157edo: Difference between revisions

Line 3:

== Theory ==

157et [[~~tempering out|~~tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo| 37 -16 -5 }} (quinticosiennic comma) in the 5-limit; [[2401/2400]], [[5120/5103]], and 110592/109375 in the 7-limit (supporting the [[hemififths]] and the [[catafourth]] temperaments). Using the [[patent val]], it tempers out [[176/175]], 1331/1323, 3773/3750 and [[8019/8000]] in the 11-limit; [[351/350]], [[352/351]], [[847/845]], [[1573/1568]], and [[2197/2187]] in the 13-limit.

157et [[tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo| 37 -16 -5 }} (quinticosiennic comma) in the 5-limit; [[2401/2400]], [[5120/5103]], and 110592/109375 in the 7-limit (supporting the [[hemififths]] and the [[catafourth]] temperaments). Using the [[patent val]], it tempers out [[176/175]], 1331/1323, 3773/3750 and [[8019/8000]] in the 11-limit; [[351/350]], [[352/351]], [[847/845]], [[1573/1568]], and [[2197/2187]] in the 13-limit.

=== Odd harmonics ===

Line 26:

| {{monzo| 249 -157 }}

| {{mapping| 157 249 }}

| ~~−0~~.388

| −0.388

| 0.388

| 5.08

Line 33:

| 78732/78125, {{val| 37 -16 -5 }}

| {{mapping| 157 249 365 }}

| ~~−0~~.760

| −0.760

| 0.614

| 8.04

Line 40:

| 2401/2400, 5120/5103, 78732/78125

| {{mapping| 157 249 365 441 }}

| ~~−0~~.737

| −0.737

| 0.533

| 6.98

Line 47:

| 176/175, 1331/1323, 2401/2400, 5120/5103

| {{mapping| 157 249 365 441 543 }}

| ~~−0~~.532

| −0.532

| 0.629

| 8.24

Line 54:

| 176/175, 351/350, 847/845, 1331/1323, 2197/2187

| {{mapping| 157 249 365 441 543 581 }}

| ~~−0~~.454

| −0.454

| 0.600

| 7.86

Line 61:

| 176/175, 256/255, 351/350, 442/441, 715/714, 2197/2187

| {{mapping| 157 249 365 441 543 581 642 }}

| ~~−0~~.461

| −0.461

| 0.556

| 7.28

Line 68:

| 176/175, 256/255, 286/285, 351/350, 361/360, 442/441, 476/475

| {{mapping| 157 249 365 441 543 581 642 667 }}

| ~~−0~~.420

| −0.420

| 0.531

| 6.95

Line 119:

| [[Catafourth]]

|}

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

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

@@ Line 3: / Line 3: @@
 == Theory ==
-et [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo| 37 -16 -5 }} (quinticosiennic comma) in the 5-limit; [[2401/2400]], [[5120/5103]], and 110592/109375 in the 7-limit (supporting the [[hemififths]] and the [[catafourth]] temperaments). Using the [[patent val]], it tempers out [[176/175]], 1331/1323, 3773/3750 and [[8019/8000]] in the 11-limit; [[351/350]], [[352/351]], [[847/845]], [[1573/1568]], and [[2197/2187]] in the 13-limit.
+et [[tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo| 37 -16 -5 }} (quinticosiennic comma) in the 5-limit; [[2401/2400]], [[5120/5103]], and 110592/109375 in the 7-limit (supporting the [[hemififths]] and the [[catafourth]] temperaments). Using the [[patent val]], it tempers out [[176/175]], 1331/1323, 3773/3750 and [[8019/8000]] in the 11-limit; [[351/350]], [[352/351]], [[847/845]], [[1573/1568]], and [[2197/2187]] in the 13-limit.
 === Odd harmonics ===
@@ Line 26: / Line 26: @@
 | {{monzo| 249 -157 }}
 | {{mapping| 157 249 }}
-| &minus;0.388
+| −0.388
 | 0.388
 | 5.08
@@ Line 33: / Line 33: @@
 | 78732/78125, {{val| 37 -16 -5 }}
 | {{mapping| 157 249 365 }}
-| &minus;0.760
+| −0.760
 | 0.614
 | 8.04
@@ Line 40: / Line 40: @@
 | 2401/2400, 5120/5103, 78732/78125
 | {{mapping| 157 249 365 441 }}
-| &minus;0.737
+| −0.737
 | 0.533
 | 6.98
@@ Line 47: / Line 47: @@
 | 176/175, 1331/1323, 2401/2400, 5120/5103
 | {{mapping| 157 249 365 441 543 }}
-| &minus;0.532
+| −0.532
 | 0.629
 | 8.24
@@ Line 54: / Line 54: @@
 | 176/175, 351/350, 847/845, 1331/1323, 2197/2187
 | {{mapping| 157 249 365 441 543 581 }}
-| &minus;0.454
+| −0.454
 | 0.600
 | 7.86
@@ Line 61: / Line 61: @@
 | 176/175, 256/255, 351/350, 442/441, 715/714, 2197/2187
 | {{mapping| 157 249 365 441 543 581 642 }}
-| &minus;0.461
+| −0.461
 | 0.556
 | 7.28
@@ Line 68: / Line 68: @@
 | 176/175, 256/255, 286/285, 351/350, 361/360, 442/441, 476/475
 | {{mapping| 157 249 365 441 543 581 642 667 }}
-| &minus;0.420
+| −0.420
 | 0.531
 | 6.95
@@ Line 119: / Line 119: @@
 | [[Catafourth]]
 |}
-<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct