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Magic extensions: Difference between revisions

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[[Magic]] has various competing [[extension]]s to the 11- and 13-limit. The following temperaments are discussed in this article:
{{Breadcrumb|Magic}}


* '''Tridecimal magic''' (19 & 22f) – tempering out 100/99, 105/104, 144/143, and 196/195;
[[Magic]] has various competing [[extension]]s to the [[11-limit|11-]] and [[13-limit]]. The following temperaments are discussed in this article:
* '''Necromancy''' (19f & 22) – tempering out 100/99, 225/224, 245/243, and 275/273;
* '''Witchcraft''' (19e & 22ef) – tempering out 105/104, 196/195, 245/243, and 275/273;
* '''Sorcery''' (19 & 22) – tempering out 65/64, 78/77, 91/90, and 100/99;
* '''Intuition''' (19e & 22f) – tempering out 55/54, 66/65, 99/98, and 105/104;
* '''Telepathy''' (19e & 22) – tempering out 55/54, 65/64, 91/90, and 99/98.  


The most important of these is tridecimal magic, where primes 11 and 13 are mapped such that 10/9 and 11/10 are tempered together and that 14/13 and 16/15 are tempered together. Necromancy takes the same mapping of 11 as magic, but swaps in a more complex mapping for 13, enabling the possibility of a higher-accuracy harmony. Similarly, witchcraft takes the same mapping of 13 as magic, but swaps in a more complex mapping for 11.  
* '''Tridecimal magic''' ({{nowrap| 19 & 22f }}) – tempering out 100/99, 105/104, 144/143, and 196/195;
* '''Necromancy''' ({{nowrap| 19f & 22 }}) – tempering out 100/99, 225/224, 245/243, and 275/273;
* '''Witchcraft''' ({{nowrap| 19e & 22ef }}) – tempering out 105/104, 196/195, 245/243, and 275/273;
* '''Sorcery''' ({{nowrap| 19 & 22 }}) – tempering out 65/64, 78/77, 91/90, and 100/99;
* '''Intuition''' ({{nowrap| 19e & 22f }}) – tempering out 55/54, 66/65, 99/98, and 105/104;
* '''Telepathy''' ({{nowrap| 19e & 22 }}) – tempering out 55/54, 65/64, 91/90, and 99/98.  


Sorcery swaps in a less complex and less accurate mapping for prime 13, as it finds ~16/13 where magic will find ~26/21, which is of course conflated with ~5/4. Likewise, intuitive uses a less complex and less accurate mapping for prime 11. Finally, telepathy adopts the changes of both sorcery and intuition, resulting in a very low-accuracy temperament.  
The most important of these is tridecimal magic, where primes 11 and 13 are mapped such that 10/9 and 11/10 are tempered together and that 14/13 and 16/15 are tempered together. Necromancy takes the same mapping of 11 as magic, but swaps in a more complex mapping for 13, enabling the possibility of a higher-accuracy harmony. Similarly, witchcraft takes the same mapping of 13 as magic, but swaps in a more complex mapping for 11. Necromancy is the {{nowrap| 41 & 63 }} temperament [[support]]ed by [[104edo]], whereas witchcraft is the {{nowrap| 41 & 60e }} temperament supported by [[101edo]] in the 101cd [[val]].
 
Sorcery swaps in a less complex and less accurate mapping for prime 13, as it finds ~16/13 where magic will find ~26/21, which is of course conflated with ~5/4. Likewise, intuition uses a less complex and less accurate mapping for prime 11. Finally, telepathy adopts the changes of both sorcery and intuition, resulting in a very low-accuracy temperament.
 
See [[Magic family #Magic]], [[Magic family #Necromancy|#Necromany]], [[Magic family #Witchcraft|#Witchcraft]], [[Magic family #Sorcery|#Sorcery]], [[Magic family #Intuition|#Intuition]], and [[Magic family #Telepathy|#Telepathy]] for technical data.  


