Miracle: Difference between revisions

+definition in the opening paragraph. -duplicate info
Tunings: +target tunings, extracted from the spectrum
Line 222: Line 222:
| 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 }}
|}
|}


Line 228: Line 277:
|-
|-
! Edo<br>generator
! Edo<br>generator
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]*
! Generator (¢)
! Generator (¢)
! Comments
! Comments
Line 281: Line 330:
| 116.505
| 116.505
|  
|  
|-
|
| {{monzo| 0 -27 25 5 }}
| 116.573
| 7-odd-limit least squares
|-
|
| {{monzo| 0 -19 20 }}
| 116.578
| 5-odd-limit least squares
|-
|-
|  
|  
Line 321: Line 360:
| 116.667
| 116.667
|  
|  
|-
|
| {{monzo| 0 17 -11 -6 11 }}
| 116.672
| 11-odd-limit least squares
|-
|-
|  
|  
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
|-
|
| {{monzo| 0 117 -44 -19 }}
| 116.721
| 9-odd-limit least squares
|-
|-
|  
|  
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 ==