18edo: Difference between revisions
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18edo is also known as the '''third-tone''' system. | 18edo is also known as the '''third-tone''' system. | ||
== Theory == | == Theory == | ||
18edo does not approximate the 3rd harmonic at all, unless a >30¢-error is considered acceptable, and it approximates the 5th, 7th and 9th harmonics equally well (or equally poorly) as 12edo does. It does, however, render more accurate tunings of 7/6, 21/16, 15/11, 12/7, and 13/7. It is also the smallest edo to approximate the harmonic series chord 5:6:7 without tempering out 36/35 (and thus without using the same interval to approximate both 6/5 and 7/6). | 18edo does not approximate the 3rd harmonic at all, unless a >30¢-error is considered acceptable, and it approximates the 5th, 7th and 9th harmonics equally well (or equally poorly) as 12edo does. It does, however, render more accurate tunings of 7/6, 21/16, 15/11, 12/7, and 13/7. It is also the smallest edo to approximate the harmonic series chord 5:6:7 without tempering out 36/35 (and thus without using the same interval to approximate both 6/5 and 7/6). | ||
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== Representations of JI intervals == | == Representations of JI intervals == | ||
{| class="wikitable center-all right-2" | {| class="wikitable center-all right-2" | ||
! Degree | ! Degree | ||
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[[File:18-ED2-JI-approximations-2.png|alt=18-ED2-JI-approximations-2.png|18-ED2-JI-approximations-2.png]] | [[File:18-ED2-JI-approximations-2.png|alt=18-ED2-JI-approximations-2.png|18-ED2-JI-approximations-2.png]] | ||
== Commas == | == Regular temperament properties == | ||
=== Uniform maps === | |||
{{Uniform map|13|17.5|18.5}} | |||
=== Commas === | |||
18edo [[tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 18 29 42 51 62 67 }}.) | 18edo [[tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 18 29 42 51 62 67 }}.) | ||