742edo: Difference between revisions

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== Theory ==

742edo is a very strong 19-limit system and a [[zeta peak edo]], and is [[consistency|distinctly consistent]] in the [[21-odd-limit]]. ~~The equal temperament~~ [[~~tempering out|~~tempers out]] the [[vishnuzma]] and the fortune comma in the 5-limit, [[support]]ing [[vishnu]] and [[fortune]]; [[2401/2400]] in the 7-limit, [[9801/9800]] in the 11-limit, [[4096/4095]], [[6656/6655]], [[10648/10647]] in the 13-limit, [[1701/1700]], [[2058/2057]], [[2601/2600]], [[4914/4913]], [[5832/5831]] in the 17-limit, 2376/2375, 2432/2431, 2926/2925, 3136/3135, 4200/4199, 5776/5775, 5929/5928, 5985/5984, 6860/6859 in the 19-limit.

742edo is a very strong 19-limit system and a [[zeta peak edo]], and is [[consistency|distinctly consistent]] in the [[21-odd-limit]]. It [[tempers out]] the [[vishnuzma]] and the fortune comma in the 5-limit, [[support]]ing [[vishnu]] and [[fortune]]; [[2401/2400]] in the 7-limit, [[9801/9800]] in the 11-limit, [[4096/4095]], [[6656/6655]], [[10648/10647]] in the 13-limit, [[1701/1700]], [[2058/2057]], [[2601/2600]], [[4914/4913]], [[5832/5831]] in the 17-limit, 2376/2375, 2432/2431, 2926/2925, 3136/3135, 4200/4199, 5776/5775, 5929/5928, 5985/5984, 6860/6859 in the 19-limit.

=== Prime harmonics ===

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=== Subsets and supersets ===

Since 742 factors into {{factorization|742}}, 742edo has subset edos {{EDOs| 2, 7, 14, 53, 106, and 371 }}, of which [[7edo]], [[14edo]] and [[53edo]] are very notable. It supports [[silicon]] (224 & 518) with period 14 in the 13-limit, and [[iodine]] (159 & 583f) with period 53 in the 17-limit.

Since 742 factors into {{factorization|742}}, 742edo has subset edos {{EDOs| 2, 7, 14, 53, 106, and 371 }}, of which [[7edo]], [[14edo]] and [[53edo]] are very notable. It supports [[silicon]] ({{nowrap|224 & 518}}) with period 14 in the 13-limit, and [[iodine]] ({{nowrap|159 & 583f}}) with period 53 in the 17-limit.

== Regular temperament properties ==

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| {{monzo| 23 6 -14 }}, {{monzo| -84 53 }}

| {{mapping| 742 1176 1723 }}

| ~~−0~~.0157

| −0.0157

| 0.0555

| 3.43

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| 2401/2400, 14348907/14336000, {{monzo| 23 6 -14 }}

| {{mapping| 742 1176 1723 2083 }}

| ~~−0~~.0035

| −0.0035

| 0.0525

| 3.24

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| 2401/2400, 9801/9800, 172032/171875, 1240029/1239040

| {{mapping| 742 1176 1723 2083 2567 }}

| ~~−0~~.0123

| −0.0123

| 0.0501

| 3.10

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| 2401/2400, 4096/4095, 6656/6655, 9801/9800, 39366/39325

| {{mapping| 742 1176 1723 2083 2567 2746 }}

| ~~−0~~.0302

| −0.0302

| 0.0608

| 3.76

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| 1701/1700, 2058/2057, 2401/2400, 2601/2600, 4096/4095, 6656/6655

| {{mapping| 742 1176 1723 2083 2567 2746 3033 }}

| ~~−0~~.0317

| −0.0317

| 0.0564

| 3.49

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| 1701/1700, 2058/2057, 2376/2375, 2401/2400, 2432/2431, 2601/2600, 3213/3211

| {{mapping| 742 1176 1723 2083 2567 2746 3033 3152 }}

| ~~−0~~.0295

| −0.0295

| 0.0531

| 3.28

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| 1197/1196, 1496/1495, 1701/1700, 2025/2024, 2058/2057, 2401/2400, 2601/2600, 3213/3211

| {{mapping| 742 1176 1723 2083 2567 2746 3033 3152 3357 }} (742i)

| ~~−0~~.0468

| −0.0468

| 0.0699

| 4.32

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| [[Iodine]]

