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Temperaments 2. Quasi-Pythagorean temperament. 11. Temperament and harmony.: Ex.1 Du Fay, ‘Mon chier amy’ (GB-Ob Can.misc.213, fasc.9, p.314), end of the penultimate section

Temperaments 2. Quasi-Pythagorean temperament. 11. Temperament and harmony.: Ex.1 Du Fay, ‘Mon chier amy’ (GB-Ob Can.misc.213, fasc.9, p.314), end of the penultimate section

Temperaments 2. Quasi-Pythagorean temperament.: Ex.2 Matteo da Perugia, ‘Pres du soloil’ (I-MOe α.M.5.24, f.16), excerpt

Temperaments 2. Quasi-Pythagorean temperament.: Ex.2 Matteo da Perugia, ‘Pres du soloil’ (I-MOe α.M.5.24, f.16), excerpt

Temperaments 3. Regular mean-tone temperaments to 1600.: Ex.3 Paumann (D-Mbs Cim 325b, f.104v)

Temperaments 3. Regular mean-tone temperaments to 1600.: Ex.3 Paumann (D-Mbs Cim 325b, f.104v)

Temperaments 3. Regular mean-tone temperaments to 1600.: Ex.4 Bull (GB-Och Mus. 1113, p.227)

Temperaments 3. Regular mean-tone temperaments to 1600.: Ex.4 Bull (GB-Och Mus. 1113, p.227)

Temperaments 3. Regular mean-tone temperaments to 1600.: Ex.5 G. Gabrieli (I-Tn Giordano II, f.28v)

Temperaments 3. Regular mean-tone temperaments to 1600.: Ex.5 G. Gabrieli (I-Tn Giordano II, f.28v)

Temperaments 3. Regular mean-tone temperaments to 1600.: Ex.6 Valente (Libro secondo, Naples, 1580, p.27)

Temperaments 3. Regular mean-tone temperaments to 1600.: Ex.6 Valente (Libro secondo, Naples, 1580, p.27)

Temperaments 3. Regular mean-tone temperaments to 1600.: Ex.7 Cabezón (Obras de música, Madrid, 1578, f.62v)

Temperaments 3. Regular mean-tone temperaments to 1600.: Ex.7 Cabezón (Obras de música, Madrid, 1578, f.62v)

Grammateus’s method for determining the geometrical mean between two pipe lengths in the ratio 9:8

Grammateus’s method for determining the geometrical mean between two pipe lengths in the ratio 9:8

Temperaments 4. Irregular keyboard temperaments to 1680.: Ex.8 Schlick (Tabulaturen etlicher Lobgesang, Mainz, 1512, p.44)

Temperaments 4. Irregular keyboard temperaments to 1680.: Ex.8 Schlick (Tabulaturen etlicher Lobgesang, Mainz, 1512, p.44)

Temperaments 4. Irregular keyboard temperaments to 1680.: Ex.9 Schlick (op. cit., p.51)

Temperaments 4. Irregular keyboard temperaments to 1680.: Ex.9 Schlick (op. cit., p.51)

Temperaments 4. Irregular keyboard temperaments to 1680.: Ex.10 L. Couperin (F-Pn Mus. Rés. Vm7 675, f.74r)

Temperaments 4. Irregular keyboard temperaments to 1680.: Ex.10 L. Couperin (F-Pn Mus. Rés. Vm7 675, f.74r)

Temperaments 4. Irregular keyboard temperaments to 1680.: Ex.11 Chambonnières (Les pièces de clavessin, Paris, 1670, p.40)

Temperaments 4. Irregular keyboard temperaments to 1680.: Ex.11 Chambonnières (Les pièces de clavessin, Paris, 1670, p.40)

Temperaments 6. Regular mean-tone temperaments from 1600.: Ex.12 Anon: contemporary transcr. of Lully, overture to Bellérophon (1679)

Temperaments 6. Regular mean-tone temperaments from 1600.: Ex.12 Anon: contemporary transcr. of Lully, overture to Bellérophon (1679)

Circle of 5ths indicating the relative amount of tempering of 3rds in characteristic 18th-century keyboard tuning

Circle of 5ths indicating the relative amount of tempering of 3rds in characteristic 18th-century keyboard tuning

Temperaments 7. Irregular temperaments from 1680.: Ex.13 Platti, op.4 no.3 (Nuremberg, c1746)

Temperaments 7. Irregular temperaments from 1680.: Ex.13 Platti, op.4 no.3 (Nuremberg, c1746)

Temperaments 7. Irregular temperaments from 1680.: Ex.14 Fischer (Ariadne musica neo-organoedum, Schlackenwerth, 1702)

Temperaments 7. Irregular temperaments from 1680.: Ex.14 Fischer (Ariadne musica neo-organoedum, Schlackenwerth, 1702)

Temperaments 7. Irregular temperaments from 1680.: Ex.15 Schubert, Piano sonata in C (d 840), beginning

Temperaments 7. Irregular temperaments from 1680.: Ex.15 Schubert, Piano sonata in C (d 840), beginning

Partly schematic representation of a typical 16th-century lute fretting

Partly schematic representation of a typical 16th-century lute fretting

Temperaments 9. Fretted instruments.: Ex.16 Milán (El maestro, Valencia, 1536)

Temperaments 9. Fretted instruments.: Ex.16 Milán (El maestro, Valencia, 1536)

Temperaments 11. Temperament and harmony.: Ex.17 Schütz, Die so ihr den Herren fürchtet (swv364), beginning of the last section

Temperaments 11. Temperament and harmony.: Ex.17 Schütz, Die so ihr den Herren fürchtet (swv364), beginning of the last section

Temperaments 11. Temperament and harmony.: Ex.18 S.L. Weiss, isolated enharmonic modulation, captioned ‘He who is knowledgeable will understand’ (Chi sá/L’intenderá; from the Stammbuch of C.A. Schmid, 15 August 1742; originally lute tablature)

Temperaments 11. Temperament and harmony.: Ex.18 S.L. Weiss, isolated enharmonic modulation, captioned ‘He who is knowledgeable will understand’ (Chi sá/L’intenderá; from the Stammbuch of C.A. Schmid, 15 August 1742; originally lute tablature)

Temperaments 11. Temperament and harmony.: Ex.19 Du Fay, Belle, plaissant et graciese (GB-Ob can.misc.213, fasc.2, p.22), tenor part, the last note of the first section and the entire second section

Temperaments 11. Temperament and harmony.: Ex.19 Du Fay, Belle, plaissant et graciese (GB-Ob can.misc.213, fasc.2, p.22), tenor part, the last note of the first section and the entire second section

Distribution of the Pythagorean comma in 12 ‘good’ temperaments

Distribution of the Pythagorean comma in 12 ‘good’ temperaments

Some neo-Baroque organ temperaments: (a), (b) Queens College, Oxford, in the 1980s and as improved in 1992; (c), (d) Grosvenor Chapel, London, originally and as improved; (e), (f) Memorial Chapel, Stanford, original and improved; (g) Jatobtiche, Hamburg

Some neo-Baroque organ temperaments: (a), (b) Queens College, Oxford, in the 1980s and as improved in 1992; (c), (d) Grosvenor Chapel, London, originally and as improved; (e), (f) Memorial Chapel, Stanford, original and improved; (g) Jatobtiche, Hamburg

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