Yahoo Tuning Groups Ultimate Backup tuning Gesualdo / intonation / Meantone / FAQ

Hi,
let me answer to several postings around these topic/s

> Date: Mon, 19 Feb 2001 15:08:25 -0500
> From: "Paul H. Erlich" <PERLICH@ACADIAN-ASSET.COM>

> I wrote,

> >> ....However, even today, the vast
> >> majority of trained singers are singing essentially in 12-tET,

> Ibo wrote,

> >I don't believe that - most of have not any good idea about intonation,
> >because even their teachers don't know what a pure major third is (not
> >to speak of minor and major semitones)

> Sounds like you're agreeing rather than disagreeing.

Do singers really sing in 12-ET? - I think it is a myth. 12-ET is
basically just to be found in electronic instruments.
Very few come close (sometimes) to "flexible just intonation" (as pure
as possible above the lowest sounding note), but most sing their notes
"somehow". Major thirds often much higher than in 12-ET ("leading tone"
trained), halftones reversed etc.

> ---------------------------------------------------

> Date: Mon, 19 Feb 2001 12:15:14 -0800
> From: Kraig Grady <kraiggrady@anaphoria.com>

> It is interesting that vibrato is used more frequently in his music
> that any other music of the period. (or so it seems)

Vibrato more frequently used in Gesualdo's music?

Where does that info come from (source?). It is hard to imagine that
vibrato would be frequent in Gesualdo's time. I regard it as an
ornament, which implies that it is used only as a "spice".

> ---------------------------------------------------

>
> Date: Tue, 20 Feb 2001 22:35 +0000 (GMT Standard Time)
> From: graham@microtonal.co.uk
> Subject: Re: Gesualdo

> > Graham wrote,

...
> assume 12 pitch classes. If it was customary for singers to narrow
> leading tones, why didn't composers write narrow leading tones into the
> music?

Please explain, why "narrow" (in meantone temperament, which we are
speaking of heree in relation to Gesualdo)?
In "meantone" temperament a major semitone (the "leading" tone in a
discant clause) would have 117 cents, the minor semitone 76 cents
chromatic. Depending on the bass line (not a part, but as a "basso
seguente", taking always the lowest sounding note...) the leading tone
might even be larger
(s. even below) ...

> ---------------------------------------------------

Johnny Reinhard wrote

> The use of the term "quartertones" can mean most any
> interval smaller than a semitone.

Yes, I found this term "Vierteltï¿½ne" just in a description from 1814
about the subsemitones still extant by then in a Brustwerk which
Stellwagen added (among other work) in 1645-48 to the Scherer-organ
(1624-5) in St. Aegidien church in Lï¿½beck

> ---------------------------------------------------

> Message: 24
> Date: Wed, 21 Feb 2001 09:44:26 +0100
> From: "Daniel Wolf" <djwolf1@matavnet.hu>
> Subject: Re: Draft: What is meantone (MT)?

> WHAT IS MEANTONE (MT)?

> (First draft of a FAQ entry)

> Meantone (MT) is a temperament where the syntonic comma (81:80; 21.5
> cents) is
> distributed equally among a fixed number of successive fifths. The
> standard, or
> _quarter-comma MT_, distributes the comma among four fifths, so that their
> octave-reduced sum is a just major third (5:4, 386.3 cents). The fifth in
> quarter-comma MT has a size of 696.6 cents. This can be tuned by ear by first
> setting a just major third and then tempering the intermediate fifths.

In practice it works better to start with the fifths and use the thirds
to check (Michael Praetorius 2. Art on p. 154 of "Syntagma musicum" Vol.
II De Organographia). To set a good meantone temperament is *not easy
and .

> The major variants of MT include:

> Third-comma MT

> Fifth-comma, where an octave-reduced just major seventh (15:8, 1088.3
> cents) is
> the sum of five fifths of 697.6 cents),

and the beat rates of the major third and the fifths are virtually the
same, making this type of temperament very "harmonious" - works
especially well on organs.

> Sixth-comma, where an octave-reduced just augmented fourth (45:32, 590.2 cents)
> is the sum of six fifths of 698.4 cents). After quarter-comma MT,
> sixth-tone temperament was the most widely used, especially in organs of
> the late baroque and classical eras.

I wonder a bit whether this can be established from analysis of existing instruments

> with each additional tone adding an additional available tonality. MT
> instruments with more than 12 keys per octave were not unknown,

Not unknown? Rather frequent, in certain places, at certain times.
I think it was rather frequent at places with a professional music in
Italy (mid-15th century to mid 17th century) and spreading to German
speaking or German influenced countries where we know of orgas with up
to 16 keys per octave in the time from 1612 to 1721.
From a literature survey I count now more than 70 organs from small
positives to 3-manual instruments which have had subsemitones.

An overview [in Dutch] and the most recent list (understandable to
anyone, even if not reading Dutch) can be found here

Ibo Ortgies: "Subsemitoetsen bij historische orgels tussen 1468 en 1721
[Split keys on historical organs between 1468 and 1721]."
Het Orgel [Netherlands] 96, no. 6 (2000): 20-26. [includes an english
summary, but very short]

The same article in Swedish or German, only that the lists do not
contain one resp. two organs which I found later.
ï¿½ï¿½ï¿½. "Subsemitoner i historiska orglar. En ï¿½verblick ï¿½ver utvecklingen
mellan 1468 och 1721."
Tidig Musik [Sweden], no. 2 (2000): 26-31.
ï¿½ï¿½ï¿½. "Subsemitonien in historischen Orgeln. Ein ï¿½berblick ï¿½ber die
Entwicklung zwischen 1468 und 1721."
Concerto [Germany] 17, no. 156 (2000): 22-25.

