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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

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