Medieval instrumental music & early 5-limit

Many thanks to Margo for her extremely informative post about
medieval instrumental music. Apologies for the inordinate length
of this response. This is partly the result of quoting Margo's
already long post in its entirety, but that was so tightly
organized that I couldn't bring myself to omit any of it, and
hopefully I will be forgiven for my excess.

[Margo Schulter, TD 206.14]
>
> First, I'd much like to thank Joe Monzo for calling to my
> attention that Salinas published his 1/3-comma meantone tuning
> (and also a very interesting just intonation scheme) in 1577,
> not 1571 as I surmised in a response to Bill Alves.

OK, I'll accept your thanks and respond with 'you're welcome'.

But in truth, since I get the postings in Digest form, I wasn't
actually calling it to *your* attention specifically. I was
responding directly to Bill myself, and had sent my post long
before I ever read yours. As you yourself pointed out here
once, sometimes the nature of email leads to unintended
miscommunication. Certainly not a big deal in any case. :)

[Schulter]
>
> Secondly, as to the role of instrumental music in late medieval
> and Renaissance Europe, I would certainly agree that vocal music
> is both the prevalent form and the "perfect" ideal of these eras.
> However, this does not mean that instrumental music was
> inconsequential, or that its influence on vocal intonations was
> necessarily negligible.

In connection with this comment, I'd like to quote Richard H.
Hoppin, 1978, _Medieval Music_, from the chapter _Polyphony in
the 13th Century_, p 347-349, concerning the time-period about a
century prior to that of which you speak further on. Hoppin is
here discussing the very end of the _Ars Antiqua_ [c. 1300]:

[Hoppin]
>
> The dearth of manuscript evidence for instrumental music in
> the Middle Ages is both astonishing and mysterious. Writers
> and theorists make countless references to instruments and
> their practical uses. Manuscript illustrations and cathedral
> sculptures depict a wide variety of instruments, often in
> connection with singing or dancing, but sometimes in ways that
> suggest either solo or ensemble performances. Peasants
> reportedly played instruments for their rustic dances.
> Jongleurs were expected to play as many as ten instruments
> according to the _Conseils aux Jongler_ written by Guiraut de
> Calanson in 1210. Troubadours and trouveres presumably sang
> their songs to instrumental accompaniment. In short, there
> is abundant evidence that instruments played a vital role in
> medieval musical life at every social level, yet only a handful
> of purely instrumental pieces has been preserved. Several
> factors probably account for this situation. Instrumental
> performance seems to have been largely the province of jongleurs,
> whose music has either been lost or, as is more likely, was never
> written down. Peasants too probably had a repertory of both song
> and dance tunes that were passed on solely by oral tradition.
> And at all levels of society, apparently, vocal music provided
> the chief source of material for instrumental performance.
> Numerous poems speak of musicians playing chansons or lais or
> ballades on a variety of instruments, and Johannes de Grocheo
> says that 'a good artist plays on the viol every _cantus_ and
> _cantilena_ and every musical form in general' [quoted in
> Gustave Reese, 1940, _Music in the Middle Ages_, p. 327].
>
> Most of the references to instrumental performance, either in
> poems or in theoretical treatises, are concerned with monophonic
> songs and dances. It is probable, however, that players
> provided troubadour and trouvere songs with simple improvised
> accompaniments. We have also noted the likelihood that
> instruments took over the performance of motet tenors and thus
> introduced accompanied duets and trios as well as solo songs.
> Instrumental doubling of the vocal lines is a further probability
> from which it is but a short step to the substitution of
> instruments for voices. It has been suggested that the caudae
> of conducti were designed for instrumental performance and 'may
> prove to be a valuable source for 13th-century dance music' [New
> Oxford History of Music, 1954, vol 2, p 337]. Such an assumption
> is a bit farfetched, perhaps, but vocal polyphony undoubtedly did
> provide music for instrumental ensembles. A few pieces in vocal
> forms even appear to have been intended for instrumental
> performance.
> ...
> [for example:] ...the 'instrumental motets' in the Bamberg Codex
> (# 102-108). ...Like the later secular motets, these pieces would
> seem to have lost all connection with organum, and their textless
> state, together with their use of hocket, makes the assumption of
> instrumental performance unavoidable.

