Telemann, Werckmeister, 'pure' meantone and the break away from it

I am continually surprised at Brad's capacity for exaggeration...
though I guess I shouldn't be. Thinks he is the reincarnation of Bach,
Tosi and Telemann all at once - at least, he argues from that premise.
The Lehman Principle: Never mind weight of documentary evidence, what
I personally like the sound of on my harpsichord this week is more
likely to be historically correct.

But what would happen if Brad had set up in 1/4-comma or 1/5-comma
instead? Maybe it would have sounded even better, once the
instrumentalists had adjusted to the more unequal sound world. (Never
underestimate the conditioning of modern ears to 12-ET!)

The old-ish recording of Schmelzer and Muffat by London Baroque uses
1/4-comma and sounds perfectly fine. The generic problem with saying
'I like the sound of X' is: you don't know if 'Y' would sound even
better. (Example of 'Y': Francois Couperin Prelude no.1, tuned with
F-A, C-E and G-B pure.)

It is clearly documented that Telemann's 55-comma system was *not* a
keyboard tuning. (Which is obvious, since it doesn't accommodate
enharmonic equivalents.) He wrote so himself. It was rather an
approximate model of what singers and violinists were likely to do. To
tune an ordinary harpsichord to 1/6 comma meantone and say without a
blush 'This was Telemann's own tuning' is .. how shall I put it ..
using a loose definition.

Did Telemann ever actually measure the intonation of any singers or
violinists to find out *how* accurate the model might be? Or was he
satisfied to have found one example of relatively purer intonation
with some size of enharmonic discrepancy?

Did he actually even calculate that the model, if taken with
mathematical precision, implied rather sharp major thirds and flat
minor ones? (Sorge did later...) How much mathematics does it take to
get from Telemann's theoretical description to find out just how flat
one ought to tune every fifth? What harpsichordist would bother with
such calculations?

If one *does* deviate adaptively from a given meantone, it becomes
practically adaptive JI, and the semitones and tones of the melodic
parts no longer follow the supposedly 'correct' intervallic ratios of
the model. Tosi said his semitone distinction was only useful when
singing with string orchestra accompaniment - where no such meantone
model can or need apply - with a keyboard, there was no point in
trying to observe it. Brad has, inadvertently, proved the opposite of
his intended point: 1/6-comma is a temperament for keyboard
instruments, not a tuning for melody instruments.

Yes, 1/6 comma *is* a reasonable keyboard tuning for some 18th century
music - now Telemann was quite some time after the 17th century and
Tosi's salad days, and also quite some time post-Werckmeister.

Werckmeister in the 1690's is the first person in the modern era to
try and argue that thirds ought be more out of tune than fifths - an
essential feature of 1/6 comma, and all points towards ET. If you
accept this then circular tuning becomes simple, almost trivial.

The problem with believing that anyone was musically accustomed to
anything like 1/6-comma in the 17th century is that the great majority
of practical keyboard tuning instructions from that time result in
something between 1/4- and 1/5-comma: privileging thirds over fifths.
If you believe that Brad's 'deductions' from Tosi apply that far back,
you have to disbelieve Denis, Mersenne, Praetorius, all the simple and
easily applicable instructions that lead to pure thirds and extend
well into the 18th century in some countries.

Concerning the 17th century, we have a conflict. On the one hand, some
theories, or brief references to them, which are supposed to define
and explain an entire meantone system by referring to a difference
between diatonic and chromatic semitones. If given the full rigid
mathematical treatment, their thirds turn out more mistuned than their
fifths. But the sources themselves never once tell you straight out
how to tune a fifth or a third. Most of them never even mention
temperament or keyboard tuning.

On the other hand, some keyboard tuning instructions which tell you
how to tune the fifths and the thirds, and the octaves too, and even
in what order to play the keys to get your tuning sequence logical and
correct. They also say clearly that the thirds are perfect, or at most
about as mistuned as the fifths.

Both *cannot* be realistic descriptions of the same intonational
practice. If keyboards were routinely tuned to 1/4-to-1/5-comma, there
is no point to considering the exact melodic implications of such and
such a theory of semitones - it would simply be unnecessarily out of
tune with the keyboard, with the general-bass and with the harmony.

