Diagram archive
GID: 2_3
Designation: Descartes: Pitch Circle of Hexachords
Description: Circular pitch diagram. Three hexachords (ut-re-mi-fa-sol-la) are displayed on three concentric rings. This leads to a tone system with two ambiguous tones d and g as well as b-rotundum (b-flat) and b-quadratum (b).

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


GID: 1_107
Year: 1664
Description: During 1664-1665 Newton prepared an essay on music and made a series of related calculations. As part of his notes we find this diagram, clearly modeled on those of Descartes (compare image 95). Descartes shows not three but five different scales simultaneously.


GID: 1_112
Year: 1668
Description: 1668_descartes_buzon_2012_104.jpg


GID: 1_115
Year: 1684
Description: This anonymous diagram shows three octaves of the diatonic scale and combines two aspects of pitch. Whereas the angular position of a point on the spiral indicate its pitch class, the radial distance from the centre of the circle is related to the time period of a sound. However, the width of the spiral is not exactly halved after a full rotation.


GID: 1_157
Year: 1635
Description: 1635_Descartes_Compendium_Musicae__Leiden_MS_copy__Hexachords_Circle.jpg


GID: 1_162
Year: 1640
Description: 1640_Descartes_Compendium_Musicae__Groningen_MS_copy__Hexachords_Circle.jpg


GID: 1_85
Year: 1628
Description: 1628_beeckman 171v-172r_HexachordsCircle_detail.jpg




gid: 2_3 / keyword: pitch diagram / id_keyword: 1
--> 1_100 / Desig: 1653_descartes_compendium_en_032_diatonicCircle_1.jpg
--> 1_101 / Desig: 1653_descartes_compendium_en_032_diatoniccircle_2.jpg
--> 1_102 / Desig: 1653_descartes_compendium_en_035_hexachords.jpg
--> 1_103 / Desig: 1653_descartes_compendium_en_070_animadv_consonanceCircle.jpg
--> 1_104 / Desig: 1653_descartes_compendium_en_074_animadv_diatonicScale_01.jpg
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--> 1_107 / Desig: 1664_65_c_newton_TuningProblem_gouk_140_4_33.jpg
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--> 1_153 / Desig: 1635_Descartes_Compendium_Musicae__Leiden_MS_copy__Consonance_Circle.jpg
--> 1_154 / Desig: 1635_descartes_compendium_musicae__leiden_ms_copy__diatonic_scale_1.jpg
--> 1_155 / Desig: 1635_descartes_compendium_musicae__leiden_ms_copy__diatonic_scale_2.jpg
--> 1_156 / Desig: 1635_Descartes_Compendium_Musicae__Leiden_MS_copy__Diatonic_Scales.jpg
--> 1_157 / Desig: 1635_Descartes_Compendium_Musicae__Leiden_MS_copy__Hexachords_Circle.jpg
--> 1_158 / Desig: 1640_Descartes_Compendium_Musicae__Groningen_MS_copy__Consonance_Circle.jpg
--> 1_159 / Desig: 1640_descartes_compendium_musicae__groningen_ms_copy__diatonic_scale_1.jpg
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--> 1_161 / Desig: 1640_Descartes_Compendium_Musicae__Groningen_MS_copy__Diatonic_Scales.jpg
--> 1_162 / Desig: 1640_Descartes_Compendium_Musicae__Groningen_MS_copy__Hexachords_Circle.jpg
--> 1_163 / Desig: 1680_PhiloMus_A_B__Synopsis_of_Vocal_Musick_1.jpg
--> 1_164 / Desig: 1680_PhiloMus_A_B__Synopsis_of_Vocal_Musick_2.jpg
--> 1_165 / Desig: 1656_descartes_ConsonanceCircle_brockt_1978_20.jpg
--> 1_166 / Desig: 1656_descartes_DiatonicScale_A_brockt_1978_36.jpg
--> 1_167 / Desig: 1656_descartes_DiatonicScale_B_brockt_1978_36.jpg
--> 1_168 / Desig: 1656_descartes_HexachordCircle_brockt_1978_40.jpg
--> 1_28 / Desig: 1617_fludd_uch_1_0098.jpg
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--> 1_82 / Desig: 1628_beeckman_166v-167r_detail_ConsonanceCircle.jpg
--> 1_83 / Desig: 1628_beeckman_170v-171r_diatoniccircles_detail_a.jpg
--> 1_84 / Desig: 1628_beeckman_170v-171r_diatoniccircles_detail_b.jpg
--> 1_85 / Desig: 1628_beeckman_171v-172r_HexachordsCircle_detail.jpg
--> 1_91 / Desig: 1650_1704_descartesNewton_kreise.jpg
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--> 1_95 / Desig: 1650_descartes_buzon_2012_105.jpg
--> 1_99 / Desig: 1653_descartes_compendium_en_017_intervalCircle.jpg
--> 2_2 / Desig: Descartes: Circular Diatonic Scale 1
--> 2_4 / Desig: Descartes: Consonance circle
--> 2_5 / Desig: Ms Middleburg 1627-28 (Beeckman)

gid: 2_3 / 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_19 / Desig: A.B. Philomus

gid: 2_3 / keyword: hexachord / id_keyword: 5
--> 2_17 / Desig: Newton's treatment of the tuning problem