1817edo: Difference between revisions

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1817edo distinctly [[consistent]] in the [[17-odd-limit]], and a fairly strong 17-limit system.

1817edo is distinctly [[consistent]] in the [[17-odd-limit]], and a fairly strong 17-limit system. Past that, adding the mapping for [[29/16|29]] is worth considering.

In the 5-limit, it is a strong tuning for [[alphatricot]]. It also [[tempering out|tempers out]] {{monzo| 128 13 -64 }}, corresponding to the 323 & 1171 temperament, which divides the [[3/1|third harmonic]] into 64 equal parts, as well as {{monzo| -89 -42 67 }} and {{monzo| -50 -71 70 }}. In the 7-limit, it tempers out [[4375/4374]] (ragisma). In the 11-limit it tempers out 117649/117612, 2097152/2096325, and tunes rank-3 temperaments [[heimdall]] and [[bragi]]. In the 13-limit, it tempers out [[4096/4095]], [[6656/6655]], and in the 17-limit, [[12376/12375]] and [[14400/14399]].

In the 17-limit and the 2.3.5.7.11.13.17.37 subgroup (17-limit add-37), the [[patent val]] tunes the [[gold]] temperament which divides the octave into 79 parts, though it is worth noting that the error on the 37th harmonic is quite large.

=== Prime harmonics ===

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=== Subsets and supersets ===

Since 1817 factors into {{~~factorization~~|~~1817~~}}, 1817edo contains [[23edo]] and [[79edo]] as subsets.

Since 1817 factors into primes as {{nowrap| 23 × 79 }}, 1817edo contains [[23edo]] and [[79edo]] as subsets.

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|1817}}
+{{ED intro}}
-edo distinctly [[consistent]] in the [[17-odd-limit]], and a fairly strong 17-limit system.
+edo is distinctly [[consistent]] in the [[17-odd-limit]], and a fairly strong 17-limit system. Past that, adding the mapping for [[29/16|29]] is worth considering.
+In the 5-limit, it is a strong tuning for [[alphatricot]]. It also [[tempering out|tempers out]] {{monzo| 128 13 -64 }}, corresponding to the 323 & 1171 temperament, which divides the [[3/1|third harmonic]] into 64 equal parts, as well as {{monzo| -89 -42 67 }} and {{monzo| -50 -71 70 }}. In the 7-limit, it tempers out [[4375/4374]] (ragisma). In the 11-limit it tempers out 117649/117612, 2097152/2096325, and tunes rank-3 temperaments [[heimdall]] and [[bragi]]. In the 13-limit, it tempers out [[4096/4095]], [[6656/6655]], and in the 17-limit, [[12376/12375]] and [[14400/14399]].
+In the 17-limit and the 2.3.5.7.11.13.17.37 subgroup (17-limit add-37), the [[patent val]] tunes the [[gold]] temperament which divides the octave into 79 parts, though it is worth noting that the error on the 37th harmonic is quite large.
 === Prime harmonics ===
@@ Line 8: / Line 12: @@
 === Subsets and supersets ===
-Since 1817 factors into {{factorization|1817}}, 1817edo contains [[23edo]] and [[79edo]] as subsets.
+Since 1817 factors into primes as {{nowrap| 23 × 79 }}, 1817edo contains [[23edo]] and [[79edo]] as subsets.