Global
Flattening
Whilst the possibility that increased
levels of atmospheric carbon dioxide could give rise to global warming has been
widely publicised, a concomitant phenomenon of interest to practicioners of
early music, namely global flattening of pitch, has hardly received any
attention. The pitch of a wind instrument is inversely proportional to its
length and to the density of the gas it contains. In calculating the pitch of
the many surviving wind instruments from earlier centuries it has hitherto
always been assumed that the latter factor is a constant. Clearly however
this is not the case: if we calculate the effect of the increase in carbon
dioxide levels the change in pitch is by no means negligible. The atomic
weight of nitrogen is 14, of oxygen 16 and carbon is 12 (ignoring trace amounts
of carbon-14). Nitrogen and oxygen are divalent, so their molecular
weights are 28 and 32 respectively. The resulting molecular weight of the
mixture of nitrogen and oxygen in the ratio found in air is approximately
28.8. However the molecular weight of carbon dioxide is 44 and thus even
small amounts of this compound make a significant contribution to the density of
the resulting gas.
Calculation of the fall in pitch
resulting from this over the period from 1700 to the present day is a problem
too complex for these pages, but an article from the Journal of Theoretical and
Applied Accoustics, published at the beginning of this month, suggests a figure
of 5.5%. This means that the pitch of a baroque instrument which today is
a=415 would at the time of construction actually have been A=438, i.e. almost
exactly the modern concert pitch of A=440. Clearly the TVEMF committee
should give serious consideration to standardising on modern tuninbg for all its
events in future!
D. Arrowsmith