The Stellwagen Brustwerk in Aegidien, Lï¿½beck, mentioned above, I
discovered later, could not be included, but in my later "catalogue"
still to be published it will be in detail.

> and G.F.Hï¿½ndel owned instruments with 14 and 16 keys per octave.

Please give the source - until now I could only find that the Parker
organ in the foundling hospital had a lever system (no split keys for
the subsemitones - but that was built ca. 10 years after Handel's death.

Of course there was also Bernard Smith's (Bernhard Schmidt) organ in
Temple church, London, with it's eb/d#-s and g#/ab-s

> ... Common usage of MT or MT
> variants continued well into the 19th century with its final replacement by
> various well temperaments and 12tet occuring definitively only around
> 1850. MT
> has been widely revived for performances of early music; modern tracker organs
> in MT are not uncommon.

Unfortunately they *are still uncommon, only a few around evreywhere...

> ... qualities of MT were assumed by composers and
> positively reflected in musical repertoire.
> ... when minor, a preference for g)

or d

> ; a limited range of usable tonalities (typically Eb to A);
> a leading tone significantly lower than that of pythagorean or 12tet;

s. above

> ... (indeed, the MT augmented sixth is a good approximation of a 7:4).

Which seems to have been used by composers like G.Frescobaldi,
J.J.Froberger, J.C.F.Fischer
(wonder why all begin with F, which I instantly remember)

Very good FAQ-start!

> DJW

Kind regards
Ibo Ortgies

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

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

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

Answer to several postings

"Graham Breed" <graham@microtonal.co.uk>
"Paul H. Erlich" <PERLICH@ACADIAN-ASSET.COM>
Dale Carr <d.c.carr@obgron.nl>
Herman Miller <hmiller@IO.COM>
"Daniel Wolf" <djwolf1@matavnet.hu>

kind regards
Ibo Ortgies

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

Date: Wed, 21 Feb 2001 17:50:21 -0000
From: "Graham Breed" <graham@microtonal.co.uk>
Subject: Re: Gesualdo / intonation / Meantone / FAQ

Ibo Ortgies wrote:

talking of leading tones
> > Please explain, why "narrow" (in meantone temperament, which we are
> > speaking of heree in relation to Gesualdo)?

Graham Breed:

> I'm taking "leading tone" to mean any semitone used in a resolution.

depending on the point of departure

Ll. S. Lloyd ("Intervals, Scales and Temperaments" London, 1963, 1978),
p. 48
"Then there is the violinist's practice of closing the leading note as
to bring it nearer to the tonic in a melodic line when there is no
dominant sounding with it to control its intonation."

> It's generally considered that the smaller leading tones of
> Pythagorean intonation are preferable to the larger ones of meantone.

"Generally" - hmm, as generally as this example:
If you look in legion of music books, encyclopedias, etc. it is also
"generally" considered that Bach used 12-ET, and that it was invented by Werckmeister

> I don't know if this is accurate for Gesualdo's time, but hey, I'm
> not a historian.

But hey, it's historic stuff we are talking about... without historical
knowledge we'll land pretty soon off-road

Percy Buck (1871-1947):
"Music came first; then the scales accrued after ages of experiment;
then came the theorists to explain them. And as they know more
about mathematics than of musical history they laid down laws
which, in actual fact, no human being had ever obeyed."

I wouldn't agree wholly with his statement, but I believe the root of
the matter is that we should regard history and the math, both necessary
to understand phenomena better.

> 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

> > In "meantone" temperament a major semitone (the "leading" tone in a
> > discant clause) would have 117 cents, the minor semitone 76 cents
> > chromatic. Depending on the bass line (not a part, but as a "basso
> > seguente", taking always the lowest sounding note...) the leading
> > tone might even be larger (s. even below) ...

> As an example, take a G7-C cadence. That has two semitone steps, B-C
> and F-E. You can narrow either of these to a minor semitone by
> replacing B with B^(Cb) or F with Fv(E#). The former happens to give
> you a 9-limit chord, the latter a 7-limit one.

> But let's put 9-limit harmony aside. In which case, a seventh chord
> is dissonant however you spell it. So why is it used? To give
> semitonal motion. A note is added to the G major chord to give it a
> semitone from a note in the C major chord.

In the music of the vocal polyphony "meantone era" it was not added -
treatment of dissonances was a part of counterpoint/voice leading. An
"f" above "g" in a piece of Gesualdo could only be a (meantone) f. The
sequence g-e#-e (replacing g-f-d) would not occur. And: we talking about
vocal compositions, which probably were rehearsed and accompanied with
19- or 31 note keyboards.

> If you have 12 pitch
> classes, it doesn't matter if that note is F or E#, but you call it F
> because it fits a C major key and gives a minor third B-F.

minor third: D-F (?)

...
> If Gesualdo were using 19 pitch classes, and expected his singers to
> narrow leading tones,

... 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.

> 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?

> So either leading tones were
> not in fashion, he was cloth-eared, or he was using 12 pitch classes
> and tuning/spelling for 5-limit intervals.

Nothing of this I regard as right
- leading tones (as large semitones) occurred in evrey discant clause
- that Gesualdo might have been cloth-eared,
- 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)
- he would have used the terminology of his time, one aspect of which
might be describable with the modern X-limit-concept.

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

> 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?

> The upshot of all this is that the use of meantone by Gesualdo (and,
> it appears, his contemporaries) isn't that interesting.

Not intersting to you (what a pity)
- and again, how can you judge without referring to the historical background?
No one has the *full historical background of course, but we are
striving, hopefully.

