Beethoven Symphony #1

Beethoven #1 second movement

Beethoven #1 third movement

Beethoven #1 fourth movement

Stars and Stripes Forever

2/7-comma meantone

Ratwolf is very similar in tuning to 2/7-comma meantone, which was the first meantone to be explicitly described (by Zarlino, in 1558.) It was discussed by a number of theorists of the sxiteenth and seventeeth centuries, and one might conjecture that the reason for that is that a fifth of about the size of the 2/7-comma fifth, 695.81 cents, 0.027 cents flatter than the ratwolf fifth, was in actual use during this period. Below is a piece by John Bull (1562-1628) who composed during the period that music theorists were discussing 2/7-comma. It would be easy to conclude that this piece, Ut re mi fa sol la, must be intended for a well-temperament, since it visits the complete circle of fifths, but to conclude that would really require evidence people knew and used well-temperaments during this period. Similarly we would like evidence that something other than lutes and guitars were tuned to equal temperament before counting that as at all likely; the same remarks apply to mild versions of meantone.

An alternative theory is that Bull tuned his harpsichord to 2/7-comma or something like it. If we use a tuning from Eb up, the 20/13 wolf is at Ab, and Ab and Db are the least-visited chords in this piece. Bull may not have found the 20/13 magic triad and the supermajor triads in the remote keys to be intolerably unmusical, and simply have proceeded to use them.

Here is Ut re mi fa sol la, scored for bassoon, clarinet, flute, horn and cello, in 2/7-comma meantone.

Utremifasola 5.48 mb