Ed4/3: Difference between revisions

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Centered the article on 4/3 (removed content about 15/11 and 7/5 can be recovered from the page history if necessary)
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The utility of the fourth as a base is apparent by being used at the base of so much Neo-Medieval harmony. Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy, but which context(s), if any, it is very perceptually important in is as yet an open question.
The utility of the fourth as a base is apparent by being used at the base of so much Neo-Medieval harmony. Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy, but which context(s), if any, it is very perceptually important in is as yet an open question.


Incidentally, one way to treat 4/3 as an equivalence is the use of the 12:13:14:(16) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]]. Whereas in meantone it takes (an octave-reduced stack of) four 3/2 to get to 5/1, here it takes (a fourth-reduced stack of) eight 7/6 to get to 13/12 (tempering out the comma [[5764801/5750784]]). So, doing this yields 13, 15, and 28 note MOS for ed4/3s. While the notes are rather closer together, the scheme is uncannily similar to meantone.
Incidentally, one way to treat 4/3 as an equivalence is the use of the 12:13:14:(16) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]]. Whereas in meantone it takes (an octave-reduced stack of) four [[3/2]] to get to [[5/4]], here it takes (a fourth-reduced stack of) eight [[7/6]] to get to [[13/12]] (tempering out the comma [[5764801/5750784]]). So, doing this yields 13, 15, and 28 note [[MOS scale]]s for ed4/3s. While the notes are rather closer together, the scheme is uncannily similar to meantone.


== Individual pages for ed4/3s ==
== Individual pages for ed4/3s ==