date:

Fri, 20 Jun 2008 14:37:08 -0400

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (207 lines)

First, a bit of housekeeping in the music:

Here is a roster of Buxtehude's extant suites and variations, giving the 
notes these pieces require.  This is from going straight through 
Breitkopf 8077 (Beckmann ed) from first page to last:

C suite 226: Bb to G#
C suite 227: Bb to G#
C suite 228: Bb to G#
C suite 230: Eb to G#
C suite 231: Bb to G#
D suite 232: C to G# +A#
d suite 233: Eb to G#
d suite 234: Eb to G#
e suite 235: F to A#
e suite 236: C to A#
e suite 237: F to A#
F suite 238: Eb to C#
F suite 239: Eb to C#
G suite 240: F to D#
g suite 241: Ab to C#
g suite 242: Ab to C#
A suite 243: G to B# (yes, B sharp! no surprise in A-major music)
a suite 244: F to D#
C aria/var 246: Bb to D#
C More Palatino 247: Bb to D#
d Rofilis 248: Eb to G#
G La Capricciosa 250: Eb to D#
a Aria/var 249: Bb to D#
a Courante Simple 245: F to D#
d Courante (Anhang 6): Bb to C#
C suite 229 (Lebegue?): Bb to G#
G Simphonie (Anhang 8 - Lebegue?): F to G#

And here is Georg Böhm's harpsichord music, from Breitkopf 6634 (Wolgast 
ed).  Breitkopf redid this later with Beckmann, as I'll note below.

C praeludium/fuge (organ): Eb to A#
a p/f (organ): Bb to D#
F praeludium: Eb to C#
d p/f (organ): Eb to G#
D capriccio: Bb to E#
g p/f/postludium: Ab to C#
c suite: Ab to C#
D suite: Bb to A#
d suite: Ab to G#
d suite: Bb to G#
Eb suite (= Froberger's Rhine journey: see Rampe): Ab to F#
Eb suite: Gb to F#
F suite: Db, Eb to G#
f suite: Db to B (this is the suite with the Ciacona in it)
f suite: Db to B
G suite: F to A#
a suite: F to D#
G menuett: C to C#
C partita "Jesu du bist allzu schöne": Bb to G#

Supplementing this from Beckmann's edition, Breitkopf 8086:

G chaconne: Eb to D#

Furthermore, more than half of Böhm's "organ" music can also be played 
just fine on harpsichord (and I've done so for years), at least the 
_manualiter_ chorale partitas.  Here are all those _manualiter_ pieces 
from the Breitkopf 8087 organ edition (Beckmann again):

a "Ach wie nichtig": Bb to G#
g "Auf meinen lieben Gott" (3 of the 4 stanzas are manualiter): Db to C#
F "Aus tiefer Not" stanza 1 (st 2 needs pedal): Eb to C#
g "Christe, der du bist Tag und Licht" st 1-2: Ab to G#
d "Christ lag in Todesbanden" (**): Bb to G#
G "Freu dich sehr": Eb to G#
F "Gelobet seist du": Ab to G#
F "Herr Jesu Christ" st 2: Bb to B
C "Jesu, du bist allzu schöne": Bb to G# (same as above in Wolgast ed)
d "Vater unser in Himmelreich" (2 manuals): Bb to G#
a "Wer nur den lieben Gott": F to D#

(** Beckmann gives a pedal part but it works fine _manualiter_)

=====

Now, all that said, for many of these pieces one *could* adopt a 
basically meantone approach (anything from about 1/4 comma to 1/6, 
plausibly), adjusting the endpoints: flipping the Eb to a D#, the Bb 
occasionally to an A#, and occasionally the G# to an Ab.  Böhm goes 
further into the flats than Buxtehude does, so there would be some 
flipping of the C# occasionally to Db.  Both composers occasionally get 
to E#, although I wouldn't expect anyone to move F...or to move C, 
catching Buxtehude's use of B#.

I consider this meantone enharmonic-swapping to be probably a dead end, 
anyway, for one obvious reason: both of these composers sometimes take 
us to 13 or even 14 different notes *within the same piece*.  If we keep 
things as regular as possible (and assuming no split keys on the 
keyboard), we still run into problems.  For example, in that Böhm C 
major prelude/fugue for organ, we need all of Eb, D#, Bb, and A#. 
So...at least those several notes need to be compromised toward one 
another.  And in one of those Böhm E-flat major suites, we have to 
handle a patch of E-flat minor with a good Gb, but we also have a long 
F# bass note a page earlier.

