Diagram archive
GID: 2_18
Designation: Brouncker contra 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: 1_99
Year: 1653
Description: When Descartes's Compendium musicae was published in an English translation in 1653, the diagrams were printed in a badly distorted form. The editor or printer represented not Descartes's logarithmic scale of pitches but the positions of frets on a musical string, with the whole circle corresponding to the difference between the open string and the octave fret half way along the string.

GID: 1_103
Year: 1653
Description: 1653_descartes_compendium_en_070_animadv_consonanceCircle.jpg

GID: 1_93
Year: 1650
Description: Constructed on a similar plan to image 92, this diagram from Descartes's Compendium musicae shows the interval sizes for a complete diatonic scale. The numbers around the edge are the lengths of string needed to produce the notes, assuming the lowest note comes from a string 540 units long. As the diagram illustrates, the use of just intonation produces some imperfections, here dealt with by having two different versions of one of the pitches, separated by a 'schisma' (syntonic comma).

GID: 1_100
Year: 1653
Description: 1653_descartes_compendium_en_032_diatonicCircle_1.jpg

GID: 1_104
Year: 1653
Description: 1653_descartes_compendium_en_074_animadv_diatonicScale_01.jpg

GID: 1_105
Year: 1653
Description: 1653_descartes_compendium_en_075_animadv_diatonicScale_02.jpg

GID: 1_94
Year: 1650
Description: Another image similar to no. 93, from Descartes's Compendium musicae. This time the notes of the scale are labelled with musical pitch names, from F upwards. In this different form of the scale from image 93 the 'schism' is put in a different place. The sizes of some intervals are strikingly inaccurate, despite the evident intention to make their angles correspond to their logarithmic sizes.

GID: 1_101
Year: 1653
Description: 1653_descartes_compendium_en_032_diatoniccircle_2.jpg

GID: 1_106
Year: 1653
Description: 1653_descartes_compendium_en_076_animadv_diatonicScale_03.jpg

GID: 1_95
Year: 1650
Description: The final circular diagram of musical pitch from Descartes' Compendium musicae. Here three different musical scales are shown together, and the diagram enables us to understand how they differ. Their starting notes are F, C and G; they use slightly different selections of pitches, but the use of just intonation also means that their versions of certain pitches - such as D - differ from one another by a 'schism' (syntonic comma).

GID: 1_102
Year: 1653
Description: 1653_descartes_compendium_en_035_hexachords.jpg