> ... They were using a few keyboards with more than 12
> notes to the octave,

Especially at the Italian centers of madrigal-composition there were many:
See:

Stembridge, Christopher: "The Cimbalo Cromatico and other Italian
Keyboard Instruments with Nineteen or More Divisions to the Octave."
Performance Practice Review 6 (1993): 33-59.

Stembridge, Christopher, and Denzil Wraight: "Italian Split-keyed
Instruments with Fewer than Nineteen divisions to the Octave."
Performance Practice Review 7 (1994): 150-181.

Stembridge, Christopher: "Italian organ music to Frescobaldi." In The
Cambridge Companion to the Organ, edited by Nicholas J. Thistlethwaite
and Geoffrey Webber, 148-163. Cambridge, 1998.

> 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.

> They don't stand as models for the modern Xenharmonicist in the way
> that Vicentino does.

> That's what I'm arguing. It's entirely consistent with received
> opinion,

sorry, I disagree completely - it's your opinion and certainly the
opinion of other, also honorable people, too

> but I had to go to the scores to convince myself of it.

Yes, do that, I'd like to do it much more myself, too.

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

Date: Wed, 21 Feb 2001 17:00:53 -0500
From: "Paul H. Erlich" <PERLICH@ACADIAN-ASSET.COM>
Subject: RE: Gesualdo / intonation / Meantone / FAQ

> Ibo wrote,

> >Do singers really sing in 12-ET? - I think it is a myth.

> Well, clearly they're not exact like a synthesizer, but also, wouldn't you
> agree that intervals today are sung much closer to 12-tET than how they were
> sung c.1480-1725?

certainly I'd agree with the last part of sentence. But the degree of
exactness which modern trained singers reach with deviaton of let's say
+/- 10 cent per tone, + Vibrato of something between another +/-10 to
+/-40 cent leaves it pretty menaingless that they have (usually) any
clue of intonation at all. And since this is hardly any adressed in
public criticism (how false sings Pavarotti?) it get's never out of
"our" circles.

> > > ... After quarter-comma MT,
> > > sixth-tone temperament was the most widely used, especially in organs of
> > > the late baroque and classical eras.

> I've seen some analyses to this effect, but typically the accuracy is not
> sufficient to distinguish 1/6-comma from, say, 1/5-comma or 1/7-comma.

To my knowledge temperaments can sometimes be analyzed quite good - if
there are pipes basically untouched, seldom, but occurs.

> >> and G.F.Hï¿½ndel owned instruments with 14 and 16 keys per octave.

> >Please give the source

> I posted three or four sources for this -- perhaps search the archives for
> "Handel".

I couldn't find it, I tried keywords Handel, Hï¿½ndel, Handel + Ehrlich ...
Please be so kind to share the complete information as I do here:

Stephen Bicknell, the English organ expert, answered my question to the
use of instruments with split keys in Handel's time some time ago:

Bernard Smith built two well-known organs with split keys at the Temple
Church London (1684) and Durham Cathedral (1685). These had 14 keys
to the
octave, with separate keys for d#/eb and g#/ab.

In 1768 an organ was built for the Foundling Hospital, London by Thomas
Parker. This instrument replaced an unsucessful organ built in 1750 by
Justinian Morse and paid for by Handel.
Parker's organ had levers at the console, two for each of the three
manuals. One gave c# and eb at rest, c# and d# when moved to the left,
and db and eb when moved to the right. The other gave g# and bb at
rest, ab and bb when moved to the left, and g# and a# when moved to
the right.

It is often assumed that this was a 'Handel' organ, but of course Handel
died in 1759, before the Parker organ was built. It is not known whether
the Morse organ also had 'extra' notes. However, it is said that Handel
often went to hear John Stanley play at the Temple Church. I cannot give
you a source for this information but I imagine it probably comes from
Hawkins or Burney.

-------------------------------
> Date: Wed, 21 Feb 2001 16:44:39 -0500
> From: "Paul H. Erlich" <PERLICH@ACADIAN-ASSET.COM>
> Subject: RE: Draft: What is meantone (MT)?

> Daniel wrote,
> >MT was the pre-eminent keyboard tuning in the 17th and 18th centuries.

> It seems, from all of Margo's posts, that the 16th would be included as well,
...

in the second half of the 15th century already, as can be shown in instruments.
It took of course some time to switch from pythagorean tuning and music
to meantone practice.

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

> Message: 20
> Date: Wed, 21 Feb 2001 22:40:33 +0100
> From: dcc <d.c.carr@obgron.nl>
> Subject: Re: Draft: What is meantone (MT)?

> ï¿½ale C. Carr

> WHAT IS MEANTONE (MT)?

> MT instruments with more than 12 keys per octave were not unknown, and
> G.F.Hï¿½ndel owned instruments with 14 and 16 keys per octave.

> ###It would surely be more to the point to refer to split key instruments from the heyday of MT,
> the 16th and 17th centuries. Hï¿½ndel's instrument was exceptional rather than even slightly
> representative.###

We don't know whether Hï¿½ndel had that instrument all seem to think he
had (the Parker -Organ, s. above).
Judging from his music (it's dangerous) I'd say, he is a
"meantone-composer", and it's not unlikely that he had those
instruments, but not more.

> MT was the pre-eminent keyboard tuning in the 17th and 18th centuries.

I'd subtract ca. 100 years or more:
what about the 13th ct. with the Summer-canon,
making use of I-ii-I-vii/dim-III-I

A - E
/ \ / \
F - C - G - D
\ /
Bb

The Bb in the g-minor chord (ii) and the diminished chord on the seventh
step sounds strange in relation to the final
F-major chord. Meantone/flexible-just-intonation would be my preferable choice

- but Dale has also a good point here:
> ###Again, this historical statement is unjustifiably broad.

