Yahoo Tuning Groups Ultimate Backup tuning tuning in reverberant spaces

[Paul Erlich, TD 204.11]
>
>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.

This is only true of instrumental music, which was still only
a minor part of serious music-making during this time-period.

The significant compositions were purely vocal, *perhaps*
accompanied by the organ, and when not accompanied, were presumed
to be in performed in just-intonation; _a cappella_, it *couldn't*
be anything else but JI!

Instrumental music didn't gain stature in a serious way until
after the invention of opera, c. 1600.

On the one hand, the overtures of operas (called 'sinfonia') got
larger and longer, until they became substantial enough to be
performed as separate compositions in their own right, eventually
morphing into what became symphonies during the classical period
(mid-to-late 1700s).

On the other hand, the rise of instrumental virtuosi, first
on the lute and then on the keyboard, developed along with the
rise of opera, the continual improvement in instrument design
and manufacture, and changing economic and social conditions
for musicians (and European people in general).

In any case, a temperament would not be significant for European
music until the late 1500s (Vincentino, Zarlino, Salinas) at the
*earliest*.

Given the fact that I believe 5-limit JI was used in practice
by 1300 (and perhaps long before that), that leaves *at least*
two and a half centuries during which, I would argue, unaccompanied
singers routinely used 5-limit JI.

>> [me, monz]
>> 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.

Simple: it's not magic, you're just forgetting that we're
not talking about harmony here, we're talking about *monophonic*
unaccompanied plainchant.

What I meant was that if the melody were such that a certain
note may require two different tunings (say, a syntonic comma
apart) in order to make it consonant with the preceding note(s),
it would be no big deal in plainchant, because there are no
harmonies or other accompaniment notes to complicate the matter.

If a performer of plainchant wants a 'D' to be a 5:3 or 6:5
with 'F' at one point in the melody, and to be a 3:2 or 4:3
with 'G' at another, it's no problem.

Plainchant melodies are constructed in such a manner that this
type of intonational adjustment is quite possible - at least
I *think* this is true. I'd have to do a much more detailed
study of actual chants to state it unequivocally.

-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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🔗Brett Barbaro <barbaro@xxxxxxxxx.xxxx>

🔗Dale Scott <adelscot@xxx.xxxx>

adelscot@onr.com

Mr. Monzo,
concerning the use of just intonation in early a cappella vocal music, you wrote:

> The significant compositions were purely vocal, *perhaps*
> accompanied by the organ, and when not accompanied, were presumed
> to be in performed in just-intonation; _a cappella_, it *couldn't*
> be anything else but JI!
(...)
> Given the fact that I believe 5-limit JI was used in practice
> by 1300 (and perhaps long before that), that leaves *at least*
> two and a half centuries during which, I would argue, unaccompanied
> singers routinely used 5-limit JI.

While it is only natural, owing to the structure of the human psyche, that a cappella singers gravitate toward just-tuned intervals, and while it is quite probably true that early singers used 5-limit JI "routinely," it is doubtful to me that they could have used it _consistently_. I say this because if they *had* used it consistently, the result would have been to what Martin Vogel refers as "comma shifts" in any music except that which is the most simple-simon harmonically. Comma shifts are a real problem of using JI in an a cappella context, because they usually result in a lowering of overall pitch placement.

Take, for example, a simple chord succession (I know, this is a tonal example, but I think the same sort of thing would occur in a modal context) like I - IV - ii - V - I, rendered in 5-limit JI. If we measure the tonic pitch as 1, this means the submediant pitch in the IV and ii chords must measure 5/3; fine so far, but then in order for the supertonic to form a just fourth with the submediant in the ii chord, it has to measure 10/9, rather than the 9/8 that this pitch is "supposed" to be. The tonic and dominant of the final I chord end up being too low by the syntonic comma as well, measuring 80/81 and 40/27 respectively. Sing through these chords just 4 or 5 times in a row in literal just intonation, and you'll discover that the final I chord is a full half-step lower than the beginning one.

I would like to suggest, Mr. Monzo, that singers have historically (consciously or unconsciously) taken 5-limit JI as an intonational ideal, but in practice have tempered some intervals (especially melodic, rather than harmonic, ones) slightly in order to prevent comma shifts from causing pitch to drop lower...and lower...and lower...

Of course, there is the possibility that early singers didn't care if their pitch was dropping, in which case just intonation could have been used more consistently. In any case, it's doubtful that it has ever been used that accurately, seeing as perfect intonation is unattainable in an imperfect universe. :P

Oh, one more note.....personally, I don't see the value of performing plainchant in just intonation. The big advantage of JI is how pretty it makes _simultaneously held_ pitches sound. I mean, I can see how it might be used in early polyphony, such as organum, where you have long-held simultaneities, but performing monophony in JI, even in a highly-reverberant cathedral, seems like a fairly pointless endeavour to me, except perhaps as some sort of carnival stunt. And then, of course, there's still that potential comma shift problem...

Thanx for listening,
Dale Scott
Austin, Texas

🔗monz@xxxx.xxx

[Paul Erlich, posting as Brett Barbaro, TD 206.7]
>
>> >> [me, monz]
>> >> And it *is* possible to perform plainchant in a JI scale with
>> >> *every* note consonant with those already being heard
> <etc. - big snip>
>
> Joe, I meant the seconds would be dissonant no matter what.

