Vallotti for Bach

Tuning and Temperament
1

Claudio is one who advocates Vallotti for Bach for certain application. But the recipe was not published until 1779. So I wondered if it is appropriate, particularly with my current question relating to performing BWV 988.

From Wikipedia:

Vallotti’s description of his temperament appears in book 2 of his treatise, Della scienza teorica e pratica della moderna musica (On the theoretical and practical science of modern music). Although Vallotti stated that he had developed his theoretical system—presumably including the details of his temperament—by 1728, the first book of his treatise was not published until 1779, the year before he died. At the time of his death, the other three books had not been published, and remained only in manuscript form until an edition of all four books was published in 1950, under the title Trattato della moderna musica (Treatise on modern music).

Sure enough, consulting Claudio’s UT book, he lays out good reasons why it is very likely to have been known and circulating (pardon the tuning pun) well before. I find his arguments completely convincing.

Refer to p. 124, 5th edition.

I believe Claudio has more to say about Vallotti, so here is the topic to do so.

2

I proposed a topic for ChatGPT 3 to answer:

Give the instructions for tuning Vallotti.

Here is the response. Make of it what you will. :slight_smile:

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Vallotti temperament is a historical tuning system for keyboard instruments that was proposed by Francesco Antonio Vallotti in the 18th century. It is based on a meantone temperament, which is a type of tuning system that divides the octave into a series of equal intervals.

To tune an instrument in Vallotti temperament, you will need an electronic tuner or another reference pitch to tune the instrument to. Here are the steps you can follow:

Determine the reference pitch that you will use to tune the instrument. This is typically A440, which is the standard pitch for modern concert pitch.

Tune the first note, which is typically the A above middle C (A4), to the reference pitch.

Tune the remaining notes in the octave starting from A4, using the following intervals:

A4 to B4: Tune B4 to a pure major third above A4.
B4 to C5: Tune C5 to a pure major third above B4.
C5 to D5: Tune D5 to a pure major third above C5.
D5 to E5: Tune E5 to a pure major third above D5.
E5 to F5: Tune F5 to a pure major third above E5.
F5 to G5: Tune G5 to a pure major third above F5.
G5 to A5: Tune A5 to a pure major third above G5.

Tune the remaining notes in the octave, starting from A5 and following the same intervals as in step 3.

Repeat the process for the remaining octaves, starting from the reference pitch (A4) and following the same intervals as in step 3.

I hope this helps! Let me know if you have any questions or need further assistance.

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3

All the thirds are pure!

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4

Interesting. I asked the same question and got a less amusing, although
still wrong, answer:

give instructions for tuning Vallotti

Vallotti temperament is an historical tuning system that was developed
in the 18th century by Francesco Antonio Vallotti. It is a meantone
temperament that divides the octave into 31 equal parts, resulting in a
slightly larger syntonic comma than other meantone temperaments.

To tune a Vallotti temperament on a keyboard instrument, you will need a
reference pitch, such as a tuning fork or an electronic tuning device,
and a method for adjusting the intervals between pitches, such as a
tuning lever or an electronic tuning software.

Start by setting the reference pitch for your instrument. This is
usually the pitch of the A above middle C, which is typically set to 440 Hz.

Next, tune the octave from the reference pitch. In Vallotti temperament,
the octave is divided into 31 equal parts, so the size of each interval
between consecutive pitches is about 1.93 semitones.

Once the octave is tuned, proceed to tune the fifths. In Vallotti
temperament, the fifths are slightly flattened, so you will need to tune
them slightly smaller than in equal temperament. The size of the fifths
in Vallotti temperament is about 694 cents, which is slightly smaller
than the size of the fifths in equal temperament (700 cents).

After the fifths are tuned, proceed to tune the thirds. In Vallotti
temperament, the major thirds are slightly larger than in equal
temperament, so you will need to tune them slightly larger than in equal
temperament. The size of the major thirds in Vallotti temperament is
about 413 cents, which is slightly larger than the size of the major
thirds in equal temperament (400 cents).

Finally, check the temperament of your instrument by playing a sequence
of intervals and chords and comparing them to the reference pitch. Make
any necessary adjustments to achieve the desired level of tuning accuracy.

I hope these instructions are helpful! If you have any further questions
or need more detailed guidance, feel free to ask.

5

This is ChatGPT 3. I fail to be impressed in any way. It’s usually wrong when it comes to the point. I read that ChatGPT 4 will be trained on a vastly larger training dataset. But I confess I do not understand what pressing problem ChatGPT solves. What is it for except for cheating in essays and generating vast scads of disinformation quickly? I am not normally a cynical person, but I cant see how it moves us any closer to AGI (or, Strong AI) ether.

So I post this more as an amusement than anything else.

And yes Stuart, it will give different answers to the same question each time, and you can ask it to reformulate its answer and it comes back with something different. Musicologists and historians can still keep their jobs.

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6

I hope this is a joke.

7

@Peterclav it’s not so much a joke as a modern sort of entertainment, seeing how dumb ChatGPT is, despite the huge hype cycle.

i was actually hoping for a good answer, but sadly, not to be, as yet.

8

For my colleagues who argue for Vallotti or Barnes for Bach:

Please tune Vallotti, and then play through, say, the slow movement of Brandenburg 5. Please tell me if there is another word to describe the harmonies like C# major or F# major, or the melodic notes at many cadences for that matter, other than “horrid”. I could pick other examples in B minor or F# minor. To my ears, it just sounds audibly bad.

I believe CPE’s instructions, in their vagueness (or, better, flexibility), point to the true purpose of temperament: to make the instrument sound good for the intended musical purpose. No single formula, just make it sound good, like Duke Ellington said.

9

That sounds right.

Compare music theorists with temperament theorists.

Music theorists can describe music that already exists. This might not
interest musicians (Bach, supposedly, didn’t understand what Rameau was
getting at, since you could write music based on the basso continuo
without all this fancy harmony stuff), but at least they describe real
music.

Baroque temperament theorists, on the other hand, couldn’t describe real
temperaments. Insofar as musicians tuned by feel, not by formula,
theorists had no way to measure the results.

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10

Le 05/01/2023 20:19, Keith Womer via The Jackrail écrit :

For my colleagues who argue for Vallotti or Barnes for Bach:

Please tune Vallotti, and then play through, say, the slow movement of Brandenburg 5. Please tell me if there is another word to describe the harmonies like C# major or F# major, or the melodic notes at many cadences for that matter, other than “horrid”. I could pick other examples in B minor or F# minor. To my ears, it just sounds audibly bad.

I believe CPE’s instructions, in their vagueness (or, better, flexibility), point to the true purpose of temperament: to make the instrument sound good for the intended musical purpose. No single formula, just make it sound good, like Duke Ellington said.

The point of unequal temperaments is having some “nice” thirds. The
price you have to pay for this is bad thirds. Everyone has to decide how
much at the most they are willing to pay for these nice thirds. In the
Neidhardt temperament I mentioned and in two other of his circulating
temperaments, and in the four Sorge temperaments mentioned my Poletti in
his comparison, you pay at the most 17,6 cents your nice thirds. In
Vallotti, and, I assume in Barnes, though I don’t have the figures, your
thirds will cost you more, 20,2 cents. In Young, even more, 21,5 cents.
I’d say Neidhardt’s bad thirds are the most I’m willing to pay. So if
you set a threshold of, say, 18 cents, you can eliminate quite a few
German temperaments (and all the French ones) and all you have to do is
pick one of those that is left to your taste.

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