Re: [tuning] Re: The mighty strange Bohlen-Pierce scale and JI monks

Monz wrote:

>
> One thing I've read about and noticed many times myself that's
> being overlooked here: very often, people without any
> musical training, when singing in what they think is unison,
> are actually singing a 'perfect 4th' or '5th' above or below
> the 'lead' singer.
>
> Listen carefully the next time a group of non-musicians sings
> 'Happy Birthday' at a party - I guarantee you'll hear it!
>
> So '4th'- and '5th'-equivalence most definitely do exist, but
> probably more among non-musicians than among musicians. Musical
> training seems strip away that kind of perception.
>

This might be of interest. In the 9th Century an anonymous writer presented what some consider
to be the first detailed account of early polyphony, the 'Musica enchiriadis & Scholia
enchiriadis ' (Manual on Music and Commentary on the Manual). Two types of harmonisation of
chants were presented; parallel organum - duplication of the chant at the fourth, fifth or
octave and oblique organum which used oblique motion and the coming together of voices in a
unison cadence.

What I find interesting is how this early polyphony came about. I can see two possible
reasons. Communities that live and sing together (and in the case of polyphonic development
we are talking mainly about the harmonising of sacred chants by monks) will show a tendency to
make changes to their music, particularly if the same music is sung or played the same way
year in, year out. Human beings can't resist change, though the Eastern Orthodox Church claims
to have preserved its beautiful sacred chants better than the Western Church. The chants had a
limited range. If the lead singer or singers sang the chants around about the mutual zone
between bass and tenor, fine, but if the chant started off a bit too low the tenors would
struggle and probably want to harmonise at a 4/3 above. Counter-tenors must have struggled.
Given a developmental period of several hundred years I imagine the abbots of the monasteries
would tolerate change over the years.

I have been fortunate to have participated in and observed the changes that take place over
time, not with monks of course, but in a community that chanted and sang a fairly unvaried
'repertoire' several times a day year in, year out. In addition to the tendencies towards
melodic variation, extension and repetition the most obvious point to make is that girls and
women will naturally sing at the 2/1 above the men. Have we overlooked this simple fact in our
discussion of octave equivalence? However, in the middle ages, according to the theorist
Guido, octave doubling had no place. Perhaps he or 'they' disapproved of the high voices,
which in those days would have been boys or counter-tenors. Or perhaps it was dismissed as a
bad 'habit.'

Back to modern times, some singers over time began to pitch up or down a 3/2 or 4/3. These
were usually the tenors. Then the 5-limit prima donnas would start to embellish top lines
with relatively pure thirds.

Secondly, I think that the spontaneous 4th and 5th harmonisation is a very natural expression
of our basic inner harmonic template. It might be that the trained musician or the modern
person working from the intellect refines this by intellectualising the process and
consciously seeking more 'complex' intervals or higher primes. I don't think that the average
monk in a medieval monastic community thought too much about the harmony as it developed so
one conclusion might be that there was a 'natural tendency' to harmonise in fourths and
fifths. I have gathered from my readings in JI theory, in particular Partch, that we in the
Western musical world have moved from 3- to 5- and now on to 7 and above - limit in our
musical explorations. In the context of the discussion about evolution that permeated the
thread I'm following I find it intriguing to speculate that our harmonic template in the West
has evolved in a culturally specific manner over time, though more slowly than the output of
actual music. I attach no quality judgement to evolution in this sense. Perhaps we found it
more natural to harmonise in thirds as we evolved, though we needed to think a bit more about
it. I can hear some of you wondering where blues harmony, as sung or played in non12-tet, fits
into this. That's for another thread.

As for organum, I use it from time to time in my choral compositions and I find the texture
most distinctive and I would recommend the singing of organum to anyone seriously interested
in tuning. This is one case where singers will instinctively reach for the pure intervals.

JI monks - who would have believed it.

--- In tuning@egroups.com, Alison Monteith wrote:
> http://www.egroups.com/message/tuning/13676

responded to my observation about 'perfect 4th/5th'-equivalence
(in analogy to '8ve'-equivalence) with a whole lot of stuff about
the _enchiriadis_ treatises, organum, and medieval intonation,
and concluded with:

> JI monks - who would have believed it.

Well, Alison, I certainly would. Margo Schulter and I have
both posted a lot of papers here on this subject, and they're
in the archives - here are some URLs:

http://www.egroups.com/message/tuning/3350
subject: history of diatonic scale

In a post that contained what is perhaps the wildest speculating
I've ever done, I suggest that perhaps the fondness for 5-limit JI
singing was either an innate characteristic of Germanic people,
or originated with the Native-Americans, then was transmitted
via the Vikings and other Germanic tribes to England, where
it became the object of study and emulation by other Europeans.

http://www.egroups.com/message/tuning/3380 (original form)
http://www.ixpres.com/interval/td/o207.htm (webpage version)
Date: Mon, 7 Jun 1999 18:01:01 -0400
Subject: Medieval instrumental music & early 5-limit

http://www.egroups.com/message/tuning/3427
Date: Tue, 8 Jun 1999 21:31:08 -0400
Subject: Medieval intonations

Margo on 5-limit Gregorian chant:
http://www.egroups.com/message/tuning/3509

I've also written in the past on my ideas about the relationships
between music and language. Here's one:

http://www.egroups.com/message/tuning/3408
Date: Tue, 8 Jun 1999 08:52:27 -0400
Subject: musical phonemes

I've also done a ton of research on the _enchiriadis_ treatises,
and in fact started making my own translation until Erikson's
was published recently. I can't find anything on it right now
that I can publish, but eventually I'll have a webpage about it.
I have some very radical theories about what the 'Daseian'
notation meant.

Another unpublished article I should put on the web is one
where I examine the Greek-letter notation used in an example
of his book by Boethius, which I think documents conclusively
that the diatonic genus, at least in Boethius's time (Italy,
c. 500 AD) used 5-limit intervals. The notational symbols
discrimate between two notes separated by the syntonic comma
(~22 cents) but not between notes separated by the skhisma
(~ 2 cents).

In general, what I find is that theorists wrote descriptions
of music that either directly confirm or indirectly imply
5-limit JI tuning being used in practice all the way back
as far as the Sumerians (c. 3000 BC). 'Pythagorean' tuning
doctrine was certainly firmly established in Babylon 1000
years later, and the reasons why it became so firmly entrenched
in European theory were mainly historical (wish to emulate
ancient Greek theory) and partly matters of musical style.
(many papers published here by Margo document the latter)

Last but not least, and pretty much unrelated to all of this,
a few posts back you asked Paul Erlich 'what about middle-C?'.
I thought I'd dredge up an old post I wrote about how middle-C
functions in my theory, with a bit of a quote:

I wrote:
> http://www.egroups.com/message/tuning/2801
>
> If you call 'middle-C' your n^0 or 1:1, then the bottom end
> of the audible range would give a 16 Hz 'C' with the ratio
> 2^-4 or 1:16, and the note an 'octave' above '5-line high C',
> which is pretty much the useful limit for instruments and notation
> on the high end (exceptions noted) has the ratio 2^4 or 16:1.
>
> This gives a very neat symmetrical layout to the whole 'usable'
> range of pitches.
>
> An explanation with a musical example can be found in my original
> paper about my theory:
> http://www.ixpres.com/interval/monzo/article/article.htm

-monz
http://www.ixpres.com/interval/monzo/homepage.html