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The '''299 equal divisions of the octave''' divides the octave into 299 parts of 4.013 cents each. In the 5-limit it tempers out the [[kleisma]], 15625/15552, in the 7-limit [[10976/10935]], in the 11-limit [[385/384]]; and in the 13-limit [[325/324]], [[625/624]] and [[676/675]]. It provides the [[optimal patent val]] for the 13-limit rank-3 [[enlil]] temperament, and the rank-4 temperament tempering out 325/324 and 385/384.   
{{Infobox ET}}
{{ED intro}}
 
== Theory ==
In the 5-limit, 299et [[tempering out|tempers out]] the [[kleisma]], 15625/15552, in the [[7-limit]] [[10976/10935]], in the [[11-limit]] [[385/384]]; and in the [[13-limit]] [[325/324]], [[625/624]] and [[676/675]]. It provides the [[optimal patent val]] for the 13-limit rank-3 [[enlil]] temperament, and the rank-4 temperament tempering out 325/324 and 385/384.   
 
=== Prime harmonics ===
{{Harmonics in equal|299}}
 
=== Subsets and supersets ===
Since 299 factors into 13 × 23, 299edo contains [[13edo]] and [[23edo]] as subsets.
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{Monzo| 474 -299 }}
| {{Mapping| 299 474 }}
| −0.1218
| 0.1218
| 3.04
|-
| 2.3.5
| 15625/15552, {{monzo| 80 -49 -1 }}
| {{Mapping| 299 474 694 }}
| +0.0665
| 0.2844
| 7.09
|-
| 2.3.5.7
| 10976/10935, 15625/15552, 823543/819200
| {{Mapping| 299 474 694 839 }}
| +0.1925
| 0.3291
| 8.20
|-
| 2.3.5.7.11
| 385/384, 6250/6237, 10976/10935, 12005/11979
| {{Mapping| 299 474 694 839 1034 }}
| +0.2399
| 0.3092
| 7.70
|-
| 2.3.5.7.11.13
| 325/324, 385/384, 625/624, 10648/10647, 10976/10935
| {{Mapping| 299 474 694 839 1034 1106 }}
| +0.2779
| 0.2948
| 7.34
|-
| 2.3.5.7.11.13.17
| 325/324, 385/384, 595/594, 625/624, 2058/2057, 8624/8619
| {{Mapping| 299 474 694 839 1034 1106 1222 }}
| +0.2595
| 0.2767
| 6.89
|-
| 2.3.5.7.11.13.17.19
| 325/324, 343/342, 385/384, 595/594, 625/624, 1216/1215, 1445/1444
| {{Mapping| 299 474 694 839 1034 1106 1222 1270 }}
| +0.2424
| 0.2627
| 6.54
|}
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>ratio*
! Temperaments
|-
| 1
| 25\299
| 100.33
| 1323/1250
| [[Heptacot]] (7-limit)
|-
| 1
| 79\299
| 317.06
| 6/5
| [[Hanson]]
|-
| 1
| 124\299
| 497.66
| 4/3
| [[Cotoneum]] (7-limit)
|-
| 1
| 124\299
| 505.69
| 75/56
| [[Marfifths]]
|}
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct


[[Category:Equal divisions of the octave]]
[[Category:Enlil]]
[[Category:Enlil]]
[[Category:Keenanismic]]
[[Category:Keenanismic]]
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