== Interval chain ==
== Interval chain ==
Line 16: Line 20:


{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
! rowspan="3" | #
! rowspan="3" | #
! rowspan="3" | Cents*
! rowspan="3" | Cents*
Line 262: Line 267:
<nowiki/>* In 7-limit [[CWE tuning]]
<nowiki/>* In 7-limit [[CWE tuning]]


== Tuning spectra ==
== Tunings ==
=== Magic ===
=== Target tunings ===
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Target tunings (magic)
|-
! rowspan="2" | Target
! colspan="2" | Minimax
! colspan="2" | Least squares
|-
! Generator
! Eigenmonzo*
! Generator
! Eigenmonzo*
|-
| 11-odd-limit
| ~5/4 = 380.700{{c}}
| 11/9
| ~5/4 = 380.714{{c}}
| {{Monzo| 0 85 -14 52 -68 }}
|-
| 13-odd-limit
| ~5/4 = 380.354{{c}}
| 13/11
| ~5/4 = 380.377{{c}}
| {{Monzo| 0 56 -31 46 -94 88 }}
|-
| 15-odd-limit
| ~5/4 = 380.354{{c}}
| 13/11
| ~5/4 = 380.389{{c}}
| {{Monzo| 0 58 -29 52 -108 100 }}
|}
 
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Target tunings (necromancy)
|-
! rowspan="2" | Target
! colspan="2" | Minimax
! colspan="2" | Least squares
|-
! Generator
! Eigenmonzo*
! Generator
! Eigenmonzo*
|-
| 13-odd-limit
| ~5/4 = 380.709{{c}}
| 13/9
| ~5/4 = 380.705{{c}}
| {{Monzo| 0 -179 -10 -87 53 158 }}
|-
| 15-odd-limit
| ~5/4 = 380.709{{c}}
| 13/9
| ~5/4 = 380.817{{c}}
| {{Monzo| 0 -222 -53 -93 67 187 }}
|}
 
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Target tunings (witchcraft)
|-
! rowspan="2" | Target
! colspan="2" | Minimax
! colspan="2" | Least squares
|-
! Generator
! Eigenmonzo*
! Generator
! Eigenmonzo*
|-
| 11-odd-limit
| ~5/4 = 380.343{{c}}
| 11/8
| ~5/4 = 380.278{{c}}
| {{Monzo| 0 -38 -55 11 137 }}
|-
| 13-odd-limit
| ~5/4 = 380.119{{c}}
| 11/7
| ~5/4 = 380.218{{c}}
| {{Monzo| 0 -67 -72 5 152 47 }}
|-
| 15-odd-limit
| ~5/4 = 380.113{{c}}
| 15/11
| ~5/4 = 380.193{{c}}
| {{Monzo| 0 -106 -111 11 179 59 }}
|}
 
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Target tunings (sorcery)
|-
! rowspan="2" | Target
! colspan="2" | Minimax
! colspan="2" | Least squares
|-
! Generator
! Eigenmonzo*
! Generator
! Eigenmonzo*
|-
| 13-odd-limit
| ~5/4 = 380.700{{c}}
| 11/9
| ~5/4 = 380.427{{c}}
| {{Monzo| 0 -113 12 -65 75 26 }}
|-
| 15-odd-limit
| ~5/4 = 380.700{{c}}
| 11/9
| ~5/4 = 380.457{{c}}
| {{Monzo| 0 134 9 71 -89 -33 }}
|}
 
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Target tunings (intuition)
|-
! rowspan="2" | Target
! colspan="2" | Minimax
! colspan="2" | Least squares
|-
! Generator
! Eigenmonzo*
! Generator
! Eigenmonzo*
|-
| 13-odd-limit
| ~5/4 = 380.029{{c}}
| 13/8
| ~5/4 = 380.568{{c}}
| {{Monzo| 0 -10 -53 24 38 66 }}
|-
| 15-odd-limit
| ~5/4 = 380.029{{c}}
| 13/8
| ~5/4 = 380.562{{c}}
| {{Monzo| 0 -30 -73 30 46 78 }}
|}
 
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Target tunings (telepathy)
|-
! rowspan="2" | Target
! colspan="2" | Minimax
! colspan="2" | Least squares
|-
! Generator
! Eigenmonzo*
! Generator
! Eigenmonzo*
|-
| 11-odd-limit
| ~5/4 = 381.923{{c}}
| 11/10
| ~5/4 = 381.380{{c}}
| {{Monzo| 0 19 -36 30 42 }}
|-
| 13-odd-limit
| ~5/4 = 380.719{{c}}
| 13/11
| ~5/4 = 380.676{{c}}
| {{Monzo| 0 47 -34 43 57 -48 }}
|-
| 15-odd-limit
| ~5/4 = 380.719{{c}}
| 13/11
| ~5/4 = 380.691{{c}}
| {{Monzo| 0 46 -35 49 65 -55 }}
|}
 