I'd be very interested in seeing some studies done on the
intonations implied by the design of medieval and Renaissance
woodwind instruments. As a former woodwind player myself,
and with the current increased interest in using 'historical
instruments' in performance and recording, I'm surprised that
this hasn't been done (or perhaps I just don't know about it
- those who know, references would be appreciated)

[Schulter]
>
> Mark Lindley, for example, argues with due caution that the new
> modified Pythagorean tunings of the early 15th century, possibly
> sometimes implemented on keyboards with more than 12 notes per
> octave, may have influenced the vocal writing of composers such
> as Dufay, intriguing them with the sound of nearly pure schisma
> thirds involving written sharps.
>
> Lindley also shows how, around 1400-1450, keyboard sources such
> as the Italian Faenza Codex and the German Buxheimer Organ Book
> used prominent sonorities with schisma thirds as a very popular
> "special effect," indeed sometimes a "stock in trade," as he
> puts it. While the "explosion" in lute and keyboard tablatures
> around 1500 was yet to come, these trends may have played a role
> in the stylistic change around 1420-1450 which marked what
> Tinctoris (1477) regarded as the beginning of truly "modern"
> music. In current historical terms, this is often regarded as
> the Gothic/Renaissance transition.

What Hoppin says at the end of _Medieval Music_, p 522-524, has
a direct bearing on some of the points you make here, as well as
on the question of tuning in general, and England's role:

[Hoppin]
>
> If Dunstable [?-1453] was in [the Duke of] Bedford's service on
> the continent, as we must assume he was, he would have had ample
> opportunities for meeting and influencing musicians at the
> Burgundian court. A contemporary poet, Martin le Franc, bears
> witness ... in ... _Le Champion des dames)_ [1441-2]. After
> proclaiming the superiority of Dufay and Binchois over their
> French predecessors, le Franc credits their excellence to their
> having followed Dunstable and adopted the 'English countenance',
> by which means they found a new way of using 'sprightly concords'
> to create song of marvelous pleasure, joyous and memorable.
>
> ...we can only admire the poet's acuity if critical judgment in
> putting his finger on the one aspect of English music -- and of
> Dunstable's in particular -- that was chiefly responsible for
> its influence on continental composers... a new treatment of
> consonance and dissonance...[which] began when composers rejected
> medieval permissiveness in the combination of harmonic intervals
> in favor of a 'panconsonant' style that required each voice to
> be consonant with all the others. Hand in hand with this
> elimination of dissonance from the essential tones of vertical
> combinations went a much more restricted and controlled use of
> dissonance to ornament the harmonic tones. The unprepared and
> accented dissonances so characteristic of 14th-century music now
> disappear almost entirely.
> ...
> We must recognize Dunstable as the greatest English composer
> of his day. We must also recognize that, for perhaps the only
> time, the prestige and influence of English composers changed
> the course of music history thru-out western Europe. By these
> recognitions we confirm the judgment of Tinctoris, altho we may
> rephrase his statement to make English composers, with Dunstable
> at their head, the fount and origin of the musical Renaissance.
> In their works, and in the works of continental contemporaries
> who added the English countenance to their earlier mixture of
> French _subtilitas_ with Italian _dulcedo_, music moves beyond
> the scope of the present study. For the music of the Middle
> Ages, the end had come.

IMO, Hoppin may be making a few rather broad generalizations,
but overall I think these comments by another expert on medieval
music provide pretty good evidence that 'sweetening' of '3rds'
and '6ths' (from 3- to 5-limit ratios) had long been an important
part of English musical performance, especially if one considers
both the writings of Odington and Theinred and the observation
I've been making about the lag of theoretical description behind
musical practice.

In connection with this, it's interesting to consider the
heterogenous ethnic base of medieval England, a mixture of the
original inhabitants, and successive waves of Celtic, Roman,
German (Anglo-Saxon, then Danish, then Norwegian), and finally
Norman (= Celtic + Roman + German [Frank] + Norwegian) invaders.
I wonder if this had anything to do with intonational preferences
or their evolution?

The fact that the shift from 3- to 5-limit was noticed by Theinred
so soon (little more than a century) after the Norman invasion of
1066 seems to me to indicate either that the people already living
in England before that may have been using 5-limit harmonies, or,
still more likely, that it was a characteristic shared by the
inhabitants of both England and Normandy.

This might lead one to believe that perhaps it springs
ultimately from unrecorded sources in Scandinavia. The presence
of the Vikings would be the main ethnic differentiation between
England/Normandy and the rest of literate Europe around 1100.

And the Vikings had sailed to America just before this, so perhaps
they got 5-limit from Native Americans? I'm speculating wildly
here, but 5-limit singing does seem to have suddenly appeared
shortly after this in the Anglo-Norman lands, and there is the
possibility...

Can anyone give some insight into the earliest manuscripts of
Scandinavian compositions or theoretical treatises?

