s in
the list is 12.78"; that of the nontransposing group is 10.45". This
suggests a separation between the two groups of about a major third
since the first average is roughly 5/4 of the second. However, the fact
that the separation of the two averages is not great enough to
positively indicate a perfect fourth--the first average would have to
be 4/3 of the second to do so--does not disprove the theory of
transposition by a fourth. In the first place, a considerable variety of
pitches is no doubt represented in both groups since a universal pitch
standard did not exist in the 16th and 17th centuries. Also, a margin of
error of only a semitone is as good as could be expected considering the
small number of examples on which the averages are based.

A further possible justification for the relationship of the two
averages is found in Praetorius' discussion of the pitch standards with
which he was familiar.[6] He states that choir pitch was a major second
lower than chamber pitch and that _tertiam minorem_ was a minor third
lower than chamber pitch. Praetorius says of _tertiam minorem_:[7]

But in Italy and in various Catholic choirs in Germany, the said
lower pitch is much in use. For some Italians, not unjustly, take
no pleasure in high singing, and maintain it is not beautiful, and
the words cannot be properly understood, and it sounds like
crowing, yelling, singing at the top of one's voice....

Possibly some of the nontransposing instruments were tuned to choir
pitch and others to _tertiam minorem_, while the transposing instruments
were set a fourth lower than choir pitch.

Three of the instruments listed are ottavinas, small instruments tuned
an octave higher than usual. Ottavinas correspond to a four-foot
register. Mersenne[8] mentions that they existed in two sizes, one a
fifth above the usual pitch and the other an octave above. The three
ottavinas included in the table are considered to be of the size
sounding an octave above the usual pitch because they have _C/E_ to
_c'''_ ranges and pitch _C_ string lengths about half the average length
of the other instruments in the nontransposing group. Although no
examples were found for inclusion in this study, it is probable that
some ottavinas a fifth above the usual pitch--and therefore an octave
higher than the transposing instruments in our listing--survive. Such
instruments would be expected to have apparent ranges of _C/E_ to _f'''_
a