Breed family
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Breed is a 7-limit microtemperament which tempers out 2401/2400. While it is so accurate it hardly matters what is used to temper it, or whether it is tempered at all, 2749et will certainly do the trick. ===Vital statistics=== Comma c = 2401/2400 7- and 9-limit minimax tuning: 3 and 5 just, 7 1/4c flat Eigenmonzos: 6/5 and 5/4 (or 4/3) Lattice basis: 49/40 length 0.7858 8/7 length 1.1241 Angle(49/40, 8/7) = 107.367 degrees Map to lattice: [<0 2 -1 0|, <0 0 -2 -1|] Generators: 2, 49/40, 10/7 EDOs: 441, 612, 2308, 2749 ==11-limit children== ===Jove, aka Wonder=== Jove, formerly known as wonder, tempers out 243/242 and 441/440. Wonder has been deprecated as a name due to conflict with another temperament also given that name. Jove converts breed into an 11-limit temperament via 441/440, which equates 49/40 with 11/9, and 243/242, which tells us 11/9 can serve as a neutral third. While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. 72, 130 and 171 are good edos for jove, and if that doesn't suit there's 476edo. 11-limit Commas: 243/242, 441/440 Minimax tuning [|1 0 0 0 0>, |1/5 0 0 0 2/5>, |13/5 0 2 -2 1/5>, |13/5 0 1 -1 1/5>, |0 0 0 0 1>] Eigenmonzos: 7/5,11/8 13-limit Commas: 243/242, 441/440, 364/363 13-limit minimax [|1 0 0 0 0 0>, |17/11 -12/11 2/11 0 0 4/11>, |34/11 -46/11 15/11 0 0 8/11>, |35/11 -26/11 8/11 0 0 5/11>, |37/11 -30/11 5/11 0 0 10/11>, |34/11 -46/11 4/11 0 0 19/11>] Eigenmonzos: 2, 10/9, 13/10 (or 13/9) 15-limit minimax [|1 0 0 0 0 0>, |2 -1/4 1/2 -3/4 0 1/4>, |7/2 -1/8 9/4 -19/8 0 1/8>, |7/2 -1/8 5/4 -11/8 0 1/8>, |9/2 -5/8 5/4 -15/8 0 5/8>, |11/2 -11/8 7/4 -25/8 0 11/8>] Eigenmonzos: 2, 15/13, 7/5 17-limit minimax [|1 0 0 0 0 0 0>, |7/3 -1/3 4/3 -5/3 0 0 1/3>, |11/3 -1/6 8/3 -17/6 0 0 1/6>, |11/3 -1/6 5/3 -11/6 0 0 1/6>, |16/3 -5/6 10/3 -25/6 0 0 5/6>, |22/3 -11/6 19/3 -49/6 0 0 11/6>, |6 -3/2 3 -9/2 0 0 3/2>] Eigenmonzos: 2, 17/15, 7/5 Map: [<1 1 1 2 2 1 3|, <0 2 1 1 5 11 9|, <0 0 2 1 0 -1 -3|] Generators: 2, 11/9, 10/7 Edos: 72, 130, 171, 243, 274, 346, 435, 476 ===Freya=== 11-limit Commas: 2401/2400, 3025/3024 11-limit minimax [|1 0 0 0 0>, |0 1 0 0 0>, |11/10 11/10 0 4/5 -4/5>, |9/5 4/5 0 2/5 -2/5>, |9/5 4/5 0 -3/5 3/5>] Eigenmonzos: 2, 14/11, 4/3 Map: [<1 1 3 3 2|, <0 2 3 2 1|, <0 0 -4 -2 3|] Generators: 2, 49/40, 55/42 Edos: 270, 342, 612 ===Baldur=== 11-limit Commas: 2401/2400, 9801/9800 11-limit minimax [|1 0 0 0 0>, |3/4 0 1/2 1/2 -1/2>, |0 0 1 0 0>, |23/16 0 5/8 1/8 -1/8>, |23/16 0 5/8 -7/8 7/8>] Eigenmonzos: 5/4, 14/11 Map: [<2 0 1 3 7|, <0 2 1 1 -2|, <0 0 2 1 3|] Generators: 99/70, 343/198, 10/7 Edos: 612, 742, 1012, 1084, 1696, 2308
Original HTML content:
<html><head><title>Breed family</title></head><body>Breed is a 7-limit microtemperament which tempers out 2401/2400. While it is so accurate it hardly matters what is used to temper it, or whether it is tempered at all, 2749et will certainly do the trick.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h3> --><h3 id="toc0"><a name="x--Vital statistics"></a><!