Yahoo Tuning Groups Ultimate Backup tuning meantone / Gesualdo / Handel

Dear list-members

Reply to several postings by

graham@microtonal.co.uk
PERLICH@ACADIAN-ASSET.COM
"M. Schulter" <MSCHULTER@VALUE.NET>

---------------------
> Date: Fri, 23 Feb 2001 20:38 +0000 (GMT Standard Time)
> From: graham@microtonal.co.uk
> Subject: Re: Gesualdo / intonation / Meantone / FAQ

> Ibo Ortgies wrote:

> > > Some people have suggested that singers would have
> > > narrowed the leading tones, so let's consider that hypothesis.

> > narrowed, it can be by raising the "leading note" or as could be also
> > reaching the resolved note at a lower pitch, which happens in practic

> Does that mean lowering the tonic below its original point,

this would be an example in a cadence

g# - a
e - A

if you use JI the third e-g# will have 386,3 ct and since the fifth A-e
is supposed to be pure (702 ct) the diatonic semitone will be 111,7 ct
(1200-702-386,3). As this is regarded by the prevailing opinion of the
majority (outside this list) a too big step for "leading tone" the third
is usually raised - the amount, how much it is raised, practically being
undefined. In practice this might lead to thirds (on the "dominant" or
V-th grade) which are much closer to a diminished fourth than a third.

> > > If Gesualdo were using 19 pitch classes, ...

> > ... we cannot assume that they narrowed leading tones since a discant
> > clause, where tyhe leading note would occur, would be the large semitone
> > (16:15) resp. it's meantone approximation.

> Why can't we assume that?

I explained that, just after the "since" (maybe I should have written
"because" - my English is not that good, sorry)

> What does "discant clause" mean?

[This was explained later by Margo Schulter ...]

> > > I would expect him to use dissonances in the
> > > manner outlined above to give motion by minor semitones. I don't know
> > > of a single example of him doing this.

> > Then, why would you expect it?

> That's a deceptively short question.

Not as I understood what you said: you say, that you don't know any
example of him doing this and I only wondered why we would expect
something from Gesualdo without knowing it from a single example by him.

> The word "then" means I'm not sure what

Again, my bad English. I'm sorry that it contributes to our dispute ...
maybe "If it is so, why would you expect it" would have been the right
way to ask?

[Daniel Wolf made a very polite and good statement about the use of a
foreign language]

> > Nothing of this I regard as right
> > - leading tones (as large semitones) occurred in evrey discant clause

> As I don't know what this means, I can't say if I ever suggested it.

Margo Schulter explains it in one of her following mails much better
than I could do it (not speaking of language ability again).

...
> > - 12 pitches* per octave, or more per piece up to 19 (talking abstractly
> > here, as if talking about keyboards - in vocal intonation there would
> > be ideally more pitches, mainly the pure fifths)

> Not sure what you mean by this. I'm not sure he ever used more than 12 pitches (as
> written) in a piece although he may have used as many as 20. I haven't counted.
> But what's its relevance?

Again I refer to Mrs. Schulter's mail(s)

May be an example: If he used different pitches as sometimes represented
by split keys in instruments (for Gesualdo you might extend this to Gb
on the flat-side and to B# on the sharp side)

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

Here the dashes indicate
- meantone fifths
/ pure major thirds
\ minor thirds (as defined by the two previous)

Here you have 14 distinctive pitches, because for example G# and Ab (and
Eb and D# as well) are two different pitches, separated by the smaller
diï¿½sis (of 41 ct or ~1/5 tone). The Ab cannot be used as a G# or vice
versa (as in 12-ET).
Therefore you have 14 pitch classes.
I think Margo Schulter has made this point clear in one of her following mails.

> > - he would have used the terminology of his time, one aspect of which
> > might be describable with the modern X-limit-concept.

> That looks obviously true to me. So is it still what you don't regard as right?

> > * the modern concept of pitch class doesn't add anything to the argument

> You obviously have a low opinion of my argument, because it would fall to the
> ground immediately without the idea of pitch classes.

