940edo: Difference between revisions

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940edo is ~~uniquely~~ [[~~consistent~~|consistent]] through the 11-limit, tempering out 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it [[support]]s [[~~Breedsmic_temperaments#Decoid|~~decoid ~~temperament~~]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives the [[~~Optimal_patent_val|~~optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for [[~~The_Archipelago#Rank tree temperaments|~~greenland]] and [[~~The_Archipelago#Rank tree temperaments|~~baffin]] temperaments, and for the rank ~~five temperament~~ temperament tempering out 676/675.

940edo is [[consistency|distinctly consistent]] through the [[11-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]] in the 7-limit and [[5632/5625]] and [[9801/9800]] in the 11-limit, which means it [[support]]s [[decoid]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]] and [[4225/4224]], so that it supports and gives the [[optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for the [[greenland]] and [[baffin]] temperaments, and for the rank-5 temperament tempering out 676/675.

The non-patent val {{val|940 1491 2184 2638 3254 3481}} gives a tuning almost identical to the POTE tuning for the 13-limit [[~~Hemifamity_family#Pele|~~pele ~~temperament~~]] tempering out 196/195, 352/351 and 364/363.

The non-patent val {{val| 940 1491 2184 2638 3254 3481 }} gives a tuning almost identical to the [[POTE tuning]] for the 13-limit [[pele]] temperament, tempering out 196/195, 352/351 and 364/363.

In higher limits, it is a satisfactory no-13's 23-limit tuning. Another thing to note is that its 15th harmonic is just barely off of the sum of mappings for 3rd and 5th harmonics, which adds a peculiarity to it where it has good 3/2 and 5/4, but 15/8 is one step off from the closest location.

In higher limits, it is a satisfactory no-13s 23-limit tuning. Another thing to note is that its 15th harmonic is just barely off of the sum of mappings for 3rd and 5th harmonics, which adds a peculiarity to 940edo's theory in 5-prime-limit where it has good 3/2 and 5/4, but 15/8 is one step off from the "expected" location.

=== Odd harmonics ===

=== Subsets and supersets ===

940edo has subset edos {{EDOs|1, 2, 4, 5, 10, 20, 47, 94, 188, 235, 470}}, of which [[94edo]] is notable.

Since 940 factors into {{factorization|940}}, 940edo has subset edos {{EDOs| 2, 4, 5, 10, 20, 47, 94, 188, 235, 470 }}, of which 94edo is notable.

[[1880edo]], which doubles 940edo, provides good correction for harmonics 13 ~~and 15 and uses a new mapping for 5 which consistently leads~~ to ~~15.~~

[[1880edo]], which doubles 940edo, provides good correction for harmonics 5 and 13, though the error of 3 has accumulated to the point of inconsistency in the 9-odd-limit.

~~[[Category:Equal divisions~~ of the ~~octave|###]] <!~~-- ~~3-digit number -->~~

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 {{Infobox ET}}
-{{EDO intro|940}}
+{{ED intro}}
-edo is uniquely [[consistent|consistent]] through the 11-limit, tempering out 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it [[support]]s [[Breedsmic_temperaments#Decoid|decoid temperament]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives the [[Optimal_patent_val|optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for [[The_Archipelago#Rank tree temperaments|greenland]] and [[The_Archipelago#Rank tree temperaments|baffin]] temperaments, and for the rank five temperament temperament tempering out 676/675.
+edo is [[consistency|distinctly consistent]] through the [[11-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]] in the 7-limit and [[5632/5625]] and [[9801/9800]] in the 11-limit, which means it [[support]]s [[decoid]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]] and [[4225/4224]], so that it supports and gives the [[optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for the [[greenland]] and [[baffin]] temperaments, and for the rank-5 temperament tempering out 676/675.
-The non-patent val {{val|940 1491 2184 2638 3254 3481}} gives a tuning almost identical to the POTE tuning for the 13-limit [[Hemifamity_family#Pele|pele temperament]] tempering out 196/195, 352/351 and 364/363.
+The non-patent val {{val| 940 1491 2184 2638 3254 3481 }} gives a tuning almost identical to the [[POTE tuning]] for the 13-limit [[pele]] temperament, tempering out 196/195, 352/351 and 364/363.
+In higher limits, it is a satisfactory no-13's 23-limit tuning. Another thing to note is that its 15th harmonic is just barely off of the sum of mappings for 3rd and 5th harmonics, which adds a peculiarity to it where it has good 3/2 and 5/4, but 15/8 is one step off from the closest location.
-In higher limits, it is a satisfactory no-13s 23-limit tuning. Another thing to note is that its 15th harmonic is just barely off of the sum of mappings for 3rd and 5th harmonics, which adds a peculiarity to 940edo's theory in 5-prime-limit where it has good 3/2 and 5/4, but 15/8 is one step off from the "expected" location.
 === Odd harmonics ===
-{{harmonics in equal|940}}
+{{Harmonics in equal|940}}
 === Subsets and supersets ===
-edo has subset edos {{EDOs|1, 2, 4, 5, 10, 20, 47, 94, 188, 235, 470}}, of which [[94edo]] is notable.
+Since 940 factors into {{factorization|940}}, 940edo has subset edos {{EDOs| 2, 4, 5, 10, 20, 47, 94, 188, 235, 470 }}, of which 94edo is notable.
-[[1880edo]], which doubles 940edo, provides good correction for harmonics 13 and 15 and uses a new mapping for 5 which consistently leads to 15.
+[[1880edo]], which doubles 940edo, provides good correction for harmonics 5 and 13, though the error of 3 has accumulated to the point of inconsistency in the 9-odd-limit.
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->