another meantone question!

Hello everyone.

I have another question about meantone (I hope this is no problem!)

In the temperament section of the New Grove dictionary Lindley (I think) says that Bartolomeo Ramis de Pareja, in his Musica Practica, presented a scheme which indicated a meantone temperament, as it contained a wolf fifth and 'good' and 'bad' semitones, etc. However, in Partch's Genesis of a Music he writes that Ramis de Pareja's substitution of complex Pythagorean intervals for the simple ratios of 5/4 and 10/9 ".hardly constitutes temperament, either in fact or in attitude."

My questions are:-
Are Partch and Lindley discussing different Ramis de Pareja schemes?
If they are not - was Ramis de Pareja suggesting a meantone temperament?

If anyone knows the answers to these questions I would be really grateful for their help. Alternatively, is it possible to get hold of Ramis de Pareja's book - I have not been successful in finding it.

cheers,

Tim

--- In tuning@y..., "tim oram" <tim_oram@h...> wrote:
> Hello everyone.
>
> I have another question about meantone (I hope this is no problem!)
>
> In the temperament section of the New Grove dictionary Lindley (I
think) says that Bartolomeo Ramis de Pareja, in his Musica Practica,
presented a scheme which indicated a meantone temperament, as it
contained a wolf fifth and 'good' and 'bad' semitones, etc. However,
in Partch's Genesis of a Music he writes that Ramis de Pareja's
substitution of complex Pythagorean intervals for the simple ratios
of 5/4 and 10/9 ".hardly constitutes temperament, either in fact or
in attitude."
>
> My questions are:-
> Are Partch and Lindley discussing different Ramis de Pareja
schemes?

Maybe.

> If they are not - was Ramis de Pareja suggesting a meantone
temperament?

The only proposal by him that I know of was not meantone, but was
simply two chains of just fifths, tuned to one another by just thirds:

A---E---B---F#--C#--G#
/ \ / \ / \ /
Eb--Bb--F---C---G---D

However, I'm not sure if Ramis also described something
more "practical" tantamount to meantone. I wouldn't be surprised
because theorists like Zarlino, in roughly the same era, felt they
needed to present just theoretical tunings even while advocating
meantone in practice.

Most likely, meantone was beginning to be used in Ramis' time in
practice but no one had yet figured out how to explain it
theoretically.

Hello, there, Tim Oram and everyone, and please let me try quickly to
answer at least the basic question you have raised about Bartolomeo
Ramos and his description (1482) of a keyboard very likely in some
kind of meantone -- in the same treatise where he also describes a
monochord using pure ratios based on 5.

As Mark Lindley[1] has noted, these seem clearly two different tuning
systems, and Paul has correctly anticipated Lindley's explanation. The
5-limit JI monochord is for the instruction of beginners, and Ramos
himself explains that simpler ratios like 5:4 or 6:5 for thirds may be
easier to follow than the more complex divisions of a traditional
Pythagorean scheme. Of course, this change also appears to reflect the
shift in 15th-century tastes toward more blending and restful thirds
in this era of Ockeghem and other composers of his generation.

The keyboard, in contrast, is a 12-note instrument, and Ramos presents
the question of whether Ab or G# is the more prudent note to include,
opting for Ab as more useful. His locations on the keyboard of "good"
and "bad" thirds, as Lindley observes, seem to fit meantone rather
than a typical 15th-century Pythagorean tuning, where the diminished
fourths or augmented seconds would actually approximate pure 5-based
intervals, hardly "bad" by likely late 15th-century standards.

There's more about Ramos and his discussion of the Ab/G# question at:

http://www.medieval.org/emfaq/harmony/hex.html

In sum, I agree with Lindley that the keyboard Ramos describes is very
likely in some kind of meantone, with the process of _participatio_ or
tempering of fifths first specifically mentioned by Gafurius in 1496
as something done as standard practice by organ tuners.

The alternative hypothesis would be that Ramos is describing a 12-note
keyboard in some kind of Pythagorean tuning or the like. One possible
bit of evidence making this a bit more unlikely, and also pointed out
by Lindley, is that Ramos mentions a proposal by his friend Tristan de
Silva for an extra key between F and G -- something that Ramos finds
without purpose. (He recognized more merit for including both Ab and
G#, the choice whose debate he addresses in his discussion.)

In a typical 15th-century Pythagorean tuning, Gb-B, a true F# key
would be a very logical option for an extra note, because it would fix
the Pythagorean Wolf fifth B-Gb. By 1482, however, meantone had
evidently become widespread enough on keyboards that Ramos did not see
the relevance of the Gb/F# question. His preferring tuning scheme is
Ab-C#, with the Wolf between these notes, rather than the Eb-G# which
became the standard tuning by around the second quarter of the 16th
century, I might guess.

A keyboard tuned according to the instructional monochord of Ramos
would have a Wolf of the 5-limit JI variety (40:27 or 27:20) at D-G,
not the most practical arrangement, unless one adds extra versions of
notes to handle the commas, and even there likely a highly
experimental option.

Thus I strongly agree both with Lindley's thesis and with Paul's
accurate guess as to that thesis: Ramos used JI for pedagogical
purposes, but in his description of a practical 12-note keyboard was
describing some more or less regular tuning, more likely meantone
rather than Pythagorean for reasons Lindley presents at some length.

----
Note
____

1. Mark Lindley, "Fifteenth-Century Evidence for Meantone
Temperament," _Proceedings of the Royal Musical Association_ 102
(1976), pp. 37-51.

Most appreciatively,

Margo Schulter
mschulter@value.net

Hi Margo Schulter and Paul Erlich,

I would just like to thank you both for your very informative and interesting answers to my meantone question. Both posts have been extremely useful for my research.

There was just one thing in your post, Margo, that I didn't understand (I'm still quite new to this tuning stuff! - I hope the questions aren't too elementary).

In your post you said:
"In a typical 15th-century Pythagorean tuning, Gb-B, a true F# key would be a very logical option for an extra note, because it would fix
the Pythagorean Wolf fifth B-Gb."

I'm a bit unsure of what you're saying here and I wondered if you would take the time to explain it to me - a sort of idiots guide!

cheers,

Tim Oram