31edf: Difference between revisions
Created page with "'''Division of the just perfect fifth into 31 equal parts''' (31EDF) is almost identical to 53 edo, but with the 3/2 rather than the 2/1 being just. The octa..." Tags: Mobile edit Mobile web edit |
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Lookalikes: [[53edo]], [[84edt]] | Lookalikes: [[53edo]], [[84edt]] | ||
=Just Approximation= | |||
31edf provides excellent approximations for the classic 5-limit [[just]] chords and scales, such as the Ptolemy-Zarlino "just major" scale. | |||
{| class="wikitable" | |||
|- | |||
! |interval | |||
! |ratio | |||
! |size | |||
! |difference | |||
|- | |||
| |perfect octave | |||
| |2/1 | |||
| style="text-align:center;" |31 | |||
| | +0.12 cents | |||
|- | |||
| |major third | |||
| |5/4 | |||
| style="text-align:center;" |17 | |||
| |−1.37 cents | |||
|- | |||
| |minor third | |||
| |6/5 | |||
| style="text-align:center;" |14 | |||
| | +1.37 cents | |||
|- | |||
| |major tone | |||
| |9/8 | |||
| style="text-align:center;" |9 | |||
| |−0.12 cents | |||
|- | |||
| |minor tone | |||
| |10/9 | |||
| style="text-align:center;" |8 | |||
| |−1.25 cents | |||
|- | |||
| |diat. semitone | |||
| |16/15 | |||
| style="text-align:center;" |5 | |||
| | +1.49 cents | |||
|}One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds. | |||
The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO is practically equal to an extended Pythagorean. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. In addition, the 43-degree interval is only 4.85 cents away from the just ratio 7/4, so 31EDF can also be used for 7-limit harmony, tempering out the [[septimal kleisma]], 225/224. | |||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||