374edo: Difference between revisions

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== Theory ==

374et is in[[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[5/1|5]] is about halfway between its steps. Omitting the harmonic 5, it is consistent to the [[31-odd-limit]].

Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[5120/5103]], 1071875/1062882, 1500625/1492992 ~~and~~ [[2100875/2097152]], 9765625/9680832 in the 7-limit; 1375/1372, 4375/4356, 12005/11979, and [[41503/41472]] in the 11-limit. It [[support]]s [[quintakwai]] and [[quartemka]].

Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[5120/5103]], 1071875/1062882, 1500625/1492992, [[2100875/2097152]], and 9765625/9680832 in the 7-limit; 1375/1372, 4375/4356, 12005/11979, and [[41503/41472]] in the 11-limit. It [[support]]s [[quintakwai]] and [[quartemka]].

=== Prime harmonics ===

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== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

|-

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list|Comma List]]

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| {{monzo| 593 -374 }}

| {{mapping| 374 593 }}

| -0.2268

| −0.2268

| 0.2267

| 7.07

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| {{monzo| 4 -22 11 }}, {{monzo| 51 -18 -8 }}

| {{mapping| 374 593 1050 }}

| -0.1699

| −0.1699

| 0.2018

| 6.29

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| 41503/41472, 1362944/1361367, 70493667328/70027449129

| {{mapping| 374 593 1050 1294 }}

| -0.1675

| −0.1675

| 0.1748

| 5.45

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| 10648/10647, 20449/20412, 41503/41472, 652288/649539

| {{mapping| 374 593 1050 1294 138 4}}

| -0.1401

| −0.1401

| 0.1656

| 5.16

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| 2058/2057, 8281/8262, 8624/8619, 22528/22491, 34816/34749

| {{mapping| 374 593 1050 1294 1384 1529 }}

| -0.1546

| −0.1546

| 0.1546

| 4.82

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| 1729/1728, 2058/2057, 2912/2907, 5929/5928, 22528/22491, 34816/34749

| {{mapping| 374 593 1050 1294 1384 1529 1589 }}

| -0.1622

| −0.1622

| 0.1444

| 4.50

|}

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|374}}
+{{ED intro}}
 == Theory ==
 et is in[[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[5/1|5]] is about halfway between its steps. Omitting the harmonic 5, it is consistent to the [[31-odd-limit]].
-Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[5120/5103]], 1071875/1062882, 1500625/1492992 and [[2100875/2097152]], 9765625/9680832 in the 7-limit; 1375/1372, 4375/4356, 12005/11979, and [[41503/41472]] in the 11-limit. It [[support]]s [[quintakwai]] and [[quartemka]].
+Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[5120/5103]], 1071875/1062882, 1500625/1492992, [[2100875/2097152]], and 9765625/9680832 in the 7-limit; 1375/1372, 4375/4356, 12005/11979, and [[41503/41472]] in the 11-limit. It [[support]]s [[quintakwai]] and [[quartemka]].
 === Prime harmonics ===
@@ Line 15: / Line 15: @@
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
 ! rowspan="2" | [[Comma list|Comma List]]
@@ Line 27: / Line 28: @@
 | {{monzo| 593 -374 }}
 | {{mapping| 374 593 }}
-| -0.2268
+| −0.2268
 | 0.2267
 | 7.07
@@ Line 34: / Line 35: @@
 | {{monzo| 4 -22 11 }}, {{monzo| 51 -18 -8 }}
 | {{mapping| 374 593 1050 }}
-| -0.1699
+| −0.1699
 | 0.2018
 | 6.29
@@ Line 41: / Line 42: @@
 | 41503/41472, 1362944/1361367, 70493667328/70027449129
 | {{mapping| 374 593 1050 1294 }}
-| -0.1675
+| −0.1675
 | 0.1748
 | 5.45
@@ Line 48: / Line 49: @@
 | 10648/10647, 20449/20412, 41503/41472, 652288/649539
 | {{mapping| 374 593 1050 1294 138 4}}
-| -0.1401
+| −0.1401
 | 0.1656
 | 5.16
@@ Line 55: / Line 56: @@
 | 2058/2057, 8281/8262, 8624/8619, 22528/22491, 34816/34749
 | {{mapping| 374 593 1050 1294 1384 1529 }}
-| -0.1546
+| −0.1546
 | 0.1546
 | 4.82
@@ Line 62: / Line 63: @@
 | 1729/1728, 2058/2057, 2912/2907, 5929/5928, 22528/22491, 34816/34749
 | {{mapping| 374 593 1050 1294 1384 1529 1589 }}
-| -0.1622
+| −0.1622
 | 0.1444
 | 4.50
 |}