[CAUT] "HT for Dummies"

[Elwood Doss]

I am very much interested in bearing settings for historical
temperaments since I tune aurally.  I'd like to try some of the
historical temperaments on my piano faculty.

Joy!

Elwood

 

Elwood Doss, Jr., M.M.E., RPT

Piano Technician/Technical Director

Department of Music

145 Fine Arts Building

The University of Tennessee at Martin

Martin, TN  38238

731/881-1852

FAX: 731/881-7415

HOME: 731/587-5700

________________________________

From: caut-bounces at ptg.org [mailto:caut-bounces at ptg.org] On Behalf Of
Jim Busby
Sent: Thursday, February 26, 2009 8:12 PM
To: caut at ptg.org
Subject: Re: [CAUT] "HT for Dummies"

 

Thanks Fred,

 

"Big Red" makes me sleepy just looking at it. (G) I'll get the other
books.

 

Tuning a harpsichord with an ETD seems like overkill when I watch these
harpsichordists easily tune in a just few minutes without one. 

 

Now that you and Ed got me (three years ago) tuning WT I have 3
professors who demand it. Here are the temperaments I regularly tune,
all by ETD;

 

Harpsichord - Werkmeister III (He demands that tuning...)

Harpsichord - Meantone (I think it is 1/6 comma?)

Kawai Grand, and a Disklavier upright - Broadwoods Best 

 

If I had a good "recipe" for those I'd be happy.

 

Best,

Jim

 

 

 

From: caut-bounces at ptg.org [mailto:caut-bounces at ptg.org] On Behalf Of
Fred Sturm
Sent: Thursday, February 26, 2009 6:46 PM
To: caut at ptg.org
Subject: Re: [CAUT] "HT for Dummies"

 

On Feb 26, 2009, at 12:17 PM, Jim Busby wrote:

 

Hi Don,

 

Maybe Fred, the Eds (Aren't you the same? ;-) or someone else could
answer this as well, but is there any source that lays out bearing
setting for these aurally, w/o offsets? Maybe a "HT for Dummies"
booklet? Maybe I missed it in all the many posts.

 

Thanks.

 

Jim Busby

 

Hi Jim,

            Actually Jorgensen's "Big Red" isn't very useful for finding
historical "tuning recipes." It is mostly taken up with his argument
about 19th century tuning practice, and most of the tuning instructions
are from that point of view - things published in the 1800s - early
1900s in England. His earlier book (1977), Tuning the Historical
Temperaments by Ear, is much more useful, if you can manage to decipher
the extraordinarily long and convoluted titles he gives the tunings.
This one we've been discussing would be in the chapter "Tuning the
Theoretically Correct Jean Baptiste Romieu 1/7 Syntonic Meantone
Temperament in the Acoustic Tonality of C Major and A Minor." (There is
also another book, "Equal-Beating Temperaments," that I have never seen,
which may have more recipes.)

            Or you can open the attachment Aaron Bousel just sent, which
gives beat rates for 4ths, 5ths and M3s. I doubt you'll find 1/7 comma
much of anywhere else, other than as a set of cents offsets, as it seems
to have been based on just a single mention in the theoretical work of
one person. Here is what Murray Barbour wrote:

"Romieu mentioned temperaments of 1/7, 1/8, 1/9, and 1/10 

commas, but did not consider them sufficiently important to dis- 

cuss." 

(Barbour's book is available as a free text or pdf download, and in
various formats to read on line:
http://www.archive.org/details/turningandtemper027139mbp).

                So essentially these are a 20th (and 21st) century
phenomenon, with no real historical practice connection.

                All that said, the way I would tune it aurally follows:
Starting with A, tune 5ths in each direction. ADGCFB-flatE-flat and
AEBF#C#G#. All 5ths should be half again as large in deviation as ET
(IOW, about 1 bps) and 4ths the same (about 1.5 bps). As you create M3s
from these strings of 5ths, they should beat at about 2/3 the rate of ET
(if it was 6 bps, it should be 4). The final, wolf 5th, E-flatG# should
be wide, beating between 3 and 4 bps. As a final verification, check
stacked M3s. There will be 4 wolf M3s, spelled as diminished 4ths:
F#B-flat, G#C, BE-flat, C#F. These will beat about 1 2/3 times their
rate in ET (and the same as "Pythagorean M3s", or M3s produced when you
tune 4 consecutive pure 5ths). And when you play series of contiguous
M3s (including the "wolves"), the wolves should beat about 2x the rate
of the "true" M3s (though the proportion will vary depending whether
they are "low or high" in the sequence).

            Again, I'll put in a plug for Thomas Donahue's A Guide to
Musical Temperament. Among other things, it has instructions for a very
useful spreadsheet, into which you can insert cents offset, or comma
proportions in cents, or another way of expressing cents (based on C as
0 and counting all notes up from there, as done in Barbour, Helmholtz
and others), and come up with beat rates for 4ths, 5ths, M3s, m3s and
M6s, as well as other parameters like hertz for each note. So that way,
faced with something like this, you can do research on the web, find a
set of offsets, and generate beat rate tables. Then all you have to to
do is use your brain to come up with an aural tuning sequence that makes
sense. His spreadsheet gives the same numbers (within a couple tenths of
a cent) as Jorgensen or what Rousel posted from Farley, with the
addition of intervals they don't include.

            That's the best I can do in terms of HT for Dummies. (I have
entered Donahue's figures in a spreadsheet, which I posted on this list
maybe a year or so ago. I have since found that one of the worksheets
seems to have a problem, and I haven't yet looked into it - I probably
entered a formula wrong into one of the cells - or more than one. The
first two work seem to work fine, though).
Regards,

Fred Sturm

University of New Mexico

fssturm at unm.edu

 

 

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