> A historical atlas of the spread of
> MT in Europe would be fascinating; so far as I am aware, nobody has yet attempted it.

Great idea, in my subsemitone-organ research at least a pattern can be
seen, how that field spread (Dale knows it)
Starting (as much as we know) in Italy, probably already by
splitting/adding keys in pythagorean tuned instruments. It spread
probably first to related areas, f. ex. Spain (only a few instruments
known right now),
beginning of the 17th century Germany, which was totally dominated by
Italian musical culture then became the northern turntable (in Italy the
last instrument known to me now, was built in the late 1660ies). German
organ builders working took the idea to the Netherlands, Denmark,
Switzerland, Sweden, and Britain. Only in Sweden, heavily German
influenced, domestic/native swedish organ builders are known to have
taken over the practice.

All this depends of course from the amount of evidence and it's evaluation.

> In Italy,
> England, & France it may indeed have been common *for organs* until the late 18th C.,

In Britain and some parts of the USA (New England) it seems to have been frequent.
Again quotin Lloyd (p.66):
"The tuning of organs in mean-tone temperament was the rule in the first
half of the 19th century."

In Britain pianos seem to have been *often tuned in meantone tuning
(quarter comma) until ca. 1850, as well.

Until the end of the century this was a controversial matter among
musicians, instrument builders, musicologists.

References:
Lloyd
and
Owen, Barbara. The Organ in New England. An Account of its Use and
Manufacture to the End of the Nineteenth Century.
Raleigh: The Sunbury Press, 1979.
Owen, Barbara. "Pitch and Tuning in eighteenth- and nineteenth-century
American Organs." The Organ Yearbook. A Journal for
the Players & Historians of Keyboard Instruments
[Netherlands] XV (1984): 54-59.

We might agree state, that the prevalence of meantone temperament was in
the time of renaissance vocal polyphony and it's aftermath,
ca. mid 15th century until the end of the 17th century
and it took ca. 150 years before and after to rise and demise.

> The
> earliest recorded description of a MT tuning procedure is usually
> attributed to Pietro Aron in his _Toscanella_ (Venice, 1523).

Aaron's "Toscanello" offers a temperament - a description taken from an
ANONYMOUS letter, so it can not be stated safely, that this is AARONS
way of temperament/tuning! - which at best only approximates
meantone-temperament.
Lindley and Ratte have questioned the 1/4-comma-meantone-interpretation.
Ratte states that Aaron otherwise strictly acts for the pythagorean
theory and that the theorists of the 16th century didn't interpret the
instruction quoted by Aaron as 1/4-comma temperament.

The first theoretical description, leaving no doubt, seems to be
Zarlino's "Dimostrationi harmoniche", Venezia 1571, which he calls "un
nouo Temperamento" - "a new temperament".

> Common usage of MT or
> MT
> variants continued well into the 19th century with its final
> replacement by
> various well temperaments and 12tet occuring definitively only around
> 1850. MT
> has been widely revived for performances of early music; modern
> tracker organs
> in MT are not uncommon.

> ###I wish it were so! By far the most non-ET modern organs are tuned in something between MT &
> 12-tet. Even historical organs when 'historically' restored are far too often tuned to a
> temperament which makes possible performance of Bach's organ works, whether this repertoire is
> relevant to the style of the instrument or not.###

sigh! - yes. I know of one organ where the original temperament (1797)
could be detected having 1/3-comma and 1/6-comma tempered fifths. This
was "equalized" in the restoration to a more regular 1/6-comma modified
meantone. I think they should first try out the original temperament.
When it is completely unuseful, from the point of the improvisational
practice of the time of its origin and of repertoire which might have
been available at that place, then it might be considered to be possible
to modify it slightly. And when arriving at that conclusion, hesitate
ten times before doing that to an original instrument. [not to be
misunderstood, this is not a reminder to Dale, whom I know, is perfectly
aware of this]

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

> Message: 2
> Date: Wed, 21 Feb 2001 23:39:17 -0500
> From: Herman Miller <hmiller@IO.COM>
> Subject: Re: Re: EDO and meantone for faq

> On Wed, 21 Feb 2001 14:08:31 +0200 (IST), Robert C Valentine
> <BVAL@IIL.INTEL.COM> wrote:

> >Experiences in 55 from list members?

just a question here, why isn't 53-ET adressed, basically a extension of
pythagorean tuning

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

> Date: Wed, 21 Feb 2001 23:45:58 -0500
> From: "Paul H. Erlich" <PERLICH@ACADIAN-ASSET.COM>
> Subject: RE: Re: Gesualdo

>. . . but who cares -- if you make good music, that's all that matters.

I disagree, otherwise we could immediately stop discussing our items
here. (but I'm not sure whether Paul's statement was meant ironically)

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

> Date: Wed, 21 Feb 2001 23:52:42 -0500
> From: "Paul H. Erlich" <PERLICH@ACADIAN-ASSET.COM>
> Subject: RE: Re: Gesualdo.2

> Johnny wrote,

> >Now, it would be nice if people had the abilities you want to register for
> >them, ability to memorize complex tempered relationships on an archicembalo
> >or related extra-keyed instrument,

> Nothing needs to be memorized except the familiar sizes of common melodic
> intervals ... Singing a melody
> within a strict-JI rendered counterpoint will necessitate a great deal more
> complexity than a near-enough-meantone singing.

