Notes to pages 75–80 293
- Dickreiter 1973 , 135.
- Ibid. , 137.
- Caspar 1993 , 248; KGW 17:254. For Kepler ’ s reading of Vincenzo, see Gingerich 1993, 396 – 398.
- Dickreiter (1973 , 138 – 139) argues that Kepler ’ s knowledge of music theory was “ not very many-sided. ”
Indeed, Kepler manuscripts in the Pulkowa library reveal that he had read only three-quarters of Galilei ’ s book. - Caspar 1993 , 266.
- Where Boethius and Macrobius defined the major third as 81:64 (two whole tones, each 9:8) and the minor
third as 32:27, Kepler advocated the simpler intervals of just intonation (5:4 and 6:5, respectively). - HW 137 (KGW 6:99). Though praising Ptolemy for including just intonation, Kepler still criticized him for
not finally advocating it; HW 138 (KGW 6:99). HW 192 (KGW 6:139) is the unique mention of Zarlino in
Kepler ’ s text. - Walker 1978 , 35 – 53. Here I go beyond Walker ’ s comparison of mathematics and music as “ parallels ” (39 – 40)
drawn from a single archetype. - See Pesic 2000b , 57 – 59.
- HW 138 (KGW 6:99).
- Kepler goes past the commonplaces dating back to medieval theorists about allowed melodic intervals; see
Hucbald et al. 1978. - HW 217 (KGW 6:158).
- Here he refers to “ Euclid ” for a vocabulary of melodic devices, by which he means the Introductio harmonica
now attributed to Cleonides, a student of Aristoxenus. See HW 218n125; there is a parallel passage defining this
terminology in Aristides Quintilianus ( Barker 2004 , 2:430 – 431). - HW 218 (KGW 6:158). In the case of Victimae paschali , Kepler shows how the direct motion of agog ē
(as in the setting of the words “ paschali laudes ” or of “ immolent ” ) sets off the continuous intonation ( ton ē ) of
“ -demit oves Christus in- ” and the “ playing ” alternations ( petteia ) of “ -cens ... re- ... li- ... peccat-. ” In contrast,
the Turkish chant uses “ a pure plok ē , although not a natural one, ” throughout its course, meaning the continuous
twisting or twining of the melodic line. - Walker 1978 , 38 – 40; see also Tomlinson 1993 , 76 – 84.
- Sacrae cantiones quinque vocem (Lasso 1894, 9:49 – 52), cited at HW 221, 234, 239 (KGW 6:161, 171, 174).
Kepler mentions Lasso ’ s Ubi est Abel and Tristis est anima mea at HW 253 (KGW 6:184). - HW 243 (KGW 6:177). For the fame of this motet, see Braun et al. 1994 , 2:139 – 142. See also Boetticher
1954 , cited by Lossius 1570 , book 1, chapter 7, a book in Kepler ’ s school library in Linz ( Dickreiter 1973 , 145). - Musica autoschediastik ē (1601), expanded in his Musica poetica (1606); see Burmeister 1993 , 205 – 206; see
the translation and commentary Palisca 1972. For a discussion of this motet and its performance practice, see
Smith 2011 , 111 – 124. Concerning Burmeister, see Ruhnke 1955 , 130 – 135, 162 – 165. That we possess no specific
reference to this motet might be explained by the disappearance of some of Kepler ’ s letters to Seth Calvisius in
which Burmeister might well have been discussed; see Dickreiter 1973 , 60 – 61. - HW 221 (KGW 6:161). Kepler writes the same slightly incorrect rhythm both times he cites this passage,
probably quoting from memory and indicating how familiar this motet is to him, as noted by Dickreiter 1973 ,
175 – 176; Braun et al. 1994 , 141. For the authentic text, see Lasso 1894, 9:49. Even Kepler ’ s mistake is revealing;
by incorrectly citing the opening e' as dotted, he has the expressive minor sixth e' – c' arrive on the downbeat
in the cantus, an accented dissonance, whereas the authentic text lacks his dot and consequently arrives on
the offbeat, resolving by suspension. Thus, Kepler ’ s rhythmic mistake throws the expressive semitonal descent
c' – b' – a' into higher relief. - HW 239 (KGW 6:174).
- HW 238 (KGW 6:173).
- HW 441 (KGW 6:323).
- HW 449 – 450 (KGW 6:329).
- HW 430 (KGW 6:316). For further discussion of planetary songs, see Tomlinson 1993 , 63 – 100.
- HW 423 (KGW 6:311).