<HTML>In a message dated 12/13/00 8:08:33 AM Central Standard Time, mstore@nic.fi (martin store) writes: <BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">what is the difference between 4-2 octave and 6-3 ??? </XMP></BLOCKQUOTE> Dear Martin, I've been reading your posts and the exchanges with interest.  In the past, I have debated this topic long and hard.  In one sense, there is no temperament which is "better" than any other since for every compromise made, there is a consequence.  However, Equal Temperament (ET) was an arbitrary idea and decision proposed seriously for the first time in the middle of the 19th Century by the scientist (not musician), Helmholtz.  His idea of dividing the octave into 12 equal parts appealed to the logical mind rather than the artistic realities of music as it existed then and still do today. In the early 20th Century, the piano technician (again NOT musician but *technician*), Dr. William Braide White wrote a definitive book on caring for the piano in which tuning was only part of the instruction.  It was the principal source for information about piano technology for most of the 20th Century.  White embraced Helmolz's idea.  In doing so, he dismissed by ignoring (not mentioning or documenting in any way) all of the many ways that people had tuned keyboard instruments until that time.  He makes it seem as though there was only one, outdated way to tune called "Meantone" and the new modern way called ET. Most piano tuners and/or technicians of the time were not musicians but factory workers who had learned a mechanical trade.  They had no basis on which to question or criticize White's teachings.  Over the years, White's teaching of ET became the one and only appropriate way to tune a piano.   Unfortunately, his instructions were somewhat incomplete.  Following them, a tuner could possibly produce an ET but more than likely, an infinite number of unintended effects were the actual result.   Since these effects were not anticipated nor discussed by White, most tuner-technicians did not recognize them.  They believed in ET and only ET and ET became whatever any particular person attempted.  Thus, without realizing it, tuner-technicians produced a wide variety of results and variations in tuning without ever realizing it.  Yet, the firm and steadfast belief was in ET and ET only.  Any challenge to that belief became a challenge to one's entire body of thought.  This has produced highly excited and inflamed reactions from many people:  technicians, musicians, piano teachers, manufacturers and virtually anyone associated with the profession when any other idea about how to tune was proposed. You can easily find information about the ways keyboard instruments have been tuned in the past.  However, you must be aware of three important things:   the fear and resistance factor that I have just outlined, the fact that virtually all of these methods were used on *precursors* to the modern piano and lastly, the present day *expected* way the piano is supposed to sound.   You might try virtually every temperament ever designed and never be satisfied with a single one. That has been my experience.  Therefore, about 9 years ago, I set out to design my own temperament based on historical precedents which would satisfy both the need for what is called "color" in the temperament and yet not offend the expectations that the "contemporary ear" has.  I have not tuned any piano for anyone for any reason in ET for some 11 years.  As soon as I say this, it raises eyebrows and evokes accusations of "unethical conduct" nearly every time.  I just brush it all off and continue to do what I do being happy that I could see through all of the misguided teaching that I had received and that continues today. I'll leave it to others to describe what "partials" are and what the different kinds of octaves are.  Although I understand these, I am not concerned about them at all because the compromise I make has to with the entire premise of the kind of temperament I tune.  The concept is called Equal Beating.  It is done aurally and it is surprisingly easy to learn and as easy to be at least as consistent as people who use Electronic Tuning Devices (ETD) claim that these devices afford. I'll send you the material that I have written privately.  Good luck with your endeavor. Bill Bremmer RPT Madison, Wisconsin</HTML>