3889edo: Difference between revisions

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== Theory ==

3889edo is [[consistent]] to the [[27-odd-limit]], [[tempering out]] [[~~12376/12375~~]], [[~~14400/14399~~]], [[~~6175~~/~~6174~~]]~~, 8625/8624, 89376/89375~~, [[123201/123200]]~~, 1549184/1549125~~ and [[1990656/1990625]] in the [[23-limit]]~~. It is strong~~ in the ~~2.3.5.7.13.~~17~~.19.23.31~~ [[~~subgroup~~]], ~~tempering out~~ 6175/6174, 14365/14364, ~~426496~~/~~426465~~, ~~52326~~/~~52325~~, ~~52003~~/~~52000~~, ~~1549184~~/~~1549125~~, ~~1990656/1990625~~ and ~~22816~~/~~22815. The equal temperament also tempers out [[19251/19250]]~~ in the ~~2.3.5.7.11.23.31 subgroup and~~ [[~~5440/5439~~]] ~~in the 2.3.5.7.17.37 subgroup~~.

3889edo is [[consistent]] to the [[27-odd-limit]], and except for [[29/19]] and its [[octave complement]], it is consistent to the [[31-odd-limit]].

As an equal temperament, it [[tempering out|tempers out]] the [[pirate comma]], the [[starscape comma]], and the [[quartisma]]. Some of the simpler commas it tempers out in the higher limits include [[6656/6655]], [[123201/123200]] and [[1990656/1990625]] in the [[13-limit]]; [[12376/12375]], [[14400/14399]] in the [[17-limit]]; [[5776/5775]], [[6175/6174]], 14365/14364, 23409/23408, 28900/28899, 43681/43680 in the [[19-limit]]; [[5083/5082]], 7866/7865, and 8625/8624 in the [[23-limit]].

=== Prime harmonics ===

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|-

| 2.3.5.7

| ~~{{Monzo| -4 17 1 -9 }}~~, {{monzo| 2 -20 14 -1 }}, {{monzo| 46 -14 -3 -6 }}

| 645700815/645657712, {{monzo| 2 -20 14 -1 }}, {{monzo| 46 -14 -3 -6 }}

| {{Mapping| 3889 6164 9030 10918 }}

| −0.0101

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|-

| 2.3.5.7.11

| ~~21437500~~/~~21434787~~, ~~47265625~~/~~47258883~~, ~~56953125~~/~~56942116~~, 104857600/104825259

| 1771875/1771561, 3294225/3294172, 14348907/14348180, 104857600/104825259

| {{Mapping| 3889 6164 9030 10918 13454 }}

| −0.0129

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|-

| 2.3.5.7.11.13

| 6656/6655, 123201/123200, 492128/492075, 1990656/1990625~~, 29046875/29042496~~

| 6656/6655, 123201/123200, 492128/492075, 823680/823543, 1990656/1990625

| {{Mapping| 3889 6164 9030 10918 13454 14391 }}

| −0.0106

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|-

| 2.3.5.7.11.13.17

| 12376/12375, ~~14400/14399, 123201~~/~~123200~~, 37180/37179, ~~1990656~~/~~1990625~~, ~~361250~~/~~361179~~

| 6656/6655, 12376/12375, 28561/28560, 37180/37179, 361250/361179, 937125/937024

| {{Mapping| 3889 6164 9030 10918 13454 14391 15896 }}

| −0.0075

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is [[consistent]] to the [[27-odd-limit]], [[tempering out]] [[12376/12375]], [[14400/14399]], [[6175/6174]], 8625/8624, 89376/89375, [[123201/123200]], 1549184/1549125 and [[1990656/1990625]] in the [[23-limit]]. It is strong in the 2.3.5.7.13.17.19.23.31 [[subgroup]], tempering out 6175/6174, 14365/14364, 426496/426465, 52326/52325, 52003/52000, 1549184/1549125, 1990656/1990625 and 22816/22815. The equal temperament also tempers out [[19251/19250]] in the 2.3.5.7.11.23.31 subgroup and [[5440/5439]] in the 2.3.5.7.17.37 subgroup.
+edo is [[consistent]] to the [[27-odd-limit]], and except for [[29/19]] and its [[octave complement]], it is consistent to the [[31-odd-limit]].
+As an equal temperament, it [[tempering out|tempers out]] the [[pirate comma]], the [[starscape comma]], and the [[quartisma]]. Some of the simpler commas it tempers out in the higher limits include [[6656/6655]], [[123201/123200]] and [[1990656/1990625]] in the [[13-limit]]; [[12376/12375]], [[14400/14399]] in the [[17-limit]]; [[5776/5775]], [[6175/6174]], 14365/14364, 23409/23408, 28900/28899, 43681/43680 in the [[19-limit]]; [[5083/5082]], 7866/7865, and 8625/8624 in the [[23-limit]].
 === Prime harmonics ===
@@ Line 39: / Line 41: @@
 |-
 | 2.3.5.7
-| {{Monzo| -4 17 1 -9 }}, {{monzo| 2 -20 14 -1 }}, {{monzo| 46 -14 -3 -6 }}
+| 645700815/645657712, {{monzo| 2 -20 14 -1 }}, {{monzo| 46 -14 -3 -6 }}
 | {{Mapping| 3889 6164 9030 10918 }}
 | −0.0101
@@ Line 46: / Line 48: @@
 |-
 | 2.3.5.7.11
-| 21437500/21434787, 47265625/47258883, 56953125/56942116, 104857600/104825259
+| 1771875/1771561, 3294225/3294172, 14348907/14348180, 104857600/104825259
 | {{Mapping| 3889 6164 9030 10918 13454 }}
 | −0.0129
@@ Line 53: / Line 55: @@
 |-
 | 2.3.5.7.11.13
-| 6656/6655, 123201/123200, 492128/492075, 1990656/1990625, 29046875/29042496
+| 6656/6655, 123201/123200, 492128/492075, 823680/823543, 1990656/1990625
 | {{Mapping| 3889 6164 9030 10918 13454 14391 }}
 | −0.0106
@@ Line 60: / Line 62: @@
 |-
 | 2.3.5.7.11.13.17
-| 12376/12375, 14400/14399, 123201/123200, 37180/37179, 1990656/1990625, 361250/361179
+| 6656/6655, 12376/12375, 28561/28560, 37180/37179, 361250/361179, 937125/937024
 | {{Mapping| 3889 6164 9030 10918 13454 14391 15896 }}
 | −0.0075