Resources for medieval musicology and liturgy
I've tried using just intonation on the portative organ in music of the turn of the 16th century and it works surprisingly well.
I did this melodically in music to 3 voices with my students (that is, in 3 organetti consort), starting with a meantone tuning and then adjusting the open fifths. (One voice, the tenor, keeps the intervals constant). They managed to do it with much precision in relatively short time.
So, yes...One can be quite precise with most of the bellows that are being made today (wether the bellows were this dynamic and precise in the 15th century is another question), and just intonation is possible. If it was used or not by practical musicians, is hard to tell.
Michael Shields said:
Many thanks for your help, and helpful doubt. I know and admire Mark Lindley's observation of near-pure thirds over D, A, E in a Pythagorean tuning and their use in some music examples. I think he is still talking about a strict Pythagorean tuning (wolf H: F#) with some useable pure thirds in the black notes, but pure untempered fifths (at most, Lindley suggests one should take care that the fifths are not tuned wide).
I am interested in just tunings, with pure thirds and fifths on the white notes in the more common keys, over C, D, G or possibly F, and with resulting wolf intervals elsewhere - similar to those found in the two Heilsbronn (so-called Erlangen tunings, Erlangen Universitätsbibliothek MS 554) clavichord tunings with wolf A:E (method 1) or wolf A:D (method 2). Players on instruments tuned in these would either have to avoid using the wolf fourths and fifths as consonances, or adjust the pitch in some way, or maybe use the wolf vibrato in the low notes for expressive effect. I would imagine such tunings being used as an occasional alternative to pythagorean tunings.
So my question is really: When a 15th-century portative organ, pre-tuned in a just intonation (eg. with triads CEG, DFA and GHD pure and wolf A:E), is used as a single-melody instrument, can one use varying pressure to adjust the pitch of one or two bad notes when needed? I think this would depend whether the pipes used were constructed to give variations in pitch (not just amplitude).
Maybe there is an article that discusses 15th-century organ pipe scaling/voicing and might help to answer this question? (I am not optimistic: the surviving information may be too ambiguous to interpret.) It would also be useful to know whether there are any textual descriptions or iconograpy of people tuning their portative organs as they did their harp.
I would be grateful for bibliographical advice, or advice in the form of practical experience of small organs. I know of a number of 16th-century just tunings for organ, and these look like conservative survivals from a period before meantone became widespread.
I think to remember that the Erlangen tuning is one of the "schismatic tunings" discussed by Lindley. These tunings are strictly Pythagorean, but they indeed also could be considered early examples of just intonation.
In Pythagorean tuning, Gb is a Pythagorean comma lower than F#, while the F# a pure major third above D is a syntonic comma lower than the same F#. The difference between these two commas is a schisma, about 2 cents. That is to say that the Pythagorean "third" D-Gb is a schisma narrower than a pure one. A cycle of fifths displaced to include Gb would indeed produce the wolf at H-Gb (for H-F#, of Cb-Gb).
There is some logic in the idea that only "black" keys would be tuned in this manner, adjusting the ficta notes causa pulchritudinis. The medieval musicians may have discovered the trick by realizing that the Eb, the most distant fifth of the chain, also produced a good third above B. By continuing the chain of fifths flatwards, they obtained Ab, Db and Gb, good thirds above E, A and D respectively.
Lindlay made the hypothesis that the position of the thirds so tuned depended on the music played, and he imagined different variants of the same tuning. All these variants would have been obtained by pure fifths exclusively (one did not yet tune pure thirds directly), but I do not think many of them are really documented.
One point with Mark Lindley is that he has a fantastic ear, gained I presume after years of fine tuning. The question, which will never be answered, is whether medieval musicians had the same intransigence. The same question could be asked for J.S. Bach's time: in Leipzig, he called military musicians to play the trumpet parts when needed; I cannot believe that these were known for the exactness in intonation. I believe that our demands about tuning are much higher than they ever were before. But of course, there is no way to prove that.
As to al-Urmawī, there is not much to be learned from his treatise. The only point is that he described the schismatic tuning about a century before Western theorists; but he was interested in monodic music exclusively.