=== Tuning spectra ===
==== Magic ====
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
! Edo<br>generator
! Edo<br>generator
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
! Generator (¢)
! Generator (¢)
! Comments
! Comments
|-
|
| 21/13
| 369.747
|
|-
|-
|  
|  
Line 310: Line 490:
| 379.890
| 379.890
|  
|  
|-
|
| 27/20
| 379.968
| 5-odd-limit least squares
|-
|-
| 19\60
| 19\60
Line 339: Line 514:
| 7/5
| 7/5
| 380.228
| 380.228
|
|-
|
| 21/20
| 380.279
|  
|  
|-
|-
Line 345: Line 525:
| 380.354
| 380.354
| 13- and 15-odd-limit minimax
| 13- and 15-odd-limit minimax
|-
|
| {{monzo| 0 56 -31 46 -94 88 }}
| 380.377
| 13-odd-limit least squares
|-
|
| {{monzo| 0 36 -23 32 }}
| 380.384
| 9-odd-limit least squares
|-
|
| {{monzo| 0 58 -29 52 -108 100 }}
| 380.389
| 15-odd-limit least squares
|-
|-
|  
|  
Line 372: Line 537:
|-
|-
|  
|  
| {{monzo| 0 1 -7 15 }}
| 21/16
| 380.506
| 380.634
| 7-odd-limit least squares
|  
|-
|-
|  
|  
Line 380: Line 545:
| 380.700
| 380.700
| 11-odd-limit minimax
| 11-odd-limit minimax
|-
|
| {{monzo| 0 85 -14 52 -68 }}
| 380.714
| 11-odd-limit least squares
|-
|-
|  
|  
Line 395: Line 555:
| 380.769
| 380.769
| 104ff val
| 104ff val
|-
|
| 21/11
| 380.779
|
|-
|-
|  
|  
Line 427: Line 592:
|-
|-
|  
|  
| 15/88
| 15/8
| 381.378
| 381.378
|  
|  
Line 452: Line 617:
|}
|}


=== Necromancy ===
==== Necromancy ====
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
! Edo<br>generator
! Edo<br>generator
! Eigenmonzo<br>(unchanged-interval)
! Unchanged interval<br>(eigenmonzo)
! Generator (¢)
! Generator (¢)
! Comments
! Comments
Line 468: Line 633:
|  
|  
| 378.947
| 378.947
| 19f val
| 19f val, lower bound of 9- and 11-odd-limit diamond monotone
|-
|-
|  
|  
Line 474: Line 639:
| 379.733
| 379.733
|  
|  
|-
|
| 27/20
| 379.968
| 5-odd-limit least squares
|-
|-
| 19\60
| 19\60
Line 501: Line 661:
|-
|-
|  
|  
| {{monzo| 0 36 -23 32 }}
| 21/20
| 380.384
| 380.279
| 9-odd-limit least squares
|  
|-
|-
|  
|  
Line 513: Line 673:
|  
|  
| 380.488
| 380.488
| Lower bound of 13- and 15-odd-limit diamond monotone
|-
|  
|  
|-
| 21/16
| 380.634
|  
|  
| {{monzo| 0 1 -7 15 }}
| 380.506
| 7-odd-limit least squares
|-
|-
|  
|  
Line 529: Line 689:
| 380.709
| 380.709
| 13- and 15-odd-limit minimax
| 13- and 15-odd-limit minimax
|-
|
| {{monzo| 0 85 -14 52 -68 }}
| 380.714
| 11-odd-limit least squares
|-
|-
|  
|  
Line 543: Line 698:
| 7/4
| 7/4
| 380.735
| 380.735
|
|-
|
| 21/13
| 380.756
|  
|  
|-
|-
Line 556: Line 716:
|-
|-
|  
|  
| {{monzo| 0 -179 -10 -87 53 158 }}
| 21/11
| 380.785
| 380.779
| 13-odd-limit least squares
|  
|-
|-
|  
|  
Line 564: Line 724:
| 380.809
| 380.809
|  
|  
|-
|
| {{monzo| 0 -222 -53 -93 67 187 }}
| 380.817
| 15-odd-limit least squares
|-
|-
|  
|  
Line 588: Line 743:
|  
|  
| 380.952
| 380.952
|  
| Upper bound of 13- and 15-odd-limit diamond monotone
|-
|-
|  
|  
Line 628: Line 783:
|  
|  
| 381.818
| 381.818
|  
| Upper bound of 9- and 11-odd-limit diamond monotone
|-
|-
|  
|  
Line 641: Line 796:
|}
|}


