Ed4/3: Difference between revisions
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An '''equal division of the fourth''' ('''ed4/3''') is an [[equal-step tuning]] in which the perfect fourth ([[4/3]]) is [[Just intonation|justly tuned]] and is divided in a given number of equal steps. The fourth can be treated as an [[equave]], but it is not necessary and, more importantly, it is not well known whether most listeners can hear it as such. | An '''equal division of the fourth''' ('''ed4/3''') is an [[equal-step tuning]] in which the perfect fourth ([[4/3]]) is [[Just intonation|justly tuned]] and is divided in a given number of equal steps. The fourth can be treated as an [[equave]], but it is not necessary and, more importantly, it is not well known whether most listeners can hear it as such. | ||
The expression ''equal division of the fourth'' could be interpreted as applying to other [[interval]]s in the region of the fourth (see [[:Category:Fourth]]), such as [[15/11]]. However, these should be named more specifically and be treated on other pages to avoid any confusion. | The expression ''equal division of the fourth'' could be interpreted as applying to other [[interval]]s in the region of the fourth (see [[:Category: Fourth]]), such as [[15/11]]. However, these should be named more specifically and be treated on other pages to avoid any confusion. | ||
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 [[5/4]], 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 [[ | 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 ed4/3's. While the notes are rather closer together, the scheme is uncannily similar to meantone. | ||
== Individual pages for ed4/3s == | == Individual pages for ed4/3s == | ||
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* [[Square root of 13 over 10]] (previously listed here as an "edIV") | * [[Square root of 13 over 10]] (previously listed here as an "edIV") | ||
[[Category: | [[Category:Ed4/3| ]] <!-- main article --> | ||
[[Category:Edonoi]] | |||
[[Category:Lists of scales]] | |||