(But incorrect theory, such as trying to think of nine commas, is no
obstacle to excellent practice among singers and instrumentalists who
use their ears.)

The question is quite simple: Who gets more share of the purity, the
third or the fifth. Brad says that, so far as there was a conflict,
the fifth always got the advantage. I disagree and bring up a host of
17th century keyboard tuning instructions in which the third was
either favoured, or shared the prize equally. I argue further that 1/4
comma is clearly the best framework if one wants to have the least
trouble in getting close to pure major and minor triads.
I also say the first person to say that the fifth should be favoured
was Werckmeister, and I suspect that he was the vanguard of a new
trend which valued modulatory freedom over pure harmonic intonation.

If anyone has the relevant quotation from Musurgia Universalis, I'd be
happy to consider it.

Previous discussion on HPSCHD-L came to the point that Kircher was
more likely to have been considering 53-division, which has very
nearly pure thirds and fifths and is not meantone at all. It is quite
possible that Barbour etc. were misled by their enthusiasm for
applying keyboard/meantone thinking to everything...

Kircher has been mentioned here as involved with the 53-division.
/tuning/topicId_29025.html#29025

I stick by my point and think it is no coincidence, for example, that
1/6-comma was not included by Rossi in his 1666 enumeration of
musically useful tunings.

~~~T~~~

Well, gee. With all this energy wasted making up ludicrous straw-man
"Lehman Principles" and other complaints about a fictitiously stupid
"Brad" who allegedly believes impossible things, we're losing focus on
the material. There are some other good points interleaved with it,
but the vitriol against the straw-Lehman chokes them out.

Take a look at the _New Grove_ pages about regular 17th century
temperaments, and the prevalence of non-1/4-comma layouts. Lindley's
article here even cites a presentation of the 55-division from as
early as 1626! Here's a scan.
/tuning/files/Bradley_Lehman/

I also re-read Bruce Haynes's excellent 1991 article again this
morning, to re-acquaint myself with the things he does and doesn't
say, and from which sources. Recommended.

And as for Bach, I don't believe he cared much (if at all) about which
comma was being whacked around, or measured anything. It's not a
mathematical thing. Just nudge the designated 5ths/4ths slightly off
pure by the single or double amounts, with the tuning lever, with
taste and experience. Yes, I believe it *worked out* to something in
the 1/6 and 1/12 comma range, in result, but the conceptual model here
is tasteful nudges on the tuning lever, not calculation or counting of
anything.

Brad Lehman (the real one, not a straw construction)

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
>
> I am continually surprised at Brad's capacity for exaggeration...
> though I guess I shouldn't be. Thinks he is the reincarnation of Bach,
> Tosi and Telemann all at once - at least, he argues from that premise.
> The Lehman Principle: Never mind weight of documentary evidence, what
> I personally like the sound of on my harpsichord this week is more
> likely to be historically correct.
>
> But what would happen if Brad had set up in 1/4-comma or 1/5-comma
> instead? Maybe it would have sounded even better, once the
> instrumentalists had adjusted to the more unequal sound world. (Never
> underestimate the conditioning of modern ears to 12-ET!)
>
> The old-ish recording of Schmelzer and Muffat by London Baroque uses
> 1/4-comma and sounds perfectly fine. The generic problem with saying
> 'I like the sound of X' is: you don't know if 'Y' would sound even
> better. (Example of 'Y': Francois Couperin Prelude no.1, tuned with
> F-A, C-E and G-B pure.)
>
> It is clearly documented that Telemann's 55-comma system was *not* a
> keyboard tuning. (Which is obvious, since it doesn't accommodate
> enharmonic equivalents.) He wrote so himself. It was rather an
> approximate model of what singers and violinists were likely to do. To
> tune an ordinary harpsichord to 1/6 comma meantone and say without a
> blush 'This was Telemann's own tuning' is .. how shall I put it ..
> using a loose definition.
>
> Did Telemann ever actually measure the intonation of any singers or
> violinists to find out *how* accurate the model might be? Or was he
> satisfied to have found one example of relatively purer intonation
> with some size of enharmonic discrepancy?
>
> Did he actually even calculate that the model, if taken with
> mathematical precision, implied rather sharp major thirds and flat
