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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|988}}
{{ED intro}}


== Theory ==
== Theory ==
988edo provides excellent tuning for the 2, 3, 5, 11, 13, 19, 37, 43, 47, 53, 59th harmonics and a reasonable tuning for 23, 29, 31, 41st harmonics, making a strong higher-limit system. In lower limits, it is [[enfactored]] in the [[17-limit]], with the same tuning as [[494edo]], which is notable for being a zeta edo. If considered in the 19-limit, it provides a good correction for the 19th harmonic over 494edo. The comma basis for 988edo in the 19-limit is {1156/1155, 1275/1274, 1445/1444, 1716/1715, 2080/2079, 2431/2430, 4096/4095}.
988edo is [[enfactoring|enfactored]] in the [[17-limit]], with the same tuning as [[494edo]], which is notable for being a [[zeta edo]]. If considered in the 19-limit, it provides a good correction for the 19th harmonic over 494edo. A [[comma basis]] for 988edo in the 19-limit is {[[1156/1155]], [[1275/1274]], [[1445/1444]], [[1716/1715]], [[2080/2079]], [[2431/2430]], [[4096/4095]]}. An alternate mapping for 17 would be the 988g val, where it tempers out [[2025/2023]], 13013/13005, 15625/15606, 31213/31212.
 
In addition, in the 988ccd val provides a tuning that is extremely close to the [[POTE tuning]] for [[quadritikleismic]] temperament in the 7-limit.
 
=== Prime harmonics ===
{{Harmonics in equal|988|columns=11}}


An alternate mapping for 17 would be the 988g val, where it tempers out 2025/2023, 13013/13005, 15625/15606, 31213/31212. In addition, in the 988ccd val it is a tuning for [[quadritikleismic]] temperament in the 7-limit.
=== Higher limits ===
=== Higher limits ===
988edo provides excellent approximations for harmonics 2, 3, 5, 11, 13, 19, 37, 43, 47, 53, and 59, and reasonable approximations for harmonics 23, 29, 31, and 41, making it a strong higher-limit system.
In the 2.5.11.13.19.29.31 it supports period-52 temperament called [[french deck]], with the tempering out of [[6656/6655]] inherited from 494edo.
In the 2.5.11.13.19.29.31 it supports period-52 temperament called [[french deck]], with the tempering out of [[6656/6655]] inherited from 494edo.


988edo is similar to [[2016edo]] in the fact that both tune well the 2.5.11.13.19.41.47 subgroup. The result is the 988 & 2016 temperament, which reaches [[13/8]] in four generators and has a comma basis {7943/7942, 322465/322373, 16777475/16777216, 22151168/22150865, 12998046875/12994428928}.
988edo is similar to [[2016edo]] in the fact that both tune well the 2.5.11.13.19.41.47 subgroup. The result is the 988 & 2016 temperament, which reaches [[13/8]] in four generators and has a comma basis {7943/7942, 322465/322373, 16777475/16777216, 22151168/22150865, 12998046875/12994428928}.
=== Subsets and supersets ===
=== Subsets and supersets ===
988edo has subset edos {{EDOs|1, 2, 4, 13, 19, 26, 38, 52, 76, 247, 494}}.
Since 988 factors into {{factorization|988}}, 988edo has subset edos {{EDOs| 2, 4, 13, 19, 26, 38, 52, 76, 247, and 494 }}.


One step of 988edo is named ''semisqub'', given the strong relation to 494edo and the fact that 1 step of 494edo is called a squb.
One step of 988edo is named ''semisqub'', given the strong relation to 494edo and the fact that 1 step of 494edo is called a squb.
=== Prime harmonics ===
{{Harmonics in equal|988|columns=11}}


== Regular temperament properties ==
== Regular temperament properties ==
=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
Note: temperaments represented by 494edo are not included.
Note: 17-limit temperaments supported by 494edo are not included.
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
!Periods<br>per 8ve
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
! Generator<br>(Reduced)
|-
! Cents<br>(Reduced)
! Periods<br />per 8ve
! Associated<br>Ratio
! Generator*
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
| 4
| 4
| 261\988<br>(14\988)
| 261\988<br />(14\988)
| 317.004<br>(17.004)
| 317.004<br />(17.004)
| 6/5<br>(126/125)
| 6/5<br />(126/125)
| [[Quadritikleismic]] (988ccd)
| [[Quadritikleismic]] (988ccd)
|-
|-
| 19
| 19
| 141\988<br>(37\988)
| 141\988<br />(37\988)
| 171.255<br>(44.939)
| 171.255<br />(44.939)
| 6545/5928<br>(?)
| 6545/5928<br />(?)
| [[Kalium]]
| [[Kalium]]
|-
|-
| 52
| 52
| 325\988<br>(2\988)
| 325\988<br />(2\988)
| 394.736<br>(2.429)
| 394.736<br />(2.429)
| 134560000/107132311<br>(?)
| 134560000/107132311<br />(?)
|[[French deck]]
| [[French deck]]
|}
|}
<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


== Music ==
== Music ==
* [https://www.youtube.com/watch?v=c7BW2xnQBb4 Alien ethnic motive in 13edo and 12rdo] by [[Eliora]]
; [[birdshite stalactite]]
* "clagworks" from ''clagworks / it's probably gout'' (2024) &ndash; [https://open.spotify.com/track/1Abk4KcVUHoRkKxYNSYm0F Spotify] | [https://birdshitestalactite.bandcamp.com/track/clagworks Bandcamp] | [https://www.youtube.com/watch?v=S0zS0rYtT2Y YouTube]
 
; [[Eliora]]
* [https://www.youtube.com/watch?v=c7BW2xnQBb4 ''Alien ethnic motive in 13edo and 12rdo''] (2023)


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Listen]]
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