1 Franchino Gafurio, Practιca Musιce (Milan, 1496), book iii, chapter 3, rule 2; Eng tr, Clement A Miller (American Institute of Musicology, 1968), 125, Eng tr, Irwin Young (Madison, 1969), 133Google Scholar

2 James Murray Barbour, Tuning and Temperament, a Historical Survey (second edition, East Lansing, 1953), 5.Google Scholar

3 Bartolomé Ramos, Musica practica (Bologna, 1482), 4 5; ed. Johannes Wolf (Leipzig, 1901), 4 5 his passage is translated in Oliver Strunk, Source Readings in Music History (New York, 1950), 201 2.Google Scholar

4 Ramos, op. cit., 80; ed. Wolf, 99; translation in Strunk, op cit., 204 The system of intonation which we commonly refer to as ‘Pythagorean’ Rames more specifically associates with Boethius.Google Scholar

5 Ramos, op. cit., 27 31; ed. Wolf, 34 40.Google Scholar

6 John Hothby, La Calliopea legale, in Edmond de Coussemaker, Histore de l'Harmonte au Moyen-. Ige (Paris, 1982), 297 349, and Anton Wilhelm Schmidt, Die Calliopea legale des John Hothby (Leipzig, 1897), see Riemann, Hugo, History of Musιe Theory, tr. R H Haggh (Loincoln, Nebraska, 1962), 260 62.Google Scholar

7 The discrepancy between this and a pure fifth is tailed a schisma and amounts theoretically to 1 95 cents. In equal temperament each fifth is tempered by 1/12 of the Pythagorean comma, which consists of 12 008 schismasGoogle Scholar

8 Ramos, op cit., 80 81; ed Wolf, 99 100Google Scholar

9 Ibid.Google Scholar

10 Arnolt Schlick, Spiegel der Orgelmacher und Orgamsten (Speyer, 1511), ff 16v 17r, ed Robert Eitner in Monatshefte fur Musikgeschichte. i (1869), 103 4 See Lindley, Mark, ‘Early 16th-Century Keyboard Temperaments’, Musica Disciplina, \\\in (1974). 134, 137 8Google Scholar

11 Prosdocimo de Beldomandi, Parvus tractatulus de modo monochordum dividendt (Padua, 1413), in Edmond de Coussemaker, Sinptorum dr Musica Medu Arm, ili (Paris, 1869), 248 58 For further discussion of Prosdocimo and Ugolino of Orvieto in this regard, see Lindley, Mark, ‘Pythagorean Intonation and the Rise of the Triad’, Research Chronicle (forthcoming).Google Scholar

12 Hugo Spechtshart de Reutlingen, Flores musicae omnis cantus Gregoriam (Strasbourg, 1488) The Ab monochord which appears in chapter 2 of this publication is not by Hugo Spechtshart, who died in 1359 or 1360, but by an anonymous commentator. Hugo's chromatic monochord, described in the 1343 version of his treatise, had no semitone between C and A See Karl-Werner Gumpel, Hugo Spechtshart von Reutlingen, Flores Musicae (1332/42) (Wiesbaden, 1958), 65 72Google Scholar

13 See above, p 39.Google Scholar

14 Gιovannι Spataro, Erion de Franchino Gafw da Lodi (Bologna, 1521), ff 21v 22rGoogle Scholar

15 Franchino Gafurio, Apologιa Aranihinu Gafuru Musict aduervus Ioannem Spatarum & complues musicos Bonemenses (Turin, 1520), last page but seven. Cafurio attributes this statement to Spataro and then concedes its validityGoogle Scholar

16 Franchino Cafurio, De Harmonia Musicorum Instrumentorum (Milan. 1518), f 64r; see Young, Irwin, Franchimus Gafurius, Renaissance Theorist and Composer (1451–1522) (unpublished dissertation, University of California at Los Angeles, 1954), 130.Google Scholar

17 Gafurio, Practica Musice, book ni, chapter 3, rule 2Google Scholar

18 Gafurio, De Harmonia Musicorum Instrumentorum, f. 68v, see Young, op. cit., 352–3.Google Scholar

19 Gafurio, Theorica Musice (Milan, 1492), book v, chapter 5Google Scholar

20 Cafurio, Dr Harmonia Musicorum Instrumentorum, f. 18v The ancillary diagrams referred 10 in this paragraph (on ff 60v and 82r) had already appeared in Gafurio's Angelicum ac divinum opus musice (Milan. 1508)Google Scholar

