130edo: Difference between revisions

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== Theory ==

130edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo, and is the first [[Trivial temperament|~~non-trivial~~]] edo to be consistent in the 14-[[~~Odd~~ prime sum limit|odd-prime-sum-limit]]. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the rank-three temperament [[jove]], tempering out [[243/242]] and [[441/440]], plus [[364/363]] for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[Schismatic family #Sesquiquartififths|sesquart]] and 13-limit [[harry]].

130edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo, and is the first [[Trivial temperament|nontrivial]] edo to be consistent in the 14-[[odd prime sum limit|odd-prime-sum-limit]]. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the rank-three temperament [[jove]], tempering out [[243/242]] and [[441/440]], plus [[364/363]] for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[Schismatic family #Sesquiquartififths|sesquart]] and 13-limit [[harry]].

=== Prime harmonics ===

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| 2.3.5.7

| 2401/2400, 3136/3125, 19683/19600

| [{{~~val~~| 130 206 302 365 }}]

| {{mapping| 130 206 302 365 }}

| -0.119

| 0.311

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| 2.3.5.7.11

| 243/242, 441/440, 3136/3125, 4000/3993

| [{{~~val~~| 130 206 302 365 450 }}]

| {{mapping| 130 206 302 365 450 }}

| -0.241

| 0.370

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| 2.3.5.7.11.13

| 243/242, 351/350, 364/363, 441/440, 3136/3125

| [{{~~val~~| 130 206 302 365 450 481 }}]

| {{mapping| 130 206 302 365 450 481 }}

| -0.177

| 0.367

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|+Table of rank-2 temperaments by generator

! Periods per 8ve

! Generator~~ (Reduced)~~

! Generator*

! Cents~~ (Reduced)~~

! Cents*

! Associated Ratio

! Associated Ratio*

! Temperaments

|-

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| [[Bosonic]]

|}

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

== Scales ==

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo, and is the first [[Trivial temperament|non-trivial]] edo to be consistent in the 14-[[Odd prime sum limit|odd-prime-sum-limit]]. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the rank-three temperament [[jove]], tempering out [[243/242]] and [[441/440]], plus [[364/363]] for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[Schismatic family #Sesquiquartififths|sesquart]] and 13-limit [[harry]].
+edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo, and is the first [[Trivial temperament|nontrivial]] edo to be consistent in the 14-[[odd prime sum limit|odd-prime-sum-limit]]. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the rank-three temperament [[jove]], tempering out [[243/242]] and [[441/440]], plus [[364/363]] for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[Schismatic family #Sesquiquartififths|sesquart]] and 13-limit [[harry]].
 === Prime harmonics ===
@@ Line 336: / Line 336: @@
 | 2.3.5.7
 | 2401/2400, 3136/3125, 19683/19600
-| [{{val| 130 206 302 365 }}]
+| {{mapping| 130 206 302 365 }}
 | -0.119
 | 0.311
@@ Line 343: / Line 343: @@
 | 2.3.5.7.11
 | 243/242, 441/440, 3136/3125, 4000/3993
-| [{{val| 130 206 302 365 450 }}]
+| {{mapping| 130 206 302 365 450 }}
 | -0.241
 | 0.370
@@ Line 350: / Line 350: @@
 | 2.3.5.7.11.13
 | 243/242, 351/350, 364/363, 441/440, 3136/3125
-| [{{val| 130 206 302 365 450 481 }}]
+| {{mapping| 130 206 302 365 450 481 }}
 | -0.177
 | 0.367
@@ Line 362: / Line 362: @@
 |+Table of rank-2 temperaments by generator
 ! Periods<br>per 8ve
-! Generator<br>(Reduced)
+! Generator*
-! Cents<br>(Reduced)
+! Cents*
-! Associated<br>Ratio
+! Associated<br>Ratio*
 ! Temperaments
 |-
@@ Line 463: / Line 463: @@
 | [[Bosonic]]
 |}
+<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
 == Scales ==