296edo: Difference between revisions

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The ''296 equal temperament'' divides the octave into 296 equal parts of 4.054 cents each. In the 5-limit, it not only tempers out the semicomma of 5-limit orwell (orson) temperament, 2109375/2097152, it also provides its [[~~Optimal_patent_val|~~optimal patent val]], and tempers out the minortone comma, |-16 35 -17~~>~~. It is also an interesting temperament in higher limits, being distinctly consistent through to the 15-limit. In the 7-limit it tempers out 4375/4374 and 16875/16807, supporting 7-limit [[~~Ragismic_microtemperaments#Octoid|~~octoid ~~temperament~~]]. In the 11-limit, it tempers out 1375/1372, 6250/6237, 540/539, 4000/3993 and ~~3205~~/3024, and in the 13-limit 625/624, 729/728, 1575/1573, 1716/1715, 2080/2079, so that it also supports the 11- and 13-limit versions of octoid.

The '''296 equal temperament''' divides the octave into 296 equal parts of 4.054 cents each.

In the 5-limit, 296et not only tempers out the [[semicomma]] of 5-limit orwell (orson) temperament, 2109375/2097152, it also provides its [[optimal patent val]], and tempers out the minortone comma, {{monzo| -16 35 -17 }}. It is also an interesting temperament in higher limits, being distinctly consistent through to the 15-odd-limit. In the 7-limit it tempers out [[4375/4374]] and 16875/16807, supporting 7-limit [[octoid]] temperament. In the 11-limit, it tempers out 1375/1372, [[6250/6237]], [[540/539]], [[4000/3993]] and [[3025/3024]], and in the 13-limit [[625/624]], [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], so that it also supports the 11- and 13-limit versions of octoid.

296 is divisible by 2, 4, 8, 37, 74 and 148.

== Prime harmonics ==

[[Category:Equal divisions of the octave]]

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-The ''296 equal temperament'' divides the octave into 296 equal parts of 4.054 cents each. In the 5-limit, it not only tempers out the semicomma of 5-limit orwell (orson) temperament, 2109375/2097152, it also provides its [[Optimal_patent_val|optimal patent val]], and tempers out the minortone comma, |-16 35 -17&gt;. It is also an interesting temperament in higher limits, being distinctly consistent through to the 15-limit. In the 7-limit it tempers out 4375/4374 and 16875/16807, supporting 7-limit [[Ragismic_microtemperaments#Octoid|octoid temperament]]. In the 11-limit, it tempers out 1375/1372, 6250/6237, 540/539, 4000/3993 and 3205/3024, and in the 13-limit 625/624, 729/728, 1575/1573, 1716/1715, 2080/2079, so that it also supports the 11- and 13-limit versions of octoid.
+The '''296 equal temperament''' divides the octave into 296 equal parts of 4.054 cents each.
+In the 5-limit, 296et not only tempers out the [[semicomma]] of 5-limit orwell (orson) temperament, 2109375/2097152, it also provides its [[optimal patent val]], and tempers out the minortone comma, {{monzo| -16 35 -17 }}. It is also an interesting temperament in higher limits, being distinctly consistent through to the 15-odd-limit. In the 7-limit it tempers out [[4375/4374]] and 16875/16807, supporting 7-limit [[octoid]] temperament. In the 11-limit, it tempers out 1375/1372, [[6250/6237]], [[540/539]], [[4000/3993]] and [[3025/3024]], and in the 13-limit [[625/624]], [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], so that it also supports the 11- and 13-limit versions of octoid.
 is divisible by 2, 4, 8, 37, 74 and 148.
+== Prime harmonics ==
+{{Primes in edo|296}}
 [[Category:Equal divisions of the octave]]