It might be worth looking at singing and playing teaching books in the
meantone era and even later.
In the eighteenth century Mattheson, Walther, Quantz (traverse flute),
Agricola/Tosi (singing) , Mozart (violin), Tï¿½rk etc. refer still to the
just intervals like 5:4, 9:8, 16:15 these were books to train and to
practice with. The same authors write, that on the keyboard is a
temperament out of necessity. There you have the simultaneous dualism of intonation.
The same will be true for 17th-century writers (Bernhard, Douwes).

> >and the ability to recall and keep to the
> >exact pitch heights.

> Not so exact, and you notice it when it moves a comma.

I doubt that there practically is a comma shift.
I think continuo-practice is a key in this: it was so important to have
the strong sounding continuo, because it served an intonation aid. I
regard this aspect of continuo playing as primary, the rhythmic aspect
and keeping the ensemble "together" seems secondary. Since the bass
instruments have to provide the correct tone to intonate above and since
they have to obey the temperament.

> The musical sense does not have the grasp you attribute
> to it. The ease of providing pure harmonies independent of meantone theory
> makes much more musical and practical sense to me for Gesualdo than any
> other
> put forward. Clearly we each have areas of expertise that are greater than
> others and this may be a blind spot for either of us.

> >However, for Gesualdo, his music would have to be in
> >something fairly obvious, or he would have need to leave special
> instructions
> >for doing his music, if you get my drift.

> My drift is that a rough blurring of meantone was the only obvious tuning in
> his time and place, and unless we find any "special instructions", it's our
> best guess.

> ________________________________________________________________________
>
> Message: 25
> Date: Thu, 22 Feb 2001 10:18:05 +0100
> From: "Daniel Wolf" <djwolf1@matavnet.hu>
> Subject: Re: Meantone FAQ

> Some responses:

> (1) I stand by "modern tracker organs in MT are not uncommon". The adjective was
> very carefully chosen after doing a survey of all historical organ builders who
> have web sites. I think I turned up some 50 new or restored organs in MT, not
> including small continuo organs and the like.

Maybe today there are 50, 300, maybe 1.000 meantone organs
- of what total amount of organs (any estimate?) - 2 millions, 10 millions?

Is a percentage of certainly less than 1/1000 "not uncommon"?
It is uncommon - no doubt to me.

> (2) I have qualified the reference to the distribution of 1/6 comma meantone to
> specify a late era and specifically the association with the maker Silbermann
> (whose organs were so roundly praised by Mozart).

Silbermann seems to have used different temperaments, sometime forced
maybe by organ consultants.

...
> (4) Setting a meantone: do you start with a just third or with the fifths? I
> learned with the third first and can't imagine not having that reference point
> to work with.

that's perfectly fine with me, but others could (Praetorius) and can...

> So, here's the second draft:

> WHAT IS MEANTONE (MT)?

> (Second draft of a FAQ entry)

> The major historical variants of MT include:

How do you define "major" here? How do we find out whether a
descriptiuon of a theoretician was more or less common practice? -
especially of organ builders

> Third-comma MT, where an octave-reduced just major sixth (5:3, 884.4 cents) is
> the sum of three fifths of 693.3 cents),

> Fifth-comma, where an octave-reduced just major seventh (15:8, 1088.3 cents) is
> the sum of five fifths of 697.6 cents),

A "good" temperament, but not many historical sources to my knowledge -
how important was it?

> Sixth-comma, where an octave-reduced just augmented fourth (45:32, 590.2 cents)
> is the sum of six fifths of 698.4 cents). After quarter-comma MT, sixth-tone
> temperament was perhaps most widely used, especially in the organs of the late
> baroque and classical eras built by Silbermann.

There were many more organ builders than Silbermann and they as a
mjority use 1/6-th-comma-meantone?

...
> In quarter-comma meantone, with a keyboard of 12 keys per octave, eight major
> triads will have just major thirds, typically the triads on Eb through E.

In Italy (maybe Spain, too) it was in the beginning usually Ab - C#

> MT
> instruments with more than 12 keys per octave were not unknown,

... were in some regions rather frequent, but always a special case for
professional musicians

> 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.

> MT was the standard keyboard tuning in the 16th, 17th, and 18th centuries.
etc.

s. above

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

> Date: Thu, 22 Feb 2001 04:32:22 -0500
> From: "Paul H. Erlich" <PERLICH@ACADIAN-ASSET.COM>
> Subject: RE: Meantone FAQ

> Daniel Wolf wrote,

> >G.F.Hï¿½ndel
> >played on instruments with up to 16 keys per octave.

> up to 16 tones per octave, with enharmonic variants selected via organ stops
> rather than split keys.

again, s. above

> ________________________________________________________________________

> Date: Thu, 22 Feb 2001 11:40:39 +0100
> From: "Daniel Wolf" <djwolf1@matavnet.hu>
> Subject: Re: Keeper of the FAQ

> However, I would like to invite some others to write FAQs. If you are totally
> unwilling to do it yourself, can you help find someone who could?

> Specifically:

> Ibo Ortgies -- KEYBOARDS

agreed - coming backk soon....

> Now, who will volunteer, or be roped into volunteering, for any of the
> following:

> WHAT RECORDINGS ARE AVAILABLE IN HISTORICAL TUNINGS?

everyone...

> * If there are any list members in Japan who could do Tanaka, I'd be very
> pleased to yield on this one.

Here the report (F. Eckstein) about Anton Bruckner's fascination about
Tanaka playing on his "enharmonium" in Berlin could find a good place.

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

> Date: Thu, 22 Feb 2001 18:57:33 +0100
> From: "Daniel Wolf" <djwolf1@matavnet.hu>
> Subject: Re: Keeper of the FAQ

> Johnny Reinhard wrote:

> "The first meantone was not exactly 1/4 comma (Pietro Aaron)."

