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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Breadcrumb|Magic}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-11-17 11:39:32 UTC</tt>.<br>
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| : The original revision id was <tt>383550892</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">
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| =Tuning Spectra=
| | [[Magic]] has various competing [[extension]]s to the [[11-limit|11-]] and [[13-limit]]. The following temperaments are discussed in this article: |
| ==Spectrum of Magic Tunings by Eigenmonzos==
| |
|
| |
|
| Gencom: [2 5/4; 100/99 105/104 144/143 196/195]
| | * '''Tridecimal magic''' ({{nowrap| 19 & 22f }}) – tempering out 100/99, 105/104, 144/143, and 196/195; |
| Gencom map: [<1 0 2 -1 6 -2|, <0 5 1 12 -8 18|]
| | * '''Necromancy''' ({{nowrap| 19f & 22 }}) – tempering out 100/99, 225/224, 245/243, and 275/273; |
| ||~ Eigenmonzo ||~ Major Third ||
| | * '''Witchcraft''' ({{nowrap| 19e & 22ef }}) – tempering out 105/104, 196/195, 245/243, and 275/273; |
| || 14/13 || 378.617 ||
| | * '''Sorcery''' ({{nowrap| 19 & 22 }}) – tempering out 65/64, 78/77, 91/90, and 100/99; |
| || 6/5 || 378.910 ||
| | * '''Intuition''' ({{nowrap| 19e & 22f }}) – tempering out 55/54, 66/65, 99/98, and 105/104; |
| || 6\19 || 378.947 ||
| | * '''Telepathy''' ({{nowrap| 19e & 22 }}) – tempering out 55/54, 65/64, 91/90, and 99/98. |
| || 15/13 || 379.355 ||
| |
| || 18/13 || 379.577 || | |
| || 13/10 || 379.660 ||
| |
| || 10/9 || 379.733 ||
| |
| || 13/12 || 379.890 ||
| |
| || 27/20 || 379.968 (5 limit least squares) ||
| |
| || 19\60 || 380.000 ||
| |
| || 16/13 || 380.029 ||
| |
| || 15/14 || 380.093 ||
| |
| || 32\101 || 380.198 ||
| |
| || 7/5 || 380.228 ||
| |
| || 13/11 || 380.354 (13 and 15 limit minimax) ||
| |
| || |0 56 -31 46 -94 88> || 380.377 (13 limit least squares) ||
| |
| || |0 36 -23 32> || 380.384 (9 limit least squares) ||
| |
| || |0 58 -29 52 -108 100> || 380.389 (15 limit least squares) ||
| |
| || 4/3 || 380.391 (5, 7 and 9 limit minimax) ||
| |
| || 13\41 || 380.488 ||
| |
| || |0 1 -7 15> || 380.506 (7 limit least squares) ||
| |
| || 11/9 || 380.700 (11 limit minimax) ||
| |
| || |0 85 -14 52 -68> || 380.714 (11 limit least squares) ||
| |
| || 8/7 || 380.735 ||
| |
| || 33\104 || 380.769 ||
| |
| || 12/11 || 380.818 ||
| |
| || 14/11 || 380.875 ||
| |
| || 20\63 || 380.952 ||
| |
| || 7/6 || 380.982 ||
| |
| || 11/8 || 381.085 ||
| |
| || 15/11 || 381.211 ||
| |
| || 16/15 || 381.378 ||
| |
| || 11/10 || 381.666 ||
| |
| || 7\22 || 381.818 ||
| |
| || 9/7 || 382.458 ||
| |
| || 5/4 || 386.314 ||
| |
|
| |
|
| ==Spectrum of Necromancy Tunings by Eigenmonzos==
| | 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]]. |
|
| |
|
| Gencom: [2 5/4; 100/99 225/224 245/243 275/273]
| | 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. |
| Gencom map: [<1 0 2 -1 6 11|, <0 5 1 12 -8 -23|]
| |
| ||~ Eigenmonzo ||~ Major Third ||
| |
| || 6/5 || 378.910 ||
| |
| || 6\19 || 378.947 ||
| |
| || 10/9 || 379.733 ||
| |
| || 27/20 || 379.968 (5 limit least squares) ||
| |
| || 19\60 || 380.000 ||
| |
| || 15/14 || 380.093 ||
| |
| || 32\101 || 380.198 ||
| |
| || 7/5 || 380.228 ||
| |
| || |0 36 -23 32> || 380.384 (9 limit least squares) ||
| |
| || 4/3 || 380.391 (5, 7 and 9 limit minimax) ||
| |
| || 13\41 || 380.488 ||
| |
| || |0 1 -7 15> || 380.506 (7 limit least squares) ||
| |
| || 11/9 || 380.700 (11 limit minimax) ||
| |
| || 18/13 || 380.709 (13 and 15 limit minimax) ||
| |
| || |0 85 -14 52 -68> || 380.714 (11 limit least squares) ||
| |
| || 13/11 || 380.719 ||
| |
| || 8/7 || 380.735 ||
| |
| || 13/12 || 380.765 ||
| |
| || 33\104 || 380.769 ||
| |
| || |0 -179 -10 -87 53 158> || 380.785 (13 limit least squares) ||
| |
| || 14/13 || 380.809 ||
| |
| || |0 -222 -53 -93 67 187> || 380.817 (15 limit least squares) ||
| |
| || 12/11 || 380.818 ||
| |
| || 16/13 || 380.847 ||
| |
| || 14/11 || 380.875 ||
| |
| || 20\63 || 380.952 ||
| |
| || 15/13 || 380.957 ||
| |
| || 7/6 || 380.982 ||
| |
| || 13/10 || 381.074 ||
| |
| || 11/8 || 381.085 ||
| |
| || 15/11 || 381.211 ||
| |
| || 16/15 || 381.378 ||
| |
| || 11/10 || 381.666 ||
| |
| || 7\22 || 381.818 ||
| |
| || 9/7 || 382.458 ||
| |
| || 5/4 || 386.314 ||
| |
|
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|
| | 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. |
|
| |
|
| ==Spectrum of Sorcery Tunings by Eigenmonzos== | | == Interval chain == |
| | In the following table, odd harmonics and subharmonics 1–13 are in '''bold'''. |
|
| |
|
| Gencom: [2 5/4; 65/64 78/77 91/90 100/99]
| | {| class="wikitable center-1 right-2" |
| Gencom map: [<1 0 2 -1 6 4|, <0 5 1 12 -8 -1|]
| | |- |
| ||~ Eigenmonzo ||~ Major Third || | | ! rowspan="3" | # |
| || 16/13 || 359.472 || | | ! rowspan="3" | Cents* |
| || 13/10 || 372.893 || | | ! colspan="7" | Approximate ratios |
| || 13/12 || 376.905 || | | |- |
| || 15/13 || 378.249 || | | ! rowspan="2" | 7-limit |
| || 18/13 || 378.489 || | | ! colspan="6" | 13-limit extensions |
| || 6/5 || 378.910 || | | |- |
| || 6\19 || 378.947 || | | ! Magic |
| || 14/13 || 379.100 || | | ! Necromancy |
| || 10/9 || 379.733 || | | ! Witchcraft |
| || 27/20 || 379.968 (5 limit least squares) || | | ! Sorcery |
| || 19\60 || 380.000 || | | ! Intuition |
| || 15/14 || 380.093 || | | ! Telepathy |
| || 32\101 || 380.198 || | | |- |
| || 7/5 || 380.228 || | | | 0 |
| || |0 36 -23 32> || 380.384 (9 limit least squares) || | | | 0.0 |
| || 4/3 || 380.391 (5, 7 and 9 limit minimax) || | | | '''1/1''' |
| || |0 -113 12 -65 75 26> || 380.427 (13 limit least squares) || | | | |
| || |0 134 9 71 -89 -33> || 380.457 (15 limit least squares) || | | | |
| || 13\41 || 380.488 || | | | |
| || |0 1 -7 15> || 380.506 (7 limit least squares) || | | | |
| || 11/9 || 380.700 (11, 13 and 15 limit minimax) || | | | |
| || |0 85 -14 52 -68> || 380.714 (11 limit least squares) || | | | |
| || 8/7 || 380.735 || | | |- |
| || 33\104 || 380.769 || | | | 1 |
| || 12/11 || 380.818 || | | | 380.4 |
| || 14/11 || 380.875 || | | | '''5/4''' |
| || 20\63 || 380.952 || | | | 26/21 |
| || 7/6 || 380.982 || | | | |
| || 11/8 || 381.085 || | | | 26/21 |
| || 15/11 || 381.211 || | | | '''16/13''' |
| || 16/15 || 381.378 || | | | 26/21 |
| || 11/10 || 381.666 || | | | '''16/13''' |
| || 7\22 || 381.818 || | | |- |
| || 9/7 || 382.458 || | | | 2 |
| || 13/11 || 384.173 || | | | 760.9 |
| || 5/4 || 386.314 || | | | 14/9 |
| | | |
| | | |
| | | |