=== Witchcraft ===
==== Witchcraft ====
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
! Edo<br>generator
! Edo<br>generator
! Eigenmonzo<br>(unchanged-interval)
! Unchanged interval<br>(eigenmonzo)
! Generator (¢)
! Generator (¢)
! Comments
! Comments
|-
|
| 21/13
| 369.747
|
|-
|-
|  
|  
Line 662: Line 822:
|  
|  
| 378.947
| 378.947
| 19e val
| 19e val, lower bound of 9-odd-limit diamond monotone
|-
|-
|  
|  
Line 683: Line 843:
| 379.733
| 379.733
|  
|  
|-
|
| 27/20
| 379.968
| 5-odd-limit least squares
|-
|-
|  
|  
Line 697: Line 852:
|  
|  
| 380.000
| 380.000
| 60e val
| 60e val, lower bound of 11- to 15-odd-limit diamond monotone
|-
|-
|  
|  
| 13/8
| 13/8
| 380.029
| 380.029
|
|-
|
| 21/11
| 380.034
|  
|  
|-
|-
Line 723: Line 883:
| 380.156
| 380.156
|  
|  
|-
|
| {{monzo| 0 -106 -111 11 179 59 }}
| 380.193
| 15-odd-limit least squares
|-
|-
| 32\101
| 32\101
|  
|  
| 380.198
| 380.198
| 101cdf val
| 101cd val
|-
|
| {{monzo| 0 -67 -72 5 152 47 }}
| 380.218
| 13-odd-limit least squares
|-
|-
|  
|  
Line 745: Line 895:
|-
|-
|  
|  
| {{monzo| 0 -38 -55 11 137 }}
| 21/20
| 380.278
| 380.279
| 11-odd-limit least squares
|  
|-
|-
|  
|  
Line 763: Line 913:
| 380.343
| 380.343
| 11-odd-limit minimax
| 11-odd-limit minimax
|-
|
| {{monzo| 0 36 -23 32 }}
| 380.384
| 9-odd-limit least squares
|-
|-
|  
|  
Line 777: Line 922:
|  
|  
| 380.488
| 380.488
| Upper bound of 11- to 15-odd-limit diamond monotone
|-
|
| 21/16
| 380.634
|  
|  
|-
|-
Line 812: Line 962:
|  
|  
| 381.818
| 381.818
| 22ef val
| 22ef val, upper bound of 9-odd-limit diamond monotone
|-
|-
|  
|  
Line 825: Line 975:
|}
|}


