1/4 comma meantone tuning

[Richard Moody]

----- Original Message -----
From: <Billbrpt@AOL.COM>
To: <pianotech@ptg.org>
Sent: Friday, April 13, 2001 9:04 AM
Subject: Re: 1/4 comma meantone tuning


| Tempering each 5th by
| 5.38 will make 8 pure 3rds and leave 4 very wide (wolf) 3rds and the
last 5th
| which cannot be tuned will be over 40 cents wide.  This untuned 5th
is
| usually left between Ab-Eb but sometimes between Db-Ab.

Since the tuning progression, at least by ear, goes by 5ths up from C
to
G# this note might be better called G# instead of Ab. When speaking to
a music major if you say
"In Meantone the key of E has a pure major 3rd makes sense when that
3rd is called G# rather than Ab.  We all know musicians recognize
differences between Ab and G#.    It turns out in historical tuning
there are  differences also.  Only in ET are there not.   Which I
argue was/is a result, not a design.


| Now, because the piano has Inharmonicity, this changes all of the
above
| slightly just as it skews the values of Equal Temperament (ET) or
any other
| temperament.

Yes as far as machines are concerned.





|To come out right, the 5ths will be tempered a little less,
| more like 5.0 or 5.1 which will leave the 3rds tempered but less
than 1 cent.
|  They will still sound pure but actually have a very slow beat, not
quite 1/4
| of a beat per second.

Yes, I end up with some 3rds slightly wide. As a rule most are "pure
as the driven snow but a few drift slightly."
In re-creating the aural tuning experience especially when following
Aaron's instructions I think some of the 3rds come out a little wide
but not
more than 1/2 bps. And at this rate I would look for off 5ths to cut
it down.
This is what the ear renders (IMHO) because some are "sacrificed"
(from pure) to get the 5ths sounding "even".  The problem for me on
the modern piano aurally is getting the 5ths "even".  I think this was
the problem of our tuner ancestors also. With this in mind I would
like to try MT on harpsichords and forte pianos.

| In such a tuning, the octaves should not have the kind of stretch
you would
| usually give ET or a more modern temperament.

I agree.    Yes, some may say it (octaves wo stretech) sounds "dead"
but wait till the
playing starts.   "Dead on" is more like it as far as octaves are
concerned  even in ET.

| It's important to remember that the 1/4 Comma Meantone is at the
opposite end
| of the spectrum from ET.  While there are even more extreme
possibilities
| (the 1/3 Comma Meantone, for example), the 1/4 Comma Meantone
represents
| about as radically different kind of sound as you can get from ET.

Yes.  1/3 comma MT is supposed to give pure minor 3rds  but after that
what other results? The theoritical ramifications must be much but I
have never seen discussions on this, execpt that Zarlino (sp?) back in
15xx proposed it. Has anyone tried this?  But practically 1/4 MT is as
far from ET as one can get other than on the other side with
Pythagorean or pure 5ths tuning.
 ---2nric