Pics Pythagorean, Meantone

[Richard Moody]

You wrote.......

"The 1799 Meantone ......"

I would like to know the source of your 1799 Meantone.  It appears to be a
divergence of the traditional order of tuning Eb---G# by tempered 5ths
centered on Middle C.
  (Eb-Bb-F-C-G-D-A-E-B-F#-G#)

Since1799 was near the end of the meantone era and if this was indeed a
wide spread tuning of meantone of that time it might indicate a different
tonality (as in "color of the key") (very different perhaps) from the
Eb--G#  order.
 ---ric



----- Original Message -----
From: Jason Kanter <jkanter@rollingball.com>
To: <pianotech@ptg.org>
Sent: Friday, February 15, 2002 9:14 AM
Subject: Pics Pythagorean, Meantone


|
| The 14th Century Pythagorean is clearly designed to have pure fifths, so
ten
| of the twelve fifths are zero. The price for this is that the EB fifth is
15
| cents narrow (compared to the ET contraction of 2 cents). There are three
| varieties of thirds:  four at +6.8 cents, four at +12.8 cents, and four
at
| +21.5 cents (ET uses 13.7 cents).
|
| The 1799 Meantone is clearly designed to have the fifths and thirds match
| each other. For the major triads on C, G, D, A, D#, A#, and F, the fifths
| are at -4.3 cents and the thirds are at +4.3 cents. (This is cents, not
beat
| rates, so I'm not sure if they beat the same ... more Excel work to
come...)
| The price for this is that three of the thirds are stretched to over 30
| cents and must be unusable, and two of the fifths are actually *expanded*
to
| +8 cents and +11 cents respectively.
|
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| jason kanter * piano tuning * piano teaching
| bellevue, wa * 425 562 4127 * cell 425 831 1561
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