Mersenne’s Universal Harmony 117
played, ” by sympathetic vibration, “ since the single string of the monochords produce the
same sounds. ”^29
Mersenne goes even further when he notes that there are “ at least five different tones
at the same time, ” implying the possibility that there are still more. He hears “ still a fifth
one higher ” that “ produces the major twentieth with the natural tone. ” If so, this seventh
overtone (counting the fundamental as the first) would correspond to the note A above the
last overtone shown on figure 7.6 ; later observations placed it closer to B ♭. Given the
increasing faintness of each successive overtone, it is not surprising that he would have
had difficulty with this even fainter one, but theoretical reasons may have made him hesi-
tate. Up to this point, the overtones had coincided exactly with the well-known conso-
nances: octave, fifth, major third. Theorists soon noticed that Mersenne ’ s series of four
overtones ( figure 7.6 ) in fact sounded the ordinary triad based on the fundamental tone,
laid out in exactly the way that practitioners had found most euphonious. This was, for
many music theorists, the fundamental justification of the triad as the “ chord of nature. ”^30
Compared to that purely triadic standard, the seventh overtone is a rogue, an outlier,
rather like Boethius ’ s version of the fifth hammer in the blacksmith shop. Mersenne ’ s
hesitation about its status reflects its deviance from ordinary music theory and practice.
So strong was his commitment to the conventional intervals that he felt implicit pressure
to reduce it to one of the notes he did know (namely, the twentieth, two octaves and a
sixth above the fundamental). When he turns to wind instruments, he confirms the series
of overtones so far, which are formed by “ overblowing ” the airstream. The trumpet of his
time, a tube with a flared horn and no valves, produces this series with great clarity and
volume, including the troublesome seventh partial ( ♪ sound example 7.1). Players then
and now know that this tone lies flat from the equal-tempered scale (and also from just
intonation), so that it needs to be adjusted upward in pitch by using the tension of the lip.
Mersenne includes the trumpet in his extraordinary survey of all the instruments in the
known world, a musical tour d ’ horizon that had little precedent in earlier writings and
which remains an invaluable source about the practice of his times. He describes the history
and construction of the trumpet and lists its range, which coincides with the series of
overtones but omits the seventh, skipping from the sixth to the eighth and also omitting
two other higher overtones that sound flat ( figure 7.7a ). When he illustrates the instrument
in its military uses ( figure 7.7b ), though, he includes all these partials in one panel but not
the other, which presumably includes only the notes used in fanfares and excludes these
problematic overtones. His text is hesitant and puzzled on the whole matter; he notes
“ many difficulties ” that begin with the seventh overtone. The sequence of pure conso-
nances is broken at this point; he has heard a discordant pitch in the place of the seventh
partial but does not want to admit its existence, calling it a “ wound, ” even a “ vice. ”^31
Musical practice maintained so strong a hold over him that he tried to exorcise his experi-
mental results as numerologically impossible or devilish. Though he tried to amend the
faint seventh overtone of a viol string, the trumpet ’ s was harder to ignore.