I haven't a low opinion of you, but I think your argument really misses
the point.

> > > He did use dissonance, and a lot of chromaticism,
> > > so what I've seen so far strongly suggests 12 pitch classes.

> > While the first part of the previous sentence is undoubted,
> > the second is wrong conlusion:
> > If a piece has no more than twelve pitches then you are right, but what
> > if it makes use of g# and a-flat, which are in any case distinct pitches
> > in G's time?

> Same pitch class.

different pitch classes, since they are not interchangable ...

> I've thought about how this argument should be phrased: Gesualdo's music only
> requires 12 pitch classes.

we don't need to take this up again and again, as has been stated in
many mails now that it requires more - .
May I ask you, whether you have ever heard 16th/17th-century-music on an
instrument with split keys? I think that experience would help a lot in understanding.

> That means, if you represent the music using 12 pitch classes, it can be converted
> to the staff (and therefore meantone) exactly as Gesualdo did if you follow these
> rules, in order, 1 being the most important:

...

Talking of "split-key"-keyboards

> > > but only to allow greater range of modulation.
> > > They weren't exploiting the new sonorities those split keys gave them.

> > They were exploiting them within the frame that the music theory of the
> > time would allow - I regard that as the same degree of exploitation,
> > like Bach exploited the sonmorities which the rising well-tempered
> > tunings offered.

> Before you quoted "Music came first; then the scales ... then came the theorists to
> explain them." And you half agreed with it. Now you're saying composers are
> constrained by theory? I disagree!

I'd disagree with myself if I had said that. Where did I say that?

> But anyway, it's as much the practice of the time as Gesualdo in particular that
> I'm interested in. Gesualdo happens to be a prominent example of a highly
> chromatic composer who may have encountered split-key keyboards.

We know, he had ... as much as we can trust the sources, of course. read
again Bill Alves quote from the Grove's article by Lorenzo Bianconi.
see Alves's posting to the list:
Date: Fri, 23 Feb 2001 13:46:23 -0800
From: Bill Alves <ALVES@ORION.AC.HMC.EDU>
Subject: Re: Re: Gesualdo (Part I of II)

-----------------------------

> Date: Fri, 23 Feb 2001 22:55:30 -0000
> From: PERLICH@ACADIAN-ASSET.COM
> Subject: Re: Gesualdo / intonation / Meantone / FAQ

> --- In tuning@y..., Ibo Ortgies <ibo.ortgies@m...> wrote:

> > just a question here, why isn't 53-ET adressed, basically a
> > extension of pythagorean tuning
> That's a very odd question, Ibo. Certainly no shortage of words have
> been expended on 53-tET, both on and off this list. However, this
> particular thread started with a poster who wanted a meantone tuning,
> which 53-tET is not.

OK, sorry. I wasn't on the list, when those postings came... and you're
right, I missed the point ...

> > > . . . but who cares -- if you make good music, that's all that
> > > matters.
> ... I've made plenty of substantive claims that you
> could address instead -- and some of that comes below.

As I would do if I thought my comment would add something valuable or
disagreed for some reason. If I had to write all the time "I agree" to
your posts, then the list would be half filled with that...

> > It might be worth looking at singing and playing teaching books in
> > the meantone era and even later.
> > In the eighteenth century Mattheson, ...etc. refer still to the
> > just intervals like 5:4, 9:8, 16:15 these were books to train and to
> > practice with.
> 5:4 certainly is fine as a harmonic interval, but as for melodic
> seconds, there were no reliable means of producing such ratios except
> special tools such as the monochord, so they must be regarded as
> irrelevant to any actual training that may have taken place (unless
> monochords where a major part of musician training . . . ?)

I think these writers (and many others) were also very experienced
practitioners and wrote for the performing musician. The tool to produce
the required ratios would by the lowest sounding note on the one hand
and on the other hand practice...

