---------------------- multipart/alternative attachment Hi Phil, Too bad Prof. Jorgensen's books are out of print. I think you could=20= buy a photo-copy of '' Tuning the Historical Temperaments By Ear'' from Tim Farley RTT, he=20= is in the directory. And I suspect the little yellow 'chapbook' that came out between the ''=20= tuning the h.t.'s by ear'' and the mighty TUNING is available - do a 'google' on tuning and/or=20 harpsichords and look thru the results... One of my personal favorites is Dr. H.A. Kellner's Wohltemperirt/Bach. A=20= description and the aural bearing plan is available at: = http://ha.kellner.bei.t-online.de/ Wohltemperirt Werckmeister/J. S. Bach: Some mathematics The 19 steps of the bearing plan in detail: =A0 1 c1-c0 Descending octave from middle c 2 c1-f0 Descending pure fifth from middle c. Verify pure fourth = c0-f0 3 f0-Bb Descending pure fifth 4 Bb-bb0 Transposition by ascending octave. Verify pure fourth = f0-bb0 5 bb0-eb0 Descending pure fifth. Verify pure fourth Bb-eb0 6 eb0-eb1 Transposition by ascending octave. Verify pure fourth = bb0-eb1 7 eb1-ab0 =A0Descending pure fifth. Verify pure fourth eb0-ab0 8 g#0-c#0 =A0Descending pure fifth 9 c#0-c#1 Transposition by ascending octave. Verify pure fourth = g#0-c#1 10 c#1-f#0 Descending pure fifth, Verify pure fourth c#0-f#0 11 f#0-B Well-tempered fifth. Within the B-major triad the third = B- d#0 must beat six times faster than the fifth B-f#0 12 B-b0 Transposition by ascending octave 13 b0-e0 Descending pure fifth. Check enlarged basic third c0-e0:=20= must beat very slightly indeed from above. Verify pure fourth B-e0 14 e0-e1 Transposition by ascending octave 15 c0-g0 Well-tempered fifth, flattened. Must beat from below at=20= the same rate as the third c0-e0 beats from above within the C-major=20 triad. Beats slightly faster - virtually at the same pace - as the=20 well-tempered fifth B-f#0 a semitone below 16 g0-d1 Well-tempered fifth. Flattened to beat 3/2-times faster=20= than c0-g0 17 d1-d0 Transposition by descending octave 18 d0-a0 Well-tempered fifth. Beats hardly faster - virtually at=20= the same rate - as c0-g0,=A0 a whole tone below 19 a0-e1 Check: This must be a well-tempered fifth; e1 must not = be=20 changed. Compare beat-rate with g0-d1 a whole tone below. Play c-e-g and=20= listen to this well-tempered C-major triad which opens the door to=20 performing music in all 24 keys, both major and minor. = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= There! I copied the Bearing Plan from the web site: Get to it! Hmm....I think you might find in a PTG Journal from 10 or 12 years ago a=20= Jousse/Ressel Victorian Well Temperament- Jousse lived in the 19th century, Ressel is our contemporary, and=20 'translated' Jousse's bearing plan into beat rates, etc. that a 20th century trained piano tuner would understand. You will find some aural bearing plans here: = http://www.music.indiana.edu/som/piano_repair/temperaments/ Ah! Google is wonderful! = http://www.hubharp.com/books_forsale.htm B-007: The Equal-Beating Temperaments by Owen Jorgensen $21.00 postpaid in U.S. A handbook for tuning harpsichords and fortepianos, with tuning=20 techniques and tables of fifteen historical temperaments. = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D I am partial (oh, a pun) to these 'equal beating' temperaments.=20 Generally they start with a partial series of just fifths from C or=20 sometimes from F, going in the direction of flats, 'down' by fifths, to Gb. Then=20= there will be a strategy of tempering the remaining white or long keys by equal beating or simple proportional beating temperament=20 decisions/checks. No abstract grabbing a beat rate out of thin air. In my experience and in my opinion, the equal beating temperaments that=20= have 21.5 cent thirds in the keys of Gb, Db and maybe Ab and maybe B sound smoother and more resonant than some of the=20 'theoretically correct' temperaments that also have a few 21.5 cent=20 thirds in the right places, and look better balanced 'on paper'....but there is something=20= to be said, for instance, for the Thomas Young Representative 18th=20 Century Temperament; its sounds do exactly represent the form of the notation =20= system. It might be good to learn one or two 'milder' or Victorian style well=20 temperaments - those 21.5 cent thirds push the tolerance envelope for a lot of modern ears - in fact, Valotti had a bearing plan for his 1/6=20 comma well temperament that was a little more difficult to tune, but=20 resulted in the largest thirds being just a smidge smaller than 'pythagorean' . = Paul Bailey = Modesto CA On Wednesday, May 8, 2002, at 04:32 PM, Phil Bondi wrote: Hi Paul. Having fully investigated Bill Bremmer's EBVT( and for the most part I=20= like it), I feel I am ready to involve myself with the World Of Well. I prefer to tune aurally. Do you know where I can find a aural procedure that will tell me how to set a good Well Temp.? Thanks, -Phil Bondi (Fl.) tito@philbondi.com ---------------------- multipart/alternative attachment A non-text attachment was scrubbed... Name: not available Type: text/enriched Size: 6382 bytes Desc: not available Url : https://www.moypiano.com/ptg/pianotech.php/attachments/43/45/1e/d9/attachment.bin ---------------------- multipart/alternative attachment--
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