> Aron's tuning description can be reasonable read as an eleven tone quarter-comma

s. also bove

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

> Message: 25
> Date: Thu, 22 Feb 2001 15:33:33 EST
> From: Afmmjr@aol.com
> Subject: Re: Keeper of the FAQ
>
> Dear Daniel Wolf,

> ...

> It was of great interest to read why you chose certain things. Your reason
> to leave out your own meantone-tuned opera

Very interesting - where do/did you get singer's which are able to
perform that as intended.

> was similar to that of Walther
> (who was certainly deserving of being included in his Lexikon, but chose not
> to mention himself in his monumental work.
...

🔗graham@microtonal.co.uk

Ibo Ortgies wrote:

> > I don't know if this is accurate for Gesualdo's time, but hey, I'm
> > not a historian.
>
> But hey, it's historic stuff we are talking about... without historical
> knowledge we'll land pretty soon off-road

Yes, but I don't have to supply it.

> Percy Buck (1871-1947):
> "Music came first; then the scales accrued after ages of experiment;
> then came the theorists to explain them. And as they know more
> about mathematics than of musical history they laid down laws
> which, in actual fact, no human being had ever obeyed."
>
> I wouldn't agree wholly with his statement, but I believe the root of
> the matter is that we should regard history and the math, both necessary
> to understand phenomena better.

And music.

> > 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, or correcting for a
gradual upward drift?

> > If you have 12 pitch
> > classes, it doesn't matter if that note is F or E#, but you call it F
> > because it fits a C major key and gives a minor third B-F.
>
> minor third: D-F (?)

Looks like it.

> ...
> > If Gesualdo were using 19 pitch classes, and expected his singers to
> > narrow leading tones,
>
> ... 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? What does "discant clause" mean?

I've checked the definition of "leading note" and, sure enough, it isn't the
concept I intended. I was talking about all semitonal motion in a cadence.

> > 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. The word "then" means I'm not sure what
you're asking. Do you not see how motion by minor semitones would tend to follow
from the narrowing of semitones?

I now have that one example.

> > So either leading tones were
> > not in fashion, he was cloth-eared, or he was using 12 pitch classes
> > and tuning/spelling for 5-limit intervals.
>
> 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.

> - that Gesualdo might have been cloth-eared,

Indeed not. I never expected anybody to agree with that one.

> - 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?

> - 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.

> > 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. Saying something adds nothing to the argument, and then showing
the argument to be absurd without it is low rhetoric.

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

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:

1) Use 5-limit intervals vertically
2) No double sharps
3) Use 5-limit intervals for direct melodic steps
4) Use diatonic intervals melodically
5) Favour nominals

Everything I've seen so far obeys these rules. Note that this is a falsifiable
hypothesis! Find an examples that doesn't translate from 12 pitch classes to the
score following these rules, an it will show that Gesualdo did use more than 12
pitch classes.

In fact, I fully expect such an example to exist. I'm told he used augmented sixth
chords, and they would typically break rule 1. It may be more complex rules
operate, or different rules for different pieces, or there are a few special cases.
However, the majority of the music follows these rules, hence predominantly
requires only 12 pitch classes.

Note that rule 2 is added since the last message.

> > The upshot of all this is that the use of meantone by Gesualdo (and,
> > it appears, his contemporaries) isn't that interesting.
>
> Not intersting to you (what a pity)

I can only speak for myself

> - and again, how can you judge without referring to the historical
> background?

and I can be wrong. But I don't clutter my prose with disclaimers.

In fact, the examples I've seen more recently show that it is more interesting than
I thought, although only those few examples.

> No one has the *full historical background of course, but we are
> striving, hopefully.

I hope so.

> > ... They were using a few keyboards with more than 12
> > notes to the octave,
>
> Especially at the Italian centers of madrigal-composition there were
> many:
> See:

Thanks for the references. I'll see if I can find any of them.

> > 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!

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.

> > That's what I'm arguing. It's entirely consistent with received
> > opinion,
>
> sorry, I disagree completely - it's your opinion and certainly the
> opinion of other, also honorable people, too

What I meant was received opinion (and I didn't express myself clearly) is that
meantone was used to provide 5-limit intervals, not the greater 9-limit, and not
chromatic semitones unless the 5-limit spelling happens to fit that. I don't think
that's what you're disagreeing with.

Graham

🔗PERLICH@ACADIAN-ASSET.COM

🔗graham@microtonal.co.uk

🔗jpehrson@rcn.com

🔗Andreas Sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, Ibo Ortgies <ibo.ortgies@...> wrote:
on
> Date: Wed, 21 Feb 2001 17:00:53 -0500
> From: "Paul H. Erlich" <PERLICH@...>
> Subject: RE: ... / intonation / Meantone / FAQ
>
>Ibo asked:
>>>Do singers really sing in 12-ET? - I think it is a myth.
>P.H.Erlich replied:
>> Well, clearly they're not exact like a synthesizer,
>> but also, wouldn't you
>> agree that intervals today are sung much closer to 12-tET
>> than how they were sung c.1480-1725?
>
> certainly I'd agree with the last part of sentence.
> But the degree of
> exactness which modern trained singers reach with deviaton of let's
> say +/- 10 cent per tone, + Vibrato of something between another
> +/-10 to +/-40 cent leaves it pretty menaingless that they have
> (usually) any clue of intonation at all.
> And since this is hardly any adressed in
> public criticism (how false sings Pavarotti?) it get's never out of
> "our" circles.

but the meanwhile late
http://en.wikipedia.org/wiki/Luciano_Pavarotti
once had gained an somewhat better accuracy
in relative precision when singing intervals.

