Diagram archive
GID: 2_19
Designation: A.B. Philomus
Description: These diagrams show a scale with a unit of about a syntonic comma, by which the greater intervals are measured. Semitone: 5 units, minor tone: 9 units, major tone: 10 units, so that the octave comprises 58 units. (The octave measures 55.798 syntonic commas.)

GID: 1_163
Year: 1680
Description: The unidentified 'A.B. Philomus' included material about tuning theory in his 1680 Synopsis of Vocal Musick, including diagrams in which the octave was represented by a circle as in Descartes' Compendium musicae. As in Descartes's diagrams different scales were shown simultaneously and compared, and the discrepancies between their versions of the 'same' pitches were illustrated. A notable difference is that this author also superimposes a division of the octave into many small parts: here the just intonation was intended to be executed not exactly but according to an approximation.

GID: 1_164
Year: 1680
Description: This second image from the Synopsis of Vocal Musick shows the sizes of various diatonic intervals in relation to its equal division of the octave: including intervals occurring in the just intonation like the greater and lesser tones and semitones. Compare image 92 from Descartes.

GID: 1_92
Year: 1650
Description: Descartes wrote his Compendium musicae in 1618 but it was published posthumously in 1650. It included circular representations in which the whole circle represents an octave, while smaller intervals are shown according to a logarithmic scale: so for instance an equal-tempered semitone would occupy a twelfth of the circle. Here Descartes shows the sizes of the thirds, fourths and fifths. Manuscript versions of these diagrams, in some cases more accurate, appear in images 82-85 and 153-162.

gid: 2_19 / keyword: syntonic comma / id_keyword: 3
--> 1_83 / Desig: 1628_beeckman_170v-171r_diatoniccircles_detail_a.jpg
--> 1_85 / Desig: 1628_beeckman_171v-172r_HexachordsCircle_detail.jpg
--> 2_17 / Desig: Newton's treatment of the tuning problem
--> 2_3 / Desig: Descartes: Pitch Circle of Hexachords

gid: 2_19 / keyword: logarithm / id_keyword: 18
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--> 1_45 / Desig: 1620_buergi_jost_logCircle_.jpg
--> 2_17 / Desig: Newton's treatment of the tuning problem