Holdrian comma: Difference between revisions

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== Historical origin ==

The origin of Holder's comma resides in the fact that the [[Ancient Greek]]s (or at least to the Roman [[Boethius]]). According to [[Boethius]], [[Pythagoras]]' disciple [[Philolaus|Philolaus of Croton]] would have said that the tone consisted in two [[diatonic semitone]]s and a comma; the diatonic semitone consisted in two [[diaschisma]]ta, each formed of two commas.<ref>Anicius Manlius Severinus Boethius - ''De institutione musica'' - book 3 ch8</ref><ref>J. Murray Barbour - ''Tuning and Temperament: A historical survey'' (1951) - p123</ref>believed that in the [[Pythagorean tuning]] the tone could be divided in nine commas, four of which forming the diatonic semitone and five the chromatic semitone. If all these commas are exactly of the same size, there results an octave of ''5 tones + 2 diatonic'' semitones, ''5 × 9 + 2 × 4 = 53 equal'' commas.

The origin of Holder's comma resides in the fact that the [[Ancient Greek]]s (or at least to the Roman [[Anicius Manlius Severinus Boethius]]). According to Boethius, [[Pythagoras]]' disciple [[Philolaus|Philolaus of Croton]] would have said that the tone consisted in two [[diatonic semitone]]s and a comma; the diatonic semitone consisted in two [[diaschisma]]ta, each formed of two commas.<ref>Anicius Manlius Severinus Boethius - ''De institutione musica'' - book 3 ch8</ref><ref>J. Murray Barbour - ''Tuning and Temperament: A historical survey'' (1951) - p123</ref>believed that in the [[Pythagorean tuning]] the tone could be divided in nine commas, four of which forming the diatonic semitone and five the chromatic semitone. If all these commas are exactly of the same size, there results an octave of ''5 tones + 2 diatonic'' semitones, ''5 × 9 + 2 × 4 = 53 equal'' commas.

Holder<ref name=Holder-1731>William Holder - ''A Treatise of the Natural Grounds, and Principles of Harmony'' (1731) - ed3 p79</ref> attributes the division of the octave in 53 equal parts to [[Nicholas Mercator]]: "The late ''Nicholas Mercator'', a Modest Person, and a Learned and Judicious Mathematician, in a Manuscript of his, of which I have had a Sight."<ref name=Holder-1731/>who himself had proposed that 1/53 of the octave be named the "artificial comma".

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 == Historical origin ==
-The origin of Holder's comma resides in the fact that the [[Ancient Greek]]s (or at least to the Roman [[Boethius]]). According to [[Boethius]], [[Pythagoras]]' disciple [[Philolaus|Philolaus of Croton]] would have said that the tone consisted in two [[diatonic semitone]]s and a comma; the diatonic semitone consisted in two [[diaschisma]]ta, each formed of two commas.<ref>Anicius Manlius Severinus Boethius - ''De institutione musica'' - book 3 ch8</ref><ref>J. Murray Barbour - ''Tuning and Temperament: A historical survey'' (1951) - p123</ref>believed that in the [[Pythagorean tuning]] the tone could be divided in nine commas, four of which forming the diatonic semitone and five the chromatic semitone. If all these commas are exactly of the same size, there results an octave of ''5 tones + 2 diatonic'' semitones, ''5 × 9 + 2 × 4 = 53 equal'' commas.
+The origin of Holder's comma resides in the fact that the [[Ancient Greek]]s (or at least to the Roman [[Anicius Manlius Severinus Boethius]]). According to Boethius, [[Pythagoras]]' disciple [[Philolaus|Philolaus of Croton]] would have said that the tone consisted in two [[diatonic semitone]]s and a comma; the diatonic semitone consisted in two [[diaschisma]]ta, each formed of two commas.<ref>Anicius Manlius Severinus Boethius - ''De institutione musica'' - book 3 ch8</ref><ref>J. Murray Barbour - ''Tuning and Temperament: A historical survey'' (1951) - p123</ref>believed that in the [[Pythagorean tuning]] the tone could be divided in nine commas, four of which forming the diatonic semitone and five the chromatic semitone. If all these commas are exactly of the same size, there results an octave of ''5 tones + 2 diatonic'' semitones, ''5 × 9 + 2 × 4 = 53 equal'' commas.
 Holder<ref name=Holder-1731>William Holder - ''A Treatise of the Natural Grounds, and Principles of Harmony'' (1731) - ed3 p79</ref> attributes the division of the octave in 53 equal parts to [[Nicholas Mercator]]: "The late ''Nicholas Mercator'', a Modest Person, and a Learned and Judicious Mathematician, in a Manuscript of his, of which I have had a Sight."<ref name=Holder-1731/>who himself had proposed that 1/53 of the octave be named the "artificial comma".