Miracle: Difference between revisions
+definition in the opening paragraph. -duplicate info |
→Tunings: +target tunings, extracted from the spectrum |
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| CBE: ~15/14 = 116.736¢ | | CBE: ~15/14 = 116.736¢ | ||
| CSBE: ~15/14 = 116.677¢ | | CSBE: ~15/14 = 116.677¢ | ||
|} | |||
=== Target tunings === | |||
{| class="wikitable center-all mw-collapsible mw-collapsed" | |||
|+ style="white-space: nowrap;" | Minimax tunings | |||
|- | |||
! Target | |||
! Generator | |||
! Eigenmonzo* | |||
|- | |||
| 5-odd-limit | |||
| ~16/15 = 116.588{{c}} | |||
| 5/3 | |||
|- | |||
| 7-odd-limit | |||
| ~15/14 = 116.588{{c}} | |||
| 5/3 | |||
|- | |||
| 9-odd-limit | |||
| ~15/14 = 116.716{{c}} | |||
| 9/5 | |||
|- | |||
| 11-odd-limit | |||
| ~15/14 = 116.716{{c}} | |||
| 9/5 | |||
|} | |||
{| class="wikitable center-all left-3 mw-collapsible mw-collapsed" | |||
|+ style="white-space: nowrap;" | Least squares tunings | |||
|- | |||
! Target | |||
! Generator | |||
! Eigenmonzo* | |||
|- | |||
| 5-odd-limit | |||
| ~16/15 = 116.578{{c}} | |||
| {{Monzo| 0 -19 20 }} | |||
|- | |||
| 7-odd-limit | |||
| ~15/14 = 116.573{{c}} | |||
| {{Monzo| 0 -27 25 5 }} | |||
|- | |||
| 9-odd-limit | |||
| ~15/14 = 116.721{{c}} | |||
| {{Monzo| 0 117 -44 -19 }} | |||
|- | |||
| 11-odd-limit | |||
| ~15/14 = 116.672{{c}} | |||
| {{Monzo| 0 17 -11 -6 11 }} | |||
|} | |} | ||
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|- | |- | ||
! Edo<br>generator | ! Edo<br>generator | ||
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]] | ! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]* | ||
! Generator (¢) | ! Generator (¢) | ||
! Comments | ! Comments | ||
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| 116.505 | | 116.505 | ||
| | | | ||
|- | |- | ||
| | | | ||
Line 321: | Line 360: | ||
| 116.667 | | 116.667 | ||
| | | | ||
|- | |- | ||
| | | | ||
Line 331: | Line 365: | ||
| 116.716 | | 116.716 | ||
| 9- and 11-odd-limit minimax, <br>Secor's definition of secor | | 9- and 11-odd-limit minimax, <br>Secor's definition of secor | ||
|- | |- | ||
| | | | ||
Line 382: | Line 411: | ||
| Upper bound of 7- and 9-odd-limit diamond monotone | | Upper bound of 7- and 9-odd-limit diamond monotone | ||
|} | |} | ||
<nowiki/>* Besides the octave | |||
== Music == | == Music == |