> > The same authors write, that on the keyboard is a
> > temperament out of necessity.
> Clearly even early authors such as Benedetti were a bit more clever.

I translated from German "aus Notwendigkeit". I meant that they regarded
the keyboard as limited... and therefore a some temperament was
regarded as necessary.

....

> From http://www.ixpres.com/interval/dict/meantone.htm: how many of
> these were "important"?

Thanks for the hint on the table...

> > In Italy (maybe Spain, too) it was in the beginning usually Ab - C#
> That's very interesting! Thanks for bringing that up.

And split keys were sometimes made so that there were only keys for
ab/g# (ab in front!)

> > > and G.F.Hï¿½ndel
> > > played on instruments with up to 16 keys per octave.
> > We don't know that of Hï¿½ndel with such certainty.
> Why don't we say 14 tones.

Because we cannot say that with enough safety.
Or, let me put it more exactly: we can speculate that Handel might have
played the Bernard-Smith-organ sometimes, but we don't know even that as
a undoubtable fact. And would we regard the mere possibility as enough
reason to couple it to his still existing music?
Right now we can only say that Handel and his music did exist at the
same time as the Smith-organ (with 14 keys/octave) - anything more is an
assumption until we discover a source relating this organ to Handel and
maybe even his music (at least one piece). Also we could think that an
organ with a shifting mechanism existed before the instruments we know
of, which were built after Handel's death - we could, but we don't have
enough evidence to state it as a undoubtable fact.
This still leaves us the possibility to think that Handel's music fits
well for meantone-tuning and a extended-meantone-instrument would help
in performance probably a lot.

----------------------

> Date: Fri, 23 Feb 2001 23:40:32 -0000
> From: PERLICH@ACADIAN-ASSET.COM
> Subject: Re: Gesualdo / intonation / Meantone / FAQ

> Ibo Ortgies <ibo.ortgies@m...> wrote:

> > > and G.F.Hï¿½ndel owned instruments with 14 and 16 keys per
> > > octave.
> > > ....- perhaps search the archives for
> > I couldn't find it, I tried keywords Handel,
> Anyway, the relevant messages are numbers:
> 7516

Thanks for the help and ..
...
> > Hï¿½ndel, Handel + Ehrlich ...
> Spelling my name right might help . . .

...I apologize for that misspelling!

------------------------

> Date: Fri, 23 Feb 2001 18:52:14 -0800 (PST)
> From: "M. Schulter" <MSCHULTER@VALUE.NET>
> Subject: Re: FAQ (?) -- _Sumer_ canon, discant cadences, meantone

> Hello, there, everyone, and I might just offer a few comments on the
> Gesualdo and meantone discussions, especially in response to some
> remarks by Ibo Ortgies and Graham Breed.
...

Talking about the history of meantone-temperament as reflected in the
writings by Aaron, Vicentino, which you discussed here concise but at
the same time in depth

> (Zarlino does define his 2/7-comma system rigorously in 1558, but
> other meantones such as 1/4-comma only in 1571).

What would you regard as the reason, that Zarlino would describe the
quarter-comma-meantone in the later publication as "new temperament", if
it was already around frequently since ca. 100 years. Or is he
referring to something else which he thinks is new in it?

This question seems especially challenging to me, because otherwise I'd
interpret the sources I know or have read about, in the same way like
you.

---------------------------

> Date: Fri, 23 Feb 2001 23:16:16 -0800 (PST)
> From: "M. Schulter" <MSCHULTER@VALUE.NET>
> Subject: Re: Gesualdo

...