Short digression into Pachelbel: his book of 95 Magnificat-fugues, 
composed during his last job (St Sebald, Nuremberg, 1695-1706), needs
14 different notes: Ab-Eb-Bb-F-C-G-D-A-E-B-F#-C#-G#-D#.  Obviously, most 
of the flat-side stuff comes up during the 7th tone pieces (two flats in 
signature), and most of the sharp-side stuff during the 4th tone pieces 
(empty signature, but E major finals).  Now, what was on *that* organ? 
Split keys on G#/Ab and D#/Eb, or an irregular temperament?  Some of 
Pachelbel's earlier organ music goes farther afield than this,
incidentally, in both directions flatward and sharpward.  Much farther. 
  But, let's get back to Buxtehude and Böhm, since that's what I'm 
playing with at the moment.

How about a tasteful and experimental irregular temperament that lets us 
play *all* this Buxtehude and Böhm music, on a standard 12-note 
harpsichord, without having to retune per piece?  I've been playing all 
the way through these books, and here's what I've come up with as 
sounding good to me.

It works out to be an approximately 1/5 syntonic comma temperament 
downtown in the naturals, but as a point of departure I started directly 
from Werckmeister III.  I determined to keep at least the notes C, F, E, 
and B where they are, and then to see and hear what works out from there.

Try this at home.

First, I really dislike 1/4 PC 5ths and 4ths, as they're so rough on the 
harpsichord...and I also dislike the way D-A and A-E are such vastly 
different sizes from one another, in W-III.  So, the first step is easy: 
square those off.  Keeping C and E where they are, raise each of G, D, 
and A a little bit from their W-III positions, until we get a smoothly 
even cycle of C-G-D-A-E.  That works out to be 3/16 PC per interval, but 
do it by ear.  We also get a nicer G-B major 3rd, incidentally.  G-B and 
F-A both end up being the same size as one another, while C-E is a 
little smaller (closer to pure).

Our remaining ugly 1/4 PC 5th is in B-F#, and let's spread that out, 
too.  By making sharps sharper, we get better flats.  Raise the F# so 
it's almost pure from B, but still slightly wavering: about 1/12 comma 
left to it.  Now we have about 2/12ths remaining to burn off, and 
they're temporarily in F#-C#.  Raise C# until it's almost pure from F#, 
dropping another 1/12 comma there.  C#-G# now has just a smidge of 
tempering, too...but go ahead and raise G#, so C#-G# becomes pure, and 
the remaining slight narrowness of about 1/12 comma is transferred into 
G#-Eb.  This takes the edge off our Pythagorean Ab-C, which is more 
important in Böhm than in Buxtehude, but it also takes care of 
Buxtehude's B# bits.  These sharp-sharpening steps have also taken the 
edge off F#-A# and Db-F.  That helps all the occurrences of Db, E#, and 
A# in the music.

Finally, to my ears, the A# is still a little bit too high: the F#-A# is 
slightly too "hot", and the leading tone is too narrow in the way B-A#-B 
occurs melodically in this music.  So, my last step is to nick A# (Bb) 
downward the slightest bit, about 1/12 comma, just barely enough so the 
Bb-F 5th starts to waver slightly.  Yes, it becomes WIDE, while Eb-Bb 
becomes the same amount narrow.  (They started off with Eb-Bb-F all 
pure, in W-III.)  What we "lose" here in this slightly "impure" Bb is 
more than paid for in the improvements to A#, in the ways it functions 
in this music.

So, what do we end up with?  I've eventually moved seven of the 12 
notes.  I left the W-III notes C, E, F, B, and Eb/D# where they were.  I 
raised six other notes a bit each (G, D, A, F#, C#, and G#), and I 
slightly lowered Bb.  [Another way of stating this: much of Werckmeister 
III sounds horribly flat and misshapen, to my ears....  To fix it, I 
have to move half its notes UPWARD if I want to hold C and E steady!]

This resulting layout sounds very good to me, playing all the way 
through the music mentioned above.  It gives strongly differentiated 
color to each key, and emphasis to the sometimes startling modulations 
of these composers.  It is also strongly resonant in C, F, and G majors.

Having done all that straightforward by-ear adjustment, I plugged those 
steps into my spreadsheets just to get a set of numbers describing the 
results:

Recipe, in Pythagorean comma fragments:

F 0 C

C -3/16 G -3/16 D -3/16 A -3/16 E  (almost identical with 1/5 syntonic)

E 0 B

B -1/12 F# -1/12 C# 0 G# -1/12 Eb

Eb -1/12 Bb +1/12 F.


Sizes of major 3rds (in 1/11ths of syntonic comma):

C 2 E 9 G#/Ab 10 C

F 4.25 A 6.75 C#/Db 10 F

Bb 7.5 D 5.5 F# 8 A#/Bb

Eb 8.75 G 4.25 B 8 D#/Eb


Have a go at it on your own harpsichords; reactions welcome, in playing 
the music....

Enjoy,

Brad Lehman

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