As far as i had listened to his records:
P's achieved an compareable degree of accuracy
as the Hillyard-ensemble:

I an questionable problematic source
there lacks the essential information
of the variance:
http://mto.societymusictheory.org/issues/mto.06.12.3/mto.06.12.3.duffin.html
Especially see there at footnote 9:
"9. Seashore and Barbour maintain that scooping and pitch wandering
make it impossible for singers to come reliably closer to a certain
frequency than about a fifth of a semitone. See Harold Seashore, "An
Objective Analysis of Artistic Singing," pp. 25-77, and Barbour Tuning
and Temperament, pp. 197-98. But the Hilliard Ensemble recording
excerpt given below, in a sampling of major chords at eleven points
throughout, gives an average major 10th (the most common voicing for
the third) with a ratio of 2.507 above the root. This compares with
the pure ratio of 2.500 and the ET ratio of 2.520, and represents a
predilection for thirds that are twice as close to pure as they are to
ET, as well as a tuning accuracy six times closer to the intended
frequency than that predicted above. The excerpt also ends with a
chord sustained with astonishingly pure tuning over a full eight
seconds duration. It takes remarkable precision and extraordinary
vocal control to maintain such a beautifully tuned chord for so long,
but this recording shows that it is possible, and that our
expectations for ensemble singing should be adjusted accordingly.
Indeed, even Ternström and Karna acknowledge that "vocal groups that
perform close harmony with one voice to a part ... strive to achieve
harmonies that are so precisely tuned and so straight in pitch that
the voices fuse together and we hear one instrumentlike chord rather
than several part singers." See "Choir," p. 280."

Thomas Dent reviewed that in:
/tuning/topicId_67834.html#67835

Unfortuantly beyond that vague speculations
R.Duffin gives no data for the corresponding variation at all.
That lack in data specification demands caution:
Hence we should touch his claimed values only carefully with a barge-pole.

At least the numerical deviation versus 5/2 can be calculated.
It amounts for:
(alleged Hillyard's octaved 3rds)/(octaved JI-3rds: 5/2 := 2*(5/4))
barely about:
1200 * ln(2.507/2.5) / ln(2) = ~4.84...Cents (+-?.??...Cents)
in difference only.
An objection stays open:
The experimental root mean standard-deviation remains unknown.

At least:
That given ~5Cents appears significant less than the 12-EDO 3rd's
1200 * ln(2.52/2.5) / ln(2) = ~13.79...Cents
chargeing the 3rds 3-times worser,
than in the above a-capella case.

There remains doubts in Duffin's interpretation
due to systematically incomplete data,

But -all in all- we may conclude carefully:
Sensitive HIP-Renaissance a-capella singers,
alike the Hillyard-ensemble, can probably
perfrom almost JI 3rds about ~3-times less beating than in 12-EDO,
especially in long lasting major chords
2:3:5
Discerning aware such audiable nuances
works only when singing fully free unaccompanied
without any continuo instrument.

But some fomous singers do pay attention to even more aspects as
for instance:
Attending the composers choice of the absolute-pitch.
Example:
Pavarotti demanded his personal preferred absolute pitch: 438Hz
May be:
probably because he judged himself that at that pitch his own voice
would sound the best.

Some evidence for that hypothesis delivers a quote from:
http://query.nytimes.com/gst/fullpage.html?res=950DE7D91239F932A35752C0A96F948260&sec=&spon=&pagewanted=all
"Mr. Pavarotti doubts that pitch will ever return to Verdi's
relatively deep standards. ''We must be careful to guard pitch at
around 440 - maybe even 438,'' he said recently. ''That is where the
juicy sound is.'' Juicy for him, that is to say. What Mr. Pavarotti
demonstrates here is that while pitch levels - and therefore written
roles - theoretically have an inviolate set of limits, individual
voices do not. Mr. Pavarotti, in other words, ''wears'' A-438
comfortably, the way a tall man might wear a suit sized 42 long."

That refers in G.Verdi's case to the dubious effords:
http://www.schillerinstitute.org/music/rev_verdituning.html

That open controversy comments critically:
http://www.dolmetsch.com/musictheory27.htm
"What one should make of these two extracts, the author leaves to his
reader, but it is worth pointing out that while the belief that Verdi
espoused the pitch a'=432 Hz. is supported by a letter from Verdi to
his librettist, Arrigo Boito, that advocated a lower pitch for
colouristic reasons, it is not at all clear that Verdi's suggestion
had any philosophical basis at all."

Never the less, another -more fertile- quote:
http://www.jackgrassel.com/pages/perfect_pitch.html
illustrates Pavarotti's insist on 438Hz
in an funny anecdote:

"One time I was to accompany Luciano Pavarotti on classical guitar at
one of his concerts. I knew that he specified in his contract that the
orchestra needed to tune to A 438. Before Luciano appeared at the
rehearsal, I heard the oboist produce an A 440 to tune the orchestra.
I didn't say anything and kept my guitar tuned to A 438.
(The "Perfect Pitch" person usually learns to keep his mouth shut
since he's in the minority)
Mr. Pavarotti came out and proceeded to start the rehearsal.
After a few bars, he stopped the orchestra and reprimanded the oboist
for tuning the orchestra to A 440.
The oboist played an A 440 and said it was A 438. Then Luciano sang a
perfect A 438, and had the orchestra tune to him."

