Tone Systems

 
Bild:  Tone Systems

Tone Systems

Daniel Muzzulini

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          Bild:  Geometric and Syntonic Division of the Octave

          Geometric and Syntonic Division of the Octave

          Isaac Newton

              Bild:  Geometric derivation of fifths and fourths according to Stevin

              Geometric derivation of fifths and fourths according to Stevin

              Isaac Beeckman

                  Bild:  Geometric division of musical intervals

                  Geometric division of musical intervals

                  Jacobus Faber Stapulensis

                      Bild:  Graphical score

                      Graphical score

                      Gaspar Schott

                          Bild:  Greek Tetrachords

                          Greek Tetrachords

                          Guillermus de Podio

                              Bild:  Greek Tetrachords

                              Greek Tetrachords

                              Walter Odington

                                  Bild:  Greek tetrachord genera

                                  Greek tetrachord genera

                                  Johannes Cochlaeus

                                      Bild:  Guido of Arezzo: Micrologus

                                      Guido of Arezzo: Micrologus

                                          Bild:  Half-clipped sinusoids

                                          Half-clipped sinusoids

                                          James H. Craig; Lloyd A. Jeffress

                                              Bild:  Harmonic and arithmetic division of the octave

                                              Harmonic and arithmetic division of the octave

                                              Gioseffo Zarlino

                                                  Bild:  Harmonic and counter-harmonic mean

                                                  Harmonic and counter-harmonic mean

                                                  Gioseffo Zarlino

                                                      Bild:  Harmonic motion

                                                      Harmonic motion

                                                      Hermann von Helmholtz