Yahoo Tuning Groups Ultimate Backup tuning Tuning in reverberant spaces

> [Paul Griffiths, New York Times review of 1999 AFMM 'Finale']
>> which was held, regrettably, in St. Paul's Chapel
>> on the Columbia University campus -- a space
>> whose long reverberation fuzzed some of the
>> subtlety of shape that made the music special.
>
> [Clif Ashcraft, TD 202.1]
> I think it no accident that music based on anything other than
> the just diatonic scale is "fuzzed" in an acoustic environment
> having a long reverberation time. The prevalence of the diatonic
> scale (or close approximations to it) in music having its roots
> in the European Classical tradition is probably a direct
> consequence of the evolution of medieval plainsong chants in
> structures (monasteries and cathedrals) having long reverberation
> times. These chants only "work" in such an environment if all
> of the notes of the scale are consonant with the reverberations
> of previously sounded notes. Simply singing a just diatonic scale
> in such an environment creates beautiful harmonies.

[Fred Reinagel, TD 202.4]
> I have always been strongly convinced that Medieval chant
> historically used strictly Pythagorean tuning (Margo?), which
> would make all the 4ths and 5ths pure, but 3rds and 6ths far from
> consonant. Also, a JI diatonic scale has a wolf 5th between the
> 2nd and 6th degrees, so it is not possible for _all_ the notes of
> the scale to be consonant with the reverberations of previously
> sounded notes.

The diatonic scale has been the 'basic' scale of European music
since the time of the ancient Greek theoretical treatises
(starting with Aristoxenus, c. 330 BC), way before plainchant and
cathedrals.

Altho Greek treatises discuss the chromatic and enharmonic genera,
they generally state that these had fallen out of use and that
the diatonic was the only one left. This is somewhat contradicted
by Ptolemy (c. 150 AD) who made accurate measurements of the intervals in
all types of scales *actually in use*, but by the
time of the beginnings of Roman-Catholic plainchant (post-
Germanic-invasion, c. 600 AD), the only genus left in use was
indeed the diatonic; this, at least, is according to all extant
theoretical descriptions.

It's also quite possible that, due to the tremendous reduction
in literacy and to the inability of the German monks to read Greek
(or Latin, for that matter), the other genera were still in use
and the theorists simply did not know how to deal with or
explain the numerical measurements: it's much easier to understand
and explain a cycle of powers of 3.

Of course, there's no way for us to be absolutely sure about
what tuning was used in purely vocal music 1000 years ago.
But evidence indicates that for vocal church music, Pythagorean
(3-limit) tuning was the one generally (or possibly even
exclusively) used until about the 1300s, by 1490 almost everyone
was arguing about whether the tuning should be Pythagorean or
Just (5-limit), and by 1558 in Italy (Zarlino) and 1612 in
Germany (Lippius) 5-limit was pretty widely accepted as the
'standard'. (And remember, theoretical description *always*
lags behind the practice it's describing.)

I've posted here before on my theory that the main reason
for the shift in tuning was the acoustical perceptions resulting
from performance in the cathedrals of Europe, whose large
enclosed spaces and high ceilings were made possible only with
the 'Gothic' architectural advances of the late 1100s. I've
argued that the long reverberation times would have reinforced
the volume or extended the apparent duration of the stronger
overtones, allowing perceptive listeners to hear higher-limit JI
harmonies arising from the mass of sound emanating from the choir.

And it *is* possible to perform plainchant in a JI scale with
*every* note consonant with those already being heard - it
just wouldn't be a type of scale that we usually recognize as
a 'basic' scale.

This really doesn't have much bearing on the question anyway,
because by the time period under consideration, unaccompanied
monodic plainchant had mostly disappeared from the church rituals.
Since the Ars Nova movement in Paris in the 1200s, most church
music thruout Europe had become quite emphatically polyphonic.

Of course, Marchetto of Padua in 1318 discussed the use of
intervals smaller than the 'standard' Pythagorean semitones.
But because of his obscure numerical descriptions, exactly what
he meant is not entirely clear. See [plug alert]:

http://www.ixpres.com/interval/monzo/marchet/marchet.htm

There is also evidence suggesting that the shift from Pythagorean
to Just was already in process in English popular music as early
as the 1200s (see Walter Odington and Theinred of Dover).

So based on my historical knowledge, it appears that the use
of polyphony, the tuning shift from 3- to 5-limit in 'serious'
music, and the building of Gothic cathedrals, are all intertwined,
taking place largely during the 1200s and 1300s.

-monz

Joseph L. Monzo monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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🔗Rosati <dante@xxx.xxxxxxxxx.xxxx>

>From: monz@juno.com
>
>The diatonic scale has been the 'basic' scale of European music
>since the time of the ancient Greek theoretical treatises
>(starting with Aristoxenus, c. 330 BC), way before plainchant and
>cathedrals.

I believe the evidence is that the greeks got the diatonic scale from the
Babylonians.