|}

<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 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|742}}
+{{EDO intro}}
 == Theory ==
-edo is a very strong 19-limit system and a [[zeta peak edo]], and is [[consistency|distinctly consistent]] in the [[21-odd-limit]]. The equal temperament [[tempering out|tempers out]] the [[vishnuzma]] and the fortune comma in the 5-limit, [[support]]ing [[vishnu]] and [[fortune]]; [[2401/2400]] in the 7-limit, [[9801/9800]] in the 11-limit, [[4096/4095]], [[6656/6655]], [[10648/10647]] in the 13-limit, [[1701/1700]], [[2058/2057]], [[2601/2600]], [[4914/4913]], [[5832/5831]] in the 17-limit, 2376/2375, 2432/2431, 2926/2925, 3136/3135, 4200/4199, 5776/5775, 5929/5928, 5985/5984, 6860/6859 in the 19-limit.
+edo is a very strong 19-limit system and a [[zeta peak edo]], and is [[consistency|distinctly consistent]] in the [[21-odd-limit]]. It [[tempers out]] the [[vishnuzma]] and the fortune comma in the 5-limit, [[support]]ing [[vishnu]] and [[fortune]]; [[2401/2400]] in the 7-limit, [[9801/9800]] in the 11-limit, [[4096/4095]], [[6656/6655]], [[10648/10647]] in the 13-limit, [[1701/1700]], [[2058/2057]], [[2601/2600]], [[4914/4913]], [[5832/5831]] in the 17-limit, 2376/2375, 2432/2431, 2926/2925, 3136/3135, 4200/4199, 5776/5775, 5929/5928, 5985/5984, 6860/6859 in the 19-limit.
 === Prime harmonics ===
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
-Since 742 factors into {{factorization|742}}, 742edo has subset edos {{EDOs| 2, 7, 14, 53, 106, and 371 }}, of which [[7edo]], [[14edo]] and [[53edo]] are very notable. It supports [[silicon]] (224 & 518) with period 14 in the 13-limit, and [[iodine]] (159 & 583f) with period 53 in the 17-limit.
+Since 742 factors into {{factorization|742}}, 742edo has subset edos {{EDOs| 2, 7, 14, 53, 106, and 371 }}, of which [[7edo]], [[14edo]] and [[53edo]] are very notable. It supports [[silicon]] ({{nowrap|224 &amp; 518}}) with period 14 in the 13-limit, and [[iodine]] ({{nowrap|159 &amp; 583f}}) with period 53 in the 17-limit.
 == Regular temperament properties ==
@@ Line 26: / Line 26: @@
 | {{monzo| 23 6 -14 }}, {{monzo| -84 53 }}
 | {{mapping| 742 1176 1723 }}
-| &minus;0.0157
+| −0.0157
 | 0.0555
 | 3.43
@@ Line 33: / Line 33: @@
 | 2401/2400, 14348907/14336000, {{monzo| 23 6 -14 }}
 | {{mapping| 742 1176 1723 2083 }}
-| &minus;0.0035
+| −0.0035
 | 0.0525
 | 3.24
@@ Line 40: / Line 40: @@
 | 2401/2400, 9801/9800, 172032/171875, 1240029/1239040
 | {{mapping| 742 1176 1723 2083 2567 }}
-| &minus;0.0123
+| −0.0123
 | 0.0501
 | 3.10
@@ Line 47: / Line 47: @@
 | 2401/2400, 4096/4095, 6656/6655, 9801/9800, 39366/39325
 | {{mapping| 742 1176 1723 2083 2567 2746 }}
-| &minus;0.0302
+| −0.0302
 | 0.0608
 | 3.76
@@ Line 54: / Line 54: @@
 | 1701/1700, 2058/2057, 2401/2400, 2601/2600, 4096/4095, 6656/6655
 | {{mapping| 742 1176 1723 2083 2567 2746 3033 }}
-| &minus;0.0317
+| −0.0317
 | 0.0564
 | 3.49
@@ Line 61: / Line 61: @@
 | 1701/1700, 2058/2057, 2376/2375, 2401/2400, 2432/2431, 2601/2600, 3213/3211
 | {{mapping| 742 1176 1723 2083 2567 2746 3033 3152 }}
-| &minus;0.0295
+| −0.0295
 | 0.0531
 | 3.28
@@ Line 68: / Line 68: @@
 | 1197/1196, 1496/1495, 1701/1700, 2025/2024, 2058/2057, 2401/2400, 2601/2600, 3213/3211
 | {{mapping| 742 1176 1723 2083 2567 2746 3033 3152 3357 }} (742i)
-| &minus;0.0468
+| −0.0468
 | 0.0699
 | 4.32
@@ Line 121: / Line 121: @@
 | [[Iodine]]
 |}
-<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