{"id":1913,"date":"2016-08-18T19:09:55","date_gmt":"2016-08-18T19:09:55","guid":{"rendered":"http:\/\/casfaculty.case.edu\/ross-duffin\/?page_id=1913"},"modified":"2017-02-02T19:54:13","modified_gmt":"2017-02-02T19:54:13","slug":"why-i-hate-vallotti-or-is-it-young-2-1","status":"publish","type":"page","link":"https:\/\/casfaculty.case.edu\/ross-duffin\/why-i-hate-vallotti-or-is-it-young-2-1\/","title":{"rendered":"Why I hate Vallotti (or is it Young?) 2.1"},"content":{"rendered":"

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

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

Some continued to use quarter comma meantone<\/span><\/a> in spite of its limitations: it\u2019s arguably still the best choice for much music of the early\u2013 to mid\u201317th century and it continued to be used for organs long after that. Others chose to compromise the purity of the thirds slightly, tempering all the fifths equally but not as much as in quarter comma meantone. These\u00a0regular meantone<\/span><\/a> systems\u20131\/5, 1\/6 comma, etc.\u2013feature good chords in the same places, but although the thirds are not as good as in quarter comma, the fifths are better, and complex harmonies are better. All of these regular meantone systems share one problem interval, however: a “wolf<\/span><\/a>“\u2013one fifth that isn\u2019t even really a fifth because it is so far out of tune.<\/p>\n

Thus, theorists were motivated to explore other tuning solutions. Many of these involved a core or “backbone” of tempered fifths, along with some fifths tempered not at all (e.g., Kirnberger), not so much (e.g., Neidhardt), or even tuned wider than pure (e.g, temp\u00e9rament ordinaire). These are all termed “irregular<\/span><\/a>” systems because they use different sizes of fifths. Those that eliminate the wolf and are serviceable in a variety of keys are called “well” temperaments<\/span><\/a>, or even“circulating” temperaments<\/span><\/a> if they can be used\u2013for better or worse\u2013in all keys without adjustment. This is the category to which belong the temperaments devised by Francesc\u2019 Antonio Vallotti and Thomas Young.<\/p>\n

Vallotti (1697\u20131780) was a theorist and composer who worked in Padua. His Trattato della scienza teorica e pratica della moderna musica<\/i> wasn\u2019t published until 1779, but he claimed his theories had all been worked out by 1728. Actually, only Book 1 out of four was published in 1779\u2013the rest languished in manuscript until 1950\u2013and his temperament discussion appeared in Book 2, chapter 4. Vallotti\u2019s temperament was not unknown, however, since it was cited in England by William Jones in 1781 (Physiological Disquisitions<\/i>) with a reference to endorsement by Tartini. This is perhaps understandable since Tartini was concertmaster of the standing orchestra under Vallotti\u2019s direction at Padua. Thomas Young (1773\u20131829) was a polymath whose temperament was given as part of an address to the Royal Society in January, 1800. (Philosophical Transactions<\/i>, pp. 143\u201347).<\/p>\n

The temperaments advocated by these two men are very similar. Vallotti\u2019s calls for a series of six fifths (F\u2014C\u2014G\u2014D\u2014A\u2014E\u2014B) to be tempered by 1\/6 of a Pythagorean comma. The rest of the fifths around the “back side” of the circle were to be tuned pure. Young\u2019s is essentially a transposition of this system. The tempered fifths are C\u2014G\u2014D\u2014A\u2014E\u2014B\u2014F#, with the rest of the fifths tuned pure. Using the modern “cent<\/span><\/a>” units (1\/100 of an ET semitone, or 1\/1200 of an octave), the two temperaments may be expressed as follows:<\/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\n
\n
Vallotti<\/b><\/div>\n<\/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#<\/b><\/td>\nA<\/b><\/td>\nB<\/b><\/td>\nB<\/b><\/td>\nC<\/b><\/td>\n<\/tr>\n
0<\/td>\n94<\/td>\n196<\/td>\n298<\/td>\n392<\/td>\n502<\/td>\n592<\/td>\n698<\/td>\n796<\/td>\n894<\/td>\n1000<\/td>\n1090<\/td>\n1200<\/td>\n<\/tr>\n
Procedure: Temper F\u2013C\u2013G\u2013D\u2013A\u2013E\u2013B by 1\/6 of a Pythagorean comma, then tune the rest of the 5ths pure to F and B.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n
\n\n
\n\n\n\n\n\n\n\n
Young<\/b><\/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#<\/b><\/td>\nA<\/b><\/td>\nBb<\/b><\/td>\nB<\/b><\/td>\nC<\/b><\/td>\n<\/tr>\n
0<\/td>\n90<\/td>\n196<\/td>\n294<\/td>\n392<\/td>\n498<\/td>\n588<\/td>\n698<\/td>\n792<\/td>\n894<\/td>\n996<\/td>\n1090<\/td>\n1200<\/td>\n<\/tr>\n
Procedure: Temper C\u2014G\u2014D\u2014A\u2014E\u2014B\u2014F# by 1\/6 of a Pythagorean comma, then tune the rest of the 5ths pure to C and F#.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n
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