>Of course, there's no way for us to be absolutely sure about
>what tuning was used in purely vocal music 1000 years ago.
>But evidence indicates that for vocal church music, Pythagorean
>(3-limit) tuning was the one generally (or possibly even
>exclusively) used until about the 1300s, by 1490 almost everyone
>was arguing about whether the tuning should be Pythagorean or
>Just (5-limit), and by 1558 in Italy (Zarlino) and 1612 in
>Germany (Lippius) 5-limit was pretty widely accepted as the
>'standard'. (And remember, theoretical description *always*
>lags behind the practice it's describing.)

Aristoxenus was already complaining in the 4th. c. B.C. that musicians
tended to "sweeten" the ditone in the enharmonic tetrachord. The way you
sweeten a ditone is move it towards 5/4. I think the urge to do this is so
deeply built into our ears, both physiologically and psychologically, that
you would have to put a gun to most singers heads to get them to sing
ditones a capella.

Archytas, Plato's bud, used 5/4 in his enharmonic tetrachord.

dante

🔗mr392@xxxxx.xxxxxxxxxxxxxxxx)

🔗David Beardsley <xouoxno@home.com>

🔗Tony Butera <mr392@webtv.net>

🔗Paul H. Erlich <PErlich@xxxxxxxxxxxxx.xxxx>

>Clif Ashcraft wrote:

>>These chants only "work" in such an environment if _all_ of the notes of
the scale are >_consonant_ with the >reverberations of previously sounded
notes. Simply singing a _just_ >diatonic scale in such an environment
>creates beautiful harmonies.

Fred Reinagel wrote,

>I have always been strongly convinced that Medieval chant historically
>used strictly Pythagorean tuning (Margo?), which would make all the 4ths
>and 5ths pure, but 3rds and 6ths far from consonant.

As Margo replied, the Pythagoean 3rds and 6ths are "relatively concordant"
-- noticably worse than those of 12-tET, but still useable enough to act as
consonances in some fast-paced 18th century music when keys with lots of
accidentals were employed in typical varieties of well-temperament.

>Also, a JI
>diatonic scale has a wolf 5th between the 2nd and 6th degrees, so it is
>not possible for _all_ the notes of the scale to be consonant with the
>reverberations of previously sounded notes.

>- Fred

I would use not JI but meantone tuning to ensure that a diatonic scale
maximizes self-consonance (in the 5-limit), and 40:27 wolf fifths are
avoided. However, diatonic seconds, sevenths, and the tritone will always
create dissonance (by 5-limit standards) against the reverberations, so the
goal of having _all_ notes consonant with all others is unattainable anyway.
Nevertheless, a heavily reverberating diatonic "mush" is one of the most
pleasant sounds in the world. In addition to the meantone and Pythagorean
varieties, I would add (you guessed it) the 22-tET diatonic scale (in
"Pythagorean" rather than "just" conception), where the fifths are
acceptable, the minor thirds are very close to 7:6, the major thirds are
extremely close to 9:7, and the minor sevenths are decent approximations of
7:4s. The minor seconds of 55 cents are very dissonant but very beautiful in
the context of these higher-limit yet comprehensible consonances. Many JI
composers (such as Micheal Harrison) have used a similar scale, 1/1 9/8 7/6
4/3 3/2 14/9 7/4, for droney reverberant stuff, but 22-tET eliminates the
"wolf" fifth of 32:21 between the 7/4 and the 4/3, much as meantone tunings
eliminate the 40:27 wolf.

Joe Monzo wrote,

>and by 1558 in Italy (Zarlino) and 1612 in
>Germany (Lippius) 5-limit was pretty widely accepted as the
>'standard'.

5-limit was accepted as the standard as an ideal for each consonant
interval, but in practice, the 5-limit JI scale had very little importance.
Meantone tuning was accepted as the standard during this period (Zarlino was
no exception!), and if you like to start with the 5-limit JI scale as your
ideal, meantone tuning was necessary in order to eliminate the one wolf
fifth and the one Pythagoean minor third from the former.

>And it *is* possible to perform plainchant in a JI scale with
>*every* note consonant with those already being heard - it
>just wouldn't be a type of scale that we usually recognize as
>a 'basic' scale.

OK, Joe, tell us how this magic is done.

🔗David J. Finnamore <dfin@xxxxxxxxx.xxxx>

dante wrote:

>Aristoxenus was already complaining in the 4th. c. B.C. that musicians
>tended to "sweeten" the ditone in the enharmonic tetrachord. The way you
>sweeten a ditone is move it towards 5/4. I think the urge to do this is so
>deeply built into our ears, both physiologically and psychologically, that
>you would have to put a gun to most singers heads to get them to sing
>ditones a capella.

You could resort to threats of violence. Or you could
simply start musicians on piano lessons at an early age.
It's my perception that most pianists who also sing, tend to
intone closer to 12t-ET than to JI.