> To Bill Alves:

> The Canzona is beautiful, and has lots of the ornamentation and
> "fantastical" quality of keyboard music from this epoch around 1600.
> Maybe most relevantly for this discussion, it has a 14-note range of
> Eb-A#. Thus it could be played either on a 19-note (or larger)
> chromatic harpsichord of Neapolitan vogue, or on a somewhat smaller
> instrument with the appropriate split keys.

yes, and you might check the needed extra-keys with the interesting list
of compasses and split sharps in the article by Wraight/Stembridge:
Italian split keyed instruments ... Performance Practice review, 1994,
Vol 7. Nr. 2 (see my recent mail)
In this article I read about one instrument by
Boni (working in Rome, not in Florence, as D.Wraight corrected in a
short errata-list)
having the compass GG (or AA?) - c'''
split keys being F#, G# to complete the sshort octave and then
d#/eb (d#s in front!), g#/ab, bb/a#, d#'/eb', g#'/ab', bb'/a#'

Another unattributed (and undated) instrument having
C/E-c'''
and eb/d#, g#/ab, bb/a#, eb'/d#', g#'/ab', bb'/a#'

> Again, if we assume a keyboard performance, or maybe an ensemble with
> a keyboard as a "foundation" instrument (one manuscript has a "basso
> continuo" identical to the lowest sounding voice of Gesualdo's piece),

Reminds me of my previous mail in which I referred to continuo-practice

> either a 19-note or larger keyboard, or a smaller instrument with a
> split Bb/A# key, would cover the range.

...
> To Ibo Ortgies:

> Thank you for bringing to this thread both your general erudition and
> your special knowledge of keyboards with split keys or "subsemitones."
> It's very pleasing how this discussion of Gesualdo is bringing out
> more information on this general topic, including your most extensive
> contributions here and on the World Wide Web.

Thanks a lot for your kind words - certainly I have learnt more from you...

...

> Margo Schulter
> mschulter@value.net
------------------------

Kind regards
Ibo Ortgies

Ibo Ortgies wrote:

> > > > If Gesualdo were using 19 pitch classes, ...
>
> > > ... we cannot assume that they narrowed leading tones since a
discant
> > > clause, where tyhe leading note would occur, would be the large
semitone
> > > (16:15) resp. it's meantone approximation.
>
> > Why can't we assume that?
>
> I explained that, just after the "since" (maybe I should have
written
> "because" - my English is not that good, sorry)

I don't think that refutes what I was suggesting. With 19 pitch
classes, you're free to choose whatever semitone you want in any
context. If the choice is made for you, that surely means you don't
have 19 pitch classes available?

> > What does "discant clause" mean?
>
> [This was explained later by Margo Schulter ...]

No, she gave multiple definitions like my encyclopedia. I still don't
know what you mean in this contecxt.

> > > > I would expect him to use dissonances in the
> > > > manner outlined above to give motion by minor semitones. I
don't know
> > > > of a single example of him doing this.
>
> > > Then, why would you expect it?
>
> > That's a deceptively short question.
>
> Not as I understood what you said: you say, that you don't know any
> example of him doing this and I only wondered why we would expect
> something from Gesualdo without knowing it from a single example by
him.

This logic is backward. What I said was, roughly,

IF
19 pitch classes
AND
minor semitones good
AND
dissonance
THEN
dissonance used to give minor semitones

So I was looking for examples of gratuitous use of minor semitones to
support the hypothesis I was investigating. If this argument is
correct (it makes sense to me) and Gesualdo did use dissonance (we're
agreed on that) but he didn't use it to give minor semitones, then it
would follow that either he wasn't freely using 19 pitch classes or he
didn't favour minor semitones.

So I wasn't expecting to find these kind of minor semitones. I was
looking for them to see if the hypothesis was true. And I was
assuming the hypothesis in order to prove or disprove it. After that,
I looked for the evidence.

If I could prove he was using 19 pitch classes, and not using
dissonance to bring out minor semitones, that would prove that he
didn't favour minor semitones. In fact, I can't prove he used more
than 12 pitch classes, so the use of minor semitones is still an open
question.

There is that one passage where I think he was specifically rigging
the harmony to get minor semitones. But the motive was specific to
that context, and not general to his work.

> > The word "then" means I'm not sure what
>
> Again, my bad English. I'm sorry that it contributes to our dispute
...
> maybe "If it is so, why would you expect it" would have been the
right
> way to ask?

