Hemififths: Difference between revisions
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'''Hemififths''' is the [[temperament]] [[tempering out]] the breedsma, [[2401/2400]], and the hemifamity comma, [[5120/5103]], and as the name suggests, uses a neutral | '''Hemififths''' is the [[temperament]] [[tempering out]] the breedsma, [[2401/2400]], and the hemifamity comma, [[5120/5103]], and as the name suggests, uses a neutral third as a generator. '''Hemif''' is the no-5 subgroup version of hemififths. It is supported by [[41edo|41-]], [[58edo|58-]], and [[99edo|99et]]. | ||
Hemififths was named by [[Gene Ward Smith]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10541.html Yahoo! Tuning Group (Archive) | ''Names for important high-complexity temperaments'']</ref>. | Hemififths was named by [[Gene Ward Smith]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10541.html Yahoo! Tuning Group (Archive) | ''Names for important high-complexity temperaments'']</ref>. | ||
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In the following table, odd harmonics 1–21 are labeled in '''bold'''. | In the following table, odd harmonics 1–21 are labeled in '''bold'''. | ||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
! rowspan="2" | # | ! rowspan="2" | # | ||
! rowspan="2" | Cents* | ! rowspan="2" | Cents* | ||
! colspan="2" | Approximate Ratios | ! colspan="2" | Approximate Ratios | ||
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| | | | ||
|} | |} | ||
<nowiki>* | <nowiki />* In 7-limit CTE tuning | ||
== Notation == | == Notation == | ||
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{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|- | |- | ||
! Edo<br>generator | ! Edo<br />generator | ||
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]* | ! [[Eigenmonzo|Eigenmonzo<br />(unchanged-interval)]]* | ||
! Generator (¢) | ! Generator (¢) | ||
! Comments | ! Comments | ||
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| | | | ||
| 351.220 | | 351.220 | ||
| Lower bound of 11- to 15-odd-limit<br>and 13-limit 21-odd-limit diamond monotone | | Lower bound of 11- to 15-odd-limit<br />and 13-limit 21-odd-limit diamond monotone | ||
|- | |- | ||
| | | | ||
| Line 416: | Line 416: | ||
| | | | ||
| 352.941 | | 352.941 | ||
| Upper bound of 7- to 15-odd-limit<br>and 13-limit 21-odd-limit diamond monotone | | Upper bound of 7- to 15-odd-limit<br />and 13-limit 21-odd-limit diamond monotone | ||
|- | |- | ||
| | | | ||
| Line 428: | Line 428: | ||
| | | | ||
|} | |} | ||
<nowiki>* | <nowiki />* Besides the octave | ||
== Notes == | == Notes == | ||
[[Category:Temperaments]] | [[Category:Temperaments]] | ||
[[Category:Hemififths| ]] <!-- | [[Category:Hemififths| ]] <!-- Main article --> | ||
[[Category:Breedsmic temperaments]] | [[Category:Breedsmic temperaments]] | ||
[[Category:Hemifamity temperaments]] | [[Category:Hemifamity temperaments]] | ||
[[Category:Hemimage temperaments]] | [[Category:Hemimage temperaments]] | ||