Magic: Difference between revisions

m Interval chain: + ratios
Tunings: target tunings
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== Tunings ==
== Tunings ==
=== Target tunings ===
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Target tunings
|-
! rowspan="2" | Target
! colspan="2" | Minimax
! colspan="2" | Least squares
|-
! Generator
! Eigenmonzo*
! Generator
! Eigenmonzo*
|-
| 5-odd-limit
| ~5/4 = 380.391{{c}}
| 3/2
| ~5/4 = 379.968{{c}}
| {{Monzo| 0 3 -1 }}
|-
| 7-odd-limit
| ~5/4 = 380.391{{c}}
| 3/2
| ~5/4 = 380.506{{c}}
| {{Monzo| 0 1 -7 15 }}
|-
| 9-odd-limit
| ~5/4 = 380.391{{c}}
| 3/2
| ~5/4 = 380.384{{c}}
| {{Monzo| 0 36 -23 32 }}
|}
=== Tuning spectrum ===
=== Tuning spectrum ===
This tuning spectrum reflects 7-limit magic; for the tuning spectrum of tridecimal magic, see [[Magic extensions#Magic|the page on magic extensions]].
This tuning spectrum reflects 7-limit magic; for the tuning spectrum of tridecimal magic, see [[Magic extensions#Magic|the page on magic extensions]].
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|-
|-
! Edo<br>generator
! Edo<br>generator
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]*
! Generator (¢)
! Generator (¢)
! Comments
! Comments
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| 379.733
| 379.733
|  
|  
|-
|
| 27/20
| 379.968
| 5-odd-limit least squares
|-
|-
| 19\60
| 19\60
Line 187: Line 214:
|  
|  
| 380.198
| 380.198
| 101cde val
| 101cd val
|-
|-
|  
|  
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| 380.279
| 380.279
|  
|  
|-
|
| {{monzo| 0 36 -23 32 }}
| 380.384
| 9-odd-limit least squares
|-
|-
|  
|  
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| 380.488
| 380.488
|  
|  
|-
|
| {{monzo| 0 1 -7 15 }}
| 380.506
| 7-odd-limit least squares
|-
|-
|  
|  
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|  
|  
|}
|}
<nowiki/> * Besides the octave


== Music ==
== Music ==