Richard Moody wrote: >`Thanks Paul for posting the "Rules". It is one more incentive (esp >to me) to buy his book. However I am wondering if >"Tuning The Historical Temperaments By Ear" by Owen Jorgensen is a >different work from "Tuning" (by Jorgensen) listed as #572629 in the >American Piano Supply Co (APSCO) catalog. >What I am really wondering is, are there "Instructions" as to how >tune WT? : To my knowledge, there are three books by Owen Jorgensen: 1. TUNING THE HISTORICAL TEMPERAMENTS BY EAR Northern Michigan University Press, 1977 Unfortunately, this is out of print. Ch.I is HOW THE MUSICAL SCALE DEVELOPED THROUGH THE JUST TUNINGS. This book is a great resource for education and also for practical use. 2. THE EQUAL-BEATING TEMPERAMENTS-A Handbook for tuning harpsichords and forte-pianos,with tuning techniques and tables of fifteen historical temperaments. Raleigh: the Sunbury press, 1981. I think you might find this at: HARPSICHORD CLEARING HOUSE Glenn Giuttari 9 Chestnut St. Rehoboth MA, 02769 800-252-4304 It's a slim paperback,only about 35 pages. In a sense it's the most concentrated wealth of practical knowledge of the three. The equal beating temperaments don't depend on accurate estimation of absolute beat rates, or pitch levels. The results are often more musical than "theoretically correct" temperaments. Equal Beating Temperaments are probably more similar to what was done in the past. Fred Tremper has worked out the cents dev. from ET for the 15 temperaments of THE EQUAL BEATING TEMPERAMENTS, perhaps he would still send copies to those who send him a stamped, self-addressed envelope. 3. TUNING Containing The Perfection of 18th Century Temperaments, The Lost Art of 19th Century Temperament and The Science of Equal Temperament with Instructions for Aural and Electronic Tuning. Michigan State University Press East Lansing 1991 >My novice, (some might argue tyro) understanding of temps other than >ET, the size of the intervals is dictated (for lack of a better word) >by where one starts. Usually from middle C (older) or A above >middle C (modern). Would WT also be thus affected? The sizes of the thirds is determined by the amount of tempering of the four conjunct fifths that intervene. 'for instance, C E is 21.5 cents wider than pure if CG , GD , DA and AE are all just fifths. If each fifth is contracted from pure by 1.95 cents, CE will be 21.5 -( 4 x 1.95)=13.7cents; and if each fifth is reduced by (21.5 / 4 ) cents, CE will be pure. One reason most 'older' temperaments started from C is; many well temperaments have just fifths from C to F to Bb to Eb to Ab to Db to Gb (F#) ; and then the remaining 'long' keys are tempered to create equal beating pairs of intervals. For instance, since Bb and F# were tuned in the partial cycle of just fifths , D could be tempered to create two equal beating thirds between Bb D and D F#. Several well temperaments have this characteristic. If the conjunct thirds Bb D and D F# have the same beat rate, they are equal beating thirds. If Bb D and D F# have a beat rate ratio of 4:5 they will be the same width in cents, and "theoretically correct", in contrast to equal beating. >Now Jim mentioned figuring it out by spread sheets. They (mine) >can only give beats per second of intervals, or cents deviation from >each note in ET. I am willing to give it a try. >Richard Moody You can learn a lot by sketching circles of fifths, thinking of the fifths as just until you deduct so many cents from them, then the thirds will be the size of 21.5 cents minus the total cents tempering in the four in-between fifths. Play around with this on paper, and patterns will emerge....keep in mind you have a total of 23.4 cents of tempering of the fifths to play with before you will induce a wide fifth and the resultant 'harmonic waste'. Paul Bailey RPT
This PTG archive page provided courtesy of Moy Piano Service, LLC