988edo: Difference between revisions

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== 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. The 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 it is a tuning for [[quadritikleismic]] temperament in the 7-limit.

=== Prime harmonics ===

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 ===

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.

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 ===

988edo has subset edos {{EDOs|1, 2, 4, 13, 19, 26, 38, 52, 76, 247, 494}}.

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.

~~=== Prime harmonics ===~~

~~{{Harmonics in equal|988|columns=11}}~~

== Regular temperament properties ==

=== 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"

!Periods per 8ve

! Periods per 8ve

! Generator~~ (Reduced)~~

! Generator*

! Cents~~ (Reduced)~~

! Cents*

! Associated Ratio

! Temperaments

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| 394.736 (2.429)

| 134560000/107132311 (?)

|[[French deck]]

| [[French deck]]

|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct

== Music ==

* [https://www.youtube.com/watch?v=c7BW2xnQBb4 Alien ethnic motive in 13edo and 12rdo] ~~by [[Eliora]]~~

; [[Eliora]]

* [https://www.youtube.com/watch?v=c7BW2xnQBb4 ''Alien ethnic motive in 13edo and 12rdo''] (2023)

~~[[Category:Equal divisions of the octave|###]] ~~

@@ Line 3: / Line 3: @@
 == Theory ==
-edo 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}.
+edo 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. The 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 it is a 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 ===
+edo 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.
 edo 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 ===
-edo has subset edos {{EDOs|1, 2, 4, 13, 19, 26, 38, 52, 76, 247, 494}}.
+edo 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.
-=== Prime harmonics ===
-{{Harmonics in equal|988|columns=11}}
 == Regular temperament properties ==
 === 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"
-!Periods<br>per 8ve
+! Periods<br>per 8ve
-! Generator<br>(Reduced)
+! Generator*
-! Cents<br>(Reduced)
+! Cents*
 ! Associated<br>Ratio
 ! Temperaments
@@ Line 44: / Line 46: @@
 | 394.736<br>(2.429)
 | 134560000/107132311<br>(?)
-|[[French deck]]
+| [[French deck]]
 |}
+<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
 == Music ==
-* [https://www.youtube.com/watch?v=c7BW2xnQBb4 Alien ethnic motive in 13edo and 12rdo] by [[Eliora]]
+; [[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 -->