<HTML>In a message dated 4/15/01 10:30:42 AM Central Daylight Time, remoody@midstatesd.net (Richard Moody) writes: <BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">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.</BLOCKQUOTE> 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</HTML>