Meantone: Difference between revisions
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In the following tables, odd harmonics 1–15 are labeled in '''bold'''. | In the following tables, odd harmonics 1–15 are labeled in '''bold'''. | ||
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{| class="wikitable sortable center-1 right-2" | {| class="wikitable sortable center-1 right-2" | ||
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| Line 333: | Line 333: | ||
| [[9/5]] | | [[9/5]] | ||
| 691.202 | | 691.202 | ||
| [[1/2-comma meantone|1/2 comma]], tunings flatter than this do not fit the original sense of meantone, since their whole tones are no longer between 9/8 and 10/9, a.k.a. lower bound of 9-odd-limit diamond tradeoff | | [[1/2-comma meantone|1/2-comma]], tunings flatter than this do not fit the original sense of meantone, since their whole tones are no longer between 9/8 and 10/9, a.k.a. lower bound of 9-odd-limit diamond tradeoff | ||
|- | |- | ||
| [[59edo|34\59]] | | [[59edo|34\59]] | ||
| Line 353: | Line 353: | ||
| [[27/25]] | | [[27/25]] | ||
| 693.352 | | 693.352 | ||
| [[2/5-comma meantone|2/5 comma]] | | [[2/5-comma meantone|2/5-comma]] | ||
|- | |- | ||
| | | | ||
| Line 403: | Line 403: | ||
| {{nowrap| ''f''<sup>4</sup> − 2''f'' − 2 {{=}} 0 }} | | {{nowrap| ''f''<sup>4</sup> − 2''f'' − 2 {{=}} 0 }} | ||
| 695.630 | | 695.630 | ||
| 1–3–5 equal-beating tuning, Wilson's "metameantone" ([[DR]] 4:5:6), virtually 5/17 comma | | 1–3–5 equal-beating tuning, Wilson's "metameantone" ([[DR]] 4:5:6), virtually 5/17-comma | ||
|- | |- | ||
| [[69edo|40\69]] | | [[69edo|40\69]] | ||
| Line 413: | Line 413: | ||
| [[25/24]] | | [[25/24]] | ||
| 695.810 | | 695.810 | ||
| [[2/7-comma meantone|2/7 comma]], virtually also [[DR]] 10:12:15 | | [[2/7-comma meantone|2/7-comma]], virtually also [[DR]] 10:12:15 | ||
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| Line 421: | Line 421: | ||
|- | |- | ||
| | | | ||
| | | 3125/2304 | ||
| 695.981 | | 695.981 | ||
| [[5/18-comma meantone|5/18 comma]] | | [[5/18-comma meantone|5/18-comma]] | ||
|- | |- | ||
| | | | ||
| Line 443: | Line 443: | ||
| [[78125/73728]] | | [[78125/73728]] | ||
| 696.165 | | 696.165 | ||
| [[7/26-comma meantone|7/26 comma]], 5-odd-limit least squares | | [[7/26-comma meantone|7/26-comma]], 5-odd-limit least squares | ||
|- | |- | ||
| {{nowrap| (8 − φ)\11 }} | | {{nowrap| (8 − φ)\11 }} | ||
| Line 506: | Line 506: | ||
|- | |- | ||
| | | | ||
| | | 1875/1024 | ||
| 696.895 | | 696.895 | ||
| [[4/17-comma meantone|4/17 comma]]; 5-limit [[CEE]] tuning | | [[4/17-comma meantone|4/17-comma]]; 5-limit [[CEE]] tuning | ||
|- | |- | ||
| | | | ||
| Line 528: | Line 528: | ||
| [[75/64]] | | [[75/64]] | ||
| 697.176 | | 697.176 | ||
| [[2/9-comma meantone|2/9 comma]] | | [[2/9-comma meantone|2/9-comma]] | ||
|- | |- | ||
| | | | ||
| {{nowrap|''f''<sup>4</sup> + 2''f'' − 8 {{=}} 0}} | | {{nowrap|''f''<sup>4</sup> + 2''f'' − 8 {{=}} 0}} | ||
| 697.278 | | 697.278 | ||
| 1–3–5 equal-beating tuning ([[DR]] 3:4:5), virtually 5/23 comma | | 1–3–5 equal-beating tuning ([[DR]] 3:4:5), virtually 5/23-comma | ||
|- | |- | ||
| [[74edo|43\74]] | | [[74edo|43\74]] | ||
| Line 546: | Line 546: | ||
|- | |- | ||
| | | | ||
| | | 1125/1024 | ||
| 697.347 | | 697.347 | ||
| [[3/14-comma meantone|3/14 comma]] | | [[3/14-comma meantone|3/14-comma]] | ||
|- | |- | ||
| {{nowrap|(√(10) − 2)\2}} | | {{nowrap|(√(10) − 2)\2}} | ||
| Line 563: | Line 563: | ||
| [[15/8]] | | [[15/8]] | ||
| 697.654 | | 697.654 | ||
| [[1/5-comma meantone|1/5 comma]] | | [[1/5-comma meantone|1/5-comma]] | ||
|- | |- | ||
| [[43edo|25\43]] | | [[43edo|25\43]] | ||
| Line 613: | Line 613: | ||
| [[45/32]] | | [[45/32]] | ||
| 698.371 | | 698.371 | ||
| [[1/6-comma meantone|1/6 comma]] | | [[1/6-comma meantone|1/6-comma]] | ||
|- | |- | ||
| [[67edo|39\67]] | | [[67edo|39\67]] | ||
| Line 621: | Line 621: | ||
|- | |- | ||
| | | | ||
| | | {{monzo|-23 9 4}} | ||
| 698.514 | | 698.514 | ||
| [[4/25-comma meantone|4/25 comma]] | | [[4/25-comma meantone|4/25-comma]] | ||
|- | |- | ||
| | | | ||
| Line 638: | Line 638: | ||
| [[135/128]] | | [[135/128]] | ||
| 698.883 | | 698.883 | ||
| [[1/7-comma meantone|1/7 comma]] | | [[1/7-comma meantone|1/7-comma]] | ||
|- | |- | ||
| [[91edo|53\91]] | | [[91edo|53\91]] | ||
| Line 668: | Line 668: | ||
| | | | ||
| '''700.000''' | | '''700.000''' | ||
| '''Upper bound of 7- and 9-odd-limit diamond monotone''', 1/12 Pythagorean comma, virtually [[1/11-comma meantone|1/11 comma]]† | | '''Upper bound of 7- and 9-odd-limit diamond monotone''', 1/12 Pythagorean comma, virtually [[1/11-comma meantone|1/11-comma]]† | ||
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