Who invented ET

[Richard Moody]

----- Original Message -----
From: <A440A@AOL.COM>
To: <pianotech@ptg.org>
Sent: Thursday, January 04, 2001 5:33 AM
Subject: Re: Who invented ET

Ed writes....

Greetings,
   Not really intending to nit-pic-ric, but I got a few questions:

ric posted earlier.....
<<There are mentions that the Chinese knew the concept 3000 years ago>

Ed.......
I have nothing to do but agree with that, (just because I've been told
this often....)

Ric replies....
    Yes we need an exact reference. But I have seen it "several" places.

ric rote earlier.....
>>Aristoxenes gave the math concept in 400 BC (ca)<<

Ed replies.......
   It was my understanding that Aristoxenes promotoed a 12 notes scale
consisting of 10 equal steps and two larger ones.  If this is correct, I
don't think we should consider Aris to have been promoting what we are
pointing to as ET

ric replies to Ed's reply.
    yes that rings a faint bell. Once again we need to state references to
really get this sorted out. But with so much reading and with what comes
online these days it is impossible to keep track only by memory.  It is my
recollection that Aristoxenes may have proposed both, or addressed one while
proposing the other ie, a scale equally divided by a mathamatical formula.
That this got into the debate of what was "beauty"  He said let the ears
decide.  The "others" said beauty is related to simple proportions.  But
then there were those commas.

<Vicenzo Galilei in 1581 for ET on the lute. (18/17 ratio)>
  Yes,  dang close to ET, but did he not admit to the slight compromise?
    ++  I don't know.... The strings when pressed down make up for this, I
read some where but again forgot where.  It might have been VG himself....
it is 99 cents (98.95)...so close how did they really know it was a "slight
compromise"?

<<Mersenne gives very close monochord lengths for ET in 1635.>
   I read Jorgensen to state that Mersenne gave the definitive mathematical
ratios for ET.
++That is how Mersenne got them, multiplying ideal monochord lengths by
1000. Or giving a hypothetical monochord in 1200 units.... to establish the
math.

<<James Broadwood writes how to tune it in 1811.>>
    I was not aware that Broadwood wrote "how" to tune it, just that his
factory was then using "ET",( but Hipkins and Ellis seem to offer a
different
point of view>
++ Yes this reference is not in in Jorgensen or Lindley in the Groves
article "Temperaments". It is in the London Journal of Philosphic Sciences,
or something like that.  I have not seen this. I haven't yet emailed
Cambridge to scan it and send it back. It might also be in the Library of
Congress.  This is one I want to dig out and do an article on. ---ric


<<Claude Montal tuning instructions of 1837>>
    Were not the Montal writings published in 1832?  (Not sure on this one
either)    Regards all,
Ed Foote RPT

++Egads, the Groves bibliography to the "Temperaments" article by Lindley
gives 1834.  The title page from a modern facsimile gives 1836.  So 1837 is
for sure at least.
   ---ric



For the latest on Aristoxenes............


(Aristoxenus)

      Title: Apollo's lyre : Greek music and music theory in antiquity
          and the Middle Ages / Thomas J. Mathiesen.
      Library: University of Minnesota, Twin Cities
      Authors: Mathiesen, Thomas J.
      Published: Lincoln, Neb. : University of Nebraska Press, c1999.
      Description: xv, 806 p. : ill., 3 maps ; 24 cm.
      Series: Publications of the Center for the History of Music
          Theory and Literature ; v. 2
      Subjects: Music, Greek and Roman -- History and criticism.
          Music, Greek and Roman -- History and criticism --
          Bibliography.
          Music -- Theory -- To 500.
          Music -- Theory -- 500-1400.
      Notes: Includes indexes.
          The bibliography (p. 669-783), intended to be comprehensive
          for the field, updates and expands: A bibliography of
          sources for the study of ancient Greek music / Thomas J.
          Mathiesen. Hackensack, N.J. : J. Boonin, 1974.
      Contents: Introduction -- Musical Life in Ancient Greece. Music
          and Melos. Types of Music and Their Function. Music for the
          Gods. Music in the Theatre. Music for the Mortals -- Musical
          Instruments. Idiophones and Membranophones. Krotala.
          Kroupezai or Kroupala. Kumbala or Krembala. Seistron and
          Rhombos. Rhoptron and Tumpana. Aerophones. Aulos. Syrinx.
          Hydraulis. Salpinx and Horn. Chordophones. Origin, History,
          and Types. Lyres. Psalteria -- Music Theory I: The Sources,
          Aristoxenus, and the Sectio canonis. Overview of the
          Sources. Aristoxenus. Harmonica. The Sectio Canonis -- Music
          Theory II: The Revival. Plutarch. Cleonides. Nicomachus of
          Gerasa. Theon of Smyrna. Claudius Ptolemy -- Music Theory
          III: Late Antiquity. Gaudentius. Porphyrius. Aristides
          Quintilianus. Bacchius. Alypius -- The Tradition in the
          Middle Ages.
      Summary: "Apollo's Lyre is aimed principally at the reader
          interested in the musical typologies, the musical
          instruments, and especially the historical development of
          music theory and its transmission through the Middle
          Ages."--BOOK JACKET.
      ISBN: 0803230796 (cloth : alk. paper)
      ---------- Holdings ----------
      Library: University of Minnesota, Twin Cities
      Location: MUSIC
      Call No: ML169 .M39 2000
      Item Status:
      Volume: Item:
      Status: Available