-- ws:end:WikiTextHeadingRule:0 -->Vital statistics</h3> Comma c = 2401/2400<br /> 7- and 9-limit minimax tuning: 3 and 5 just, 7 1/4c flat<br /> Eigenmonzos: 6/5 and 5/4 (or 4/3)<br /> Lattice basis: 49/40 length 0.7858 8/7 length 1.1241<br /> Angle(49/40, 8/7) = 107.367 degrees<br /> Map to lattice: [<0 2 -1 0|, <0 0 -2 -1|]<br /> Generators: 2, 49/40, 10/7<br /> EDOs: 441, 612, 2308, 2749<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x-11-limit children"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit children</h2> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x-11-limit children-Jove, aka Wonder"></a><!-- ws:end:WikiTextHeadingRule:4 -->Jove, aka Wonder</h3> Jove, formerly known as wonder, tempers out 243/242 and 441/440. Wonder has been deprecated as a name due to conflict with another temperament also given that name. Jove converts breed into an 11-limit temperament via 441/440, which equates 49/40 with 11/9, and 243/242, which tells us 11/9 can serve as a neutral third. While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. 72, 130 and 171 are good edos for jove, and if that doesn't suit there's 476edo.<br /> <br /> 11-limit<br /> Commas: 243/242, 441/440<br /> <br /> Minimax tuning<br /> [|1 0 0 0 0>, |1/5 0 0 0 2/5>, <br /> |13/5 0 2 -2 1/5>, |13/5 0 1 -1 1/5>, <br /> |0 0 0 0 1>]<br /> Eigenmonzos: 7/5,11/8<br /> <br /> 13-limit<br /> Commas: 243/242, 441/440, 364/363<br /> <br /> 13-limit minimax<br /> [|1 0 0 0 0 0>, |17/11 -12/11 2/11 0 0 4/11>, |34/11 -46/11 15/11 0 0 8/11>, <br /> |35/11 -26/11 8/11 0 0 5/11>, <br /> |37/11 -30/11 5/11 0 0 10/11>, <br /> |34/11 -46/11 4/11 0 0 19/11>]<br /> Eigenmonzos: 2, 10/9, 13/10 (or 13/9)<br /> <br /> 15-limit minimax<br /> [|1 0 0 0 0 0>, |2 -1/4 1/2 -3/4 0 1/4>, <br /> |7/2 -1/8 9/4 -19/8 0 1/8>, <br /> |7/2 -1/8 5/4 -11/8 0 1/8>, <br /> |9/2 -5/8 5/4 -15/8 0 5/8>,<br /> |11/2 -11/8 7/4 -25/8 0 11/8>]<br /> Eigenmonzos: 2, 15/13, 7/5<br /> <br /> 17-limit minimax<br /> [|1 0 0 0 0 0 0>, |7/3 -1/3 4/3 -5/3 0 0 1/3>, |11/3 -1/6 8/3 -17/6 0 0 1/6>, <br /> |11/3 -1/6 5/3 -11/6 0 0 1/6>, <br /> |16/3 -5/6 10/3 -25/6 0 0 5/6>, <br /> |22/3 -11/6 19/3 -49/6 0 0 11/6>, <br /> |6 -3/2 3 -9/2 0 0 3/2>]<br /> Eigenmonzos: 2, 17/15, 7/5<br /> <br /> Map: [<1 1 1 2 2 1 3|, <0 2 1 1 5 11 9|, <0 0 2 1 0 -1 -3|]<br /> Generators: 2, 11/9, 10/7<br /> Edos: 72, 130, 171, 243, 274, 346, 435, 476<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="x-11-limit children-Freya"></a><!-- ws:end:WikiTextHeadingRule:6 -->Freya</h3> 11-limit<br /> Commas: 2401/2400, 3025/3024<br /> <br /> 11-limit minimax<br /> [|1 0 0 0 0>, |0 1 0 0 0>, <br /> |11/10 11/10 0 4/5 -4/5>, <br /> |9/5 4/5 0 2/5 -2/5>, |9/5 4/5 0 -3/5 3/5>]<br /> Eigenmonzos: 2, 14/11, 4/3<br /> <br /> Map: [<1 1 3 3 2|, <0 2 3 2 1|, <0 0 -4 -2 3|]<br /> Generators: 2, 49/40, 55/42<br /> Edos: 270, 342, 612<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><a name="x-11-limit children-Baldur"></a><!-- ws:end:WikiTextHeadingRule:8 -->Baldur</h3> 11-limit<br /> Commas: 2401/2400, 9801/9800<br /> <br /> 11-limit minimax<br /> [|1 0 0 0 0>, |3/4 0 1/2 1/2 -1/2>, <br /> |0 0 1 0 0>, |23/16 0 5/8 1/8 -1/8>, <br /> |23/16 0 5/8 -7/8 7/8>]<br /> Eigenmonzos: 5/4, 14/11<br /> <br /> Map: [<2 0 1 3 7|, <0 2 1 1 -2|, <0 0 2 1 3|]<br /> Generators: 99/70, 343/198, 10/7<br /> Edos: 612, 742, 1012, 1084, 1696, 2308</body></html>