| | | 20/13 |
| | | 11/7 |
| | | 11/7, 20/13 |
| | |- |
| | | 3 |
| | | 1141.4 |
| | | 27/14 |
| | | 52/27, 64/33 |
| | | 64/33 |
| | | 52/27 |
| | | 64/33 |
| | | 21/11, 52/27 |
| | | 21/11 |
| | |- |
| | | 4 |
| | | 321.8 |
| | | 6/5 |
| | | 40/33 |
| | | 40/33 |
| | | |
| | | 40/33 |
| | | 11/9, 13/11 |
| | | 11/9 |
| | |- |
| | | 5 |
| | | 702.3 |
| | | '''3/2''' |
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
| | |- |
| | | 6 |
| | | 1082.7 |
| | | 15/8, 28/15 |
| | | 13/7 |
| | | |
| | | 13/7 |
| | | 24/13 |
| | | 13/7 |
| | | 24/13 |
| | |- |
| | | 7 |
| | | 263.2 |
| | | 7/6 |
| | | |
| | | |
| | | |
| | | 13/11 |
| | | |
| | | |
| | |- |
| | | 8 |
| | | 643.7 |
| | | 35/24 |
| | | 13/9, '''16/11''' |
| | | '''16/11''' |
| | | 13/9 |
| | | '''16/11''' |
| | | 13/9, 22/15 |
| | | 22/15 |
| | |- |
| | | 9 |
| | | 1024.1 |
| | | 9/5 |
| | | 20/11 |
| | | 20/11 |
| | | |
| | | 20/11 |
| | | 11/6 |
| | | 11/6 |
| | |- |
| | | 10 |
| | | 204.6 |
| | | '''9/8''' |
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
| | |- |
| | | 11 |
| | | 585.0 |
| | | 7/5 |
| | | |
| | | |
| | | |
| | | 18/13 |
| | | |
| | | 18/13 |
| | |- |
| | | 12 |
| | | 965.5 |
| | | '''7/4''' |
| | | 26/15 |
| | | |
| | | 26/15 |
| | | |
| | | 26/15 |
| | | |
| | |- |
| | | 13 |
| | | 146.0 |
| | | 35/32 |
| | | 12/11, 13/12 |
| | | 12/11 |
| | | 13/12 |
| | | 12/11, 14/13 |
| | | 11/10, 13/12 |
| | | 11/10, 14/13 |
| | |- |
| | | 14 |
| | | 526.4 |
| | | 27/20 |
| | | 15/11 |
| | | 15/11 |
| | | |
| | | 15/11 |
| | | '''11/8''' |
| | | '''11/8''' |
| | |- |
| | | 15 |
| | | 906.9 |
| | | 27/16, 42/25 |
| | | |
| | | 22/13 |
| | | 22/13 |
| | | |
| | | |
| | | 22/13 |
| | |- |
| | | 16 |
| | | 87.3 |
| | | 21/20 |
| | | |
| | | |
| | | 22/21 |
| | | 27/26 |
| | | |
| | | 27/26 |
| | |- |
| | | 17 |
| | | 467.8 |
| | | 21/16 |
| | | 13/10 |
| | | |
| | | 13/10 |
| | | |
| | | 13/10 |
| | | |
| | |- |
| | | 18 |
| | | 848.2 |
| | | 49/30 |
| | | '''13/8''', 18/11 |
| | | 18/11 |
| | | '''13/8''' |
| | | 18/11, 21/13 |
| | | '''13/8''' |
| | | 21/13 |
| | |- |
| | | 19 |
| | | 28.7 |
| | | 49/48, 81/80, 126/125 |
| | | 45/44 |
| | | 45/44 |
| | | |
| | | 45/44 |
| | | 33/32 |
| | | 33/32 |
| | |- |
| | | 20 |
| | | 409.2 |
| | | 63/50 |
| | | 14/11 |
| | | 14/11 |
| | | |
| | | 14/11 |
| | | |
| | | |
| | |- |
| | | 21 |
| | | 789.6 |
| | | 63/40 |
| | | |
| | | |
| | | 11/7 |
| | | |
| | | |
| | | |
| | |- |
| | | 22 |
| | | 1170.1 |
| | | 49/25, 63/32 |
| | | 39/20 |
| | | |
| | | 39/20 |
| | | |
| | | 39/20 |
| | | |
| | |} |
| | <nowiki/>* In 7-limit [[CWE tuning]] |
|
| |
|
| | == Tunings == |
| | === 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 }} |
| | |} |
|
| |
|
| ==Spectrum of Telepathy Tunings by Eigenmonzos== | | {| 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 }} |
| | |} |
|
| |
|
| Gencom: [2 5/4; 55/54 65/64 91/90 99/98]
| | {| class="wikitable center-all left-5 mw-collapsible mw-collapsed" |
| Gencom map: [<1 0 2 -1 -1 4|, <0 5 1 12 14 -1|]
| | |+ style="white-space: nowrap;" | Target tunings (witchcraft) |
| ||~ Eigenmonzo ||~ Major Third || | | |- |
| || 16/13 || 359.472 || | | ! rowspan="2" | Target |
| || 13/10 || 372.893 || | | ! colspan="2" | Minimax |
| || 13/12 || 376.905 || | | ! colspan="2" | Least squares |
| || 15/13 || 378.249 || | | |- |
| || 18/13 || 378.489 ||
| | ! Generator |
| || 6/5 || 378.910 ||
| | ! Eigenmonzo* |
| || 6\19 || 378.947 ||
| | ! Generator |
| || 14/13 || 379.100 ||
| | ! Eigenmonzo* |
| || 10/9 || 379.733 || | | |- |
| || 27/20 || 379.968 (5 limit least squares) || | | | 11-odd-limit |
| || 19\60 || 380.000 || | | | ~5/4 = 380.343{{c}} |
| || 15/14 || 380.093 || | | | 11/8 |
| || 32\101 || 380.198 || | | | ~5/4 = 380.278{{c}} |
| || 7/5 || 380.228 ||
| | | {{Monzo| 0 -38 -55 11 137 }} |
| || |0 36 -23 32> || 380.384 (9 limit least squares) || | | |- |
| || 4/3 || 380.391 (5, 7 and 9 limit minimax) ||
| | | 13-odd-limit |
| || 13\41 || 380.488 ||
| | | ~5/4 = 380.119{{c}} |
| || |0 1 -7 15> || 380.506 (7 limit least squares) || | | | 11/7 |
| || |0 47 -34 43 57 -48> || 380.676 (13 limit least squares) || | | | ~5/4 = 380.218{{c}} |
| || |0 46 -35 49 65 -55> || 380.691 (15 limit least squares) ||
| | | {{Monzo| 0 -67 -72 5 152 47 }} |
| || 13/11 || 380.719 (13 and 15 limit minimax) || | | |- |
| || 8/7 || 380.735 || | | | 15-odd-limit |
| || 33\104 || 380.769 || | | | ~5/4 = 380.113{{c}} |
| || 20\63 || 380.952 ||
| | | 15/11 |
| || 7/6 || 380.982 ||
| | | ~5/4 = 380.193{{c}} |
| || 16/15 || 381.378 || | | | {{Monzo| 0 -106 -111 11 179 59 }} |
| || |0 19 -36 30 42> || 381.380 (11 limit least squares) ||
| | |} |
| || 7\22 || 381.818 || | |
| || 11/10 || 381.923 (11 limit minimax) || | |
| || 11/8 || 382.237 || | |
| || 9/7 || 382.458 ||
| |
| || 15/11 || 382.881 ||
| |
| || 12/11 || 383.263 || | |
| || 5/4 || 386.314 ||
| |
| || 11/9 || 386.852 || | |
| || 14/11 || 391.246 || | |
|
| |
|
| | {| 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 }} |
| | |} |
|
| |
|
| ==Spectrum of Witchcraft Tunings by Eigenmonzos== | | {| 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 }} |
| | |} |
|
| |
|
| Gencom: [2 5/4; 105/104 196/195 245/243 275/273]
| | {| class="wikitable center-all left-5 mw-collapsible mw-collapsed" |
| Gencom map: [<1 0 2 -1 -7 -2|, <0 5 1 12 33 18|]
| | |+ style="white-space: nowrap;" | Target tunings (telepathy) |
| ||~ Eigenmonzo ||~ Major Third || | | |- |
| || 14/13 || 378.617 || | | ! rowspan="2" | Target |
| || 6/5 || 378.910 || | | ! colspan="2" | Minimax |
| || 6\19 || 378.947 || | | ! colspan="2" | Least squares |
| || 15/13 || 379.355 || | | |- |
| || 18/13 || 379.577 ||
| | ! Generator |
| || 13/10 || 379.660 ||
| | ! Eigenmonzo* |
| || 10/9 || 379.733 ||
| | ! Generator |
| || 27/20 || 379.968 (5 limit least squares) ||
| | ! Eigenmonzo* |
| || 13/12 || 379.890 || | | |- |
| || 19\60 || 380.000 || | | | 11-odd-limit |
| || 16/13 || 380.029 ||
| | | ~5/4 = 381.923{{c}} |
| || 15/14 || 380.093 ||
| | | 11/10 |
| || 15/11 || 380.113 (15 limit minimax) ||
| | | ~5/4 = 381.380{{c}} |
| || 14/11 || 380.119 (13 limit minimax) || | | | {{Monzo| 0 19 -36 30 42 }} |
| || 11/10 || 380.156 ||
| | |- |
| || |0 -106 -111 11 179 59> || 380.193 (15 limit least squares) || | | | 13-odd-limit |
| || 32\101 || 380.198 ||
| | | ~5/4 = 380.719{{c}} |
| || |0 -67 -72 5 152 47> || 380.218 (13 limit least squares) || | | | 13/11 |
| || 7/5 || 380.228 || | | | ~5/4 = 380.676{{c}} |
| || |0 -38 -55 11 137> || 380.278 (11 limit least squares) || | | | {{Monzo| 0 47 -34 43 57 -48 }} |
