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, ~~and 59th harmonics~~, ~~making a strong higher-limit system. It is double the famous~~ [[~~494edo~~]]~~, and with the same~~ mapping for ~~the~~ 17~~-limit. To break~~ the ~~contorsion~~, ~~988d val can be used~~.

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 the ~~2.5.11.13.19.41.47 it supports~~ a ~~988 &~~ [[~~2016edo|2016~~]] temperament.~~~~

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 ===

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

=== 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 ===

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.

== Regular temperament properties ==

=== Rank-2 temperaments ===

Note: 17-limit temperaments supported by 494edo are not included.

{| class="wikitable center-all left-5"

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ratio*

! Temperaments

|-

| 4

| 261\988 (14\988)

| 317.004 (17.004)

| 6/5 (126/125)

| [[Quadritikleismic]] (988ccd)

|-

| 19

| 141\988 (37\988)

| 171.255 (44.939)

| 6545/5928 (?)

| [[Kalium]]

|-

| 52

| 325\988 (2\988)

| 394.736 (2.429)

| 134560000/107132311 (?)

| [[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 ==

; [[birdshite stalactite]]

* "clagworks" from ''clagworks / it's probably gout'' (2024) – [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:Listen]]

@@ Line 1: / Line 1: @@
-{{EDO intro|988}}
+{{Infobox ET}}
+{{ED intro}}
 == Theory ==
-edo provides excellent tuning for the 2, 3, 5, 11, 13, 19, 37, 43, 47, 53, and 59th harmonics, making a strong higher-limit system. It is double the famous [[494edo]], and with the same mapping for the 17-limit. To break the contorsion, 988d val can be used.
+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. 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 the 2.5.11.13.19.41.47 it supports a 988 & [[2016edo|2016]] temperament.<!-- why is it notable? -->
+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}}
+{{Harmonics in equal|988|columns=11}}
-[[Category:Equal divisions of the octave]]
+=== 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 ===
+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.
+== Regular temperament properties ==
+=== Rank-2 temperaments ===
+Note: 17-limit temperaments supported by 494edo are not included.
+{| 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
+|-
+| 4
+| 261\988<br />(14\988)
+| 317.004<br />(17.004)
+| 6/5<br />(126/125)
+| [[Quadritikleismic]] (988ccd)
+|-
+| 19
+| 141\988<br />(37\988)
+| 171.255<br />(44.939)
+| 6545/5928<br />(?)
+| [[Kalium]]
+|-
+| 52
+| 325\988<br />(2\988)
+| 394.736<br />(2.429)
+| 134560000/107132311<br />(?)
+| [[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 ==
+; [[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:Listen]]