Temperaments and tuning systems

TC/LB Temperament
TC Monza Temperament
Vallotti
Young
Temperament Links

TC/LB Temperament

A simple tuning based on Vallotti but with the fifths A-E and E-B set slightly wider than 1/6-coma. Good for use with string players and used by London Baroque for the last 10 years. 

Method

Set tenor A at 415Hz

1. Tune Ten A to Ten F wide of pure (just over 3 beats per second)

2. Temper the 5^th A-E 1/12 narrow (an equal tempered 5^th)

3. From F tune five perfect 5ths, F-Bb, Bb-Eb, Eb-G#, G#-C# and F-C

4. Temper six of the remaining 5ths 1/6th coma narrow of pure, ie  C-G, G-D, D-A, E-B, B-F#

5. The last fifth (F#-C#) should now be an equally tempered 5^th, ie 1/12 coma narrow.

Cent deviation values (approx.) for use with a Tuning machine;  

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TC/Monza Temperament

An irregular tuning for 18th century Italian music based on contemporary tuning systems and specially devised for a recording of Monza's harpsichord music. To tune this temperament, the fifths F#-C#, Eb-Bb, Bb-F and F-C are set pure and the fifths C#-G# and G#-Eb set wide by 1/10 coma. The remaining fifths are a narrow by 1/5 coma.

Cent deviation values (approx.) for use with a Tuning machine;  

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Vallotti (mid 18th century)

Francesco Antonio Vallotti (1697-1780). Italian composer and theorist. This elegant keyboard tuning system is recorded in his Delia Scienza teorica, e pratica, delta modema Musica. (The first volume of which was published in Padua in 1779 while the remaining three books had to wait until 1950 -mod. ed. Trattato delta modema Musica, Padua, 1950). The temperament was first reported, somewhat opaquely, by Vallotti's colleague and fellow theorist in Padua, Giuseppe Tartini in his Trattato di Musica secondo la vera Scienta deli Armonia (Padua, 1754), p. 100. Although many (myself among them) feel this temperament is misused in the perfomance of Baroque music today - see Ross Duffin's article 'Why I hate Vallotti (or is it Young)', it is still very easy to tune and an excellent starting point for those new to tuning unequal temperaments. To tune this temperament, set the fifths F-Bb-Eb-G#-C#-F#-B pure and then temper the rest by 1/6 of a Pythagorean comma.

Cent deviation values (approx.) for use with a Tuning machine;  

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Young Temperament (1800) [=Shifted Vallotti]

Thomas Young (1773-1829). Famous English polymath and scientific investigator. Recently described by Andrew Robinson as “the last man who knew everything” (Robinson, A. The Last Man Who Knew Everything, Oxford, 2007). Among his many achievements he proved Newton wrong, explained how we see and deciphered the Rosetta Stone. His now famous temperament is described in "Of the temperament of musical intervals." Philosophical Transactions of the Royal Society of London for the year 1800. London, The Royal Society, 1800. It is sometimes referred to as 'Young II'. To tune this temperament, set the fifths C-F-Bb-Eb-G#-C#-F# pure and temper the rest by 1/6 of a Pythagorean comma. 

 Cent deviation values (approx.) for use with a Tuning machine;    

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Temperament Links

LB Temperament
Temperament (Edgar Hunt Article)
Bach's Tuning, B Lehman
Claudio di Veroli, Unequal Temperaments
Temperament: A Beginner's Guide
Graphic view of Historical Temperaments
Harpsichord Tuning & Repair
Lehmann's Temperament Calculator
Tuning & Temperament Bibliography
Violab "Pitchman" Electronic Tuners
Marc Vogel Tuning Sets
Korg Electronic tuners
Reyburn CyberTuner
WinTemper

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