----- 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
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