Tuning (Owen Jorgenson) [PDF]

Zitiervorschau

·~~ TU§J?ERFECTION OF EIGHTEENTH,CENTURY TEMPERAMENT

IHE LOST ART OFNINETEENTH:-CENTURY TEMPERAMENT AND THE SCIENCE OF EQUAL TEMPERAMENT

yy~ THE PERFECTION OF EIGHTEENTH-CENTURY TEMPERAMENT THE LOST ART OF NINETEENT:ltl:CliNTURY TEMPERAMENT AND THE SCIENCE OF EQUAL TEMPERAMENT

INSTRUCTIONS FOR AURAL AND liLECTRONIC TUNING

OWEN

H.

JORGENSEN

Michigan State University Press East Lansing

1991

To my wife Barbara who made this book possible

CONTENTS OF TABLES FOR ELECTRONIC TUNING .................................................. xv Temperaments Used as Substitutes for Equal Temperament Regular Meantone ·Temperaments Modified Meantone Temperaments Well Temperaments Quasi-equal Temperaments LIST OF TABLES SHOWING THE SIZES OF MAJOR THIRDS IN CENTS IN PERSPECTIVES Temperaments Used as Substitutes for Equal Temperament Regular Meantone Temperaments Modified Meantone Temperaments Well Temperaments Quasi-equal Temperaments

xvii

LIST OF MISCELLANEOUS TABLES .......................................................... xix LIST OF FIGURES SHOWING THE FORMS OF TONALITY OR HARMONIC BALANCES ............ xx PREFACE ........................................................... ·........................ xxi HINTS ON HOW TO USE THIS BOOK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................ xxii SECTIONS 1. Equal was notpracticed on pianos in 1885 ... , .............................. . Why was not on before the twentieth century . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Nomenclature..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. "These Half-tones whether be or 1t rn a in 1636 . . . . . . . . . . . . . . . 5. "He that desires to know the true Proportions ... let him read ... Mersennus" . . . . . . . . . . . . . . 6. The ratios of equal Marin Mersenne in 1636 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Monsieur Boulliau' s fourteenth-century Pythagorean temperament . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Tuning the Boulliau tn'.lrestrictive irregular circulating Pythagorean temperament of 1373 in the theoretically correct manner. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. Tuning the Boulliau unrestrictive irregular circulating Pythagorean temperament of 13 73 in the equal-beating manner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10. Tuning the Boulliau unrestrictive irregular circulating Pythagorean temperament in the style of Henricus Grammateus of 1518.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Marin Mersenne and meantone temperament in 1636 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pietro Aaron's restrictive regular noncirculating one-fourth syntonic comma 12. meantone keyboard temperament of 1523 in the theoretically correct manner. . . . . . . . . . . . . . . . William Holder and meantone temperament 1694....................................... 14. An authentic way to tune seventeenth-century meantone temperament. . . . . . . . . . . . . . . . . . . . . . . . . 15. and of the 'Characters

4 8 11 13 15 18

21 24

26 28 31 37 39

44 --,,.,,,urn•K meantone

tPn'"!l'IP•r(>site (J..:sna1rp. In this case, the tuner is expected to turn his dial so that the tone for G-sharp will read 5 cents flat flat) and then tune accordingly. The dial is set 5 cents flat because there is a minus sign in front is a plus sign in front of a number, then the dial should be set to read sharp for the note to be tuned. finished setting the temperament, the tone A will be at standard pitch, but all the other tones will ch~,,.,.,,,,. than the same tones in equal temperament in most cases. If the tuner wishes to set a temperament then all the figures in a table must be reduced accordingly by the arbitrarily chosen number for electronic tuning are listed on pages xv-xvi. ~h~l2(kJ1lethods

outlined in this book are categorized under the following classifications. The numbers refer to the.sections containing tuning instructions. The instructions for electronic tuning follow the instructions for aural tun~rig in most cases. Topic

Sections with Tuning Instructions

Substitutes for Equal Temperament ............ 8, 9, 10, 91, 92, 129, 135, 136, 190 Regular Meantone Temperaments ............. 11, 12, 14, 18, 29, 30, 33, 36, 94, 95, 103, 106, 114, 146 Modified Meantone Temperaments ............. 16, 56, 66, 68, 71, 83, 107 Weil Temperaments .......................... 22, 25, 27, 38, 40, 41, 46, 47, 49, 50, 52,58,60,61, 70, 71, 73, 75, 76, 78, 79, 88, 89, 116, 122, 123, 124, 163, 164, 165

.... 86,

100, 109, 111, 127, 131, 137, 138, 141, 143, 147, 149, 150, 154, 155, 156, 157, 159, 168, 172, 173, 180, 181, 188, methods, 194, 199, 201, 206, 207, 209, 211, 212, 216

Equal Temperament. ......................... 98, 119, 133, 145, 170, 178, 184, 185, 186, 195, 196, 202, 204, 213, 215, 217, 221, 225

1.;' .·; ~· .;~ ;.'~fore.1~85, '({···:··

·u·e·n~ies

anai;;·~.··· usi~~;t~d~us

•. th.e.. fteq··. ...()·t· to·.ne. s were by sirens and electr·o·W;tgnetic devic.es ..T.he . ·/ tuning.fork tonometer.was inventedin 1834.by Johann Heinrich Scheibler. This consisted of 52 tuning forks .·... f~~!~n~.Clc~\{e, ..A tQ ·A, For. anal.ysis,. dlis pr()ved s¥peri.or tQ the other deyices .. The acoqstician Alexander John Ellis ·· · used. a bighfy. refln.ed tono1lleter. col).sis'tj,ng...o:(.•W~.•NnbtgfQtlcs ranging f:rom; A below middle C to· a rattJer flat D, i1,~j~.ninth abo'{e D!ll~o). ,!J'~~y t)rlfnt()fedthela'ccepted tempetan,tellts'as·usedihy'i~eyboard musiciatts. Later iii tfitif 1iVes,:theylfo'1ame'Utofeplli.Jbsl>pftic at!d, ilsmafitre old men, they promoted the avant~garde notion that equal teffffterttm:ent'slt()uld b~'applied;, oh keyhoorct~instrumefits •.. ItiS''iiffipbttantmtOOii:tefhat th'e• ltm~ingpro}'.fMentsdfeqoal'tempei'ament such·as:' Metsettne;. Werckmeister, Neidhardt, Ra)'neau, and· Marpurg, were• sirilplyia\tant;,garde theorists who were proposing a phllos~phk ideal. They furnished rttf ttining iflstroctiofis containittgifh'e'{leces~aty.'informanorl on wh:ere to listen; for bearing fimong the nearly-coinciding harmonics; how fast eaclH:i.eatill1' fr~ttency s~outa. t>e, o,r the' fact that any intewal. when pfayed chromatically up the 1ootcsstaKtliat A1fl'~.1an\es Hi~JUffs intf()dtic~e~wdlemper~nHo tli~ Broadwood ·· · · · ·· · · · · ·· · t'Jt1~rl!Jtl~nt ~as · ~.S~~(!le~~ ~¥ l ~s~. 'fhe .following para't~~k:iruts liftd o... . . \vhti4ltlv~afbm4i~·understan