| || 11/9 || 380.322 || | | |- |
| || 12/11 || 380.334 || | | | 15-odd-limit |
| || 11/8 || 380.343 (11 limit minimax) || | | | ~5/4 = 380.719{{c}} |
| || |0 36 -23 32> || 380.384 (9 limit least squares) || | | | 13/11 |
| || 4/3 || 380.391 (5, 7 and 9 limit minimax) || | | | ~5/4 = 380.691{{c}} |
| || 13\41 || 380.488 ||
| | | {{Monzo| 0 46 -35 49 65 -55 }} |
| || 13/11 || 380.719 ||
| | |} |
| || 8/7 || 380.735 || | |
| || 33\104 || 380.769 || | |
| || 20\63 || 380.952 || | |
| || 7/6 || 380.982 ||
| |
| || 16/15 || 381.378 ||
| |
| || 7\22 || 381.818 ||
| |
| || 9/7 || 382.458 ||
| |
| || 5/4 || 386.314 ||
| |
|
| |
|
| | === Tuning spectra === |
| | ==== Magic ==== |
| | {| class="wikitable center-all left-4" |
| | |- |
| | ! Edo<br>generator |
| | ! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]] |
| | ! Generator (¢) |
| | ! Comments |
| | |- |
| | | |
| | | 21/13 |
| | | 369.747 |
| | | |
| | |- |
| | | |
| | | 13/7 |
| | | 378.617 |
| | | |
| | |- |
| | | |
| | | 5/3 |
| | | 378.910 |
| | | |
| | |- |
| | | 6\19 |
| | | |
| | | 378.947 |
| | | Lower bound of 9- to 15-odd-limit diamond monotone |
| | |- |
| | | |
| | | 15/13 |
| | | 379.355 |
| | | |
| | |- |
| | | |
| | | 13/9 |
| | | 379.577 |
| | | |
| | |- |
| | | |
| | | 13/10 |
| | | 379.660 |
| | | |
| | |- |
| | | |
| | | 9/5 |
| | | 379.733 |
| | | |
| | |- |
| | | |
| | | 13/12 |
| | | 379.890 |
| | | |
| | |- |
| | | 19\60 |
| | | |
| | | 380.000 |
| | | |
| | |- |
| | | |
| | | 13/8 |
| | | 380.029 |
| | | |
| | |- |
| | | |
| | | 15/14 |
| | | 380.093 |
| | | |
| | |- |
| | | 32\101 |
| | | |
| | | 380.198 |
| | | 101cde val |
| | |- |
| | | |
| | | 7/5 |
| | | 380.228 |
| | | |
| | |- |
| | | |
| | | 21/20 |
| | | 380.279 |
| | | |
| | |- |
| | | |
| | | 13/11 |
| | | 380.354 |
| | | 13- and 15-odd-limit minimax |
| | |- |
| | | |
| | | 3/2 |
| | | 380.391 |
| | | 5-, 7- and 9-odd-limit minimax |
| | |- |
| | | 13\41 |
| | | |
| | | 380.488 |
| | | |
| | |- |
| | | |
| | | 21/16 |
| | | 380.634 |
| | | |
| | |- |
| | | |
| | | 11/9 |
| | | 380.700 |
| | | 11-odd-limit minimax |
| | |- |
| | | |
| | | 7/4 |
| | | 380.735 |
| | | |
| | |- |
| | | 33\104 |
| | | |
| | | 380.769 |
| | | 104ff val |
| | |- |
| | | |
| | | 21/11 |
| | | 380.779 |
| | | |
| | |- |
| | | |
| | | 11/6 |
| | | 380.818 |
| | | |
| | |- |
| | | |
| | | 11/7 |
| | | 380.875 |
| | | |
| | |- |
| | | 20\63 |
| | | |
| | | 380.952 |
| | | 63f val |
| | |- |
| | | |
| | | 7/6 |
| | | 380.982 |
| | | |
| | |- |
| | | |
| | | 11/8 |
| | | 381.085 |
| | | |
| | |- |
| | | |
| | | 15/11 |
| | | 381.211 |
| | | |
| | |- |
| | | |
| | | 15/8 |
| | | 381.378 |
| | | |
| | |- |
| | | |
| | | 11/10 |
| | | 381.666 |
| | | |
| | |- |
| | | 7\22 |
| | | |
| | | 381.818 |
| | | 22f val, upper bound of 9- to 15-odd-limit diamond monotone |
| | |- |
| | | |
| | | 9/7 |
| | | 382.458 |
| | | |
| | |- |
| | | |
| | | 5/4 |
| | | 386.314 |
| | | |
| | |} |
|
| |
|
| ==Spectrum of Muggles Tunings by Eigenmonzos== | | ==== Necromancy ==== |
| | {| class="wikitable center-all left-4" |
| | |- |
| | ! Edo<br>generator |
| | ! Unchanged interval<br>(eigenmonzo) |
| | ! Generator (¢) |
| | ! Comments |
| | |- |
| | | |
| | | 5/3 |
| | | 378.910 |
| | | |
| | |- |
| | | 6\19 |
| | | |
| | | 378.947 |
| | | 19f val, lower bound of 9- and 11-odd-limit diamond monotone |
| | |- |
| | | |
| | | 9/5 |
| | | 379.733 |
| | | |
| | |- |
| | | 19\60 |
| | | |
| | | 380.000 |
| | | 60f val |
| | |- |
| | | |
| | | 15/14 |
| | | 380.093 |
| | | |
| | |- |
| | | 32\101 |
| | | |
| | | 380.198 |
| | | 101cdeff val |
| | |- |
| | | |
| | | 7/5 |
| | | 380.228 |
| | | |
| | |- |
| | | |
| | | 21/20 |
| | | 380.279 |
| | | |
| | |- |
| | | |
| | | 3/2 |
| | | 380.391 |
| | | 5-, 7- and 9-odd-limit minimax |
| | |- |
| | | 13\41 |
| | | |
| | | 380.488 |
| | | Lower bound of 13- and 15-odd-limit diamond monotone |
| | |- |
| | | |
| | | 21/16 |
| | | 380.634 |
| | | |
| | |- |
| | | |
| | | 11/9 |
| | | 380.700 |
| | | 11-odd-limit minimax |
| | |- |
| | | |
| | | 13/9 |
| | | 380.709 |
| | | 13- and 15-odd-limit minimax |
| | |- |
| | | |
| | | 13/11 |
| | | 380.719 |
| | | |
| | |- |
| | | |
| | | 7/4 |
| | | 380.735 |
| | | |
| | |- |
| | | |
| | | 21/13 |
| | | 380.756 |
| | | |
| | |- |
| | | |
| | | 13/12 |
| | | 380.765 |
| | | |
| | |- |
| | | 33\104 |
| | | |
| | | 380.769 |
| | | |
| | |- |
| | | |
| | | 21/11 |
| | | 380.779 |
| | | |
| | |- |
| | | |
| | | 13/7 |
| | | 380.809 |
| | | |
| | |- |
| | | |
| | | 11/6 |
| | | 380.818 |
| | | |
| | |- |
| | | |
| | | 13/8 |
| | | 380.847 |
| | | |
| | |- |
| | | |
| | | 11/7 |
| | | 380.875 |
| | | |
| | |- |
| | | 20\63 |
| | | |
| | | 380.952 |
| | | Upper bound of 13- and 15-odd-limit diamond monotone |
| | |- |
| | | |
| | | 15/13 |
| | | 380.957 |
| | | |
| | |- |
| | | |
| | | 7/6 |
| | | 380.982 |
| | | |
| | |- |
| | | |
| | | 13/10 |
| | | 381.074 |
| | | |
| | |- |
| | | |
| | | 11/8 |
| | | 381.085 |
| | | |
| | |- |
| | | |
| | | 15/11 |
| | | 381.211 |
| | | |
| | |- |
| | | |
| | | 15/8 |
| | | 381.378 |
| | | |
| | |- |
| | | |
| | | 11/10 |
| | | 381.666 |
| | | |
| | |- |
| | | 7\22 |
| | | |
| | | 381.818 |
| | | Upper bound of 9- and 11-odd-limit diamond monotone |
| | |- |
| | | |
| | | 9/7 |
| | | 382.458 |
| | | |
| | |- |
| | | |
| | | 5/4 |
| | | 386.314 |
| | | |
| | |} |
|
| |
|
| Gencom: [2 5/4; 45/44 65/64 78/77 126/125]
| | ==== Witchcraft ==== |
| Gencom map: [<1 0 2 5 0 4|, <0 5 1 -7 11 -1|]
| | {| class="wikitable center-all left-4" |
| ||~ Eigenmonzo ||~ Major Third || | | |- |
| || 11/9 || 347.408 ||
| | ! Edo<br>generator |
| || 16/13 || 359.472 || | | ! Unchanged interval<br>(eigenmonzo) |
| || 15/11 || 372.610 || | | ! Generator (¢) |
| || 13/10 || 372.893 || | | ! Comments |
| || 12/11 || 374.894 || | | |- |
| || 8/7 || 375.882 || | | | |
| || 13/11 || 375.899 || | | | 21/13 |
| || 11/10 || 376.500 || | | | 369.747 |
| || 14/11 || 376.805 || | | | |
| || 13/12 || 376.905 || | | |- |
| || 7/5 || 377.186 || | | | |
| || 11/8 || 377.393 (11, 13 and 15 limit minimax) || | | | 13/7 |
| || |0 113 -12 -68 58 -26> || 377.630 (13 limit least squares) || | | | 378.617 |
| || |0 -21 -5 27> || 377.640 (7 limit least squares) || | | | |
| || |0 134 9 -81 63 -33> || 377.718 (15 limit least squares) || | | |- |
| || |0 85 -14 -62 46> || 377.758 (11 limit least squares) || | | | |
| || 7/6 || 377.761 (7 limit minimax) || | | | 5/3 |
| || 15/13 || 378.249 || | | | 378.910 |
| || 15/14 || 378.419 || | | | |
