{"id":1917,"date":"2016-08-18T19:10:06","date_gmt":"2016-08-18T19:10:06","guid":{"rendered":"http:\/\/casfaculty.case.edu\/ross-duffin\/?page_id=1917"},"modified":"2017-02-23T19:03:59","modified_gmt":"2017-02-23T19:03:59","slug":"why-i-hate-vallotti-or-is-it-young-4-1","status":"publish","type":"page","link":"https:\/\/casfaculty.case.edu\/ross-duffin\/why-i-hate-vallotti-or-is-it-young-4-1\/","title":{"rendered":"Why I hate Vallotti (or is it Young?) 4.1"},"content":{"rendered":"

<\/a><\/p>\n

Why I hate Vallotti – cont.<\/b><\/p>\n

I believe the answer is 1\/6 comma meantone<\/span><\/a>, a regular meantone<\/span><\/a> system where all the fifths but one (the wolf<\/span><\/a>) are narrowed by 1\/6 of a sytonic comma. The resultant temperament has several keys that are equally consonant, several M3rds of good quality, predictable semitones of two different sizes\u2013one for diatonic<\/span><\/a> and\u00a0one for chromatic semitones<\/span><\/a>\u2013as well as other musical assets. Threaded throughout the discussion in Bruce Haynes\u2019s superb 1991 Early Music article (pp. 357\u201381), “Beyond temperament: non\u2013keyboard intonation in the 17th and 18th centuries,” is the frequent re\u2013appearance of 1\/6 comma meantone. Already widely known today as Silbermann\u2019s temperament (after the organ builder and friend of J. S. Bach), it corresponds to ideals for temperaments given by Telemann, Tosi, Quantz, and Geminiani, among others, and is described by the French theorist Sauveur (1707) as the temperament of “ordinary musicians”. The historical evidence as presented by Haynes speaks for itself, and is a stunning endorsement. What better temperament to use as a standard for Baroque music than the one employed by everyday musicians at the time? So, from an historical standpoint for music from the earlier 18th century, 1\/6 comma beats Vallotti and Young. Its cents chart (with rounded approximations) is given here:<\/p>\n\n\n\n\n
\n
Fig 1.<\/b> Vallotti and Young “Circulating” Temperaments in Cents<\/div>\n<\/td>\n<\/tr>\n
\n\n\n\n\n\n\n\n
Fig 2. 1\/6 Comma Meantone Temperament in Cents<\/td>\n<\/tr>\n
C<\/b><\/td>\nC#<\/b><\/td>\nD<\/b><\/td>\nEb<\/b><\/td>\nE<\/b><\/td>\nF<\/b><\/td>\nF#<\/b><\/td>\nG<\/b><\/td>\nG# \/ Ab<\/b><\/td>\nA<\/b><\/td>\nBb<\/b><\/td>\nB<\/b><\/td>\nC<\/b><\/td>\n<\/tr>\n
0<\/td>\n88.6<\/td>\n196.7<\/td>\n304.9<\/td>\n393.5<\/td>\n501.6<\/td>\n590.2<\/td>\n698.4<\/td>\n787 \/ 806.5<\/td>\n895.1<\/td>\n1003.3<\/td>\n1091.9<\/td>\n1200<\/td>\n<\/tr>\n
Procedure: Temper all 5ths by 1\/6 of a syntonic comma<\/a><\/span>, leaving the wolf at Eb\u2014G# or at Ab\u2014C#.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n
Listen to theabove example with Ab (click below)<\/p>\n\n