OK - I already conceded to Margo that consideration of the
dissonance of the '2nds' got past me.

[Dale Scott, TD 206.13]
>
> Mr. Monzo,
> concerning the use of just intonation in early a cappella vocal
> music, you wrote:
>
>> The significant compositions were purely vocal, *perhaps*
>> accompanied by the organ, and when not accompanied, were
>> presumed to be in performed in just-intonation; _a cappella_,
>> it *couldn't* be anything else but JI!
> (...)
>> Given the fact that I believe 5-limit JI was used in practice
>> by 1300 (and perhaps long before that), that leaves *at least*
>> two and a half centuries during which, I would argue,
>> unaccompanied singers routinely used 5-limit JI.
>
> While it is only natural, owing to the structure of the human
> psyche, that a cappella singers gravitate toward just-tuned
> intervals, and while it is quite probably true that early singers
> used 5-limit JI "routinely," it is doubtful to me that they could
> have used it _consistently_.

Please note that I said 'routinely' but never said 'consistently'.

I suppose it was a poor choice of words to use
"it *couldn't* be anything else but JI!" to express my thought.

[Scott]
> I say this because if they *had* used it consistently, the result
> would have been to what Martin Vogel refers as "comma shifts" in
> any music except that which is the most simple-simon harmonically.

I've already ackowledged this in the past; it's not a matter
of opinion, it's mathematical and acoustical fact.

[Scott]
> Comma shifts are a real problem of using JI in an a cappella
> context, because they usually result in a lowering of overall > pitch
placement.

This, however, is an opinion, and I disagree. See below.

[Scott]
> I would like to suggest, Mr. Monzo, that singers have historically
> (consciously or unconsciously) taken 5-limit JI as an intonational
> ideal, but in practice have tempered some intervals (especially
> melodic, rather than harmonic, ones) slightly in order to prevent
> comma shifts from causing pitch to drop lower...and lower...and
> lower...

I don't have any problem with this statement. It's been argued
here before by Paul Erlich and others, and my Beethoven experiment
pretty much confirms exactly what you're saying, albeit in a
different context from medieval _a cappella_ vocal music.

[Scott]
> Of course, there is the possibility that early singers didn't
> care if their pitch was dropping, in which case just intonation
> could have been used more consistently.

Ah... here's the crux of the matter, and why I disagree with your
statement that 'comma shifts are a *real problem* of using JI in
an a cappella context' [emphasis mine].

I don't possess 'absolute (i.e., perfect) pitch', so a small
amount of drift doesn't bother me one bit. If it's small enough,
I won't notice it at all, unless I'm *REALLY* paying attention
specifically to it, and I'd bet that this is the case for
others like me.

I've never performed any experiments to measure my own tolerance
of 'drift', but I wouldn't be surprised if it's as large as a
'whole tone' (9 or 10 successive commatic shifts), maybe even
larger.

I think it's also worth noting that the recorded reference
frequency for 'A' in European history has varied from 373.1 Hz
to 567.3 Hz - a difference of over 725 cents (more than a '5th')!
[see Ellis's 'Appendix XX, Section H', in Helmholtz]

For those who *do* have absolute pitch, it's a different story,
but one that I can't really discuss, since I lies beyond my
ability to experience.

I suppose Vogel and others who've complained about commatic drift
must possess absolute pitch, because I can't see it bothering them
otherwise.

(For the record, Schoenberg and Partch both had absolute pitch.)

Perhaps any value my theoretical work has for others lies in
the fact that I represent those who don't have absolute pitch.

[Scott]
> In any case, it's doubtful that it has ever been used that
> accurately, seeing as perfect intonation is unattainable in an
> imperfect universe. :P

Well, basically I can agree with this.

What exactly *is* 'perfect intonation'?
That's the whole point of all the discussion we have here. :)

And how do we *know* that the universe is imperfect?
I suggest that the universe is too large for us to ever know it
adequately enough to place upon it a value judgment like that.
:P :P

[Scott]
> Oh, one more note.....personally, I don't see the value of
> performing plainchant in just intonation.

I didn't mean to imply that there was any value in it.
I was simply responding to an idea in someone else's post.

Certainly, it was more likely that plainchant was performed
with a variety of different intervals, some Pythagorean, some
5-limit, some... who knows?

The point I felt worth addressing (and the original subject of
this thread) was the idea that the long reverberation times in
Gothic cathedrals would induce performers with good intonation/ears
to sing notes which form '3rds' and '6ths' with the lingering
previous notes as 5-limit ratios.

As pointed out already by Margo Schulter and Paul Erlich, in
cases where the following notes formed '2nds' with the lingering
notes, 5-limit tuning would not necessarily apply. And certainly
where the intervals form '4ths' and '5ths', Pythagorean intonation
would automatically be considered first.

[PS - my comment on excessive formality, in another post,
was intended for this one. Please call me monz.]

Joseph L. Monzo monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

tuning in reverberant spaces

🔗monz@xxxx.xxx

🔗Brett Barbaro <barbaro@xxxxxxxxx.xxxx>

🔗Dale Scott <adelscot@xxx.xxxx>

🔗monz@xxxx.xxx

🔗perlich@xxxxxxxxxxxxx.xxx

🔗D. Stearns <stearns@xxxxxxx.xxxx>