| || 18/13 || 378.489 || | | |- |
| || 9/7 || 378.534 (9 limit minimax) || | | | 6\19 |
| || |0 93 -4 -44> || 378.554 (9 limit least squares) || | | | |
| || 14/13 || 378.617 || | | | 378.947 |
| || 6/5 || 378.910 || | | | 19e val, lower bound of 9-odd-limit diamond monotone |
| || 6\19 || 378.947 || | | |- |
| || 10/9 || 379.733 || | | | |
| || 27/20 || 379.968 (5 limit least squares) || | | | 15/13 |
| || 19\60 || 380.000 || | | | 379.355 |
| || 32\101 || 380.198 || | | | |
| || 4/3 || 380.391 (5 limit minimax) || | | |- |
| || 13\41 || 380.488 || | | | |
| || 33\104 || 380.769 ||
| | | 13/9 |
| || 20\63 || 380.952 ||
| | | 379.577 |
| || 16/15 || 381.378 || | | | |
| || 7\22 || 381.818 ||
| | |- |
| || 5/4 || 386.314 ||</pre></div> | | | |
| <h4>Original HTML content:</h4>
| | | 13/10 |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Magic extensions</title></head><body><br />
| | | 379.660 |
| <br />
| | | |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Tuning Spectra"></a><!-- ws:end:WikiTextHeadingRule:0 -->Tuning Spectra</h1>
| | |- |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Tuning Spectra-Spectrum of Magic Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:2 -->Spectrum of Magic Tunings by Eigenmonzos</h2>
| | | |
| <br />
| | | 9/5 |
| Gencom: [2 5/4; 100/99 105/104 144/143 196/195]<br />
| | | 379.733 |
| Gencom map: [&lt;1 0 2 -1 6 -2|, &lt;0 5 1 12 -8 18|]<br />
| | | |
| | |- |
| | | |
| | | 13/12 |
| | | 379.890 |
| | | |
| | |- |
| | | 19\60 |
| | | |
| | | 380.000 |
| | | 60e val, lower bound of 11- to 15-odd-limit diamond monotone |
| | |- |
| | | |
| | | 13/8 |
| | | 380.029 |
| | | |
| | |- |
| | | |
| | | 21/11 |
| | | 380.034 |
| | | |
| | |- |
| | | |
| | | 15/14 |
| | | 380.093 |
| | | |
| | |- |
| | | |
| | | 15/11 |
| | | 380.113 |
| | | 15-odd-limit minimax |
| | |- |
| | | |
| | | 11/7 |
| | | 380.119 |
| | | 13-odd-limit minimax |
| | |- |
| | | |
| | | 11/10 |
| | | 380.156 |
| | | |
| | |- |
| | | 32\101 |
| | | |
| | | 380.198 |
| | | 101cd val |
| | |- |
| | | |
| | | 7/5 |
| | | 380.228 |
| | | |
| | |- |
| | | |
| | | 21/20 |
| | | 380.279 |
| | | |
| | |- |
| | | |
| | | 11/9 |
| | | 380.322 |
| | | |
| | |- |
| | | |
| | | 11/6 |
| | | 380.334 |
| | | |
| | |- |
| | | |
| | | 11/8 |
| | | 380.343 |
| | | 11-odd-limit minimax |
| | |- |
| | | |
| | | 3/2 |
| | | 380.391 |
| | | 5-, 7- and 9-odd-limit minimax |
| | |- |
| | | 13\41 |
| | | |
| | | 380.488 |
| | | Upper bound of 11- to 15-odd-limit diamond monotone |
| | |- |
| | | |
| | | 21/16 |
| | | 380.634 |
| | | |
| | |- |
| | | |
| | | 13/11 |
| | | 380.719 |
| | | |
| | |- |
| | | |
| | | 7/4 |
| | | 380.735 |
| | | |
| | |- |
| | | 33\104 |
| | | |
| | | 380.769 |
| | | 104eeff val |
| | |- |
| | | 20\63 |
| | | |
| | | 380.952 |
| | | 63eef val |
| | |- |
| | | |
| | | 7/6 |
| | | 380.982 |
| | | |
| | |- |
| | | |
| | | 15/8 |
| | | 381.378 |
| | | |
| | |- |
| | | 7\22 |
| | | |
| | | 381.818 |
| | | 22ef val, upper bound of 9-odd-limit diamond monotone |
| | |- |
| | | |
| | | 9/7 |
| | | 382.458 |
| | | |
| | |- |
| | | |
| | | 5/4 |
| | | 386.314 |
| | | |
| | |} |
|
| |
|
| | ==== Sorcery ==== |
| | {| class="wikitable center-all left-4" |
| | |- |
| | ! Edo<br>generator |
| | ! Unchanged interval<br>(eigenmonzo) |
| | ! Generator (¢) |
| | ! Comments |
| | |- |
| | | |
| | | 13/8 |
| | | 359.472 |
| | | |
| | |- |
| | | |
| | | 13/10 |
| | | 372.893 |
| | | |
| | |- |
| | | |
| | | 13/12 |
| | | 376.905 |
| | | |
| | |- |
| | | |
| | | 15/13 |
| | | 378.249 |
| | | |
| | |- |
| | | |
| | | 13/9 |
| | | 378.489 |
| | | |
| | |- |
| | | |
| | | 5/3 |
| | | 378.910 |
| | | |
| | |- |
| | | 6\19 |
| | | |
| | | 378.947 |
| | | Lower bound of 9- and 11-odd-limit diamond monotone<br>13- and 15-odd-limit diamond monotone (singleton) |
| | |- |
| | | |
| | | 13/7 |
| | | 379.100 |
| | | |
| | |- |
| | | |
| | | 21/13 |
| | | 379.459 |
| | | |
| | |- |
| | | |
| | | 9/5 |
| | | 379.733 |
| | | |
| | |- |
| | | 19\60 |
| | | |
| | | 380.000 |
| | | 60ff val |
| | |- |
| | | |
| | | 15/14 |
| | | 380.093 |
| | | |
| | |- |
| | | 32\101 |
| | | |
| | | 380.198 |
| | | 101cdefff val |
| | |- |
| | | |
| | | 7/5 |
| | | 380.228 |
| | | |
| | |- |
| | | |
| | | 21/20 |
| | | 380.279 |
| | | |
| | |- |
| | | |
| | | 3/2 |
| | | 380.391 |
| | | 5-, 7- and 9-odd-limit minimax |
| | |- |
| | | 13\41 |
| | | |
| | | 380.488 |
| | | 41f val |
| | |- |
| | | |
| | | 21/16 |
| | | 380.634 |
| | | |
| | |- |
| | | |
| | | 11/9 |
| | | 380.700 |
| | | 11-, 13- and 15-odd-limit minimax |
| | |- |
| | | |
| | | 7/4 |
| | | 380.735 |
| | | |
| | |- |
| | | 33\104 |
| | | |
| | | 380.769 |
| | | 104fff val |
| | |- |
| | | |
| | | 21/11 |
| | | 380.779 |
| | | |
| | |- |
| | | |
| | | 11/6 |
| | | 380.818 |
| | | |
| | |- |
| | | |
| | | 11/7 |
| | | 380.875 |
| | | |
| | |- |
| | | 20\63 |
| | | |
| | | 380.952 |
| | | 63ff val |
| | |- |
| | | |
| | | 7/6 |
| | | 380.982 |
| | | |
| | |- |
| | | |
| | | 11/8 |
| | | 381.085 |
| | | |
| | |- |
| | | |
| | | 15/11 |
| | | 381.211 |
| | | |
| | |- |
| | | |
| | | 15/8 |
| | | 381.378 |
| | | |
| | |- |
| | | |
| | | 11/10 |
| | | 381.666 |
| | | |
| | |- |
| | | 7\22 |
| | | |
| | | 381.818 |
| | | Upper bound of 9- and 11-odd-limit diamond monotone |
| | |- |
| | | |
| | | 9/7 |
| | | 382.458 |
| | | |
| | |- |
| | | |
| | | 13/11 |
| | | 384.173 |
| | | |
| | |- |
| | | |
| | | 5/4 |
| | | 386.314 |
| | | |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ==== Intuition ==== |
| <tr>
| | {| class="wikitable center-all left-4" |
| <th>Eigenmonzo<br />
| | |- |
| </th>
| | ! Edo<br>generator |
| <th>Major Third<br />
| | ! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]] |
| </th>
| | ! Generator (¢) |
| </tr>
| | ! Comments |
| <tr>
| | |- |
| <td>14/13<br />
| | | |
| </td>
| | | 21/13 |
| <td>378.617<br />
| | | 369.747 |
| </td>
| | | |
| </tr>
| | |- |
| <tr>
| | | |
| <td>6/5<br />
| | | 13/11 |
| </td>
| | | 372.302 |
| <td>378.910<br />
| | | |
| </td>
| | |- |
| </tr>
| | | |
| <tr>
| | | 21/11 |
| <td>6\19<br />
| | | 373.154 |
| </td>
| | | |
| <td>378.947<br />
| | |- |
| </td>
| | | |
| </tr>
| | | 13/7 |
| <tr>
| | | 378.617 |
| <td>15/13<br />
| | | |
| </td>
| | |- |
| <td>379.355<br />
| | | |
| </td>
| | | 5/3 |
| </tr>
| | | 378.910 |
| <tr>
| | | |
| <td>18/13<br />
| | |- |
| </td>
| | | 6\19 |
| <td>379.577<br />
| | | |
| </td>
| | | 378.947 |
| </tr>
| | | 19e val, lower bound of 9-odd-limit diamond monotone |
| <tr>
| | |- |
| <td>13/10<br />
| | | |
| </td>