=== Sorcery ===
==== Sorcery ====
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
! Edo<br>generator
! Edo<br>generator
! Eigenmonzo<br>(unchanged-interval)
! Unchanged interval<br>(eigenmonzo)
! Generator (¢)
! Generator (¢)
! Comments
! Comments
Line 866: Line 1,016:
|  
|  
| 378.947
| 378.947
|  
| Lower bound of 9- and 11-odd-limit diamond monotone<br>13- and 15-odd-limit diamond monotone (singleton)
|-
|-
|  
|  
| 13/7
| 13/7
| 379.100
| 379.100
|
|-
|
| 21/13
| 379.459
|  
|  
|-
|-
Line 877: Line 1,032:
| 379.733
| 379.733
|  
|  
|-
|
| 27/20
| 379.968
| 5-odd-limit least squares
|-
|-
| 19\60
| 19\60
Line 904: Line 1,054:
|-
|-
|  
|  
| {{monzo| 0 36 -23 32 }}
| 21/20
| 380.384
| 380.279
| 9-odd-limit least squares
|  
|-
|-
|  
|  
Line 912: Line 1,062:
| 380.391
| 380.391
| 5-, 7- and 9-odd-limit minimax
| 5-, 7- and 9-odd-limit minimax
|-
|
| {{monzo| 0 -113 12 -65 75 26 }}
| 380.427
| 13-odd-limit least squares
|-
|
| {{monzo| 0 134 9 71 -89 -33 }}
| 380.457
| 15-odd-limit least squares
|-
|-
| 13\41
| 13\41
Line 929: Line 1,069:
|-
|-
|  
|  
| {{monzo| 0 1 -7 15 }}
| 21/16
| 380.506
| 380.634
| 7-odd-limit least squares
|  
|-
|-
|  
|  
Line 937: Line 1,077:
| 380.700
| 380.700
| 11-, 13- and 15-odd-limit minimax
| 11-, 13- and 15-odd-limit minimax
|-
|
| {{monzo| 0 85 -14 52 -68 }}
| 380.714
| 11-odd-limit least squares
|-
|-
|  
|  
Line 952: Line 1,087:
| 380.769
| 380.769
| 104fff val
| 104fff val
|-
|
| 21/11
| 380.779
|
|-
|-
|  
|  
Line 996: Line 1,136:
|  
|  
| 381.818
| 381.818
|  
| Upper bound of 9- and 11-odd-limit diamond monotone
|-
|-
|  
|  
Line 1,014: Line 1,154:
|}
|}


=== Intuition ===
==== Intuition ====
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
! Edo<br>generator
! Edo<br>generator
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
! Generator (¢)
! Generator (¢)
! Comments
! Comments
|-
|-
|
|
| 21/13
| 369.747
|
|-
|  
| 13/11
| 13/11
| 372.302
| 372.302
|
|
|-
|
| 21/11
| 373.154
|  
|-
|-
|
|  
| 13/7
| 13/7
| 378.617
| 378.617
|
|  
|-
|-
|
|  
| 5/3
| 5/3
| 378.910
| 378.910
Line 1,040: Line 1,190:
|
|
| 378.947
| 378.947
| 19e val, lower bound of 9-odd-limit diamond monotone
|-
|  
|  
|-
|
| 15/13
| 15/13
| 379.355
| 379.355
|
|  
|-
|-
|
|  
| 13/9
| 13/9
| 379.577
| 379.577
|
|  
|-
|-
|
|  
| 13/10
| 13/10
| 379.660
| 379.660
|
|  
|-
|-
|
|  
| 9/5
| 9/5
| 379.733
| 379.733
|
|  
|-
|-
|
|  
| 13/12
| 13/12
| 379.890
| 379.890
|
|  
|-
|
| 27/20
| 379.968
| 5-odd-limit least squares
|-
|-
| 19\60
| 19\60
|
|
| 380.000
| 380.000
| 60eee val
|-
|  
|  
|-
|
| 13/8
| 13/8
| 380.029
| 380.029
| 13 and 15-odd-limit minimax
| 13- and 15-odd-limit minimax
|-
|-
|
|  
| 15/14
| 15/14
| 380.093
| 380.093
Line 1,090: Line 1,235:
|
|
| 380.198
| 380.198
| 101cdeeee val
|-
|  
|  
|-
|
| 7/5
| 7/5
| 380.228
| 380.228
|  
|  
|-
|-
|
|  
| {{monzo| 0 36 -23 32 }}
| 21/20
| 380.384
| 380.279
| 9-odd-limit least squares
|  
|-
|-
|
|  
| 3/2
| 3/2
| 380.391
| 380.391
Line 1,110: Line 1,255:
|
|
| 380.488
| 380.488
| 41e val
|-
|
| 21/16
| 380.634
|  
|  
|-
|-
|
|  
| {{monzo| 0 1 -7 15 }}
| 380.506
| 7-odd-limit least squares
|-
|
| {{monzo| 0 -30 -73 30 46 78 }}
| 380.562
| 15-odd-limit least squares
|-
|
| {{monzo| 0 -10 -53 24 38 66 }}
| 380.568
| 13-odd-limit least squares
|-
|
| 7/4
| 7/4
| 380.735
| 380.735
Line 1,135: Line 1,270:
|
|
| 380.769
| 380.769
|  
| 104eeeff val
|-
|-
| 20\63
| 20\63
|
|
| 380.952
| 380.952
| 63ef val
|-
|  
|  
|-
|
| 7/6
| 7/6
| 380.982
| 380.982
|  
|  
|-
|-
|
|  
| 15/8
| 15/8
| 381.378
| 381.378
|  
|  
|-
|
| {{monzo| 0 19 -36 30 42 }}
| 381.380
| 11-odd-limit least squares
|-
|-
| 7\22
| 7\22
|
|
| 381.818
| 381.818
| 22f val, upper bound of 9-odd-limit diamond monotone<br>11- to 15-odd-limit diamond monotone (singleton)
|-
|  
|  
|-
|
| 11/10
| 11/10
| 381.923
| 381.923
| 11-odd-limit minimax
| 11-odd-limit minimax
|-
|-
|
|  
| 11/8
| 11/8
| 382.237
| 382.237
|  
|  
|-
|-
|
|  
| 9/7
| 9/7
| 382.458
| 382.458
|  
|  
|-
|-
|
|  
| 15/11
| 15/11
| 382.881
| 382.881
|  
|  
|-
|-
|
|  
| 11/6
| 11/6
| 383.263
| 383.263
|  
|  
|-
|-
|
|  
| 5/4
| 5/4
| 386.314
| 386.314
|  
|  
|-
|-
|
|  
| 11/9
| 11/9
| 386.852
| 386.852
|  
|  
|-
|-
|
|  
| 11/7
| 11/7
| 391.246
| 391.246
Line 1,203: Line 1,333:
|}
|}


