1783edo: Difference between revisions

(2 intermediate revisions by one other user not shown)

Line 1:

'''1783edo''' divides the octave into 1783 equal parts of 0.673 cents each. It is a very strong 5-limit system, with a lower 5-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than anything until [[2513edo|2513]]. It tempers out the monzisma, | 54 -37 2 >; egads, | -36 -52 51 >; gross, | 144 -22 -47 >; and pirate, | -90 -15 49 >.

~~{{Primes in edo~~|~~1783~~|~~prec=4}}~~

1783edo is a very strong 5-limit system, with a lower 5-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] than anything until [[2513edo|2513]]. It is [[consistent]] to the [[9-odd-limit]], but there is a large relative delta for the [[harmonic]] [[7/1|7]]. Together with decent approximations to [[11/1|11]], [[13/1|13]], [[17/1|17]], and [[19/1|19]], it makes for a good no-7 19-limit tuning.

[[~~Category:Equal divisions of~~ the ~~octave~~|~~####~~]]

In the 5-limit the equal temperament [[tempering out|tempers out]] the [[monzisma]], {{monzo| 54 -37 2}}; egads, {{monzo| -36 -52 51 }}; gross, {{monzo| 144 -22 -47 }}; and pirate, {{monzo| -90 -15 49 }}.

Using the [[patent val]], it tempers out 2460375/2458624 in the 7-limit; [[3025/3024]] and 180224/180075 in the 11-limit; [[1716/1715]] and [[4096/4095]] in the 13-limit. The alternative 1783d [[val]] tempers out [[4375/4374]] in the 7-limit; 41503/41472 and 160083/160000 in the 11-limit; [[10648/10647]] in the 13-limit.

=== Prime harmonics ===

=== Subsets and supersets ===

1783edo is the 276th [[prime edo]]. [[3566edo]], which doubles it, provides a good correction to the approximation of [[7/1|harmonic 7]].

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''1783edo''' divides the octave into 1783 equal parts of 0.673 cents each. It is a very strong 5-limit system, with a lower 5-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than anything until [[2513edo|2513]]. It tempers out the monzisma, | 54 -37 2 &gt;; egads, | -36 -52 51 &gt;; gross, | 144 -22 -47 &gt;; and pirate, | -90 -15 49 &gt;.
+{{ED intro}}
-{{Primes in edo|1783|prec=4}}
+edo is a very strong 5-limit system, with a lower 5-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] than anything until [[2513edo|2513]]. It is [[consistent]] to the [[9-odd-limit]], but there is a large relative delta for the [[harmonic]] [[7/1|7]]. Together with decent approximations to [[11/1|11]], [[13/1|13]], [[17/1|17]], and [[19/1|19]], it makes for a good no-7 19-limit tuning.
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+In the 5-limit the equal temperament [[tempering out|tempers out]] the [[monzisma]], {{monzo| 54 -37 2}}; egads, {{monzo| -36 -52 51 }}; gross, {{monzo| 144 -22 -47 }}; and pirate, {{monzo| -90 -15 49 }}.
+Using the [[patent val]], it tempers out 2460375/2458624 in the 7-limit; [[3025/3024]] and 180224/180075 in the 11-limit; [[1716/1715]] and [[4096/4095]] in the 13-limit. The alternative 1783d [[val]] tempers out [[4375/4374]] in the 7-limit; 41503/41472 and 160083/160000 in the 11-limit; [[10648/10647]] in the 13-limit.
+=== Prime harmonics ===
+{{Harmonics in equal|1783|prec=4}}
+=== Subsets and supersets ===
+edo is the 276th [[prime edo]]. [[3566edo]], which doubles it, provides a good correction to the approximation of [[7/1|harmonic 7]].