It also seems to me that American recordings of Renaissance
motets and other 5-lim choral works tend to be less Just
than European recordings of the same. What would cause
that, I wonder? Anyone else noticed that? I listen with
almost obsessive compulsion to the U. S. NPR show
"Harmonia," which provides ample examples for comparative
analysis. The French and Italian groups, particularly, are
usually right in tune.

David J. Finnamore
Just tune it!

🔗David J. Finnamore <dfin@bellsouth.net>

On Thu, 3 Jun 1999, in TD 203.4, Monz wrote:

> I've posted here before on my theory that the main reason
> for the shift in tuning was the acoustical perceptions resulting
> from performance in the cathedrals of Europe, whose large
> enclosed spaces and high ceilings were made possible only with
> the 'Gothic' architectural advances of the late 1100s. I've
> argued that the long reverberation times would have reinforced
> the volume or extended the apparent duration of the stronger
> overtones, allowing perceptive listeners to hear higher-limit JI
> harmonies arising from the mass of sound emanating from the choir.

I thought I also remembered him opining something to the
effect that he would be really surprised if plain chant sung
in cathedrals was not practically always sung in 5-limit
JI. (I can't find that quote and I don't want to put words
in your mouth so please call me on it if necessary.) And,
of course, a little discussion of medieval theory and
speculation on practice ensued.

Actual audio recordings from before the 12th century being
somewhat rare, I substituted the famous "Chant" CD by the
Benedictine Monks of Santo Domingo de Silos. It was
recorded in a suitably reverberant environment (sounds like
about 8 - 10 secs. of RT60!) by real live monks who claim,
as I understand it, to be carrying on the ancient tradition
as closely as anyone knows how. (I also understand that not
everyone agrees that their methods are "authentic." Big
surprise.)

Thanks to someone's (Dante's?) mention of the Spectrogram
software, I was able to do more than analyze by ear this
time :-) So far I've only looked at one cut, "Media vita in
morte sumus," which has a relative preponderance of leaps by
third for plain chant. It even has a few "minor triads"
outlined melodically. (According to the cover, it's in Modo
IV.)

Like Margo and Paul E., I fully expected the thirds to come
out mostly Pythagorean and partly miscellaneous with no
particular bias toward 5-limit intonation. Instead, I found
that the monks did indeed tune the majority of the thirds to
5/4 and 6/5. If you account for the pitch scoops and a
gradual drift flat over the first couple of minutes
(probably not commatic, of course), the whole tuning is so
close to pure 5-limit JI so much of the time that it's just
plain scary.

Granted, these are 20th century monks, so maybe they've been
"polluted" by exposure to tonal music. Anyway, it's as
close as I know how to come to finding some evidence one way
or the other. I present it, and leave it to each judge to
weigh or throw out, as you wish.

David J. Finnamore
Just tune it!
Yeah, like the Monks of Santo Domingo de Silos do.

🔗Rosati <dante@pop.interport.net>

>From: "David J. Finnamore" <dfin@bellsouth.net>
>
>Thanks to someone's (Dante's?) mention of the Spectrogram
>software, I was able to do more than analyze by ear this
>time :-) So far I've only looked at one cut, "Media vita in
>morte sumus," which has a relative preponderance of leaps by
>third for plain chant. It even has a few "minor triads"
>outlined melodically. (According to the cover, it's in Modo
>IV.)
>
>Like Margo and Paul E., I fully expected the thirds to come
>out mostly Pythagorean and partly miscellaneous with no
>particular bias toward 5-limit intonation. Instead, I found
>that the monks did indeed tune the majority of the thirds to
>5/4 and 6/5. If you account for the pitch scoops and a
>gradual drift flat over the first couple of minutes
>(probably not commatic, of course), the whole tuning is so
>close to pure 5-limit JI so much of the time that it's just
>plain scary.
>
>Granted, these are 20th century monks, so maybe they've been
>"polluted" by exposure to tonal music. Anyway, it's as
>close as I know how to come to finding some evidence one way
>or the other. I present it, and leave it to each judge to
>weigh or throw out, as you wish.

Way to go David! This is what we need to do. If a bunch of us look at the
spectrograms of 1)A capella vocal recordings, both solo and ensemble, and 2)
Unaccompanied strings, from violin solo to string quartet to string
orchestra, I believe some light may be shed on some of the issues we hold
dear here.

You can use a program like Nexencode to rip a track off the CD and save it
as a .wav file. Then use CoolEdit to trim it to a smaller section of the
track, if appropriate. You may also want to downsample the file to 22050 to
make 11025 the highest frequency shown. Then use Spectrogram to view the
spectrum in real time and do an analysis where frequencies can be read off
with the cursor.

try mp3.com to get a cd ripper. Coodedit is at syntrillium.com and I don't
remember where I got Spectrogram, try typing something like "spectrogram
windows (or Mac) software" into a search engine.

Im sure all this can be done on a Mac too, but my krusty old Quadra cant run
powermac software so im not up on whats available floating around out there.

I've just begun looking at the Hilliard ensemble's recording of the Machaut
Mass. It will be interesting to see if highly trained singers can actually
sing in pythagorean intonation!