I completely agree, Mark Lindley's evidence is far from imprecise, he refers to clavichord mensurations (the temperament or tuning is given by the position of the tangents whose set is like a monochord with a little bit more than just five chords).
His discussion is about which of the possible ones we know about that period, had been used by Dufay at Ferrara, and his hypothesis is a conventional diatonic scale (based on Pythagorean tuning), but the fictae (more or less) in meantone intonation. Not exactly what Catalina describes, but she is dealing with a century later!
By the way, if you go on her page you can listen her playing on a historical 16th-century harpsichord. Of course, also Mark has his pragmatic concept to tune the instrument and he does it quite fast. But the clavichord mensuration is the decision you must do, before you build the instrument!
Thank you. For clarity: The Erlangen clavichord mensuration pro clavichordys faciendis (the first of the 2 methods) tunes E as a pure third from C and H as a pure third from G, in the proportion 5:4. This is completely unambiguous in the text. That is why I call it essentiallly a just tuning- it goes against pythagorean just fifths and their wide major thirds. (Maybe I should say "mixed-just" and contrast it with pythagorean "fifth-just", terminology is not quite clear).
It does also derive D and A from a long downward chain of fifths, G>C>F>B>Eflat>Aflat>Dflat>Gflat. It takes D as a major third from this Gflat 5:4. (In this way the increasing flattening of pure fifths going down is counteracted by the smaller pure third which makes D higher.)
A is tuned a pure fifth from D. I think the reason for getting D and A this way is to try to reduce the sharpness of D and A (and the wolf A:E) which results when one derives D and A the usual way, going up C>G>D>A.
Apart from the flat D and A this tuning has strong similarities with some simple 16th-century diatonic just tunings.
I take Nicolas' point about the possibility that tunings were sometimes sloppy, strings defective etc, but medieval descriptions of musical sweetness suggest that there were also people with an incredible ear, back then, and maybe less noise to ruin their hearing, and more time to get things in tune.
Their ears were presumably much finer than those of musicians today... Unfortunately the didactic concepts at conservatories and music high schools are rather poor nowadays, when it comes to deal with certain intonation problems!
Do you think that the Erlangen tuning can be dated back to the 15th century (let us say the late 15th century) or was this part added later to the manuscript?
The wolf between D and a is nothing special during the 16th century, still Gioseffo Zarlino described the meantone tuning exactly this way! Let us say, it was one of well-known disadvantages, if you chose the meantone tuning system!
The text of pro clavichordys faciendis does not seem available on Internet, and your description does not exactly correspond to that in Murray Barbour's Tuning and Temperament. Like all just tunings, these two versions are best described on the Tonnetz, with pure fifths on the horizontal lines, pure thirds in the vertical colums. In your version, the result is this;
G C F Bb Eb G# C# F#
G#, C# and F# are tuned in a chain of fifths following Eb, thus as Ab, Db and Gb, but obviously used as sharps.
There are only four just major thirds, G:H, C:E, A:C# and D:F#, two wolf fifths, F#:H and D:G a comma smaller than pure, and another one, E:A, two commas flat: this tuning does not reduce the wolf fifth E:A, it actually makes it twice worse. (In this disposition of the Tonnetz, each fifth that jumps from one line to the one above is a comma narrower than pure.)
Murray Barbour's version (his table 83) is as follows:
C# F# B E
A D G C F Bb D# G#
with the same major thirds, and two wolf fifths, G#:C# and E:A. In addition B:D# and E:G# are "schismatic" majord thirds (Pythagorean diminished fourths), almost exactly pure.
The main difference with the earlier schismatic tunings is that in the Erlangen Ms some of the thirds are tuned pure (5:4) instead of as Pythagorean diminished fourths. Barbour mentions the Erlangen clavichord in his book in a position that indicates that he dates it later than Ramos (1482) who, he writes, was "the first known European writer to break away from the Pythagorean tuning".
Ramos' own tuning, as described by Barbour (table 81), is
C# F# B E A D
G C F Bb Eb Ab
with major thirds on G, D, F and Bb and the wolf fifth between Ab and C# (Ab-Db or G#-C#). In addition, however, Eb and Ab could be used as "schismatic" major thirds of B and E.
