1/4 comma meantone tuning

[Richard Moody]

1/4 comma MT  or simply MT may be the "original temperament".  If it
is tuned aurally or the aural instructions looked over much of the
"theory" is revealed.
    The theory is -- a series of 5ths, following the circle of 5ths,
flattened by the amount of 1/4 comma ( 5 + cents) will produce a pure
3rd.   Because they are flattened more than in ET, where the circle
ends will way off.  This traditionally was G# to Eb.  When tuning,
the series runs up from C to G# and down from C to Eb.  Math theory
says that there is no such thing as 3 contiguous 5/4 3rds in a 2/1
octave.   (Music theory also says there are not 3 such thirds in an
octave as the 3rd Third is actually an augmented fourth. )  If you
tune pure C--E then E--G#, the remaining G# --C is woefully sharp.
So in MT you have one wolf 5th and 3 wolf 3rds so to speak.   For this
reason MT is said to have a "center of tonality".  The further away
you get from the key of C on both sides the more you run into the
"wolf" intervals.  All of this is not apparent from the cents offsets
a machine needs unless you arrange the notes by the circle of 5ths.
And then it is difficult to detect the "center" (starting point)
    With aural instructions, since intervals are tuned, (rather than
single notes) the intentions and results are immediate, because the
tuning starts from the "center point" or Middle C.   You know to start
playing in C to hear the "best" of MT and for the "worst" try Ab,
which doesn't actually exist since G# was tuned instead of Ab.  When
tuning the  5ths flat, the trick is to make the first 4 give a pure
3rd with the starting note.  This is like the exercise in ET of
flattening 11 fifths and having the 12th "come out" .  But with MT
there is a short cut where one can immediately tune a pure 3rd from
the starting note and only have three 5ths to jockey.  This indeed is
described by Pietro Aaron in his instructions from 1529.   He further
describes tuning 3rds inside 5ths which to my knowledge has never been
mentioned by modern writers but is ingenious and crucial to completing
a musically successful mean tone.  (I am preparing an article on this.
If anyone wants to "review" it , please send an email.)
    The trick is to have the 5ths "sound the same" just as in ET but
of course their tonality is noticeably different.  In fact as was
mentioned the "sweetness" of the triads is astonishing, it is the pure
3rds sounding with the flattened 5th not being heard as expected.  If
you want to hear a "new tonality" play and listen to pieces in the
keys of C to E and C to Bb.   To all of those (including me) who
"don't hear a difference" in the HTs,  you WILL hear a difference in
1/4 MT, which is at least intriguing, and for me delightful.    ---ric

ps---C#--G# should not be noticeably different C--G, I think G#--Eb
was meant for "the very bad 5th")


----- Original Message -----
From: Farrell <mfarrel2@tampabay.rr.com>
To: <pianotech@ptg.org>
Sent: Friday, April 13, 2001 6:52 AM
Subject: Re: 1/4 comma meantone tuning


|played some stuff in the key of C and it sounded
| so pure that it sounded like the piano was kinda dead - sounds
somewhat
| lifeless. Pretty weird. I don't really see a use for it except for
fun.
|
| Terry Farrell
| Piano Tuning & Service
| Tampa, Florida
| mfarrel2@tampabay.rr.com
|
| ----- Original Message -----
| From: "Larry" <lbeach@sfu.ca>
| To: <pianotech@ptg.org>
| Sent: Friday, April 13, 2001 12:13 AM
| Subject: 1/4 comma meantone tuning
|
|
| > Hi folks!
| >
| > How many of you have had the time to waste and put a 1/4 comma
meantone
| > tuning on your home piano? ;)  .
| Nevertheless,
| > it sure demonstrated how nice some chords can sound, and how awful
a
| couple
| > of them were.  (C#-G# is a very bad 5th!)
| >
| > Just curious today....
| >
| > Larry Beach, RPT
| > Vancouver, BC
| >
|