| | | 15/13 |
| <td>379.660<br />
| | | 379.355 |
| </td>
| | | |
| </tr>
| | |- |
| <tr>
| | | |
| <td>10/9<br />
| | | 13/9 |
| </td>
| | | 379.577 |
| <td>379.733<br />
| | | |
| </td>
| | |- |
| </tr>
| | | |
| <tr>
| | | 13/10 |
| <td>13/12<br />
| | | 379.660 |
| </td>
| | | |
| <td>379.890<br />
| | |- |
| </td>
| | | |
| </tr>
| | | 9/5 |
| <tr>
| | | 379.733 |
| <td>27/20<br />
| | | |
| </td>
| | |- |
| <td>379.968 (5 limit least squares)<br />
| | | |
| </td>
| | | 13/12 |
| </tr>
| | | 379.890 |
| <tr>
| | | |
| <td>19\60<br />
| | |- |
| </td>
| | | 19\60 |
| <td>380.000<br />
| | | |
| </td>
| | | 380.000 |
| </tr>
| | | 60eee val |
| <tr>
| | |- |
| <td>16/13<br />
| | | |
| </td>
| | | 13/8 |
| <td>380.029<br />
| | | 380.029 |
| </td>
| | | 13- and 15-odd-limit minimax |
| </tr>
| | |- |
| <tr>
| | | |
| <td>15/14<br />
| | | 15/14 |
| </td>
| | | 380.093 |
| <td>380.093<br />
| | | |
| </td>
| | |- |
| </tr>
| | | 32\101 |
| <tr>
| | | |
| <td>32\101<br />
| | | 380.198 |
| </td>
| | | 101cdeeee val |
| <td>380.198<br />
| | |- |
| </td>
| | | |
| </tr>
| | | 7/5 |
| <tr>
| | | 380.228 |
| <td>7/5<br />
| | | |
| </td>
| | |- |
| <td>380.228<br />
| | | |
| </td>
| | | 21/20 |
| </tr>
| | | 380.279 |
| <tr>
| | | |
| <td>13/11<br />
| | |- |
| </td>
| | | |
| <td>380.354 (13 and 15 limit minimax)<br />
| | | 3/2 |
| </td>
| | | 380.391 |
| </tr>
| | | 5-, 7- and 9-odd-limit minimax |
| <tr>
| | |- |
| <td>|0 56 -31 46 -94 88&gt;<br />
| | | 13\41 |
| </td>
| | | |
| <td>380.377 (13 limit least squares)<br />
| | | 380.488 |
| </td>
| | | 41e val |
| </tr>
| | |- |
| <tr>
| | | |
| <td>|0 36 -23 32&gt;<br />
| | | 21/16 |
| </td>
| | | 380.634 |
| <td>380.384 (9 limit least squares)<br />
| | | |
| </td>
| | |- |
| </tr>
| | | |
| <tr>
| | | 7/4 |
| <td>|0 58 -29 52 -108 100&gt;<br />
| | | 380.735 |
| </td>
| | | |
| <td>380.389 (15 limit least squares)<br />
| | |- |
| </td>
| | | 33\104 |
| </tr>
| | | |
| <tr>
| | | 380.769 |
| <td>4/3<br />
| | | 104eeeff val |
| </td>
| | |- |
| <td>380.391 (5, 7 and 9 limit minimax)<br />
| | | 20\63 |
| </td>
| | | |
| </tr>
| | | 380.952 |
| <tr>
| | | 63ef val |
| <td>13\41<br />
| | |- |
| </td>
| | | |
| <td>380.488<br />
| | | 7/6 |
| </td>
| | | 380.982 |
| </tr>
| | | |
| <tr>
| | |- |
| <td>|0 1 -7 15&gt;<br />
| | | |
| </td>
| | | 15/8 |
| <td>380.506 (7 limit least squares)<br />
| | | 381.378 |
| </td>
| | | |
| </tr>
| | |- |
| <tr>
| | | 7\22 |
| <td>11/9<br />
| | | |
| </td>
| | | 381.818 |
| <td>380.700 (11 limit minimax)<br />
| | | 22f val, upper bound of 9-odd-limit diamond monotone<br>11- to 15-odd-limit diamond monotone (singleton) |
| </td>
| | |- |
| </tr>
| | | |
| <tr>
| | | 11/10 |
| <td>|0 85 -14 52 -68&gt;<br />
| | | 381.923 |
| </td>
| | | 11-odd-limit minimax |
| <td>380.714 (11 limit least squares)<br />
| | |- |
| </td>
| | | |
| </tr>
| | | 11/8 |
| <tr>
| | | 382.237 |
| <td>8/7<br />
| | | |
| </td>
| | |- |
| <td>380.735<br />
| | | |
| </td>
| | | 9/7 |
| </tr>
| | | 382.458 |
| <tr>
| | | |
| <td>33\104<br />
| | |- |
| </td>
| | | |
| <td>380.769<br />
| | | 15/11 |
| </td>
| | | 382.881 |
| <td><br />
| | | |
| </td>
| | |- |
| <td>12/11<br />
| | | |
| </td>
| | | 11/6 |
| <td>380.818<br />
| | | 383.263 |
| </td>
| | | |
| </tr>
| | |- |
| <tr>
| | | |
| <td>14/11<br />
| | | 5/4 |
| </td>
| | | 386.314 |
| <td>380.875<br />
| | | |
| </td>
| | |- |
| </tr>
| | | |
| <tr>
| | | 11/9 |
| <td>20\63<br />
| | | 386.852 |
| </td>
| | | |
| <td>380.952<br />
| | |- |
| </td>
| | | |
| </tr>
| | | 11/7 |
| <tr>
| | | 391.246 |
| <td>7/6<br />
| | | |
| </td>
| | |} |
| <td>380.982<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/8<br />
| |
| </td>
| |
| <td>381.085<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/11<br />
| |
| </td>
| |
| <td>381.211<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/15<br />
| |
| </td>
| |
| <td>381.378<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/10<br />
| |
| </td>
| |
| <td>381.666<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7\22<br />
| |
| </td>
| |
| <td>381.818<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9/7<br />
| |
| </td>
| |
| <td>382.458<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5/4<br />
| |
| </td>
| |
| <td>386.314<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | ==== Telepathy ==== |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Tuning Spectra-Spectrum of Necromancy Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:4 -->Spectrum of Necromancy Tunings by Eigenmonzos</h2>
| | {| class="wikitable center-all left-4" |
| <br />
| | |- |
| Gencom: [2 5/4; 100/99 225/224 245/243 275/273]<br />
| | ! Edo<br>generator |
| Gencom map: [&lt;1 0 2 -1 6 11|, &lt;0 5 1 12 -8 -23|]<br />
| | ! Unchanged interval<br>(eigenmonzo) |
| | ! Generator (¢) |
| | ! Comments |
| | |- |
| | | |
| | | 13/8 |
| | | 359.472 |
| | | |
| | |- |
| | | |
| | | 13/10 |
| | | 372.893 |
| | | |
| | |- |
| | | |
| | | 21/11 |
| | | 373.154 |
| | | |
| | |- |
| | | |
| | | 13/12 |
| | | 376.905 |
| | | |
| | |- |
| | | |
| | | 15/13 |
| | | 378.249 |
| | | |
| | |- |
| | | |
| | | 13/9 |
| | | 378.489 |
| | | |
| | |- |
| | | |
| | | 5/3 |
| | | 378.910 |
| | | |
| | |- |
| | | 6\19 |
| | | |
| | | 378.947 |
| | | 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 |
| | | 379.100 |
| | | |
| | |- |
| | | |
| | | 21/13 |
| | | 379.459 |
| | | |
| | |- |
| | | |
| | | 9/5 |
| | | 379.733 |
| | | |
| | |- |
| | | 19\60 |
| | | |
| | | 380.000 |
| | | 60eeeff val |
| | |- |
| | | |
| | | 15/14 |
| | | 380.093 |
| | | |
| | |- |
| | | 32\101 |
| | | |
| | | 380.198 |
| | | 101cdeeeefff val |
| | |- |
| | | |
| | | 7/5 |
| | | 380.228 |
| | | |
| | |- |
| | | |
| | | 21/20 |
| | | 380.279 |
| | | |
| | |- |
| | | |
| | | 3/2 |
| | | 380.391 |
| | | 5-, 7- and 9-odd-limit minimax |
| | |- |
| | | 13\41 |
| | | |
| | | 380.488 |
| | | 41ef val |
| | |- |
| | | |
| | | 21/16 |
| | | 380.634 |
| | | |
| | |- |
| | | |
| | | 13/11 |
| | | 380.719 |
| | | 13- and 15-odd-limit minimax |
| | |- |
| | | |
| | | 7/4 |
| | | 380.735 |
| | | |
| | |- |
| | | 33\104 |
| | | |
| | | 380.769 |
| | | 104eeefff val |
| | |- |
| | | 20\63 |
| | | |
| | | 380.952 |
| | | 63eff val |
| | |- |
| | | |
| | | 7/6 |
| | | 380.982 |
| | | |
| | |- |
| | | |
| | | 15/8 |
| | | 381.378 |
| | | |
| | |- |
| | | 7\22 |
| | | |
| | | 381.818 |
| | | Upper bound of 9-odd-limit diamond monotone<br>11-odd-limit diamond monotone (singleton) |
| | |- |
| | | |
| | | 11/10 |
