48-tone harmonium

See http://www.phys.uniroma1.it/DOCS/MUSEO/acu34.htm

Click on the photo and the letter to enlarge them.
The letter has four pages. The handwriting is difficult
for me to read. Perhaps a native German list member
could read it and tell us about the tuning of this
harmonium? It could be a tuning described in Helmholtz.
Take a look at the other pages of the museum too.

Manuel

--- In tuning@y..., <manuel.op.de.coul@e...> wrote:
> See http://www.phys.uniroma1.it/DOCS/MUSEO/acu34.htm
>
> Click on the photo and the letter to enlarge them.
> The letter has four pages. The handwriting is difficult
> for me to read. Perhaps a native German list member
> could read it and tell us about the tuning of this
> harmonium? It could be a tuning described in Helmholtz.
> Take a look at the other pages of the museum too.
>
> Manuel

Hello Manuel, or, is it Italian?

Regards,
Haresh

No, the letter, from Georg Appunn to Pietro Blaserna,
is in German. All webpages are in Italian though.

Manuel

Anton Appunn's letter is a beauty. If my English were better I would love to
present a translation right now. But anyway, here are a few comments.

Actually, the letter does not refer to the instrument on the photography.
This instrument, obviously made by Appunn, has a little lever (or stop?)
attached to each key and may very well feature 48 tones per octave.

The instrument, mentioned in Appunns letter, has 36 notes per octave, and it
achieves this in a rather odd way. According to the description, all three
5-octave keyboards are tuned to "mathematically pure" fifths. While the
bottom keyboard has a = 435 Hz as a reference, the middle one is tuned a
80/81 comma lower, and the top one again lower by the same margin, so that
for instance a just major triad consists of c and g on the bottom keyboard
and e on the middle one.

The other cord examples, which Appunn gives, are not always consistent, and
much of the tuning remains open to speculation. May be that that was
intended. The price he asks for his harmonium, however, comes out very clear:
950 Reichsmark, which translate into some 50,000 nowaday's dollars (the
annual income of an industrial worker was about 500 to 600 Reichsmark at that
time). And the delivery time was just marvelous: about 2 months.

Thank you, Manuel. A very intriguing find!

-Heinz

--- In tuning@y..., HPBOHLEN@A... wrote:

> The instrument, mentioned in Appunns letter, has 36 notes per
octave, and it
> achieves this in a rather odd way. According to the description,
all three
> 5-octave keyboards are tuned to "mathematically pure" fifths. While
the
> bottom keyboard has a = 435 Hz as a reference, the middle one is
tuned a
> 80/81 comma lower, and the top one again lower by the same margin,
so that
> for instance a just major triad consists of c and g on the bottom
keyboard
> and e on the middle one.

What's so odd about that? It's basically what happens when you do 5-
limit in 72-tET -- we've referred to just this way of viewing it
as "bicycle chains".

Paul, what I find odd about Appunn's tuning is that you don't get anything
near 72 tET by making two 21.5 cents steps only.

--- In tuning@y..., HPBOHLEN@A... wrote:

> Paul, what I find odd about Appunn's tuning is that you don't get
anything
> near 72 tET by making two 21.5 cents steps only.

It's near to a _subset_ of 72-tET. It operates on basically the same
principle -- several "Pythagorean" chains of fifths, separated by
(effectively) syntonic commas, allowing many "just" triads to be
played.

Hello Heinz,

Thanks for your reply. The tuning of the organ in the letter
is probably close to a subset of 53-tET then.

Manuel

Sorry, Manuel and everybody else interested in antique microtonal
instruments: only today, with more time at hand due to the weekend, I
detected that there is not just one letter written by Anton Appunn on the
"armonium" website, but a total of three.

Number two is just a postcard, written on June 13, 1887. Obviously Appunn had
come across the weakness of his first proposal, and he hastens to tell
Blaserna in just a single sentence that he had "forgotten" to mention that 4
keyboards, offering a total of 48 tones per octave, represented a "still more
perfect" solution, with a price tag of now 1200 Reichsmark.

That seems to have convinced Blaserna. On June 21 Appunn answers a letter of
Blaserna that is dated June 18 (compare the swiftness of the post service
more than hundred years ago with today's snail mail!) and obviously contains
favorable conditions. Blaserna's eagerness makes Appunn both inventive and
bold. He has come to the conclusion that 4 keyboards might be a bit awkward
to play. Thus he offers a system of little buttons that penetrate each key
and permit playing the next higher keyboard without taking the hands from the
lower one. This way the number of keyboards can be reduced to 3 again (one is
"hidden") with still 48 tones per octave available. He is bold insofar as he
anticipates that Blaserna will order this instrument despite the fact that
the price now will go up to 1500 Reichsmark (some 70 to 80,000 dollars at
today's value). He was obviously correct in that anticipation, because the
instrument pictured on the "armonium" website corresponds to the description
above.

By the way: Appunn was well known in his days as a manufacturer not only of
musical instruments but also of scientific acoustical apparatus (compare "A
Laboratory Course in Physiological Psychology" by Edmund C. Sanford, American
Journal of Psychology, 4, 1891, pp. 303-322).

Thank you once more, Manuel, for digging this up.

-Heinz

Thanks Heinz, an interesting story. I had Anton Appunn confused with
Georg Appunn, maybe they are related.

>By the way: Appunn was well known in his days as a manufacturer not only
of
>musical instruments but also of scientific acoustical apparatus (compare
"A
>Laboratory Course in Physiological Psychology" by Edmund C. Sanford,
American
>Journal of Psychology, 4, 1891, pp. 303-322).

I believe this is a website about it:
http://psychclassics.yorku.ca/Sanford/course2.htm
Classics in the History of Psychology.

Manuel

Manuel, I didn't find anything about Georg Appunn, but here is one little
postscript to Anton Appunn's harmonium story that I found on still another
page of "armonium":
He actually got paid 1520 Reichsmarks, "pari a 1929 lire" (!), the additional
20 Marks most probably for freight, or packaging.

-Heinz

There's a reference from a Georg Appunn in the bibliography,
without publication year. I have the suspicion that the
first name is wrong and that he's the same person.

Manuel