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, tempérament ordinaire). These are all termed “irregular” 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, or even“circulating” temperaments if they can be used–for better or worse–in all keys without adjustment. This is the category to which belong the temperaments devised by Francesc’ Antonio Vallotti and Thomas Young.

Vallotti (1697–1780) was a theorist and composer who worked in Padua. His Trattato della scienza teorica e pratica della moderna musica wasn’t 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–the rest languished in manuscript until 1950–and his temperament discussion appeared in Book 2, chapter 4. Vallotti’s temperament was not unknown, however, since it was cited in England by William Jones in 1781 (Physiological Disquisitions) with a reference to endorsement by Tartini. This is perhaps understandable since Tartini was concertmaster of the standing orchestra under Vallotti’s direction at Padua. Thomas Young (1773–1829) was a polymath whose temperament was given as part of an address to the Royal Society in January, 1800. (Philosophical Transactions, pp. 143–47).

The temperaments advocated by these two men are very similar. Vallotti’s calls for a series of six fifths (F—C—G—D—A—E—B) 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’s is essentially a transposition of this system. The tempered fifths are C—G—D—A—E—B—F#, with the rest of the fifths tuned pure. Using the modern “cent” units (1/100 of an ET semitone, or 1/1200 of an octave), the two temperaments may be expressed as follows:

Cents charts are especially useful for comparison with ET. ET semitones are found by definition at the even 100s all the way up the scale, so numbers slightly below the 100s represent lower pitches and numbers above, higher pitches. As mentioned above, the two temperaments are similarly constructed but, as can be seen, they are not identical. This is my first problem–granted, a minor one–with the citing of Vallotti/Young as a temperament in use today. The two temperaments are not the same. The “naturals” of the keyboard are all the same except for the F, but the “accidentals” are different. In my experience, many people are not aware of the differences between these temperaments and often use the term “Vallotti/Young” even when they are actually tuning Vallotti. This is semantic distinction but, still, there’s no reason not to get it right. Furthermore, “Vallotti–Young,” as it appears in some places to refer to Young as a transposition of Vallotti, seems an unnecessary obfuscation.

So why are these systems so popular anyway? There are three main reasons:

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These are all valid and valuable attributes. These temperaments really are useful and can contribute to good–sounding performances. So why would I say–perhaps in an attention–grabbing overstatement–that I hate Vallotti? What’s not to like?