SV: Aaron and Meantone

[Bobby R. Sims]

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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

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