Technical Library
TEMPERAMENTS XVI: Sixth-comma Meantone
Entire Contents Copyright ©2007 CBH
Technical LibraryTEMPERAMENTS XVI: Sixth-comma Meantone Entire Contents Copyright ©2007 CBH |
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Now
that you are used to the sound of Vallotti’s sixth-comma fifths, you might
want to try Sixth-comma Meantone. Richard Kolb, sometime lutenist at the Carmel
Bach Festival, has been using this temperament successfully for some time,
and requested it for one of the Intermezzo recital programs he devized in 2007 for his last year in Carmel. From a keyboard point of view, this temperament was supposedly
favored by Silbermann and
so is sometimes found described under his name. With the exception of the wolf
which is greatly reduced in size from that of Quarter-comma Meantone, a moment’s
contemplation of the diagram will show you that all the identically-sized fifths
are here a somewhat larger sixth-comma like Vallotti. Each of the usable thirds
resulting are exactly the same in size, but wider here than the absolute purity
of Quarter-comma Meantone and so we have no pure intervals to check.
Compared to Vallotti, though, all the “white” notes of the keyboard are in exactly the same place. All usable keys sound the same, so this temperament lacks Vallotti’s variation in key color. The “black” notes for the three sharp keys are closer to their tonics (progressively flatter than Vallotti), and the two flats are closer to their thirds (sharper than Vallotti).
To change your previously-tuned Vallotti to Sixth-comma Meantone, proceed as follows:
1. Raise your bb so that instead of a perfect fifth bb–f', you have a narrow sixth-comma fifth sounding with the same roughness as the a–e' a semitone lower.
2. Raise your eb first of all to make a perfect fifth with the bb you’ve just tuned, then raise it some more to make a sixth-comma fifth eb–bb. Again this can be compared in roughness to e–b which is the same size. The two flat notes have now been found.
3. The three remaining sharps must be progressively lowered from Vallotti. Work to lower your f#' so the fifth b–f#' sounds similar to the already tuned bb–f'. Tune down an octave to determine the new f# and then lower your c#' so that again you have the same sized narrow fifth f#–c#' as f–c'. Tune down an octave to c# and make your final narrow fifth c#–g#. Verify your almost-usable wolf g#–eb' and your tuning is complete.
4. Finally, though, you can check the accuracy of your work with a chain of ascending tempered fifths. If you’ve succeeded, each one should beat just a little more than the previous as you ascend the keyboard through c#–g#, d–a, eb–bb, e–b, f–c', f#–c#', g–d', a–e', bb–f', b–f#' & c'–g'. (Your g#–eb' wolf is as expected from the diagram, so that interval doesn’t occur in this check series.) And you can even pull the same trick with your major third f–a the same three beats per second as Vallotti, and each third beating slightly faster as you ascend g–b', a–c#', bb–d', c'–e', d'–f#', eb'–g' & e'–g#'. The harsh thirds which are really fourths, do not form part of this check. They are perhaps not as vulgar as in Quarter-comma Meantone, and you might find their enharmonics almost usable: f#–bb, g#–c', b–eb' & c#'–f'. If you try to play an Ab Major triad you’ll hear that it is almost as hideous as Quarter-comma because every note is still wrong.
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