105
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

The Unification of Tonal Systems, or About the Circle of Fifths

Pages 319-334 | Published online: 20 May 2008

References

  • Barbour , J. M. ( 1951 ). Tuning and temperament: A historical survey . East Lansing MI: Michigan State Univ. Press ; reprint New York : Da Capo , 1972 .
  • Blackwood , E. 1985 . The structure of recognizable diatonic tunings , Princeton, NJ : Princeton Univ. Press .
  • Drobisch , M. W. 1853 . ber die wissenschaftliche Bestimmung der musikalischen Temperatur . Annalen der Physik und Chemie Dritte Reihe , 90 : 353 – 389 .
  • Ellis , Alexander J. ( 1875 ). Appendices to H. L. F. Helmholtz , On the sensations of tone , translated by A. J. Ellis . London : Novello ; 2nd edition, 1885 .
  • Drobisch , M. W. 1853 . ber die wissenschaftliche Bestimmung der musikalischen Temperatur . Annalen der Physik und Chemie Dritte Reihe , 90 : 353 – 389 .
  • Fokker , Adriaan D. ( 1968b ). Selections from the harmonic lattice of perfect fifths and major thirds containing 12, 19, 22, 31, 41 or 53 notes . In Proceedings of the Koninklijke Nederlandse Academie van Wetenschappen Series B , 71 , 251 – 266 .
  • Fokker , Adriaan D. ( 1969 ). Unison vector and periodicity blocks in the three-dimensional (3-5-7-) harmonic lattice of notes . In Proceedings of the Koninklijke Nederlandse Academie van Wetenschappen Series B , 72 , 153 – 168 .
  • Fokker , Adriaan D. ( 1987 ). Selected musical compositions (1948–1972) , Rudolf Rasch . Utrecht/Haarlem : Diapason Press .
  • Huygens , Christiaan ( 1986 ). Lettre touchant le cycle harmonique . Histoire des Ouvrages des Sçavans (October 1691) , pp. 78 – 88 . Rudolf Rasch ( Utrecht : Diapason Press ).
  • Lindley , Mark ( 1987 ). Stimmung und Temperatur . In Hören, Messen und Rechnen in der frühen Neuzeit pp. 109 – 331 . Darmstadt : Wissenschaftliche Buchgesellschaft, Geschichte der Musiktheorie Band 6 .
  • Lindley , Mark & Ronald Turner-Smith ( 1993 ). Mathematical models of musical scales . Bonn : Verlag für Systematische Musikwissenschaft .
  • Partch , Harry ( 1974 ). Genesis of a music , 2nd edition enlarged . New York : Da Capo ; first edition, 1949 .
  • Rasch , Rudolf A. 1985 . Relations between multiple divisions of the octave and the traditional tonal system . Interface , 14 : 75 – 108 .
  • Rasch , Rudolf A. 1988 . Farey systems of musical intonation . Contemporary Music Review , 2 : 31 – 67 .
  • Romieu , Jean-Baptiste ( 1758 ). Mémoire théorique et pratique sur les systèmes tempérés de musique . Mémoires de l'Académie Royale des Sciences , 805 – 870 .
  • Joseph Sauveur ( 1701 ). Système général des intervalles des sons, et son application à tous les sytèmes et à tous les instrumens de musique . Histoire de l'Académie Royale des sciences Année, Mémoires , 299 – 366 .
  • Facsimile edition in Joseph Sauveur ( 1984 ). Collected writings on musical acoustics (Paris 1700–1713) , Rudolf Rasch . Utrecht : Diapason Press .
  • Salinas , Francisco ( 1958 ). De musica libri VII (Salamanca 1577) . Faksimile-Nachdruck herausgegeben von Macario Santiago Kastner . Kassel : Bärenreiter .
  • Zarlino , Gioseffo , Dimostrationi armoniche (Venice 1571) .
  • Zarlino , Gioseffo , Istitutioni armoniche (Venice 1558) .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.