130edo: Difference between revisions
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== Theory == | == Theory == | ||
130edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It is [[ | 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]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 130 factors into {{ | Since 130 factors into {{Factorisation|130}}, 130edo has subset edos {{EDOs| 2, 5, 10, 13, 26, and 65 }}. | ||
[[260edo]], which divides the edostep in two, provides a strong correction for the 29th harmonic. | [[260edo]], which divides the edostep in two, provides a strong correction for the 29th harmonic. | ||
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| 2401/2400, 3136/3125, 19683/19600 | | 2401/2400, 3136/3125, 19683/19600 | ||
| {{mapping| 130 206 302 365 }} | | {{mapping| 130 206 302 365 }} | ||
| | | −0.119 | ||
| 0.311 | | 0.311 | ||
| 3.37 | | 3.37 | ||
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| 243/242, 441/440, 3136/3125, 4000/3993 | | 243/242, 441/440, 3136/3125, 4000/3993 | ||
| {{mapping| 130 206 302 365 450 }} | | {{mapping| 130 206 302 365 450 }} | ||
| | | −0.241 | ||
| 0.370 | | 0.370 | ||
| 4.02 | | 4.02 | ||
| Line 353: | Line 353: | ||
| 243/242, 351/350, 364/363, 441/440, 3136/3125 | | 243/242, 351/350, 364/363, 441/440, 3136/3125 | ||
| {{mapping| 130 206 302 365 450 481 }} | | {{mapping| 130 206 302 365 450 481 }} | ||
| | | −0.177 | ||
| 0.367 | | 0.367 | ||
| 3.98 | | 3.98 | ||
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| [[Bosonic]] | | [[Bosonic]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Scales == | == Scales == | ||
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| 9 (47/130) | | 9 (47/130) | ||
| 433.846 | | 433.846 | ||
| [[9/7]] ( | | [[9/7]] (−1.238 ¢) | ||
|- | |- | ||
| 7 (54/130) | | 7 (54/130) | ||
| Line 506: | Line 506: | ||
| 9 (76/130) | | 9 (76/130) | ||
| 701.538 | | 701.538 | ||
| [[3/2]] ( | | [[3/2]] (−0.417 ¢) | ||
|- | |- | ||
| 7 (83/130) | | 7 (83/130) | ||
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| 5 (101/130) | | 5 (101/130) | ||
| 932.308 | | 932.308 | ||
| [[12/7]] ( | | [[12/7]] (−0.821 ¢) | ||
|- | |- | ||
| 13 (114/130) | | 13 (114/130) | ||
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| 7 (121/130) | | 7 (121/130) | ||
| 1116.923 | | 1116.923 | ||
| [[21/11]] ( | | [[21/11]] (−2.540 ¢) | ||
|- | |- | ||
| 9 (130/130) | | 9 (130/130) | ||