Books by Daniel Zachariah Franks
An approach towards outlining a practical understanding of ancient music. Particularly dealing wi... more An approach towards outlining a practical understanding of ancient music. Particularly dealing with aspects of ancient Greek music, as recounted by the translated fragments of Aristoxenus, Ptolemy and others. In brief, a summary guide defining a method for practically realising harmonic relations, rhythmic poetics, the varieties of the tonal genera, and tetrachord theory using standard techniques of rational string division.
(Please note: This is an incomplete review copy and as such does not contain the full text of this manuscript. If you would like the full picture, please do get in touch with me.)
“This text is an attempt to link the historic practices and systems of harmony, including twelve ... more “This text is an attempt to link the historic practices and systems of harmony, including twelve tone theory in an expanded model of resonance relations and their harmonic implications.
Part One begins by looking at Western acoustic history together with the related histories of more ancient computations of tempered twelve tone scales and the 'microtonal' harmonic perfection of the unequal temperaments of classical Indian and Oriental music traditions. These archaic systems are seen to correlate with, and expand upon, the bare bones of the 'allegedly Greek' western modal harmonic systematization of resonant relations.
Part Two deals with pedagogic issues surrounding acoustic observations and resonant relations … an investigation of pre-piano temperaments in defining historic practices, harmonic overtone and undertone theory, 'tonal' harmonic relations, and proportion / string theory are also dealt with.
Part Three involves the general arrangement of harmonic material. Various systems of arrangement and problematisations are discussed. The theory of symmetrical geometry utilizing a simplified model of 12TET enharmony is dealt with as an aid to the visualization of harmonic relations. Circles, triangles and squares are seen to represent symmetrical harmonic intervals arranged in mathematical proportions upon circles of fifths, simplified for 12TET analysis. Equal temperament is seen to be descended from this general framework of harmony.
Part Four describes the illumination of dodecaphony by microchromatic networks of intervallic relations and unequal proportions. This article hopes to describe the interdependences of the twelvefold equal-tempered octave conception upon the more subtle, almost abstracted, octave divisions of fifty-five unequally distributed commas. …
Appendix A offers a brief pentatonic view of tonal arrangements. …
Appendix B contains a brief discussion of concepts underlying rhythmic articulation …
Appendix C offers a geometers view of the symmetrical material of harmony …
Appendix D contains further charts and diagrams used in preparing the text, to be used in illuminating it. Much of the information mapped out in the text is summarized by these diagrammatic representations. …” (From the Abstraction to the text)
''Books on any subject reflect of necessity a limited range of vision, in which some parts and qualities stand out while others retreat or vanish altogether. The readers expect to find their familiar, personal ranges of vision – ranges that might be very different from that of the author.'' (Sachs, 1953: 11)
Papers by Daniel Zachariah Franks
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Books by Daniel Zachariah Franks
(Please note: This is an incomplete review copy and as such does not contain the full text of this manuscript. If you would like the full picture, please do get in touch with me.)
Part One begins by looking at Western acoustic history together with the related histories of more ancient computations of tempered twelve tone scales and the 'microtonal' harmonic perfection of the unequal temperaments of classical Indian and Oriental music traditions. These archaic systems are seen to correlate with, and expand upon, the bare bones of the 'allegedly Greek' western modal harmonic systematization of resonant relations.
Part Two deals with pedagogic issues surrounding acoustic observations and resonant relations … an investigation of pre-piano temperaments in defining historic practices, harmonic overtone and undertone theory, 'tonal' harmonic relations, and proportion / string theory are also dealt with.
Part Three involves the general arrangement of harmonic material. Various systems of arrangement and problematisations are discussed. The theory of symmetrical geometry utilizing a simplified model of 12TET enharmony is dealt with as an aid to the visualization of harmonic relations. Circles, triangles and squares are seen to represent symmetrical harmonic intervals arranged in mathematical proportions upon circles of fifths, simplified for 12TET analysis. Equal temperament is seen to be descended from this general framework of harmony.
Part Four describes the illumination of dodecaphony by microchromatic networks of intervallic relations and unequal proportions. This article hopes to describe the interdependences of the twelvefold equal-tempered octave conception upon the more subtle, almost abstracted, octave divisions of fifty-five unequally distributed commas. …
Appendix A offers a brief pentatonic view of tonal arrangements. …
Appendix B contains a brief discussion of concepts underlying rhythmic articulation …
Appendix C offers a geometers view of the symmetrical material of harmony …
Appendix D contains further charts and diagrams used in preparing the text, to be used in illuminating it. Much of the information mapped out in the text is summarized by these diagrammatic representations. …” (From the Abstraction to the text)
''Books on any subject reflect of necessity a limited range of vision, in which some parts and qualities stand out while others retreat or vanish altogether. The readers expect to find their familiar, personal ranges of vision – ranges that might be very different from that of the author.'' (Sachs, 1953: 11)
Papers by Daniel Zachariah Franks
(Please note: This is an incomplete review copy and as such does not contain the full text of this manuscript. If you would like the full picture, please do get in touch with me.)
Part One begins by looking at Western acoustic history together with the related histories of more ancient computations of tempered twelve tone scales and the 'microtonal' harmonic perfection of the unequal temperaments of classical Indian and Oriental music traditions. These archaic systems are seen to correlate with, and expand upon, the bare bones of the 'allegedly Greek' western modal harmonic systematization of resonant relations.
Part Two deals with pedagogic issues surrounding acoustic observations and resonant relations … an investigation of pre-piano temperaments in defining historic practices, harmonic overtone and undertone theory, 'tonal' harmonic relations, and proportion / string theory are also dealt with.
Part Three involves the general arrangement of harmonic material. Various systems of arrangement and problematisations are discussed. The theory of symmetrical geometry utilizing a simplified model of 12TET enharmony is dealt with as an aid to the visualization of harmonic relations. Circles, triangles and squares are seen to represent symmetrical harmonic intervals arranged in mathematical proportions upon circles of fifths, simplified for 12TET analysis. Equal temperament is seen to be descended from this general framework of harmony.
Part Four describes the illumination of dodecaphony by microchromatic networks of intervallic relations and unequal proportions. This article hopes to describe the interdependences of the twelvefold equal-tempered octave conception upon the more subtle, almost abstracted, octave divisions of fifty-five unequally distributed commas. …
Appendix A offers a brief pentatonic view of tonal arrangements. …
Appendix B contains a brief discussion of concepts underlying rhythmic articulation …
Appendix C offers a geometers view of the symmetrical material of harmony …
Appendix D contains further charts and diagrams used in preparing the text, to be used in illuminating it. Much of the information mapped out in the text is summarized by these diagrammatic representations. …” (From the Abstraction to the text)
''Books on any subject reflect of necessity a limited range of vision, in which some parts and qualities stand out while others retreat or vanish altogether. The readers expect to find their familiar, personal ranges of vision – ranges that might be very different from that of the author.'' (Sachs, 1953: 11)