Ed4/3: Difference between revisions

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 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.

== Individual pages for ed4/3s ==

* [[Cube Root of P4|3ed4/3]] (aka Cube Root of P4)

* [[4ed4/3]]

* [[5ed4/3|5ed4/3]] (aka Quintilipyth scale{{citation needed|date=December 2021|reason=Who used that term?}})

* [[6ed4/3]] (aka Sextilipyth scale{{citation needed|date=December 2021|reason=Who used that term?}})

* [[7ed4/3]]

* [[8ed4/3]]

* [[Noleta|9ed4/3]] (aka Noleta scale)

 

* [[Square root of 13 over 10]] (previously listed here as an "edIV")