Xenharmonic Wiki

Miracle extensions: Difference between revisions

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m Text replacement - "Prime-optimized" to "Norm-based"
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m →Target tunings: consolidate tables for readability
Line 343: Line 343:


=== Target tunings ===
=== Target tunings ===
{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Minimax tunings (miracle)
|+ style="white-space: nowrap;" | Target tunings (miracle)
|-
|-
! Target
! rowspan="2" | Target
! colspan="2" | Minimax
! colspan="2" | Least squares
|-
! Generator
! Eigenmonzo*
! Generator
! Generator
! Eigenmonzo*
! Eigenmonzo*
Line 353: Line 358:
| ~16/15 = 116.588{{c}}
| ~16/15 = 116.588{{c}}
| 5/3
| 5/3
| ~16/15 = 116.578{{c}}
| {{Monzo| 0 -19 20 }}
|-
|-
| 7-odd-limit
| 7-odd-limit
| ~15/14 = 116.588{{c}}
| ~15/14 = 116.588{{c}}
| 5/3
| 5/3
| ~15/14 = 116.573{{c}}
| {{Monzo| 0 -27 25 5 }}
|-
|-
| 9-odd-limit
| 9-odd-limit
| ~15/14 = 116.716{{c}}
| ~15/14 = 116.716{{c}}
| 9/5
| 9/5
| ~15/14 = 116.721{{c}}
| {{Monzo| 0 117 -44 -19 }}
|-
|-
| 11-odd-limit
| 11-odd-limit
| ~15/14 = 116.716{{c}}
| ~15/14 = 116.716{{c}}
| 9/5
| 9/5
| ~15/14 = 116.672{{c}}
| {{Monzo| 0 17 -11 -6 11 }}
|}
|}


{| class="wikitable center-all left-3 mw-collapsible mw-collapsed"
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Least squares tunings (miracle)
|+ style="white-space: nowrap;" | Target tunings (miraculous)
|-
! rowspan="2" | Target
! colspan="2" | Minimax
! colspan="2" | Least squares
|-
|-
! Target
! Generator
! Generator
! Eigenmonzo*
! 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 }}
|}
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Minimax tunings (miraculous)
|-
! Target
! Generator
! Generator
! Eigenmonzo*
! Eigenmonzo*
Line 401: Line 395:
| ~15/14 = 116.716{{c}}
| ~15/14 = 116.716{{c}}
| 9/5
| 9/5
| ~15/14 = 116.846{{c}}
| {{Monzo| 0 141 -70 -35 84 -42 }}
|-
|-
| 15-odd-limit
| 15-odd-limit
| ~15/14 = 116.993{{c}}
| ~15/14 = 116.993{{c}}
| 3/2
| 3/2
|}
{| class="wikitable center-all left-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Least squares tunings (miraculous)
|-
! Target
! Generator
! Eigenmonzo
|-
| 13-odd-limit
| ~15/14 = 116.846{{c}}
| {{Monzo| 0 141 -70 -35 84 -42 }}
|-
| 15-odd-limit
| ~15/14 = 116.820{{c}}
| ~15/14 = 116.820{{c}}
| {{Monzo| 0 127 -84 -36 100 -44 }}
| {{Monzo| 0 127 -84 -36 100 -44 }}
|}
|}


{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Minimax tunings (benediction)
|+ style="white-space: nowrap;" | Target tunings (benediction)
|-
! rowspan="2" | Target
! colspan="2" | Minimax
! colspan="2" | Least squares
|-
|-
! Target
! Generator
! Eigenmonzo*
! Generator
! Generator
! Eigenmonzo*
! Eigenmonzo*
Line 433: Line 420:
| ~15/14 = 116.595{{c}}
| ~15/14 = 116.595{{c}}
| 13/9
| 13/9
| ~15/14 = 116.56309{{c}}
| {{Monzo| 0 -234 39 4 -115 228 }}
|-
|-
| 15-odd-limit
| 15-odd-limit
| ~15/14 = 116.588{{c}}
| ~15/14 = 116.588{{c}}
| 5/3
| 5/3
|}
{| class="wikitable center-all left-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Least squares tunings (benediction)
|-
! Target
! Generator
! Eigenmonzo
|-
| 13-odd-limit
| ~15/14 = 116.56309{{c}}
| {{Monzo| 0 -234 39 4 -115 228 }}
|-
| 15-odd-limit
| ~15/14 = 116.56348{{c}}
| ~15/14 = 116.56348{{c}}
| {{Monzo| 0 -251 22 5 -131 261 }}
| {{Monzo| 0 -251 22 5 -131 261 }}
|}
|}


{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Minimax tunings (manna)
|+ style="white-space: nowrap;" | Target tunings (manna)
|-
! rowspan="2" | Target
! colspan="2" | Minimax
! colspan="2" | Least squares
|-
|-
! Target
! Generator
! Eigenmonzo*
! Generator
! Generator
! Eigenmonzo*
! Eigenmonzo*
Line 465: Line 445:
| ~15/14 = 116.760{{c}}
| ~15/14 = 116.760{{c}}
| 13/10
| 13/10
| ~15/14 = 116.780{{c}}
| {{Monzo| 0 18 -111 -76 43 204 }}
|-
|-
| 15-odd-limit
| 15-odd-limit
| ~15/14 = 116.725{{c}}
| ~15/14 = 116.725{{c}}
| 15/13
| 15/13
|}
{| class="wikitable center-all left-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Least squares tunings (manna)
|-
! Target
! Generator
! Eigenmonzo
|-
| 13-odd-limit
| ~15/14 = 116.780{{c}}
| {{Monzo| 0 18 -111 -76 43 204 }}
|-
| 15-odd-limit
| ~15/14 = 116.764{{c}}
| ~15/14 = 116.764{{c}}
| {{Monzo| 0 -37 -166 -77 59 243 }}
| {{Monzo| 0 -37 -166 -77 59 243 }}
|}
|}


{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Minimax tunings (revelation)
|+ style="white-space: nowrap;" | Target tunings (revelation)
|-
! rowspan="2" | Target
! colspan="2" | Minimax
! colspan="2" | Least squares
|-
|-
! Target
! Generator
! Eigenmonzo*
! Generator
! Generator
! Eigenmonzo*
! Eigenmonzo*
Line 497: Line 470:
| ~15/14 = 116.164{{c}}
| ~15/14 = 116.164{{c}}
| 11/9
| 11/9
| ~15/14 = 116.198{{c}}
| {{Monzo| 0 -195 35 5 89 }}
|-
|-
| 13-odd-limit
| 13-odd-limit
| ~15/14 = 116.164{{c}}
| ~15/14 = 116.164{{c}}
| 11/9
| 11/9
| ~15/14 = 116.249{{c}}
| {{Monzo| 0 -234 39 4 102 11 }}
|-
|-
| 15-odd-limit
| 15-odd-limit
| ~15/14 = 116.164{{c}}
| ~15/14 = 116.164{{c}}
| 11/9
| 11/9
|}
{| class="wikitable center-all left-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Least squares tunings (revelation)
|-
! Target
! Generator
! Eigenmonzo
|-
| 11-odd-limit
| ~15/14 = 116.198{{c}}
| {{Monzo| 0 -195 35 5 89 }}
|-
| 13-odd-limit
| ~15/14 = 116.249{{c}}
| {{Monzo| 0 -234 39 4 102 11 }}
|-
| 15-odd-limit
| ~15/14 = 116.229{{c}}
| ~15/14 = 116.229{{c}}
| {{Monzo| 0 -251 22 5 117 13 }}
| {{Monzo| 0 -251 22 5 117 13 }}
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