| | | 381.923 |
| | | 11-odd-limit minimax |
| | |- |
| | | |
| | | 11/8 |
| | | 382.237 |
| | | |
| | |- |
| | | |
| | | 9/7 |
| | | 382.458 |
| | | |
| | |- |
| | | |
| | | 15/11 |
| | | 382.881 |
| | | |
| | |- |
| | | |
| | | 11/6 |
| | | 383.263 |
| | | |
| | |- |
| | | |
| | | 5/4 |
| | | 386.314 |
| | | |
| | |- |
| | | |
| | | 11/9 |
| | | 386.852 |
| | | |
| | |- |
| | | |
| | | 11/7 |
| | | 391.246 |
| | | |
| | |} |
|
| |
|
| | | [[Category:Magic]] |
| <table class="wiki_table">
| | [[Category:Temperament extensions]] |
| <tr>
| | [[Category:Rank-2 temperaments]] |
| <th>Eigenmonzo<br />
| |
| </th>
| |
| <th>Major Third<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>6/5<br />
| |
| </td>
| |
| <td>378.910<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6\19<br />
| |
| </td>
| |
| <td>378.947<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10/9<br />
| |
| </td>
| |
| <td>379.733<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27/20<br />
| |
| </td>
| |
| <td>379.968 (5 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19\60<br />
| |
| </td>
| |
| <td>380.000<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/14<br />
| |
| </td>
| |
| <td>380.093<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32\101<br />
| |
| </td>
| |
| <td>380.198<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/5<br />
| |
| </td>
| |
| <td>380.228<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 36 -23 32&gt;<br />
| |
| </td>
| |
| <td>380.384 (9 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td>380.391 (5, 7 and 9 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13\41<br />
| |
| </td>
| |
| <td>380.488<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 1 -7 15&gt;<br />
| |
| </td>
| |
| <td>380.506 (7 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/9<br />
| |
| </td>
| |
| <td>380.700 (11 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18/13<br />
| |
| </td>
| |
| <td>380.709 (13 and 15 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 85 -14 52 -68&gt;<br />
| |
| </td>
| |
| <td>380.714 (11 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/11<br />
| |
| </td>
| |
| <td>380.719<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8/7<br />
| |
| </td>
| |
| <td>380.735<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/12<br />
| |
| </td>
| |
| <td>380.765<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33\104<br />
| |
| </td>
| |
| <td>380.769<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>|0 -179 -10 -87 53 158&gt;<br />
| |
| </td>
| |
| <td>380.785 (13 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/13<br />
| |
| </td>
| |
| <td>380.809<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 -222 -53 -93 67 187&gt;<br />
| |
| </td>
| |
| <td>380.817 (15 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12/11<br />
| |
| </td>
| |
| <td>380.818<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/13<br />
| |
| </td>
| |
| <td>380.847<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/11<br />
| |
| </td>
| |
| <td>380.875<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20\63<br />
| |
| </td>
| |
| <td>380.952<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/13<br />
| |
| </td>
| |
| <td>380.957<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/6<br />
| |
| </td>
| |
| <td>380.982<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/10<br />
| |
| </td>
| |
| <td>381.074<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/8<br />
| |
| </td>
| |
| <td>381.085<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/11<br />
| |
| </td>
| |
| <td>381.211<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/15<br />
| |
| </td>
| |
| <td>381.378<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/10<br />
| |
| </td>
| |
| <td>381.666<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7\22<br />
| |
| </td>
| |
| <td>381.818<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9/7<br />
| |
| </td>
| |
| <td>382.458<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5/4<br />
| |
| </td>
| |
| <td>386.314<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Tuning Spectra-Spectrum of Sorcery Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:6 -->Spectrum of Sorcery Tunings by Eigenmonzos</h2>
| |
| <br />
| |
| Gencom: [2 5/4; 65/64 78/77 91/90 100/99]<br />
| |
| Gencom map: [&lt;1 0 2 -1 6 4|, &lt;0 5 1 12 -8 -1|]<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Eigenmonzo<br />
| |
| </th>
| |
| <th>Major Third<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>16/13<br />
| |
| </td>
| |
| <td>359.472<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/10<br />
| |
| </td>
| |
| <td>372.893<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/12<br />
| |
| </td>
| |
| <td>376.905<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/13<br />
| |
| </td>
| |
| <td>378.249<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18/13<br />
| |
| </td>
| |
| <td>378.489<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6/5<br />
| |
| </td>
| |
| <td>378.910<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6\19<br />
| |
| </td>
| |
| <td>378.947<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/13<br />
| |
| </td>
| |
| <td>379.100<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10/9<br />
| |
| </td>
| |
| <td>379.733<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27/20<br />
| |
| </td>
| |
| <td>379.968 (5 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19\60<br />
| |
| </td>
| |
| <td>380.000<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/14<br />
| |
| </td>
| |
| <td>380.093<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32\101<br />
| |
| </td>
| |
| <td>380.198<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/5<br />
| |
| </td>
| |
| <td>380.228<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 36 -23 32&gt;<br />
| |
| </td>
| |
| <td>380.384 (9 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td>380.391 (5, 7 and 9 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 -113 12 -65 75 26&gt;<br />
| |
| </td>
| |
| <td>380.427 (13 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 134 9 71 -89 -33&gt;<br />
| |
| </td>
| |
| <td>380.457 (15 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13\41<br />
| |
| </td>
| |
| <td>380.488<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 1 -7 15&gt;<br />
| |
| </td>
| |
| <td>380.506 (7 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/9<br />
| |
| </td>
| |
