1147edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
1147edo can be defined as the unique ET in the [[2.3.7 subgroup]] that tempers out the [[Don Page comma]]s among the intervals [[9/8]], [[8/7]], and [[7/6]], and therefore contains [[28ed4/3]] and [[32ed9/7]] within it. This edo notably also tempers out the [[quartisma]] (117440512/117406179), by virtue of 28ed4/3 mapping 7/6 to a number of steps divisible by 5 (that is, 15). Therefore, the representation of [[33/32]], as one fifth of 7/6, is accurate and the edo overall excels in the [[2.3.7.11 subgroup]], with an additional very good prime 43. | 1147edo can be defined as the unique ET in the [[2.3.7 subgroup]] that tempers out the [[Don Page comma]]s among the intervals [[9/8]], [[8/7]], and [[7/6]], and therefore contains [[28ed4/3]] and [[32ed9/7]] within it. This edo notably also tempers out the [[quartisma]] (117440512/117406179), by virtue of 28ed4/3 mapping 7/6 to a number of steps divisible by 5 (that is, 15). Therefore, the representation of [[33/32]], as one fifth of 7/6, is accurate and the edo overall excels in the [[2.3.7.11 subgroup]], with an additional very good prime 43. | ||
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=== Odd harmonics === | === Odd harmonics === | ||
One should note that its prime 11 is inherited from 37edo, which is a strong [[convergent]]. | One should note that its prime 11 is inherited from [[37edo]], which is a strong [[convergent]]. | ||
{{Harmonics in equal|1147|2|1|prec=4|columns=15|intervals=prime}} | {{Harmonics in equal|1147|2|1|prec=4|columns=15|intervals=prime}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 1147 factors into {{factorization|1147}}, 1147edo has subset edos {{EDOs| 31 and 37 }}. | Since 1147 factors into {{factorization|1147}}, 1147edo has subset edos {{EDOs| 31 and 37 }}. | ||