229edo: Difference between revisions
→Regular temperament properties: update to reflect the discussion in the theory section |
Correction and cleanup |
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It extends less well to the 13-limit. Using the [[patent val]] {{val| 229 363 532 643 792 '''847''' }}, it tempers out [[351/350]], [[1573/1568]], [[2080/2079]], and [[4096/4095]]. Using the alternative 229f val {{val| 229 363 532 643 792 '''848''' }}, it tempers out [[352/351]], [[729/728]], [[1001/1000]], and [[1716/1715]]. | It extends less well to the 13-limit. Using the [[patent val]] {{val| 229 363 532 643 792 '''847''' }}, it tempers out [[351/350]], [[1573/1568]], [[2080/2079]], and [[4096/4095]]. Using the alternative 229f val {{val| 229 363 532 643 792 '''848''' }}, it tempers out [[352/351]], [[729/728]], [[1001/1000]], and [[1716/1715]]. | ||
Higher [[harmonic]]s like [[17/1|17]], [[19/1|19]], and [[23/1|23]] are well approximated, so it shows great potential in the no-13 23-limit. It tempers out [[561/560]], [[1701/1700]] in the 17-limit; [[476/475]], [[1216/1215]], [[ | Higher [[harmonic]]s like [[17/1|17]], [[19/1|19]], and [[23/1|23]] are well approximated, so it shows great potential in the no-13 23-limit. It tempers out [[561/560]], [[1089/1088]], and [[1701/1700]] in the 17-limit; [[476/475]], [[1216/1215]], [[1445/1444]], and [[1540/1539]] in the 19-limit; and [[484/483]], [[576/575]] and [[736/735]] in the 23-limit. | ||
The 229b [[val]] supports a [[septimal meantone]] close to the [[CTE tuning]]. | The 229b [[val]] supports a [[septimal meantone]] close to the [[CTE tuning]]. | ||
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| 2.3.5.7.11.17 | | 2.3.5.7.11.17 | ||
| 561/560, 1701/1700, 2401/2400 | | 561/560, 1089/1088, 1701/1700, 2401/2400, 3136/3125 | ||
| {{mapping| 229 363 532 643 792 936 }} | | {{mapping| 229 363 532 643 792 936 }} | ||
| -0.106 | | -0.106 | ||
| Line 64: | Line 64: | ||
|- | |- | ||
| 2.3.5.7.11.17.19 | | 2.3.5.7.11.17.19 | ||
| 476/475, 561/560, 1216/1215, | | 476/475, 561/560, 1089/1088, 1216/1215, 1445/1444, 2401/2400 | ||
| {{mapping| 229 363 532 643 792 936 973 }} | | {{mapping| 229 363 532 643 792 936 973 }} | ||
| -0.130 | | -0.130 | ||
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|- | |- | ||
| 2.3.5.7.11.17.19.23 | | 2.3.5.7.11.17.19.23 | ||
| 476/475, 561/560, 576/575, | | 476/475, 484/483, 561/560, 576/575, 736/735, 1089/1088, 1216/1215 | ||
| {{mapping| 229 363 532 643 792 936 973 1036 }} | | {{mapping| 229 363 532 643 792 936 973 1036 }} | ||
| -0.129 | | -0.129 | ||