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Ill, pp. 108—9, 364—6. 39 Mersenne, Harmonie universelle, vol. Ill, p. 363. 40 Joseph Sauveur, 'Methode generale pour former les systemes temperes de musique, & du choix de celui qu'on doit suivre', Histoire de I'Academie royale des sciences  (Paris 1730), Memoires, p. 219; facsimile reprint in Joseph Sauveur: Collected Writings on Musical Acoustics, ed. Rudolf Rasch (Utrecht: The Diapason Press, 1984). 41 Praetorius, Syntagma Musicum, vol. II, p. 155. 28 Jean Denis and meantone temperament and with the same hand C, E, G, and C .
336. 29 Treatise on harpsichord tuning This description is vivid, and strongly suggests that Mersenne may have learned first-hand about the actual setting of quartercomma meantone temperament directly from Denis. In a subsequent paragraph, Mersenne provides a final clue as to the size of the diminishment of the fifth called for in Denis's Traite. As noted above, Denis states that the fifths in his temperament are to be diminished by 'MM poincf, a quantity that would seem to defy any attempt at precise definition.
Ill, pp. 349-58. 36 Jean Denis and meantone temperament an A\>, the Dorian mode could not be transposed to F. 53 These and other problems of similar nature are addressed by Jean Denis in the Traite. In response to such difficulties, a number of authors note the need for some sort of accommodation: either a compromise tuning of Djt/Eb and G|/AI> so that these keys might serve for either note, or the addition of separate keys (and corresponding strings or pipes) for Dfl and A\>, so that two additional pure thirds might be added to the quarter-comma system without any alteration of the basic temperament.