> minor ones? (Sorge did later...) How much mathematics does it take to
> get from Telemann's theoretical description to find out just how flat
> one ought to tune every fifth? What harpsichordist would bother with
> such calculations?
>
> If one *does* deviate adaptively from a given meantone, it becomes
> practically adaptive JI, and the semitones and tones of the melodic
> parts no longer follow the supposedly 'correct' intervallic ratios of
> the model. Tosi said his semitone distinction was only useful when
> singing with string orchestra accompaniment - where no such meantone
> model can or need apply - with a keyboard, there was no point in
> trying to observe it. Brad has, inadvertently, proved the opposite of
> his intended point: 1/6-comma is a temperament for keyboard
> instruments, not a tuning for melody instruments.
>
> Yes, 1/6 comma *is* a reasonable keyboard tuning for some 18th century
> music - now Telemann was quite some time after the 17th century and
> Tosi's salad days, and also quite some time post-Werckmeister.
>
> Werckmeister in the 1690's is the first person in the modern era to
> try and argue that thirds ought be more out of tune than fifths - an
> essential feature of 1/6 comma, and all points towards ET. If you
> accept this then circular tuning becomes simple, almost trivial.
>
> The problem with believing that anyone was musically accustomed to
> anything like 1/6-comma in the 17th century is that the great majority
> of practical keyboard tuning instructions from that time result in
> something between 1/4- and 1/5-comma: privileging thirds over fifths.
> If you believe that Brad's 'deductions' from Tosi apply that far back,
> you have to disbelieve Denis, Mersenne, Praetorius, all the simple and
> easily applicable instructions that lead to pure thirds and extend
> well into the 18th century in some countries.
>
>
> Concerning the 17th century, we have a conflict. On the one hand, some
> theories, or brief references to them, which are supposed to define
> and explain an entire meantone system by referring to a difference
> between diatonic and chromatic semitones. If given the full rigid
> mathematical treatment, their thirds turn out more mistuned than their
> fifths. But the sources themselves never once tell you straight out
> how to tune a fifth or a third. Most of them never even mention
> temperament or keyboard tuning.
>
> On the other hand, some keyboard tuning instructions which tell you
> how to tune the fifths and the thirds, and the octaves too, and even
> in what order to play the keys to get your tuning sequence logical and
> correct. They also say clearly that the thirds are perfect, or at most
> about as mistuned as the fifths.
>
> Both *cannot* be realistic descriptions of the same intonational
> practice. If keyboards were routinely tuned to 1/4-to-1/5-comma, there
> is no point to considering the exact melodic implications of such and
> such a theory of semitones - it would simply be unnecessarily out of
> tune with the keyboard, with the general-bass and with the harmony.
>
> (But incorrect theory, such as trying to think of nine commas, is no
> obstacle to excellent practice among singers and instrumentalists who
> use their ears.)
>
> The question is quite simple: Who gets more share of the purity, the
> third or the fifth. Brad says that, so far as there was a conflict,
> the fifth always got the advantage. I disagree and bring up a host of
> 17th century keyboard tuning instructions in which the third was
> either favoured, or shared the prize equally. I argue further that 1/4
> comma is clearly the best framework if one wants to have the least
> trouble in getting close to pure major and minor triads.
> I also say the first person to say that the fifth should be favoured
> was Werckmeister, and I suspect that he was the vanguard of a new
> trend which valued modulatory freedom over pure harmonic intonation.
>
> If anyone has the relevant quotation from Musurgia Universalis, I'd be
> happy to consider it.
>
> Previous discussion on HPSCHD-L came to the point that Kircher was
> more likely to have been considering 53-division, which has very
> nearly pure thirds and fifths and is not meantone at all. It is quite
> possible that Barbour etc. were misled by their enthusiasm for
> applying keyboard/meantone thinking to everything...
>
> Kircher has been mentioned here as involved with the 53-division.
> /tuning/topicId_29025.html#29025
>
> I stick by my point and think it is no coincidence, for example, that
> 1/6-comma was not included by Rossi in his 1666 enumeration of
> musically useful tunings.
>
> ~~~T~~~
>