<HTML>In a message dated 4/26/01 8:36:45 AM Central Daylight Time, jformsma@dixie-net.com (John M. Formsma) writes: <BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px"><< snip... Marpurg-Neidhardt Composite Quasi Equal Temperament.>> Is this one of your creations, or is it found in the Jorgensen book? </BLOCKQUOTE> No, it is actually a creation of Owen Jorgensen's.  It is found only in his hard to find second publication, the "Handbook" for tuning the Equal Beating Temperaments. If you are really a good aural tuner though, I can describe how to tune it in just a few words that you should be able to remember without even writing it down: Tune A4, A3 as usual, then F3-A3-C#4-F4 exactly the same as in ET. (4:5 contiguous 3rds).  Then, from each of those notes tunes so far, tune the 4th and 5th that can be tuned from them perfectly pure.  (From F3: Bb3 and C4.   From A3: D4 and E4.  From C#4:  F#3 and G#3.) Now there are just 3 remaining notes:  G3, B3 and D#4.  Tune each of these Equal Beating:  G3 so that it beats the same against C4 and D4.  B3 so that it beats the same against F#3 and E4.  D#4 so that it beats the same against G#3 and A#3. These tempered 4ths and 5ths will stand out markedly against all of the other pure 4ths and 5ths.  They are the same as you would have in 1/6 Comma Meantone.  However, if you will use my Tempered octaves idea, you will find that you can even "hide" that sound.  Also, when you play triads associated with these tempered intervals, the Equal Beating effect will also "hide" the tempering which is noticeable when the interval is played alone. In short, you will have an ET type sound but a far "cleaner" and "clearer" one than with any other version of ET (contracted or stretched out). This idea is not new.  It's been around for a long time.  For some tuners, it is the only temperament other than a strict ET that they will dare to try.   It is excellent for Jazz and as a concert grand tuning for a concerto.  It is, in fact, a favorite of Horace Greeley RPT.  (We argued about that choice a couple of years back on the list when he used it for the Beethoven Emperor Concerto.)  I prefer the Vallotti Temperament for that piece.  Tom Cole RPT attended the performance where Horace used it.  I'm sure he still remembers the sound. Try it sometime soon, you'll be amazed at the clarity and smoothness and particularly that the 3rds & 6ths are exactly the same as in ET.  It may sound impossible but try it for yourself and see that it really does come out that way. Bill Bremmer RPT Madison, Wisconsin</HTML>