<HTML><FONT FACE=arial,helvetica><FONT SIZE=2>In a message dated 4/13/01 8:33:16 AM Central Daylight Time, lbeach@sfu.ca
<BR>(Larry) writes:
<BR>
<BR>
<BR><BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">How many of you have had the time to waste and put a 1/4 comma meantone
<BR>tuning on your home piano? ;) I just tried it on a Yamaha C7 for fun
<BR>today. I couldn't get it to work very well unless I allowed the 3rds to
<BR>beat about 2-3 /sec, and 5ths more narrow than they should. I figured this
<BR>must be due to the greater inharmonicity of the modern grand piano compared
<BR>to relatively no inharmonicity on the organs of Bach's time. Nevertheless,
<BR>it sure demonstrated how nice some chords can sound, and how awful a couple
<BR>of them were. (C#-G# is a very bad 5th!)</BLOCKQUOTE>
<BR>
<BR>There are a couple of things confusing about your experience but basically,
<BR>I think you must have got it. The classic 1/4 Syntonic Comma Meantone tone
<BR>is constructed by making a chain of 5ths, each one tempered by 1/4 of the
<BR>value of the Syntonic Comma (21.5). 21.5 ./. 4= 5.38. Tempering each 5th by
<BR>5.38 will make 8 pure 3rds and leave 4 very wide (wolf) 3rds and the last 5th
<BR>which cannot be tuned will be over 40 cents wide. This untuned 5th is
<BR>usually left between Ab-Eb but sometimes between Db-Ab.
<BR>
<BR>Now, because the piano has Inharmonicity, this changes all of the above
<BR>slightly just as it skews the values of Equal Temperament (ET) or any other
<BR>temperament. To come out right, the 5ths will be tempered a little less,
<BR>more like 5.0 or 5.1 which will leave the 3rds tempered but less than 1 cent.
<BR> They will still sound pure but actually have a very slow beat, not quite 1/4
<BR>of a beat per second.
<BR>
<BR>In such a tuning, the octaves should not have the kind of stretch you would
<BR>usually give ET or a more modern temperament. The temperament and minimally
<BR>stretched octaves will "kill" all of the usual resonance you expect from the
<BR>piano. The piano will take on an entirely different quality. To me, it
<BR>makes it sound "antique".
<BR>
<BR>Personally, I don't really like this sound but if you really want an
<BR>authentic sound for early music which comes from J. S. Bach's time or before,
<BR>it is the temperament to tune. In a concert setting, you would likely choose
<BR>a piano with low inharmonicity and maybe one which is smaller and less
<BR>preferred. A second piano used for later compositions tuned in a later Well
<BR>Temperament or Modified Meantone would work for music from later periods.
<BR>
<BR>It's not a bad idea in one's home to have the good piano tuned in ET or a
<BR>late HT and the spinet tuned in 1/4 Comma Meantone. Children practicing
<BR>early music on the spinet in Meantone learn a different kind of sound and
<BR>harmony.
<BR>
<BR>It's important to remember that the 1/4 Comma Meantone is at the opposite end
<BR>of the spectrum from ET. While there are even more extreme possibilities
<BR>(the 1/3 Comma Meantone, for example), the 1/4 Comma Meantone represents
<BR>about as radically different kind of sound as you can get from ET.
<BR>
<BR>It is possible to tune a chain of 5ths all the same amount by many other
<BR>fractions of the Comma: 1/5, 1/6, 1/7, all the way to 1/11. The last is the
<BR>equivalent of ET. The 1/7 Comma Meantone has become popular in my area. The
<BR>last untuned 5th rather than being a "wolf" is only slightly dissonant. It
<BR>ends up making the key of Ab have a very powerful, "electrically charged"
<BR>kind of sound.
<BR>
<BR>Enjoy exploring the sound of the 1/4 Comma while you have it.
<BR>
<BR>Bill Bremmer RPT
<BR>Madison, Wisconsin</FONT></HTML>