| <td>380.700 (11, 13 and 15 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 85 -14 52 -68&gt;<br />
| |
| </td>
| |
| <td>380.714 (11 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8/7<br />
| |
| </td>
| |
| <td>380.735<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33\104<br />
| |
| </td>
| |
| <td>380.769<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>12/11<br />
| |
| </td>
| |
| <td>380.818<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/11<br />
| |
| </td>
| |
| <td>380.875<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20\63<br />
| |
| </td>
| |
| <td>380.952<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/6<br />
| |
| </td>
| |
| <td>380.982<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/8<br />
| |
| </td>
| |
| <td>381.085<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/11<br />
| |
| </td>
| |
| <td>381.211<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/15<br />
| |
| </td>
| |
| <td>381.378<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/10<br />
| |
| </td>
| |
| <td>381.666<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7\22<br />
| |
| </td>
| |
| <td>381.818<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9/7<br />
| |
| </td>
| |
| <td>382.458<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/11<br />
| |
| </td>
| |
| <td>384.173<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5/4<br />
| |
| </td>
| |
| <td>386.314<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Tuning Spectra-Spectrum of Telepathy Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:8 -->Spectrum of Telepathy Tunings by Eigenmonzos</h2>
| |
| <br />
| |
| Gencom: [2 5/4; 55/54 65/64 91/90 99/98]<br />
| |
| Gencom map: [&lt;1 0 2 -1 -1 4|, &lt;0 5 1 12 14 -1|]<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Eigenmonzo<br />
| |
| </th>
| |
| <th>Major Third<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>16/13<br />
| |
| </td>
| |
| <td>359.472<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/10<br />
| |
| </td>
| |
| <td>372.893<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/12<br />
| |
| </td>
| |
| <td>376.905<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/13<br />
| |
| </td>
| |
| <td>378.249<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18/13<br />
| |
| </td>
| |
| <td>378.489<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6/5<br />
| |
| </td>
| |
| <td>378.910<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6\19<br />
| |
| </td>
| |
| <td>378.947<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/13<br />
| |
| </td>
| |
| <td>379.100<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10/9<br />
| |
| </td>
| |
| <td>379.733<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27/20<br />
| |
| </td>
| |
| <td>379.968 (5 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19\60<br />
| |
| </td>
| |
| <td>380.000<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/14<br />
| |
| </td>
| |
| <td>380.093<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32\101<br />
| |
| </td>
| |
| <td>380.198<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/5<br />
| |
| </td>
| |
| <td>380.228<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 36 -23 32&gt;<br />
| |
| </td>
| |
| <td>380.384 (9 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td>380.391 (5, 7 and 9 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13\41<br />
| |
| </td>
| |
| <td>380.488<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 1 -7 15&gt;<br />
| |
| </td>
| |
| <td>380.506 (7 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 47 -34 43 57 -48&gt;<br />
| |
| </td>
| |
| <td>380.676 (13 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 46 -35 49 65 -55&gt;<br />
| |
| </td>
| |
| <td>380.691 (15 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/11<br />
| |
| </td>
| |
| <td>380.719 (13 and 15 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8/7<br />
| |
| </td>
| |
| <td>380.735<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33\104<br />
| |
| </td>
| |
| <td>380.769<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>20\63<br />
| |
| </td>
| |
| <td>380.952<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/6<br />
| |
| </td>
| |
| <td>380.982<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/15<br />
| |
| </td>
| |
| <td>381.378<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 19 -36 30 42&gt;<br />
| |
| </td>
| |
| <td>381.380 (11 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7\22<br />
| |
| </td>
| |
| <td>381.818<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/10<br />
| |
| </td>
| |
| <td>381.923 (11 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/8<br />
| |
| </td>
| |
| <td>382.237<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9/7<br />
| |
| </td>
| |
| <td>382.458<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/11<br />
| |
| </td>
| |
| <td>382.881<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12/11<br />
| |
| </td>
| |
| <td>383.263<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5/4<br />
| |
| </td>
| |
| <td>386.314<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/9<br />
| |
| </td>
| |
| <td>386.852<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/11<br />
| |
| </td>
| |
| <td>391.246<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Tuning Spectra-Spectrum of Witchcraft Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:10 -->Spectrum of Witchcraft Tunings by Eigenmonzos</h2>
| |
| <br />
| |
| Gencom: [2 5/4; 105/104 196/195 245/243 275/273]<br />
| |
| Gencom map: [&lt;1 0 2 -1 -7 -2|, &lt;0 5 1 12 33 18|]<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Eigenmonzo<br />
| |
| </th>
| |
| <th>Major Third<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>14/13<br />
| |
| </td>
| |
| <td>378.617<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6/5<br />
| |
| </td>
| |
| <td>378.910<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6\19<br />
| |
| </td>
| |
| <td>378.947<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/13<br />
| |
| </td>
| |
| <td>379.355<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18/13<br />
| |
| </td>
| |
| <td>379.577<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/10<br />
| |
| </td>
| |
| <td>379.660<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10/9<br />
| |
| </td>
| |
| <td>379.733<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27/20<br />
| |
| </td>
| |
| <td>379.968 (5 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/12<br />