=== Telepathy ===
==== Telepathy ====
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
! Edo<br>generator
! Edo<br>generator
! Eigenmonzo<br>(unchanged-interval)
! Unchanged interval<br>(eigenmonzo)
! Generator (¢)
! Generator (¢)
! Comments
! Comments
Line 1,219: Line 1,349:
| 13/10
| 13/10
| 372.893
| 372.893
|
|-
|
| 21/11
| 373.154
|  
|  
|-
|-
Line 1,244: Line 1,379:
|  
|  
| 378.947
| 378.947
| 19e val
| 19e val, lower bound of 9-odd-limit diamond monotone<br>2.3.5.7.13-subgroup 13-odd-limit diamond monotone (singleton)
|-
|-
|  
|  
| 13/7
| 13/7
| 379.100
| 379.100
|
|-
|
| 21/13
| 379.459
|  
|  
|-
|-
Line 1,255: Line 1,395:
| 379.733
| 379.733
|  
|  
|-
|
| 27/20
| 379.968
| 5-odd-limit least squares
|-
|-
| 19\60
| 19\60
Line 1,282: Line 1,417:
|-
|-
|  
|  
| {{monzo| 0 36 -23 32 }}
| 21/20
| 380.384
| 380.279
| 9-odd-limit least squares
|  
|-
|-
|  
|  
Line 1,297: Line 1,432:
|-
|-
|  
|  
| {{monzo| 0 1 -7 15 }}
| 21/16
| 380.506
| 380.634
| 7-odd-limit least squares
|-
|
| {{monzo| 0 47 -34 43 57 -48 }}
| 380.676
| 13-odd-limit least squares
|-
|  
|  
| {{monzo| 0 46 -35 49 65 -55 }}
| 380.691
| 15-odd-limit least squares
|-
|-
|  
|  
Line 1,340: Line 1,465:
| 381.378
| 381.378
|  
|  
|-
|
| {{monzo| 0 19 -36 30 42 }}
| 381.380
| 11-odd-limit least squares
|-
|-
| 7\22
| 7\22
|  
|  
| 381.818
| 381.818
|  
| Upper bound of 9-odd-limit diamond monotone<br>11-odd-limit diamond monotone (singleton)
|-
|-
|  
|  
Line 1,394: Line 1,514:
[[Category:Magic]]
[[Category:Magic]]
[[Category:Temperament extensions]]
[[Category:Temperament extensions]]
[[Category:Rank-2 temperaments]]
Retrieved from "https://en.xen.wiki/w/Magic_extensions"