<HTML>In a message dated 11/16/01 7:40:55 AM Central Standard Time, Tvak@AOL.COM writes: <BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">Did I misinterpret something that was posted recently in the discussion regarding temperaments?  I was surprised to learn that ET did not really exist prior to 1917.  Now, the part I'm unclear on: I believe that it was stated that this treatise, published in 1917, was the first to utilize the concept of listening to beats in order to tune a temperament.   First of all, is the above information correct?  And if it's true that tuners didn't use beats to tune a piano prior to 1917,  what did they listen to?  I can't imagine.  (I must have misunderstood the information posted.)   Certainly, tuning unisons could not be done without eliminating beats.    Perhaps tuners didn't use coincidental partials to tune prior to 1917? Straighten me out!</BLOCKQUOTE> I find it very ironic that 1917 was also the year of the Communist Revolution in Russia and that it took about the same amount of time to liberate those people as it did for people to begin to understand that there really can be more than one way to tune a piano. I concur with both Richard B. and Ed Foote.  People have always used beats to tune even if they have not recognized them for what they are or "counted" them as such.  Until at least the middle of the 19th Century it was thought that no one could discern a beat rate of more than a few beats per second.  Now, highly skilled technicians can discern rates up to 15 beats per second or maybe even more. Maybe this will ease the mind a little. "Counting" beats as such is not really the goal as much as *comparing* them is.  When I tune a temperament other than ET (which is *always*), I don't even try to follow any schemes where the only information provided is in irrational numbers (3.6, 9.7, 10.1, etc.) which are never correct anyway because they are only theoretical.  When tuning aurally, I only use methods which employ the *Equal Beating* principals because the ear can really discern very accurately when two intervals, especially the rapidly beating ones beat *exactly the same*, whatever that rate is. Unfortunately and ironically as well, *Equal Temperament* has no Equal Beating intervals to tune!  Yes, when completed, all 4ths & 5ths need to have that very slightly tempered sound which should all be alike but each of the Rapidly Beating Intervals, the 3rds and 6ths should be different from each other.  Any two 3rds which beat exactly the same indicates an error. What is important in learning to tune ET aurally is the ability to make an *estimate* and to compare.  Really, the only beat rate to learn is that first 7 beats per second that F3-A3 should have.  After establishing the first note, A4 by comparing it with the fork as a dead unison and verifying it with the F2-A4 test and ascertaining that the F2-A4 of the piano and F2-Fork beat *exaclty the same* (whatever that rate happens to be), the first octave A3-A4 is tuned. That is found by first finding an apparently beatless sound, then flattening the A3 just slightly until just the beginning of a beat can be heard.  Then, the best placement for A3 is found by making 2 comparisons which reveal the 4:2 and 6:3 type octaves.  For ET, a compromise between these two is usually best. Play F3-A3, then F3-A4.  If both intervals beat exactly the same, you have a 4:2 octave.  Play A3-C4 then C4-A4.  If both intervals beat exactly the same, you have a 6:3 octave.  The trick is to get something that falls between the two, neither one nor the other.  The beats are very rapid so don't think in terms of *counting* them but comparing very fine gradations of rapid beats.  If the piano has low inharmonicity, there won't be much distinction but if it has high inharmonicity, the distinction can be easily heard. After getting this first octave tuned, *estimate* the 7 beats per second of the F3-A3 interval.  Then tune F4 from F3 and try to find that same kind of compromise that was done between A3 and A4.  Now, fill in C#4.  If your 7 beat per second estimate for F3 was correct, you should be able to hear the all important 4:5 Ratio of Contiguous 3rds. Again, don't *count* but *compare*.  for every 4 beats in F3-A3, there should be 5 beats in A3-C#4.  For every 4 beats in A3-C#4, there should be 5 in C#4-F4.  For every 4 beats in C#4-F4, there should be 5 in F4-A4.  After practice with this concept, it will be discovered that it is easier to hear when the relationship is *incorrect* than when it is correct. If two contiguous 3rds beats exactly the same, there is an error.  If the lower one beats faster than the upper one, there is a significant error.  If the upper one beats much faster than a 4:5 ratio would be, there is an error.  The trick is to get these 4 beginning notes to have the proper relationship to each other.  After that, the rest of the notes of the temperament will fill in with comparative ease. Practicing just this 4 note beginning sequence is the best thing an aural tuner can do to achieve the kind of standards which are expected today.  If this relationship is not correct and cannot be established, the temperament can never really be what is known today as a true Equal Temperament. Incidentally, if you are at all interested in a very mild alternative to ET, you can easily learn to tune the Quasi Equal Temperament known as "Marpurg" because it starts with this very same relationship. I hope this answers more questions than it generates but if it does generate new questions, don't be afraid to ask. Bill Bremmer RPT Madison, Wisconsin</HTML>