• Nicolas Meeùs : Thank you for precising that point. Now that’s clear. Nevertheless, The point is that lowening thirds and sixth (or the contrary, make them higher than pythagorian) in pythagorian tuning, changing the air pressure (and so the pitch and the dynamic) is exactly what I do on the portativ organ, for artistic reasons, since almost 30 years now. And I beleive every skilled musician is doing so, simply because being satisfied in remaining in one tuning system, never moving the rules, is simply impossible for an artist. There is the theory, and there is the pratice. As usual. The musical works are plenty of examples of exceptions to a tuning system from the plain chant in Montpellier Ms to Codex Segovia. And more, when I played together with Martin Ehrardt three years ago, I noticed that he was not tuning his organetto with 11 pure fifth. The reason for that is that he prefers to reach the pure fifth while playing, by moving the bellows giving more air pressure. I was first surprised about that, but then, hearing him play, I was totaly convinced. In fact for any real musician, it is important to change the basic rules to make Art. Playing a big third higher than pythagorian is important because it gives more tension to the imperfection. The same with playing a big third as a pure interval, without tension. Some music of Ars antiqua and Ars nova sounds artisticly better then. And what is interresting for a musician is definitly not the theory and the rules, but the pratice and transgression of the rules. There are beautiful examples in Machault music of big thirds making more sence by playing them not pythagorian. The question on the organetto is that changing the air pressure changes the sound volume and the pitch. So it is possible to move the tuning, but it will be delicate to do it playing together with a fiddle for example. delicate but not impossible. And it will go easier by playing with a lute or a harp. And it will be totaly obvious by playing alone. Playing one note with less pressure is ok with another instrument, it will just be a lower and piano note, playing to notes together on the organetto, like a third or a sixth with another instrument will be problematic, since the the pitch will go lower on the organetto. But for that there are other solutions, moving the rings or the pipes. Ok rings are never seen on pictures, but moving the pipes (i.e. the labium) seems to be a good solution. And about tuning systems, one cannot realy go deep and far understanding the music only with theory. When we experimented on tuning with Qualia , playing the Segovia pieces, and we spent hours and hours and hours on that, we noticed that both pythagorian and meantone systems where needed for certain pieces, simply because classical Ars nova cadences work better with pythagorian thirds and sixth, and because successions of sixth or certain big thirds in a certain musical context work better with pure sixth and thirds. In the same piece, yes ! C’est la vie !

    Nevertheless, I’m realy wondering how you can make statements about playing, tuning and changing the air pressure on the organetto without being able to play the instrument yourself?!!!… This is not serious Mister !

    Michael Shileds : right, there is no evidence for tuning an organetto a positif or a big organ yet. In modern organetto playing we now use rings, but no picture has been found yet with this tuning system. The only text that one could consider is the Da Prato description of Landini moving the pipes. But that is only an interpretation and an hypothesis. Now there are at least two a nice XV. Cent. Pictures showing a man working on a pipe in a organbuilder atelier (one of those I used for my 1995 paper in the Acte du Colloques sur les Orgues gothiques at Fondation Royaumont, éditions Creaphis). Anyway, can we realy imagine organs that cannot be tuned ? And can we realy image musicians that do not change the tuning ? Is a scordatura reserved to XVIIth cent. music ? I realy don’t think so ! But all that is obviously speculation and hypothesis…

    Votre serviteur

    Christophe Deslignes

    Nicolas Meeùs said:

    It is one thing to tune an instrument in, say, Pythagorean tuning, meantone temperament, or just intonation, and quite another to pass from one of these systems to another merely by varying the wind pressure. I don't mean that the instrument cannot play "in tune", merely that I doubt that variations in wind pressure could finalize the tuning.

    Neither meantone nor just intonation are documented before the end of the 15th century -- with Ramos de Pareja's description of pure thirds (1482) being an important step in this evolution. Before that, almost pure thirds were tuned by enharmony, as Pythagorean diminished fourths (say, D-Gb for D-F#). This tuning was first described in the 13th century by Ṣafī al-Dīn al-Urmawī, in an attempt to emulate the quarter tones of Arabic music; the small intervals obtained, however, where commas, not quarter tones. In Western music, it was described among others by Arnaut de Zwolle, who mentioned one such tuning by a certain Baudecetus, who I think may have been Baudenet of Reims, late 14th century.

    Mark Lindley discussed the possible adjustments of this tuning to suit the needs of particular pieces of music, but there is no evidence that the instruments were retuned from piece to piece.

    I have little doubt that Pythagorean intonation was not used as constantly as the theorical sources seem to indicate. Yet, there is no medieval evidence of this, about which one could only speculate.

    Orgue portatif avec double soufflet
    Bonjour, quelqu'un peut-il me donner une explication au double soufflet de cet orgue ? London, British Library, Add MS 38120, 103r
  • Maybe I was not clear. As far as I understood Mark (about early tuning in Dufay's Ferrara period), it is not meantone tuning in the respect that there are clearly the proportions 9/8 x 10/9 = 5/4.

    There is still a fourth-fifth chain or palindrome which is corrupted at a certain point that it produces almost pure thirds!

    What we do discuss here (although the picture in question stems from the 14th century), in as far this concept allowed to combine fifth and third chains in the same tuning system.

    I doubt that στέφανος can mean bridge, but something which is surrounding!

  • 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.

  • 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.

  • 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.

  • 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,

    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.

    Handschriftenkataloge ONLINE
  • Now that does make sense, and I also do understand the term schismatic in this context!

  • Dear Michael,

    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;

    B   E

    G   C   F   Bb   Eb   G#   C#   F#

                                          A    D

    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

    Intonation juste
    L'intonation juste est un système d'intonation musicale dans lequel, en principe, tous les intervalles, en particulier toutes les consonances, sont j…
  • 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!

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