Hemififths: Difference between revisions

Notation: the two notations aren't mutually exclusive. Improve wording and formatting.
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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-third generator. '''Hemif''' is the no-5 subgroup version of hemififths. It is supported by [[41edo|41-]], [[58edo|58-]], and [[99edo|99et]].  
'''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" | &#35;
! 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
<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
|-
|-
|  
|  
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|  
|  
| 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
|-
|-
|  
|  
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|  
|  
|}
|}
<nowiki>*</nowiki> Besides the octave
<nowiki />* Besides the octave


== Notes ==
== Notes ==


[[Category:Temperaments]]
[[Category:Temperaments]]
[[Category:Hemififths| ]] <!-- main article -->
[[Category:Hemififths| ]] <!-- Main article -->
[[Category:Breedsmic temperaments]]
[[Category:Breedsmic temperaments]]
[[Category:Hemifamity temperaments]]
[[Category:Hemifamity temperaments]]
[[Category:Hemimage temperaments]]
[[Category:Hemimage temperaments]]