And the answer is, I assumed it first, and then looked to see if it
was true. I don't expect anything without evidence.

> [Daniel Wolf made a very polite and good statement about the use of
a
> foreign language]

In fact, your English is so good, I didn't realize you weren't a
native speaker, or at least a long-time resident in an English
speaking country.

> > > Nothing of this I regard as right

> Here you have 14 distinctive pitches, because for example G# and Ab
(and
> Eb and D# as well) are two different pitches, separated by the
smaller
> diësis (of 41 ct or ~1/5 tone). The Ab cannot be used as a G# or
vice
> versa (as in 12-ET).
> Therefore you have 14 pitch classes.
> I think Margo Schulter has made this point clear in one of her
following mails.

My understanding of the term "pitch class" is that it is an abstract
idea that can represent a number of pitches. So an "F" on the page
may not always be sung at the same pitch, but is a single pitch class.
Traditional notation can be thought of as using 12 pitch classes,
where C#=Db, D#=Eb, etc.

I don't have the reference to hand, it was a long time ago that I read
it, but at that time I didn't see any inconsistency in analysing
meantone music using such a system. And it seems to be appropriate
for Gesualdo. His compositions can be expressed in 12 pitch classes,
and mechanically converted into a higher number of pitches with very
few discrepancies. He wrote more than 12 pitches, but only 12 pitch
classes are required to analyse the overwhelming majority of his
music.

However, I don't believe you could devise an algorithm that could
restore the music after all accidentals were removed. Which means you
need more than 7 pitch classes to represent the music.

> > > While the first part of the previous sentence is undoubted,
> > > the second is wrong conlusion:
> > > If a piece has no more than twelve pitches then you are right,
but what
> > > if it makes use of g# and a-flat, which are in any case distinct
pitches
> > > in G's time?
>
> > Same pitch class.
>
> different pitch classes, since they are not interchangable ...

I know of no music, tonal or free atonal or serial, in which there are
no rules governing whether G# should be preferred over Ab. If the
idea of 12 pitch classes is to make any sense when applied to these
musics, it must mean something like what I think it means. If not,
let's reformulate the idea so it does mean something. Or find me a
different term for what I'm trying to express.

> > I've thought about how this argument should be phrased:
Gesualdo's music only
> > requires 12 pitch classes.
>
> we don't need to take this up again and again, as has been stated in
> many mails now that it requires more - .

I've given objective criteria by which my assertion can be disproved.
I can even give you the source code so you can run the tests
yourself. You can say as often as you like that I'm wrong, but I
won't believe you until you prove it.

Nothing anybody has said contradicts my idea, which may mean nobody
understands it and I'm not expressing myself well enough. But then
you must think you understand it to say it's wrong. To me, it seems
obvious in the light of the evidence.

> May I ask you, whether you have ever heard 16th/17th-century-music
on an
> instrument with split keys? I think that experience would help a lot
in understanding.

No. I'm going by the score. I can tune a keyboard to an extended
mapping, but it would be difficult to get the voicing right. I also
have a guitar with the right fretting but, again, it's not really
suitable for playing a madrigal on.

> > > They were exploiting them within the frame that the music theory
of the
> > > time would allow - I regard that as the same degree of
exploitation,
> > > like Bach exploited the sonmorities which the rising
well-tempered
> > > tunings offered.
>
> > Before you quoted "Music came first; then the scales ... then came
the theorists to
> > explain them." And you half agreed with it. Now you're saying
composers are
> > constrained by theory? I disagree!
>
> I'd disagree with myself if I had said that. Where did I say that?

Maybe this is getting pedantic. But when you say "within the frame
that music theory of the time would allow" it seems like the theory is
not allowing some things to be done.

Graham

meantone / Gesualdo / Handel

🔗Ibo Ortgies <ibo.ortgies@musik.gu.se>

🔗justin.white@davidjones.com.au

🔗Graham Breed <graham@microtonal.co.uk>

🔗PERLICH@ACADIAN-ASSET.COM