Re: tuning in reverberant spaces and AJI downward drift

Dale Scott [TD206.13]

>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.

This is the dispute that I am at present having with Paul.
It is interesting that you raise it in regard to singers, because it is
possible to actually check out what frequencies they sing and to
determine a possible method of resolving this issue with regard to AJI
electronic instruments.

>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 don't dispute that this would happen if the most obvious transition
was done at each point. However I think that the obvious approach
ignores the fact that the human memory and the feel of the piece has a
wider span than just the previous chord. For that reason I believe that
a break will happen in the above sequence and the original "I" above
will be returned to. The exact location of the break is uncertain to me
but I believe that it can best be understood through considering the
concept of centre of gravity of tuning. I have explained this
alternatively as a dancer in a spotlight where the dancer moves about a
lot but the spotlight follows more slowly. The spotlight is the centre
of gravity of the piece's tuning and the dancer the present chord. At
some point the dancer will do a larger leap back into the spotlight
rather than a smaller one out of the spotlight. Taken locally this is
incomprehensible but globally it is quite meaningful.

I believe that major confusion is caused by our naming convention where
we call D and D- (or D and D+) by the same name "D". We would never
think of playing a Db for a D or vice versa because we call these
separate names and so we should also accept that D and D- are not the
same note and that they can occur near each other in the same piece.
This is well understood in Indian music (in practice if not in theory).

Let me repeat. There is no reason why D and D- cannot occur near each
other in a piece of music.

As an example take Bach's well tempered clavichord piece. Of course it
might be considered rather low life to play a piece that was designed to
show off tempering in JI however I believe that this is possible. In
that case each arpegio is played twice and the first time has a strong
musical relationship to the second arpegio of the previous pair.
However the second plaing of the same "notes" (same note names anyway)
has a different meaning and is to be matched with the following
arpeggio. A friend described this as musical puns. I would love to
have someone do this as I describe in JI and have the responses of
people who listened to it in that manner.

>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...

Tempering is not necessary for the above reasons. However it may be
that singers actually do temper because their minds are polluted by
pianos tuned to 12 tet as you said before.

>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.

Aaaahhhhhhh!!!!

>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

Perfect intonation is attainable in this perfect universe 8^D

>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...

Several people have mentioned that in a reverberant space there are
harmonies between the present note of the melody and previous notes
which are still reverberating. Clearly even very simple music has a
greater complexity when played under such circumstances when compared to
modern music which is generally not performed in reverberant spaces.

A local modern cathedral (Auckland's Parnell) has a ceilling that has
a discontinuity in the slope so that any notes with about a 2.5 metre
wavelength will totally cancel themselves as they are reflected.
No doubt designed by some trendy architect who had no idea about
acoustics. The results were so dreadful that they installed a great big
floating baffle (I can't think of a better description) above the
orchestral or singer area so that this effect was reduced. Not only has
the art of making true harmony in music been almost lost in the last few
centuries, so has the art of making cathedrals for making music in.

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