[Schulter]
>
> While the formal vocal forms of sacred and secular polyphony
> continued to hold center stage in the 16th century, instrumental
> forms played a very important role also, and madrigals, for
> example, might be sometimes be performed by mixed consorts of
> voices and instruments. In fact, the complications and conflicts
> resulting from such mixed ensembles (e.g. meantone keyboards and
> 12-tone equal temperament or 12-tet lutes) was one topic of
> discussion in late 16th-century treatises.
>
> During the first half of the 16th century, an incredible
> flowering of instrumental forms occurred, ranging from dances
> and improvisatory lute and keyboard preludes to Willaert's
> ensemble _ricarcare_. By 1555, Vicentino was prepared to
> advocate the use of his 31-tet _archicembalo_ as a standard
> for intonation by singers.
>
> In discussing either the 3-limit JI of the Gothic era or the
> 5-limit JI of the Renaissance, it may be helpful to remember
> that these are _ideals_ of intonation, guiding singers of some
> natural variability in their intervals. In performances involving
> mixed voices and instruments, common for example in the various
> Florentine entertainments chronicled by Howard Mayer Brown,
> instrumental and vocal intonations would interact, making the
> former not irrelevant.
>
> As early as 1516, by which year Castiglione's _Courtier_ is said
> to have been completed (it was published in 1528), an author
> argues that the most pleasing court music is a vocal solo
> accompanied by the _viola a mano_ -- that is, actually, a lute
> or similar plucked instrument. Various Italian _frottole_ around
> 1500 may have performed in this manner, and arrangements of
> Italian madrigals by Verdelot, for example, for the lute may
> have represented a continuation of this tradition.
>
> This is not at all to minimize the importance of the view taken
> by various theorists of the later 16th century that there are
> three distinct types of intonation: (1) Just intonation for
> voices, specifically 5-limit; (2) Meantone for keyboards; and
> (3) 12-tet for lutes. However, in forms where these varieties
> of instruments (the voice being considered the most "perfect")
> interacted, mutual influence or accommodation might come into
> play.
>
> The influence of instrumental intonations in practice is
> suggested by Vicentino, who describes the conventional practice
> of his time as "mixed and tempered music." The "mixed" refers
> to his view that even compositions typically classified as
> "diatonic" in fact use elements of the chromatic and enharmonic
> genera; and the "tempered" evidently refers to the kind of
> accommodations made in meantone tunings for keyboard.

Hmmm... Now your comments about 'mutual influence or accommodation'
have got me wondering about the possible role of well-temperaments
during the Renaissance, whereas they are usually associated with
the Baroque period which followed.

From Anthony Baines, 1961, _Musical Instruments Through the Ages_,
chapter 7, 'The Fretted Instruments':

[Baines]
>
> four centuries ago [c. 1561] the place of the lute in musical
> life in many ways foreshadowed that of the pianoforte in modern
> times [1961], both as the chief instrument of the home and as
> the first instrument for the professional virtuoso of
> international fame.

In this same chapter, Michael W. Prynne [in his article
_I. The Lute_] calls John Dowland 'the greatest lutenist of
his day'.

These statements, on the tremendous popularity of the lute
in general and Dowland in particular during the 1500s and early
1600s, make me wonder just how widespread Dowland's lute tuning
[published 1610] may have been.

This tuning, as opposed to the lute tunings generally cited, was
most emphatically *not* 12-eq, but rather a complex rational
system (I hesitate to call it JI, as it includes no 5-limit ratios)
which functioned as a well-temperament. See my Dowland webpage:

http://www.ixpres.com/interval/monzo/fngrbds/dowland/dowland.htm

I'm also very curious as to exactly how and why Dowland chose
the particular ratios he used in this system.
Does anyone have any clues?

