This is a multi-part message in MIME format. ---------------------- multipart/alternative attachment Hello, I'm sure this will sound like a very simple question. I'm trying to = follow the conversations on these different temperaments. I have not = the slightest idea what most of them are. Is there a book that explains = the different temperaments and how to set them aurally? I'm new to this = and Equal Temp. is the only temperament that I have been introduced too. = Since it's the only one I've known, I like it but there seems to be = some very strong likes for other temperaments that I don't know. Please help. Bobby Sims sims-n-sons@ev1.net ----- Original Message -----=20 From: Billbrpt@AOL.COM=20 To: pianotech@ptg.org=20 Sent: Monday, October 22, 2001 6:38 PM Subject: Re: SV: Aaron and Meantone In a message dated 10/22/01 6:10:56 PM Central Daylight Time, = pianola@online.no (Ola Andersson) writes:=20 /7 comma and 1/8 comma must be a modern temprement. They should not = be called HT. I think tuning MT with a computer is another consept than = what Aaron and his friends was doing. I guess there is nothing wrong = with 1/7 MT but it is not a HT. It was a comment to Bill Bremmer who = called it at modern pianotuning or something wich I agree it is.=20 By the way I often tune a 1/12 comma meantone:-)=20 The 1/7 Comma Meantone is indeed an HT. It was designed by = Jean-Baptiste Romieu in France, 1755. It can be found in Owen = Jorgensen's first publication, Tuning the Historical Temperaments by = Ear. Although there are some historically documented 1/8 Comma Well = Temperaments, there is no 1/8 Comma Meantone. It, therefore, is a = modern temperament.=20 All of the different Comma Meantones are easily constructed with an = ETD. By definition, a Meantone Temperament is a chain of 5ths all = tempered exactly by the same amount. There can be variations but a pure = Meantone Temperament is constructed this way. The Comma to which they = refer is the Syntonic Comma whose value is 21.5. If you divide 21.5 by = 4, you get 5.375. Therefore, a 1/4 Comma Meantone's 5ths are all = theoretically 5.375 cents narrow.=20 You can create a Meantone of any fraction you want. A properly = constructed 1/8 Comma Meantone has 5ths of about 2.5 cents narrow (when = adjusted for inharmonicity). This will produce mild 3rds like those of = the Victorian Temperaments and a very mild "Wolf" 5th (about 5 cents = wide).=20 The Modified Meantone Temperaments are a whole class of Temperaments = which may temperament researchers ignore. What they do is to take that = "Wolf" of a Meantone Temperament and divide it between two or more of = the 5ths among the black keys. This smoothes out the dissonance of the = "Wolf" itself and the 3rds on that side of the temperament.=20 My EBVT is, in fact, an Irregular 1/8 Comma Modified Meantone = Temperament. Normally, a Modified Meantone Temperament could not = satisfy the Rules for Well Tempered Tuning written by Andreas = Werkmeister but in this case, the modifications allow it to just barely = meet those rules. It can therefore also be considered a Victorian style = Well Tempered Tuning.=20 ET is actually the equivalent of a 1/11 Syntonic Meantone Temperament. = 21.5 divided by 11 is 1.954, virtually the same as the -2 cent ET 5th. = The Ditonic (not Diatonic) Comma value is 24 cents. ET is also a 1/12 = Ditonic Comma Meantone.=20 If a customer asks me if there is a choice of how to tune the piano, I = always say, "Yes, a nice, sounding, Well Tempered Tuning or that awful = 1/11 SYN-tonic MEAN-tone tuning. Which would YOU prefer?" So far, none = has ever asked for ET. }:)=20 Bill Bremmer RPT=20 Madison, Wisconsin=20 ---------------------- multipart/alternative attachment An HTML attachment was scrubbed... URL: https://www.moypiano.com/ptg/pianotech.php/attachments/cb/08/63/43/attachment.htm ---------------------- multipart/alternative attachment--
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