Pics Pythagorean, Meantone

[Jason Kanter]

My data for the 1799 Meantone pic comes from the file supplied with TuneLab Pro, named "1799 Meantone.tem", which contains the following:

A   0.00
A# 11.72
B  -4.68
C   7.03
C# -9.37
D   2.34
D# 14.06
E  -2.34
F   9.37
F# -7.03
G   4.68
G#  0.97

----- Original Message ----- 
From: "Richard Moody" <remoody@midstatesd.net>
To: "Pianotech" <pianotech@ptg.org>
Sent: Sunday, February 17, 2002 8:19 PM
Subject: Re: Pics Pythagorean, Meantone


| 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
| | orcas island * 360 376 2799
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