User:Lhearne/Extra-Diatonic Intervals: Difference between revisions
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=== English interval names in the Baroque === | === English interval names in the Baroque === | ||
[[File:Harmonics, or The Philosophy of Musical Sounds, Section 2 figure 3.png|thumb| | [[File:Harmonics, or The Philosophy of Musical Sounds, Section 2 figure 3.png|thumb|547.986x547.986px|''Harmonics, or The Philosophy of Musical Sounds'', Edition 2, Smith, 1759, Section 2: On the Names and Notation of consonance and their intervals, Fig. 2 & 3 , pg. 10]] | ||
After English superseded Latin as the the main language of scholarship, the Latin interval names were rejected and the convention we saw in Zarlino's Italian for naming the smaller of a pair of sizes of an interval 'minor' and the larger 'major' was further applied. | After English superseded Latin as the the main language of scholarship, the Latin interval names were rejected and the convention we saw in Zarlino's Italian for naming the smaller of a pair of sizes of an interval 'minor' and the larger 'major' was further applied. | ||
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In ''An Elementary Treatise on Musical Intervals and Temperament,'' published in 1876'','' R. H. M Bosanquet refers to 5/4 as the ''perfect third'', and 81/64 as the P''ythagorean third''. Bosanquet also labels other intervals of the Pythagorean diatonic scale similarly, i.e. 256/243, the limma, is labelled the ''Pythagorean semitone'', and 27/16 the ''Pythagorean sixth''. 81/80 is labelled the ''ordinary comma'', or simple the ''comma,'' and the Pythagorean comma is defined as the difference between twelve fifths and seven octaves. The apotome of 2187/2048 is referred to as Apatomè Pythagoria. The following relationships are then described: (<span style="color:#FF0000">the image is too inappropriate to show, see pg 28 for rules regarding posting images to the Internet</span>) | In ''An Elementary Treatise on Musical Intervals and Temperament,'' published in 1876'','' R. H. M Bosanquet refers to 5/4 as the ''perfect third'', and 81/64 as the P''ythagorean third''. Bosanquet also labels other intervals of the Pythagorean diatonic scale similarly, i.e. 256/243, the limma, is labelled the ''Pythagorean semitone'', and 27/16 the ''Pythagorean sixth''. 81/80 is labelled the ''ordinary comma'', or simple the ''comma,'' and the Pythagorean comma is defined as the difference between twelve fifths and seven octaves. The apotome of 2187/2048 is referred to as Apatomè Pythagoria. The following relationships are then described: (<span style="color:#FF0000">the image is too inappropriate to show, see pg 28 for rules regarding posting images to the Internet</span>) | ||
=== Helmholtz and Ellis === | === Helmholtz and Ellis === | ||
[[File:Helmholtz consonances table.png|thumb|617x469px|Table describing the influence of the different consonances on one another, up to the 9th partial, from ''On the Sensations of Tone as a Phycological Basis for Theory of Music'', Helmholtz, 1863, Translation by Ellis, 1875, pg. 187|]] | |||
Through the investigations of Galileo (1638), Newton, Euler (1729), and Bernouilli (1771), theorist Hermann von Helmholtz was aware that ratios governing the lengths of strings existed also for the vibrations of the tones they produced. His investigation of the harmonic series associated with these ratios of vibration led him to the consideration of ratios above the 5-limit. In his seminal ''On the Sensations of Tone as a Physiological Basis for the Theory of Music'', published in German in 1863 and translated into English in 1875 by Alexander Ellis, he listed just intervals as show in the table to the right. It is interesting to note that 8:9 is labelled a 'Second' rather than a 'major Second'. The minor Seventh is shown as 5:9 rather than as 9:16 seemingly because of the 9 partial limit imposed on the table. It is also worth noting that 5:7 is labelled a subminor Fifth. 'Super', indicated in notation with a '+', raises an interval by 35:36, the septimal quarter tone, and 'sub', indicated with a '-' lowers by the same interval with the exception of the Supersecond 7:8, which lies 63:64, the septimal comma above the Second. The subminor fifth is not included in this as no minor Fifth is shown. If we assume that 'sub' lowers an interval 35:36, then the minor Fifth would be 18:25, 80:81 above Smith's 45:64 minor Fifth, however in table 2 below, Ellis labels 18:25 a ''superfluous Fourth'', and it's inverse, 25:32, an ''acute diminished Fifth'', whilst 64:45 is labelled a ''diminished Fifth'' and its inverse 32:45 a ''false Fourth or Tritone.'' If we label 9:10 as a 'major Second', and 7:8 as a 'supermajor Second' then they differ by 35:36, the major Second is the inverse of the minor Seventh, and the supermajor Second is the octave inverse of the subminor Seventh. Perhaps 'major' has been left off name of the major Fifth, and minor off the name of the minor Fourth since the time of Smith. We can add to this table the remaining octave inversions as well as the super Fourth and sub Fifth. | Through the investigations of Galileo (1638), Newton, Euler (1729), and Bernouilli (1771), theorist Hermann von Helmholtz was aware that ratios governing the lengths of strings existed also for the vibrations of the tones they produced. His investigation of the harmonic series associated with these ratios of vibration led him to the consideration of ratios above the 5-limit. In his seminal ''On the Sensations of Tone as a Physiological Basis for the Theory of Music'', published in German in 1863 and translated into English in 1875 by Alexander Ellis, he listed just intervals as show in the table to the right. It is interesting to note that 8:9 is labelled a 'Second' rather than a 'major Second'. The minor Seventh is shown as 5:9 rather than as 9:16 seemingly because of the 9 partial limit imposed on the table. It is also worth noting that 5:7 is labelled a subminor Fifth. 'Super', indicated in notation with a '+', raises an interval by 35:36, the septimal quarter tone, and 'sub', indicated with a '-' lowers by the same interval with the exception of the Supersecond 7:8, which lies 63:64, the septimal comma above the Second. The subminor fifth is not included in this as no minor Fifth is shown. If we assume that 'sub' lowers an interval 35:36, then the minor Fifth would be 18:25, 80:81 above Smith's 45:64 minor Fifth, however in table 2 below, Ellis labels 18:25 a ''superfluous Fourth'', and it's inverse, 25:32, an ''acute diminished Fifth'', whilst 64:45 is labelled a ''diminished Fifth'' and its inverse 32:45 a ''false Fourth or Tritone.'' If we label 9:10 as a 'major Second', and 7:8 as a 'supermajor Second' then they differ by 35:36, the major Second is the inverse of the minor Seventh, and the supermajor Second is the octave inverse of the subminor Seventh. Perhaps 'major' has been left off name of the major Fifth, and minor off the name of the minor Fourth since the time of Smith. We can add to this table the remaining octave inversions as well as the super Fourth and sub Fifth. | ||
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