As attested by the repertoire, the tempered system in France began to evolve at the end of the 17th century. Until then, the favourite temperament, for both harpsichord and organ, was the meantone. In the 18th century, however, the music for organ seemed to favour pure meantone temperaments. In effect, except for a few cases, the repertoire always provided meantone tonalities. On the contrary, the composers of harpsichord music were definitely more daring, which proves their tendency towards a more tempered system. 18th century French temperaments must be performed as freely as possible, according to French bon goût. Their performance, relatively complex at first glance, requires a great deal of experience in the field of tuning. It is necessary to keep in mind that the relation between the enlargement of the fifths - as shown in our diagrams - is never exact. Its essence lies in the progressive enlargement of the interval. You will either have to gradually enlarge the fifths (marked by 0+, 0++ , etc.), or to narrow them (0-). The performance of each temperament must convey the essence of this music. It is like translating the not-written rules for ornaments and notes inégales. Apart from a few known rules, many parameters for defining the fifths are unspecified.

           Historical documents prove that in Germany the musical evolution towards a "less tempered" system began very early. A quick glance at the repertoire shows that it oriented towards multitonality. This progression is perceptible in instrumental compositions both for harpsichord and organ. When we speak of German music the first name that comes to mind is Johann Sebastian Bach. Undebatably, the early 18th century is marked by musical solutions aiming at the "well-tempered" system, which will progressively lead, in the course of two centuries, to our contemporary system. The Germans tend to privilege the Pythagorean comma. The various tunings here shown provide also the graphycal diagrams for the realization of the temperaments. The arrows located on the circle of the fifths mean: "shifting of the tempered fifth"; to each arrow there corresponds, within the circle, a Roman number, marking the tuning stage.

            Historically the term meantone has been used to identify a temperament of major thirds reduced of the fifths of a ¼ syntonic comma. There are, however, meantone temperaments of major thirds more narrow, as well as larger than the pure ones. The first group comprises the temperaments whose fifth is more narrow than ¼ of syntonic comma. In this case the fraction is smaller and, consequently, the chromatic gamut becomes more and more uneven. On the contrary, the larger the fifth, the larger the third will be. The fractions from 1/5 to 1/10 of syntonic comma tend to reach the Pythagorean value, which, as we have seen, is larger than the syntonic one. In order to obtain the meantone temperaments of impure major thirds, it is necessary first of all to set the limits within which we are going to insert the fifths to be tempered. There exist some mathematical methods - that I cannot explain here for obvious reasons - which prove and support the validity of this tuning technique. For example, in order to temper to 1/4 of comma it is necessary to tune a pure major third (for example, C-E); in order to temper to 1/5 of comma it is necessary to tune a pure major third + a pure fifth (ex. C-E + E-B), and then to temper the 5 remaining fifths; in order to temper to 1/6 of comma it is necessary to tune a pure major third + two pure fifths (ex. C-E + E-B + B-F sharp), and then to temper the 6 remaining fifths; etc.. Once obtained, the temperd fifth can be used as a comparative model to produce the remaining fifths. German Temperaments Historical documents prove that in Germany the musical evolution towards a "less tempered" system began very early. A quick glance at the repertoire shows that it oriented towards multitonality. This progression is perceptible in instrumental compositions both for harpsichord and organ. When we speak of German music the first name that comes to mind is Johann Sebastian Bach. Undebatably, the early 18th century is marked by musical solutions aiming at the "well-tempered" system, which will progressively lead, in the course of two centuries, to our contemporary system. The Germans tend to privilege the Pythagorean comma. The various tunings here shown provide also the graphycal diagrams for the realization of the temperaments. The arrows located on the circle of the fifths mean: "shifting of the tempered fifth"; to each arrow there corresponds, within the circle, a Roman number, marking the tuning stage.