1/3 Comma Meantone Tuning

[Billbrpt@AOL.COM]

---------------------- multipart/alternative attachment
In a message dated 4/15/01 10:30:42 AM Central Daylight Time, 
remoody@midstatesd.net (Richard Moody) writes:


> 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
> 

Richard,

I appreciate the fact that you are an aural tuner.  I was too exclusively for 
over 20 years until I was finally persuaded to buy and learn to use the SAT.  
My first experience with the 1/4 Comma Meantone was an aural tuning on my own 
piano at home.  It's true that you can tune a "pure" 3rd first, then tune 2 
tempered 5ths which you can "even out" to where they will meet the resultant 
pure 3rds that is desired. 

As far as aural tuning goes, I know of no better approach.  It must be true 
as well that in the days when this tuning was really used, the days of 
harpsichords and the early pipe organs, people must simply have done the best 
they could even if they knew the mathematical theories.  I would agree with 
some of the other statements I have read from you about other fractions of 
the Comma.  How could anyone tune accurately a 1/3, 2/7, 3/10, 1/5 or any 
other theoretical fraction of 21.5?

For that matter, how could anyone look at a list of irrational numbers for 
any temperament, including ET, adjust them for Inharmonicity and proceed to 
tune with unquestionable accuracy?  I have heard that there is an aural test 
for a pure 3rd but I don't know what it is.  Also, I don't know of a test for 
a 2:1 (the so-called "pure") octave although I know and use the tests for 4:2 
and 6:3 octaves and the tests for pure 4ths and 5ths.

The next time I had the challenge of tuning the 1/4 Comma Meantone was for a 
recital Owen Jorgensen was giving at the PTG Annual Convention in Dearborn.  
I had proposed testing a theory I had for using the SAT to construct a 
Meantone Temperament of any fraction of the Comma that may be called for.  I 
had first used my idea with the 1/7 Comma Meantone, not having been able to 
be sure about following the aural instructions given in Owen's first 
publication, Tuning the HT's by Ear.

I declined to use deviations of an FAC program because I did not trust either 
the FAC calculation nor anyone's calculation of the so-called "Correction 
Figures".  While I know that most people attempting to tune HT's are doing it 
this way, I dislike the idea as a matter of principal, to simply use someone 
else's calculations with no way of verifying them myself.  What I did was 
along the lines of a Direct Interval approach where the SAT can show that 
coincident partials match exactly to create a pure interval or also show that 
one is tempered by exactly the desired and/or calculated amount.

I worked up in Owen's room while he was practicing 16th Century music on an 
Electronic Keyboard in ET (Uhggg!).  When I showed what I had come up with, 
he agreed that it looked correct so I was ready to go down and try it on the 
piano.  If it didn't work, the piano's temperament could have been done 
aurally, stored in the SAT and worked with from that point.  It turns out 
that my idea did work.

The piano I used was a 7 foot Kawai RX-6 Grand that had inharmonicity in the 
low end of the moderate range.  As I recall, the 5ths ended up each being 
tuned 5.2 cents narrow (instead of the theoretical -5.38).  This caused the 
3rds which were supposed to be pure theoretically, to end up tempered 0.8 
cents wide.  Whatever beat there may have been was imperceptible.

The advantage in using the SAT, of course was the ability to control the size 
of the intervals precisely to 1/10th of 1 cent and thus have the results be 
impeccable.  The idea of not stretching the octaves the way I usually do came 
from Owen.  His instructions were to tune the Meantone with "minimal stretch" 
and to tune the octaves of the other piano which was tuned in Thomas Young #1 
with "optimum stretch".  He was pleased with both tunings and it was 
interesting to compare the difference in where the high treble ended up 
between both pianos.

I must say that the Meantone piano sounded very strange to me.  All of the 
resonance it had when tuned in ET had been removed.  Although it still had 
the same sustain, the pure sounding chords sounded "dead" to me and quite 
odd, something like the odd way that antique instruments such as the viol 
sounds compared to the modern versions of that instrument, the violin family 
sound when they are played in the typical manner of today.

Even as a vocalist, I struggle with the sound required by early music.  I 
have worked so hard on developing a broad range and a controlled vibrato and 
use of portamento that I have a difficult time singing with a "pure" sound 
that might be appropriate for early music such as Gregorian Chant.  I much 
prefer the Romantic sound of 19th Century Italian Opera and 20th Century 
Musical Theater.

So, my experience with the 1/3 Comma Meantone has only been by using the SAT 
in the same manner as above.  Yes, it produces pure minor 3rds and the Major 
3rds are actually tempered narrow!  It was known to be used by the 16th 
Century composer, Thomas Salinas.  To me, it has a very mournful, "dripping" 
sound.  The chords seem to be "melting" the way that images in a Salvador 
Dali painting do.  I can imagine that funeral music in 1/3 Comma Meantone 
might bring tears to the eyes quite effectively.

I also recognized a sound from the "Wolf" keys that I have heard from the 
opposite side of the world in the Gamelon music from Southeast Asia.  The 
scales and tonalities of music from that corner of the world are completely 
different and incompatible with Western Music values (and I'm not talking 
about Waylon & Willie and the Boys either), particularly those of strict ET.

Listening to Gamelon music can open your ears to the fact that the world does 
not revolve around ET and that there are other kinds of sounds which are just 
as musical but do require getting used to hearing. 

I have often seen it written that Debussy's music should only be played in 
ET.  Of course, it all sounds smooth and nice that way but here is the 
challenge:  Listen to some Gamelon music, then prepare 2 pianos, one in ET 
and the other in 1/3 Comma Meantone.  Then hear for yourself that Debussy has 
actually captured the essence of a Gamelon Orchestra in his composition and 
that the modern piano can really mimmic this sound if tuned this way.  The ET 
version will pale in comparison,  sounding about as removed from authentic as 
a bad, fast food egg roll from an American Chinese restaurant compares with 
real Chinese food prepared in the traditional way.

You'll definitely need a piano where you are free to do something radical, 
however.  The "Wolf" will end up being 55 cents wide!  Even if your A is 
tuned at 440, your G# (Ab), will end up at -25 cents and your Eb will end up 
at +30 cents!  This will really upset the usual tuning of the piano so you 
would not want to do it on a really fine, expensive instrument.

It's worth the adventure though if you can find the right piano to take a 
trip through a "black hole" to the opposite side of the world.  One further 
note of interest:  it just so happens that the 12 notes of the 1/3 Comma 
Meantone are the same as those of the Javanese scale and those of the 
corresponding 18 tone ET scale.

Bill Bremmer RPT
Madison, Wisconsin

---------------------- multipart/alternative attachment
An HTML attachment was scrubbed...
URL: https://www.moypiano.com/ptg/pianotech.php/attachments/f1/f7/4b/53/attachment.htm

---------------------- multipart/alternative attachment--