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. If considered in the 19-limit, it is basically a spicy 494edo with the 19th harmonic. The comma basis for such regular temperament is 1445/1444, 1716/1715, ~~2601/2600, 3025/3024, 4225~~/~~4224~~, ~~10830~~/~~10829~~, ~~297440~~/~~297381~~.

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. If considered in the 19-limit, it is basically a spicy 494edo with the 19th harmonic. The comma basis for such regular temperament 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~~. In it~~, it tempers out 2025/2023, 13013/13005, 15625/15606, 31213/31212.

An alternate mapping for 17 would be the 988g val, where it tempers out 2025/2023, 13013/13005, 15625/15606, 31213/31212.

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.

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=== Prime harmonics ===

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

== Regular temperament properties ==

=== Rank-2 temperaments ===

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

!Periods

!Periods per 8ve

per ~~octave~~

! Generator (Reduced)

!Generator

! Cents (Reduced)

(~~reduced~~)

! Associated Ratio

!Cents

! Temperaments

(~~reduced~~)

!Associated

~~ratio~~

!Temperaments

|-

|52

| 52

|325\988

| 325\988 (2\988)

(2\988)

| 394.736 (2.429)

|394.736

| 134560000/107132311 (?)

(2.429)

| [[French deck]]

|134560000/107132311

|}

~~(?)~~

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

|[[~~French deck~~]]

|}

@@ Line 3: / Line 3: @@
 == 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. If considered in the 19-limit, it is basically a spicy 494edo with the 19th harmonic. The comma basis for such regular temperament is 1445/1444, 1716/1715, 2601/2600, 3025/3024, 4225/4224, 10830/10829, 297440/297381.
+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. If considered in the 19-limit, it is basically a spicy 494edo with the 19th harmonic. The comma basis for such regular temperament 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. In it, it tempers out 2025/2023, 13013/13005, 15625/15606, 31213/31212.
+An alternate mapping for 17 would be the 988g val, where it tempers out 2025/2023, 13013/13005, 15625/15606, 31213/31212.
 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.
@@ Line 14: / Line 14: @@
 === Prime harmonics ===
-{{Harmonics in equal|988}}
+{{Harmonics in equal|988|columns=11}}
-[[Category:Equal divisions of the octave|###]]
 == Regular temperament properties ==
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-!Periods
+!Periods<br>per 8ve
-per octave
+! Generator<br>(Reduced)
-!Generator
+! Cents<br>(Reduced)
-(reduced)
+! Associated<br>Ratio
-!Cents
+! Temperaments
-(reduced)
-!Associated
-ratio
-!Temperaments
 |-
-|52
+| 52
-|325\988
+| 325\988<br>(2\988)
-(2\988)
+| 394.736<br>(2.429)
-|394.736
+| 134560000/107132311<br>(?)
-(2.429)
+| [[French deck]]
-|134560000/107132311
+|}
-(?)
+[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
-|[[French deck]]
-|}<!-- 3-digit number -->