In a message dated 3/18/99 1:25:30 AM Central Standard Time, remoody@easnet.net writes: << Now if I can just find out how terms like "1/4 syntonic comma" lead to the flattening of fiths, in Meantone, and how this was determined by the tuners of the times before 1750. I mean how does 1/4 comma translate into beats per second. Yes I know some where it is written that tuners in the 1700's (18th cent) did not listen to beats, yet the organ tuners did. The exciting part of historical temperaments is that they can be rendered on modern pianos----that the predictions of physists of the 17th and 18th century can be translated into cents and therefore plugged into 20th century tuning machines. In the interest in "hearing the music as the masters did" one must realize that the instruments on which they heard their music no longer exist execpt as museum pieces or reproductions. Hearing modern pianos tuned according to concepts of their time renders the keyboard music of the Baroque and Classical eras in a new light for our times. If performers ask, "Is it possible to tune the modern piano in Meantone by ear?", I would hope to have something to offer. Now if I can just figure out how much 1/4 syntonic comma flattens fifths from the aural perspective. Richard Moody >> While all of the 5ths have the same interval *size*, they increase in speed slightly and gradually as they ascend the scale. In an F3-F4 temperament, it would be from about 1 1/2 beats per second to about 2. There is a good, theoretically correct method in Owen Jorgensen's book, "Tuning" on page 31. When tuning this or any HT on a modern piano, you have to remember to compensate for inharmonicity. As Owen Jorgensen has pointed out in his lectures, "Inharmonicity has the same effect on HT's as it does on ET." This means your octave will be wider, so will your 3rds and your 5ths will be less tempered. The figures given in Owen's book can only serve as a kind of guide. Since they are theoretical, they are not exactly right and even if they were, they are mostly what are called "irrational numbers". This means that even if you knew that your intervals should be exactly the figure indicated, there is no way on earth for you to really know if what you have done is right or not. So just *how* do you do it? For starters, when you go to tune a pure 3rd, the only thing you will have to go by is the absence of a beat. There is no test for a pure 3rd the way there is for a 4th, 5th or octave. Since you know that the entire octave must be expanded, it will be very important to not have your 3rd on the narrow side. The best way to do this is to start from the point where you hear no beat, then gradually widen the 3rd just until you start to hear the faintest beat, then back off, giving the string good, hard test blows until the 3rd just "hangs" there, *apperently* beatless. This is the same approach I would recommend for an octave although you will have some test intervals that can verify it. I would recommend what Ed did for your judgment of the 5ths. Once you have one of the "pure" 3rds tuned, you will have a series of 4ths and 5ths around it. You simply put a good, strong, "lilting" beat in them, deliberately much more than you would ever tolerate in ET. ET can also be called a 1/11 Syntonic Comma Meantone. Since you are tuning a 1/4, your tempering will be almost three times as much as it would be in ET. Just as you might in ET, however, if you see that you have made a cumulative error in your chain of 4ths and 5ths, you can back up through them until you have evened them out. The 4ths will beat a bit faster than the 5ths, just as they do in ET only proportionately much stronger. I would also recommend that you use a piano with relatively low inharmonicity such as a Mason & Hamlin, Baldwin or Kawai. While you can certainly do it on a high inharmonicity Steinway, the scale itself will resist this highly contracted tuning much the same as one of the low inharmonicity pianos resists the highly expanded ET with pure 5ths. The 1/4 Comma Meantone is a very severe departure from ET. It is not the *most* extreme (1/3 is) but it is nearly so. You can think of it as being on opposite ends of the spectrum from ET in all of the possible ways to tune a temperament. It is useful mostly for playing early music, that composed before J. S. Bach. (Some of Bach's earlier compositions are appropriately played in it too.) Some very simple compositions in the simple keys in the Classical period such as those by Mozart will sound appropriate too. It will make the modern piano take on a completely different character. It will have a kind of "antique piano" sound to it just as a result of the way you have tuned it. You should tune the most conservative (2:1) type octaves with this temperament. This will eliminate almost, if not all of the "resonance" that you are used to hearing from the modern piano. You may not like the sound, personally. (I have to admit, I really don't care for it myself). But, it is appropriate for playing these early music styles. There are certain ways of playing ornaments that you can find annotated in good editions of early music that make some of the "rough" spots in the temperament more musically palatable. When playing this music in ET, these tricks are not necessary and therefore, many performers don't use them. The original playing style has thus become lost among most performers. In his book from which the modern art of tuning draws most of its authority, "Piano Tuning and Allied Arts", Dr. William Braide White makes a final comparison between ET and what he simply refers to as "Mean-tone". He gives the impression that there are only two choices, ET and "Mean-tone". He does not acknowledge any other possibility, no Meantones of smaller commas like the 1/5, 1/6 or 1/7, no Modified Meantones where the "wolf" is split to make the temperament more versatile, no Well-Temepered tunings which can run the gamut from Kirnberger and Werkmeister to the very mild, nearly equal Victorian and no Quasi-Equal either. It is no wonder that a single person with a single authoritative publication has been able to literally polarize the entire Occidental music culture into thinking that there can be only one way to tune the piano: nice, smooth, even and resonant ET that can be used for anything. Your only alternative is awkward, dead, bizarre, rough *MEAN* tone with a *WOLF* right in the middle of it that you can't use at all. This has been a very difficult mindset to overcome but I am glad to see the beginnings of its undoing. Good luck with your Meantone adventure! Sincerely, Bill Bremmer RPT Madison, Wisconsin
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