| |
| </td>
| |
| <td>379.890<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19\60<br />
| |
| </td>
| |
| <td>380.000<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/13<br />
| |
| </td>
| |
| <td>380.029<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/14<br />
| |
| </td>
| |
| <td>380.093<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/11<br />
| |
| </td>
| |
| <td>380.113 (15 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/11<br />
| |
| </td>
| |
| <td>380.119 (13 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/10<br />
| |
| </td>
| |
| <td>380.156<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 -106 -111 11 179 59&gt;<br />
| |
| </td>
| |
| <td>380.193 (15 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32\101<br />
| |
| </td>
| |
| <td>380.198<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 -67 -72 5 152 47&gt;<br />
| |
| </td>
| |
| <td>380.218 (13 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/5<br />
| |
| </td>
| |
| <td>380.228<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 -38 -55 11 137&gt;<br />
| |
| </td>
| |
| <td>380.278 (11 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/9<br />
| |
| </td>
| |
| <td>380.322<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12/11<br />
| |
| </td>
| |
| <td>380.334<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/8<br />
| |
| </td>
| |
| <td>380.343 (11 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 36 -23 32&gt;<br />
| |
| </td>
| |
| <td>380.384 (9 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td>380.391 (5, 7 and 9 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13\41<br />
| |
| </td>
| |
| <td>380.488<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/11<br />
| |
| </td>
| |
| <td>380.719<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8/7<br />
| |
| </td>
| |
| <td>380.735<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33\104<br />
| |
| </td>
| |
| <td>380.769<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>20\63<br />
| |
| </td>
| |
| <td>380.952<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/6<br />
| |
| </td>
| |
| <td>380.982<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/15<br />
| |
| </td>
| |
| <td>381.378<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7\22<br />
| |
| </td>
| |
| <td>381.818<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9/7<br />
| |
| </td>
| |
| <td>382.458<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5/4<br />
| |
| </td>
| |
| <td>386.314<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Tuning Spectra-Spectrum of Muggles Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:12 -->Spectrum of Muggles Tunings by Eigenmonzos</h2>
| |
| <br />
| |
| Gencom: [2 5/4; 45/44 65/64 78/77 126/125]<br />
| |
| Gencom map: [&lt;1 0 2 5 0 4|, &lt;0 5 1 -7 11 -1|]<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Eigenmonzo<br />
| |
| </th>
| |
| <th>Major Third<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>11/9<br />
| |
| </td>
| |
| <td>347.408<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/13<br />
| |
| </td>
| |
| <td>359.472<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/11<br />
| |
| </td>
| |
| <td>372.610<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/10<br />
| |
| </td>
| |
| <td>372.893<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12/11<br />
| |
| </td>
| |
| <td>374.894<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8/7<br />
| |
| </td>
| |
| <td>375.882<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/11<br />
| |
| </td>
| |
| <td>375.899<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/10<br />
| |
| </td>
| |
| <td>376.500<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/11<br />
| |
| </td>
| |
| <td>376.805<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/12<br />
| |
| </td>
| |
| <td>376.905<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/5<br />
| |
| </td>
| |
| <td>377.186<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/8<br />
| |
| </td>
| |
| <td>377.393 (11, 13 and 15 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 113 -12 -68 58 -26&gt;<br />
| |
| </td>
| |
| <td>377.630 (13 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 -21 -5 27&gt;<br />
| |
| </td>
| |
| <td>377.640 (7 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 134 9 -81 63 -33&gt;<br />
| |
| </td>
| |
| <td>377.718 (15 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 85 -14 -62 46&gt;<br />
| |
| </td>
| |
| <td>377.758 (11 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/6<br />
| |
| </td>
| |
| <td>377.761 (7 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/13<br />
| |
| </td>
| |
| <td>378.249<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/14<br />
| |
| </td>
| |
| <td>378.419<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18/13<br />
| |
| </td>
| |
| <td>378.489<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9/7<br />
| |
| </td>
| |
| <td>378.534 (9 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>|0 93 -4 -44&gt;<br />
| |
| </td>
| |
| <td>378.554 (9 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/13<br />
| |
| </td>
| |
| <td>378.617<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6/5<br />
| |
| </td>
| |
| <td>378.910<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6\19<br />
| |
| </td>
| |
| <td>378.947<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10/9<br />
| |
| </td>
| |
| <td>379.733<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27/20<br />
| |
| </td>
| |
| <td>379.968 (5 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19\60<br />
| |
| </td>
| |
| <td>380.000<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32\101<br />
| |
| </td>
| |
| <td>380.198<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td>380.391 (5 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13\41<br />
| |
| </td>
| |
| <td>380.488<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33\104<br />
| |
| </td>
| |
| <td>380.769<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>20\63<br />
| |
| </td>
| |
| <td>380.952<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/15<br />
| |
| </td>
| |
| <td>381.378<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7\22<br />
| |
| </td>
| |
| <td>381.818<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5/4<br />
| |
| </td>
| |
| <td>386.314<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| </body></html></pre></div>
| |