Ed4/3

An equal division of the fourth (ed4/3) is an equal-step tuning in which the perfect fourth (4/3) is 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 intervals 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 5/4, 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 scales for ed4/3s. While the notes are rather closer together, the scheme is uncannily similar to meantone.

Individual pages for ed4/3s

• 3ed4/3 (aka Cube Root of P4)
• 4ed4/3
• 5ed4/3 (aka Quintilipyth scale^{[citation needed]})
• 6ed4/3 (aka Sextilipyth scale^{[citation needed]})
• 7ed4/3
• 8ed4/3
• 9ed4/3 (aka Noleta scale)

See also

• Square root of 13 over 10 (previously listed here as an "edIV")