21 Thomas Morley, A Plaune and Easie Introduction to Practicall Musike (London, 1597), second page of the annotations.Google Scholar

22 Pietro Aaron, Lmudano, in Musica (Venice, 1545), f. 36v and Thoscanello in Musica (Venice, 1523), chap 41. See Bergquest, EdPeter, junior. The Theoretical Writings of Pietra Aaron unpublished dissertation, Columbia University, 1964), 112 13, and Lindley, ‘Early 16th-Century Keyboard Temperaments’, 144–50.Google Scholar

23 Giovanni Maria Lanfranco, Seintille di Musica (Brescia, 1533), 97 101, 125ff, see Lindley, op cit (n 10), 144 50Google Scholar

24 Gioseffo Zarhno, Sopplimenti Musuali (Venice, 1588), 157.Google Scholar

25 Ramos, op cit, 82; ed. Wolf, 101 2Google Scholar

26 See Edwin M Ripin, ‘The Early Clavichord’, Mutual Quarterly, liii (1967), 518 38CrossRefGoogle Scholar

27 Ramos, loc cit.Google Scholar

28 See Dupont, Wilhelm, Geschichte der musikalischen Temperatur (Kassel, 1935), 48 51; John Barnes, ‘The Specious Uniformity of Italian Harpsichords’, in Edwin M. Ripin, Kryboard Instrum Studies in Keyboard Organology (Edinburgh, 1971), 1 2.Google Scholar

29 See Nerici, Luigi, Storia della Musica in Lucca (Lucca, 1879), 141 3Google Scholar

30 See Lindley, ‘Pythagorean Intonation and the Rise of the Triad’Google Scholar

31 Gioseffo Zarlino, Dimostration armauiche (Venice, 1571), 263 9Google Scholar

32 See Lindley, ‘Pythagorean Intonation and the Rise of the Triad’Google Scholar

33 Ibid.Google Scholar

34 Zarlino, Istitutiom harmoniche (Venice, 1558), 146 65.Google Scholar

35 See above, n 15.Google Scholar

36 See Lindley, ‘Early 16th-Ccntury Keyboard Temperaments’Google Scholar

37 Willi Apel, The History of Keyboard Music to 1700, tr and rev. Hans Tischler (Bloomington, 1972), 69–70 These clausulae appear in the ‘Fundamentum M C P.C.’, no 190 in the Buxheim Organ Book. No 236 is entitled ‘Magistn Paumann Contrapuncti’ Presumably the initials in the first title stand for 'Magistn Conrad Paumann ContrapunctiGoogle Scholar

38 Shohe Tanaka, ‘Studien im Gebiete der reinen Stimmung’, Vierteljahrwchrift fur Musikussenschaft, vi (1890), 61 2.Google Scholar

39 Friedrich Wilhelm Arnold, ‘Das Lochheimer Liederbuch nebst der Ars Organisandi von Conrad Paumann’, in Friedrich Chrysander, Jahrbucher fur musikalischr Wissenschaft (Leipzig, 1867), 182 224 For a recent edition of this music see Apel, Willi, ed., Keyboard Music of the Fourteenth & Fifteenth Centuries (American Institute of Musicology 1963), 32 51Google Scholar

40 See Krautwurst, Franz, 'Paumann, Die Musik in Geschuhte und Gegcuuart, (Kassel, 1962), cols. 968 71Google Scholar

41 See Lindley, 'Pythagorean Intonation and the Rise of the TriadGoogle Scholar

42 Ramos, op cit, 82, ed Wolf, 102Google Scholar

43 The exact dating of the various parts of the Buxheim repertory is uncertain; for a survey of opinions, see Robert S Lord, The Buxheim Organ Book A Study in the History of Organ Music in Southern Germany during the Fifteenth Century (unpublished dissertation, Yale University, 1960), 160–64.Google Scholar

44 Arnolt Schlick, Tabulaturen etluher lobgevang und liedhim uff die orgeln vn lauten (Maiuz, 1542), and Spiegel der Orgelmacher un[d] Organisten (Speyer, 1511, reprinted Mainz, 1959), chapter 8, ed. Robert Eitner, Monatshefte fur Musikgeschichte, i (1869). See Husmann, Heinrich, ‘Zur Characteristik der Schlicksen Temperatur’, Arha fui Musikuissenschaft, xxiv (1967), 253 65, and Lindley, ‘Early 16th-Century Keyboard Temperaments’Google Scholar