Technical Library TEMPERAMENTS XII: D’Alembert/Rousseau Entire Contents Copyright ©2005 CBH

There is much interest now in a variety of French temperaments known individually as tempérament ordinaire. In this collective group there are in fact a number of extraordinary and useful schemes, most of which favor the sharp keys at the expense of the flats.

Again, you can conveniently work from your Kirnberger III base to tune this variation of tempérament ordinaire by the famous philosophers d’Alembert and Rousseau. We can call their temperament D’Alembert/Rousseau 1752/67, and note from the diagram that it is characterized by the C–E perfect third with its enclosed four quarter-comma fifths, the fourth fifths on the flat side of C slightly wider than pure, and the four fifths on the sharp side of E narrow.

1. From your nicely tuned Kirnberger III base, retune the four perfect fifths on the sharp side of E so that each fifth is slightly narrow—in fact, a twelfth of a comma, the same amount as an equal tempered fifth. To make sure you are working on the correct side of each fifth and narrowing them, tune the fifth pure first of all and then squeeze the interval. Stop at your G^#.

2. Retune the four perfect fifths on the flat side of C so that each fifth is slightly wide the same small amount. Don’t move your G^#. To ensure you are indeed expanding the fifths, tune the fifth pure first of all and then widen it.

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