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. It is [[distinctly consistent]] to the [[15-odd-limit]] and is the first [[trivial temperament|nontrivial edo]] to be consistent in the 14-[[odd prime sum limit|odd-prime-sum-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[19683/19600]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]], and [[4000/3993]] in the 11-limit; and [[351/350]], [[364/363]], [[676/675]], [[729/728]], [[1001/1000]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.

130edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It is [[distinctly consistent]] to the [[15-odd-limit]] and is the first [[trivial temperament|nontrivial edo]] to be consistent in the 14-[[odd prime sum limit|odd-prime-sum-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[19683/19600]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]], and [[4000/3993]] in the 11-limit; and [[351/350]], [[364/363]], [[676/675]], [[729/728]], [[1001/1000]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-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-3 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]].

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-3 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]]. ~~(''See [[regular temperament]] for more about what all this means and how to use it.'')~~

=== Prime harmonics ===

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| [[Octave]] (2/1, 0{{c}})

|}

== Instruments ==

[[Lumatone mapping for 130edo]]

== Music ==

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 == Theory ==
-edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It is [[distinctly consistent]] to the [[15-odd-limit]] and is the first [[trivial temperament|nontrivial edo]] to be consistent in the 14-[[odd prime sum limit|odd-prime-sum-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[19683/19600]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]], and [[4000/3993]] in the 11-limit; and [[351/350]], [[364/363]], [[676/675]], [[729/728]], [[1001/1000]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.
+edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It is [[distinctly consistent]] to the [[15-odd-limit]] and is the first [[trivial temperament|nontrivial edo]] to be consistent in the 14-[[odd prime sum limit|odd-prime-sum-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[19683/19600]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]], and [[4000/3993]] in the 11-limit; and [[351/350]], [[364/363]], [[676/675]], [[729/728]], [[1001/1000]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-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-3 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]].
-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-3 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]]. (''See [[regular temperament]] for more about what all this means and how to use it.'')
 === Prime harmonics ===
@@ Line 549: / Line 547: @@
 | [[Octave]] (2/1, 0{{c}})
 |}
+== Instruments ==
+[[Lumatone mapping for 130edo]]
 == Music ==