An usual cat and mouse game of strategy,
that arises only
when oboist & soloist do both possess different APs.
Such little fights happen sometimes in order to fob each others.
They do continue usually only as long,
until one of them has enforced his own individual preferred AP
to the whole orchestre.
In most cases the chief-oboist wins the palm by default
against the conductor, soloists and all others, without any effort.

But in Pavarotti's particular case
the oboist lost the match embarassing
and had to cave downwards about 2Hz even until 438Hz.
That sounds remarkable ~1/3~SC flatter than normal 440Hz:

1200 * ln(440/438) / ln(2) = ~7.89...Cents

~(81:80)^(1/3) lower than the usual standard
http://en.wikipedia.org/wiki/A440

Liliana Gorini's
"In memoria di Luciano Pavarotti"
picks up that matter in Itlalian language:
http://www.movisol.org/07news143.htm
"...antanti lirici che sostennero la nostra iniziativa per tornare al
"La verdiano" (La=432 Hz, l'accordatura scientifica dell'orchestra
voluta da Giuseppe Verdi per decreto nel 1884)........
Boggio e Mezzapesa, inizialmente per rispettare il volere di Giuseppe
Verdi che nel decreto del 1884 parlava di La=432 Hz come "accordatura
scientifica", fu cambiato in La=440 Hz per compiacere i produttori di
strumenti a fiato, che altrimenti non avrebbero smaltito le loro
scorte, e l'iniziativa non ebbe quindi alcun seguito, perché non
rispettava più la volontà di Verdi..."

That confirms my own observation:
Only a few performers do still care still about proper
absolute-pitch that Verdi once wanted for his own works.

Quest:
Why insisted L.Pavarotti in his personal absolute pitch of 438cps?
as documented by his own colleauges that played along with himself?
For what reasons? we only can speculate.

Furthermore:
Would he also had liked the following 'septenarian' cycle of 5ths
for the other 11 open remaining notes
in order to complete the full dodecatonic scale:

Attempt:

A: 219 438Hz
E: 164 328 658 (< 659=3*A)
B: 491 (< 492=3*E)
F# 23 46 92 184 368 736 1472 (< 1473=3*B)
C# 69 = 3*F#
G# (13 26 52 104 208 416<)415(< 414 207 = 3*C#)
Eb 39 = 3*13
Bb 117 = 3*39
F: 175 330 (< 351 = 3*Bb)
C: 131 262 524 (< 525 = 3*F)
G: 98 196 392 (< 393 = 3*C)
D: (73 146 292 <) 293 (< 294 = 3*98)
A: 219 = 3*73

that yields in chromatically ascending order for the 12 keys:

C' 262 'middle_C'
C# 276
D' 293
Eb 312
E' 328
F' 350
F# 368
G' 392
G# 415
A' 438 Hz : Pavarotti's own choice
Bb 468
B' 491
c" 524 'tenor_C'

that dozen of integral frequencies corresponds in the:
http://www.xs4all.nl/~huygensf/scala/scl_format.html
and is equivalent the following 12 ratios:

!Pavarotti_438Hz.scl
!Proposal by A.Sparschuh for easier singing together with continuo
!
sounds best @ Luciano Pavarotti's own demanded absolute pitch: 438Hz
!
12
!
138/131 ! C#
293/262 ! D
156/131 ! Eb
164/131 ! E
175/131 ! F
184/131 ! F#
196/131 ! G
415/262 ! G#
219/131 ! A or 438Hz/262Hz = (abs. normal-pitch)/(abs. 'middle_C')
234/131 ! Bb
491/262 ! B
2/1 ! c
!
!

Who in that group here can present even better such well singable
frequency-ratios for Pavarotti's initial 438cps reference-tone?

Also attend:
The above tuning works well too
for 19.th century Hist.Inf.Perf.
in the good old times of:
http://www.mcgee-flutes.com/eng_pitch.html
http://www.musizworms.org/cgi-bin/utmw/topic_show.cgi?id=3738&bpg=1&age=0

" RECENT HISTORY

The tide was turned when, in 1859, a French government commission
made A=435 Hz law in that country. At the urging of singers in certain
German and London opera houses, this standard was adopted for a time
in opera houses and concert halls in other parts of Europe also.
(Imagine all the new wind instruments that needed to be made and
bought, also the tuning forks.) A=435 Hz was a compromise between
A=450 Hz, which was too high for singers, and A=422 Hz, which would
not please audiences that had become accustomed to much more
brilliance. Of course, other than in France, there was no reason that
bands and orchestras should consider themselves forever constrained by
A=435 Hz and the reduction in brilliance compared to the recent past.
In any case, Britain in the last decades of the nineteenth century
went its own way. In 1896, London's Royal Philharmonic Society got
around the practice of A=435 Hz in what appears to have been a
contrived way. By the 1880s, scientists were able to calculate the
amount by which the pitch of a wind instrument varies with room
temperature. In Britain it was a common, but erroneous, belief that
when the 1859 French commission decreed A=435 Hz, it had not specified
an absolute frequency, but had specified 59o F as the room temperature
under which the particular construction of the pitch-giving instrument
(oboe) played A=435 Hz. The Philharmonic Society, on the advice of
their consultant, therefore reasoned that the same instrument, at
normal room temperature, 68o F, would play the A above middle C as:
435 + [(68-59)÷1000 × 435] = 438.915 Hz

which is A=439 Hz to the nearest integer. As a result, in 1896, A=439
Hz became a recognized pitch standard in Britain. In North America,
meanwhile, the pitch of pianos and orchestras not only remained
unstandardized in the first decades of the twentieth century but
continued to creep upward..."

Try also an other view:
http://drjazz.ca/musicians/pitchhistory.html

Yours Sincerely
A.S.