The characteristic of these tunings is that they break the chain of fifths at some point and continue it a comma lower (or higher, depending on the way you look at it). Later just intonations would usually break it at two points, producing for instance three chains of four notes each, with eight pure major thirds and two wolf fifths.
I wrote a short discussion of all this on https://fr.wikipedia.org/wiki/Intonation_juste.
Now that does make sense, and I also do understand the term schismatic in this context!
My description of pro clavichordys faciendis follows the analysis of Andreas Hermert (Berlin), who corrected the text after consulting the MS and very kindly shared his findings with me. The transcription (possibly from microfilm) by Rudolf Denk in Musica Getutscht, MTU 69, p.200, contains a few transcription errors, where ruber has been mistaken for text. Barbour does not go explicitly into how the E and H are arrived at on the monochord (except implicitly: if C=15/16 H and E= 3/4 H then C:E= 5:4) and goes on to correct the tuning according to his interpretation of it.
There are other interesting things about this text. Does anybody have an idea where the word Stephanus (used with the meaning bridge/chevalet/Steg) comes from? Maybe Middle English steven "voice"?
About the dating of the text: it is hard to date entries in a commonplace-book. Compare the Erlangen manuscript catalogue by Hanns Fischer, http://bilder.manuscripta-mediaevalia.de/hs//katalogseiten/HSK0601b...
It looks as if it and the other entries on music might have been written after 1464 (date on fol. 116v) and before 1479 (date on fol.161b). I haven't seen the MS myself, however.
Thank you, Nicolas, for the link to your rich Wikipedia entry. As I think you can see, my interest is less in the history of theoretical discusssions of just tuning than in the practical use of very basic diatonic just tuning routines, some of which continue to be recommended for keyboard (especially for beginners) even into the late 18th century.
By the way, it was me who introduced Mark to Andreas during his visit in 2004, because the latter was and is one of the leading experts concerning the construction of clavichords in Berlin. They do know each other, but they never agreed about the mensura! I also do not agree in everything with Mark, but in this case it rather seems that some would like to have a certain tuning system they personally do favour. Quite common among organ players, when they start historical arguments (also Mark was often accused that he is that way)!
I already checked Fisher's catalogue (before writing here) and from the physical description it seems to be a later added. The early datation about the 1580s seems still possible, but the obvious tendence was to put the wolf at the border between meantone and Pythagorean intonation. If it is no longer between b natural and and f sharp which would reduce "meantone temperament" (including the schismatic third) to the intonation of ficta notes, it nevertheless represents a smooth shift between schismatic temperature and later tunings which became more common during the 16th century...
As far as I know, Mark's publication was the first who gave us the idea that there could be something inbetween medieval "Pythagorean" tuning (associated with the Western oktoechos and its modality) and modern trends of the 16th century connected with third and sixth gymels which became integrated in compositions like those by Josquin. Even if this must remain hypothetical, he also tried to verify the tuning in Dufay's counterpoint technique during these early years at Ferrara. I think this way to handle it is a very fine school for musicians.
Stephanus, in this meaning (the bridge), does not seem documented before the 15th century. I always thought it merely as the latin word, from the Greek stephanos, "crown" (from stephô, to crown, in any sense of the term: anything that crowns a head, a high point, a tower, etc.) But now that you ask, this derivation does not seem that obvious, indeed. The bridge in a sense must be the highest point of the string, the pressure resulting from the angle of the string on it. But in the context of monochord (or clavichord) measurements, the bridge also somehow is the high point for the measurements, marking the full length of the string from where all fractions are measured.
There also is the English steep, which might relate to the Greek stephô. But also step (Dutch stap), the degree of a scale, and which also relates to stephô.
The text is an integral part of the book layout (not marginalia) but as I say, I haven't seen it. Where datings of tuning schemes are concerned, they are so sparse in the 15th century that I feel as if I am moving in the dark. That is, I would doubt that a "progressive look" to a tuning method can function as a reliable basis for a dating in this period.
The idea of Stephanos= Crown does make sense if one thinks of the curved shape of some bridges.
LJS (ancient Greek Dictionary):