[Schulter]
>
> Because the topic of the Pythagorean-Aristoxenian-Ptolemaic
> debate is often raised here, I would like to conclude with one
> point about at least the late medieval theorists of polyphony
> and Pythagorean tuning. This really isn't addressed to any one
> previous article in particular, but maybe to a general trend of
> thought.
>
> In medieval versions of the Pythagoras story, this theorist heard
> an amazingly harmonious striking of blacksmith's hammers, and the
> set out to investigate how this could come about. Such curiosity
> led to experimentation, and the discovery of the ratios of the
> principal concords. Thus the sense of hearing and the intellect
> are partners in the kind of theorizing advocated by Pythagoreans
> such as Jacobus of Liege: concord and discord themselves are
> described in terms of smoothly blending or roughly "colliding"
> sounds, as well as in terms of numerical ratios.
>
> Further, to such medieval theorists, concord/discord
> classifications reflect style as well as mathematics. For
> Jacobus, while _stable_ concords are generally limited to the
> classic 3-(odd)-limit intervals, a variety of other intervals
> are also recognized as "medial" or "imperfect" concords. These
> include the major third (81:64), minor third (32:27), major
> second (9:8), minor seventh (16:9), and major sixth (27:16).
> Not all of these ratios are mathematically so tidy, but
> Jacobus hears the intervals as more or less blending, and so
> describes them as "concordant" to various degrees.
>
> Possibly the hallmark of "Pythagoreanism" in such a medieval
> setting is a desire to explain artistic perceptions in a
> precisely quantitized way -- something rather different from
> considering such perceptions irrelevant. Thus in the early 15th
> century, Prosdocimus portrays his fellow Paduan theorist
> Marchettus of about a century earlier as a very bad
> mathematician, but a good practical musician. In fact, without
> necessarily joining with Prosdocimus in his value judgment, one
> can say that the mathematics of Marchettus are at best a bit
> unclear, as compared with the 17-note Pythagorean scheme of the
> later theorist.
>
> Further, as Prosdocimus shows, it is quite possible to champion
> a Pythagorean approach to intonation while showing an awareness
> of the role of perception. Thus, having recognized the
> distinction between intervals such as A3-F#4 (major sixth, 27:16)
> and A3-Gb4 (diminished seventh, 32768:19683), he wonders aloud
> whether this distinction might be "imperceptible" to the ear.
>
> In my view, our answer might depend on how "perceptible" is
> interpreted. Certainly it is possible for an attuned listener
> to discern this difference of a Pythagorean comma (~23.46 cents),
> but at the same time, one might guess that in the early 15th
> century, as now, many listeners might find either interval an
> acceptable representative of the "major sixth" class. Indeed,
> keyboard works of the period which in popular keyboard tunings
> would use both flavors of sixths lend support to this view.

Your points here are very well taken, and I don't find them at
all contradictory to my views. On the contrary, I'm coming to
believe more and more that a wide variety of tunings have
always been in use in music, from all chronological periods and
in all geographical locations, and that various different
tunings of particular intervals have always been accepted by
listeners as embodying that interval's _gestalt_.

I likened this once before, in a posting, to the recognition
by linguists of the concept of a phoneme, where a particular
language's rules accept or ignore specific phonetic elements
as embodying meaninful linguistic content, and where these
rules of acceptance/ignorance change according to the language
under consideration.

I think a musical style is analagous to a language in the
same way, where specific phonetic elements would be analagous
to specific tunings of intervals, and phonemes would be
analagous to the general intervallic _gestalt_. What is
accepted or ignored as carrying meaning would change according
to the musical style under consideration.

I think this idea provides a fruitful avenue for further
research.

[Schulter]
>
> Here I wish not at all to minimize the importance of our ongoing
> dialogue regarding the traditions of Pythagorus, Ptolemy, and
> Aristoxenes, only to caution against any blanket equation of
> "Pythagorean" theory during the medieval period with an
> indifference to the evidence of the senses or to the vital
> dynamics of style.

I would like to comment here on your last clause, inasmuch as
I'm the one who posted recently on that subject.

I was referring specifically to Ptolemy's views of strict
Pythagorean theory being 'numbers divorced from acoustical
reality'. Ptolemy's attempts to reconcile the Pythagorean
(rational) and Aristoxenean (irrational) approaches was probably
a result of the neo-Pythagorean revival of his day.

From the evidence of Ptolemy's treatise, theorists c. 100 AD had
enthusastically re-embraced Pythagorean theory, and, his empirical
results not jiving with this, Ptolemy sought to include the more
musically empirical theories of Aristoxenus.

I did not mean to imply that this attitude towards Pythagorean
theory is valid for the medieval period, or that it was held
by medieval theorists themselves. I humbly bow before your
expertise in this area.

A point that I was making in earlier posts which I would like
to reiterate:

The mathematical descriptions of tunings by theorists of the
1300-1500s became proportionately more accurate and more complex
as these theorists became increasingly well acquainted with
ancient Greek treatises which used non-Pythagorean ratios
and, in the case of Aristoxenus, non-rational measurements.
However, this does not *necessarily* reflect the actual state of
musical practice before 1300 as *using* less complex tunings.
As I said, descriptive music-theory *always* lags (sometimes far)
behind practice.

(And please note that this statement does not pertain to
*proscriptive* theories like those of Yasser or Partch.)

If there's any certain conclusion I can make based on research
I've done for my book, it's that high-prime ratios have been
used in describing musical intervals since virtually the beginning
of our extant documents.

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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Monz, thanks for the extensive quote Richard Hoppin.
I was quite pleased, and almost stunned, at how well
it corroborated my last post, which I had written
just a minute or two earlier.