Mersenne and his Contradictions
by Philippe Allain-Dupré
Translated by Anne Smith from the French
The measurements of the "Fluste d'Allemand"
Mersenne gives the measurements of "one of the best flutes in the world which was curved": its total length was 1 5/6 feet or 605 mm assuming that 1 foot = 330 mm. From B, the end of the flute, to the embouchure hole there were 3 thumb-widths (pouces), that is 27.5 mm x 3 = 82.5 mm. Thus the acoustic length of 605 mm - 82.5 mm = 522.5 mm is that of a flute in d' at 440 Hz.
The interior diameter of 8 lines (lignes), that is 18.2 mm, was constant, different than that of other woodwinds because its bore was cylindrical. The distance of 18.2 mm from the cork to the embouchure hole is equal to the diameter of the bore. his characteristic is also found in Boehm flutes, whereas in cylindrical-conically bored baroque flutes the cork is further away.
The measurements of the holes are unusable because the distance between the embouchure hole and the first hole (No. 2) as well as the distance between the g and f holes are not given. One can use the divisions into 1/27ths given in the illustration of the proportions necessary for reconstructing his flute as an aid, although the regular divisions of 2/27ths differ from those mentioned in the text (30.9 mm between holes 2 and 3, 27.5 mm between 3 and 4 as well as 6 and 7, and 38.95 between 4 and 5). Equal sections of 2/27ths of 522.5 mm would give 38.7 mm between each of the holes.
Illustration of the Proportions:
The Range of the Flutes
"The flute described above is for the top part, and the other flutes are two or four times as large.":; This is unrealistic, as even a flute double the size in d would have an acoustic length of 1.04 m and would be unplayable. Mersenne surely must be confusing flutes with recorders here, as there really do exist recorders double in length (the bassette in g or f) and quadruple in length (the great bass in F) to the recorder in g', used for top parts. This error was already corrected on p. 243: "one cannot make long enough basses" and therefore one uses another bass instrument: serpent, sackbut, etc.
One could conclude that the flute consort suggested by Mersenne plays at 8 foot, at actual pitch, using two flutes in d' for the two top parts, a bass in g for the third, and another kind of instrument for the bass (see Raymond Meylan, La flute, p. 74). However the example given, the air de cour, "Sus, sus la bergère" by Guédron, appears in Van Eyck's Fluyten Lust-Hof with variations for soprano recorder or for a descant flute in g'. This indicates that Van Eyck adheres to the convention of playing flute music at 4 foot, an octave higher than the written notation.
It seems highly improbable that this tradition did not also prevail in France in 1636, even if Mersenne does not state this explicitly. His air for the flutes was surely to be played at 4 foot.
The fingering charts for the flutes
The first fingering chart has caused a lot of ink to flow, in that it gives the fingerings for a flute in g on which the octaves 12 and 13 are fingered in the same manner as their fundamentals 5 and 6. The Swiss flutist and musicologist Raymond Meylan and the French acoustician Michèle Castellengo thus concluded that this flute already had a conical bore, similar to that of the so-called Hotteterre flutes which appeared fifty years later in Lully's orchestra in 1681. This is in contradition to the passage in which Mersenne specifies that "it had a bore of equal size throughout its length".
It does not seem possible that it could be a fingering chart for a bass flute notated at pitch, as the range of two octaves and a fifth is impossible on that instrument. It seems more plausible that it is a fingering chart for a small flute or fife in g', but notated at 8 foot.
It is to be noted that the thirds and sixths are natural - b and e natural - although the fingering chart in G given by Agricola in 1545 "ad epidiatessaron" also lists b-flat and e-flat. But the forked fingerings which require small holes, are not expected of this instrument.
It could also be understood as the fingerings for a cylindrical flute with large finger holes on which the fingerings for the upper octaves are the same as the those in the first octave, even for the 5th and 6th notes. A number of fifes - Indian, South American, or folk instruments - made of cane or PVC function very well with these fingerings.
In the other hand, the second fingering chart resembles that of Virgiliano and Agricola for the cylindrical flute, except for the fact that Mersenne does not give a forked fingering for f natural and that he reproduces the sign used in the charts for flageolet and recorder for obtaining the notes in the second octave (opening the first hole partially), thus also showing that he really did not know the difference between the two instruments very well. He confesses to this in a later passage.
This is followed by a description of a fife of a very simple design, without mouldings and with holes seemingly too large for the proportions of the instrument. It is described as being much shorter and much narrower, producing much more lively and piercing sounds. It could therefore perhaps be an instrument in g', with a narrow bore (like that made by a bullet of a pistol according to Arbeau), giving preference to the major third because of the large holes, like the fife described by Praetorius.
Mersenne adds to the confusion by publishing a fingering chart for a fife in d', very similar to that of the second fingering chart for flute, although it is limited to two octaves. The fingerings are elaborate, using the third harmonic for the a in the second octave, and do not resemble those used by soldiers or for playing all sorts of airs or songs, as one would expect of a simply fingered folk instrument.
I therefore suggest the hypothesis that Mersenne, in editing his work, exchanged the fingering chart for fife with that of the first fingering chart for the flute.. Another argument for this can be found in the typography of the two charts for the flute in d which employ the same signs as those for the recorder, and that thus the fingering chart for the flute in g must come from a different source.
Assuming this is true, if we exchange them once again, we have:
1. Two fingering charts for the flute in d', one extending from d' to d''', and the other from d' to g''', with fingerings very similar to and in line with those of Agricola and Virgiliano for the cylindrical flute of the renaissance, but written an octave higher, as by that time erudite musicians had become aware of the fact that the flute was a four foot instrument. Writing earlier than Mersenne, Zacconi had already limited the flute to a range of two octaves from d to d'', and Praetorius to the two octaves d' to d''', describing the additional notes from e''' to a''' as being in "falsett".
Download the two fingering charts of Mersenne and their comparison with Agricola and Virgiliano
2. A fingering chart for fife in g, a more rudimentary folk or military instrument, with simple fingerings for playing melodies with drums or popular songs like those found in the Fluyten Lust-Hof, the 17th century's top 50. This fingering chart was notated in the older 8 foot tradition and gives the fife a very large range, that of two and a half octaves, the same as that given by van Eyck.
In view of these arguments, it no longer seems plausible to maintain that Mersenne already knew the conical flute. The first cylindrical-conical flutes were made after the publication of L'Harmonie Universelle.