Reply to John Thaden

John, fixed JI tunings were certainly not being used in the mid-1800s,
having been little more than theoretical curiosities since 1500. The choices
were meantones (remaining in England and Spain only), well-temperaments
(such as Werckmeister, but mostly ones closer to ET), and equal temperament,
which was just beginning its reign as the standard tuning. I'm sure Manuel
will be happy to give you the cents values for some of these tunings . . .
check out Jorgenson's book for hundreds of variations, with cents to about
10 decimal places . . .

I don't get your "JI" tuning. How does the perfect fourth above the tonic
end up being 27 cents flat of equal temperament?

Thanks for the historical perspective. As are the sounds already on my
website, the second phase of my project tries to produce music reminiscent
of music one might have heard in the frontier town Los Angeles in
1850-1876. I suppose there were plenty of pianos lovingly brought to L.A.,
but perhaps only one tuner to tune them? So the reality was probably that
they were either badly tuned, or tuned to that tuner's favorite
temperament. I have not met Manuel, but did receive information from
others about meantones, Werckmeisters, and the Lucy tuning, all of which I
am itching to try this evening.

As for my JI guess, I was thinking of harmonicas and got my scale degrees
wrong. The standard 10-hole harmonica is often played in the key of its
5th scale tone (e.g. A on a D harp). The 4th scale degree then becomes the
flat7th degree of the new scale, and it is that which I guessed was 27
cents flat (and actually is more like 31?). In fact, the few harmonicas
today that are advertised by the manufacturers as "just" tuned have their
4th scale note tuned ~30 cents flat of the 1st and 5th scale notes, so
apparently the "key" of the JI is not the named key of the harp, but fifth
note of that scale. I'm sure there are other egregious problems with my
hurried guess as well.

Thanks again, all.
John

At 03:17 PM 5/3/2000 -0400, you wrote:
>John, fixed JI tunings were certainly not being used in the mid-1800s,
>having been little more than theoretical curiosities since 1500. The choices
>were meantones (remaining in England and Spain only), well-temperaments
>(such as Werckmeister, but mostly ones closer to ET), and equal temperament,
>which was just beginning its reign as the standard tuning. I'm sure Manuel
>will be happy to give you the cents values for some of these tunings . . .
>check out Jorgenson's book for hundreds of variations, with cents to about
>10 decimal places . . .
>
>I don't get your "JI" tuning. How does the perfect fourth above the tonic
>end up being 27 cents flat of equal temperament?

John Thaden
Little Rock, Arkansas, USA
http://www.flash.net/~jjthaden

For instrumental temperaments Paul Erlich is right with the caveat that
meantone was more widespread than only Spain and England (one can safely
conclude from Berlioz, for example, that meantone remained an active system
in France, organs were still in the process of being equally tempered at
this time throughout the continent, and we know precious little about tuning
practices in Italy, Eastern Europe, and the Americas). Moreever, it was
precisely in the middle of the 19th century that there was an extremely
active "moveable doh" solfege movement in Great Britain (the key name here
is John Curwen) for singing unaccompanied in a version of 5-limit JI.
Though essentially an amateur movement, and the arrangements cannot be said
to represent the original intentions of the composers, the repertoire of
music arranged in the solfege notation was apparently very broad, with Ellis
noting some 40,000 titles. I would presume that Congregationalists in North
America shared this repertoire and solfege style, and further note that the
shape note singing tradition in the US was implicitly a JI system.

<From: Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>
<Subject: [tuning] Reply to John Thaden
<

<John, fixed JI tunings were certainly not being used in the mid-1800s,
<having been little more than theoretical curiosities since 1500. The
choices
<were meantones (remaining in England and Spain only), well-temperaments
<(such as Werckmeister, but mostly ones closer to ET), and equal
temperament,
<which was just beginning its reign as the standard tuning. I'm sure Manuel
<will be happy to give you the cents values for some of these tunings . . .
<check out Jorgenson's book for hundreds of variations, with cents to about
<10 decimal places . . .

Daniel, thanks for the caveats about meantone. As for JI, I was simply
saying that _fixed_ JI systems of only 12 notes were not being used at the
time. The movable doh and shape-note systems would, I presume, involve at
least two variations for the tuning of the second degree of the major scale,
and many more variations for other scale degrees would arise if any
modulation took place. John seems specifically interested in piano tunings.

>Daniel, thanks for the caveats about meantone. As for JI, I was simply
>saying that _fixed_ JI systems of only 12 notes were not being used at the
>time. The movable doh and shape-note systems would, I presume, involve at
>least two variations for the tuning of the second degree of the major scale,
>and many more variations for other scale degrees would arise if any
>modulation took place. John seems specifically interested in piano tunings.

Yes, in piano tunings, at least for this project, and specifically 12-note
fixed tunings, since that is a limitation of the microtuning software I'm
using. I tried the following JI tunings:

1/1
16/15
9/8
6/5 and also tried 7/6
5/4
4/3
7/5 and also 27/20
3/2
8/5
5/3 and also 12/7
9/5 and also 7/4
15/8
2/1

and a fixed tuning based on Lucy tuning, all with the very real possibility
of having made some math errors while converting to 'cents deviation from
12TET', but finally settled on the pleasant (for piano) Werckmeister III
tuning of 1681

1/1
256/243
192.180 cents
32/27
390.225 cents
4/3
1024/729
696.090 cents
128/81
888.270 cents
16/9
1092.180 cents
2/1

although I did base it on C rather than A, and also subtracted an
across-the-board six cents from all deviations to bring this rather sharp
tuning back into the range of my recorded harmonica parts.

Thanks again for the assistance!

John Thaden
Little Rock, Arkansas, USA
http://www.flash.net/~jjthaden