Minkowski reduced bases for Fokker groups of certain vals
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For some purposes, eg Fokker blocks, it is convenient to have a good basis for the wedgies of rank two temperaments supported by a given val. Below are listed some Minkowski reduced bases relative to [[generator complexity]] as a metric, with TE complexity used to break any ties. =5-limit= <12 19 28|: <<1 4 4||, <<3 0 -7|| <15 24 35|: <<3 0 -7||, <<3 5 1|| <17 27 39|: <<2 1 -3||, <<1 9 12|| <17 27 40|: <<1 4 4||, <<4 -1 -11|| <19 30 44|: <<1 4 4||, <<5 1 -10|| <22 35 51|: <<3 5 1||, <<2 -4 -11|| <31 49 72|: <<1 4 4||, <<8 1 -17|| <34 54 79|: <<2 -4 -11||, <<6 5 -6|| <41 65 95|: <<5 1 -10||, <<4 9 5|| <46 73 107|: <<2 -4 -11||, <<7 9 -2|| <53 84 123|: <<6 5 -6||, <<1 -8 -15|| =7-limit= ==Temperaments== ammonite7: <<9 15 19 3 5 2|| augene7: <<3 0 -6 -7 -18 -14|| august7: <<3 0 6 -7 1 14|| beatles7: <<2 -9 -4 -19 -12 16|| blacksmith7: <<0 5 0 8 0 -14|| dichotic7: <<2 1 -4 -3 -12 -12|| dominant7: <<1 4 -2 4 -6 -16|| flattone7: <<1 4 -9 4 -17 -32|| garibaldi7: <<1 -8 -14 -15 -25 -10|| godzilla7: <<2 8 1 8 -4 -20|| immunity7: <<2 13 1 16 -4 -34|| inflated7: <<3 0 9 -7 6 21|| injera7: <<2 8 8 8 7 -4|| keemun7: <<6 5 3 -6 -12 -7|| lemba7: <<6 -2 -2 -17 -20 1|| magic7: <<5 1 12 -10 5 25|| meantone7: <<1 4 10 4 13 12|| mothra7: <<3 12 -1 12 -10 -36|| nautilus7: <<6 10 3 2 -12 -21|| negri7: <<4 -3 2 -14 -8 13|| orwell7: <<7 -3 8 -21 -7 27|| pajara7: <<2 -4 -4 -11 -12 2|| porcupine7: <<3 5 -6 1 -18 -28|| progress7: <<3 -5 -6 -15 -18 0|| progression7: <<5 3 7 -7 -3 8|| schism7: <<1 -8 -2 -15 -6 18|| sensi7: <<7 9 13 -2 1 5|| sidi7: <<4 2 9 -6 3 15|| superpyth7: <<1 9 -2 12 -6 -30|| wollemia7: <<4 9 19 5 19 19|| ==Bases== <12 19 28 34|: august7, dominant7, pajara7 <15 24 35 42|: blacksmith7, inflated7, keemun7 <17 27 39 48|: dichotic7, sidi7, schism7 <17 27 40 48|: dominant7, progression7, progress7 <19 30 44 53: godzilla7, meantone7, keemun7 <22 35 51 62|: pajara7, magic7, porcupine7 <26 41 60 73|: injera7, lemba7, flattone7 <27 43 63 76|: augene7, superpyth7, sensi7 <29 46 67 81|: negri7, nautilus7, garibaldi7 <31 49 72 87|: meantone7, mothra7, orwell7 <34 54 79 95|: keemun7, immunity7, wollemia7 <37 59 86 104|: porcupine7, beatles7, ammonite7
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<html><head><title>Minkowski reduced bases for Fokker groups of certain vals</title></head><body>For some purposes, eg Fokker blocks, it is convenient to have a good basis for the wedgies of rank two temperaments supported by a given val. Below are listed some Minkowski reduced bases relative to <a class="wiki_link" href="/generator%20complexity">generator complexity</a> as a metric, with TE complexity used to break any ties.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x5-limit"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit</h1> <br /> <12 19 28|: <<1 4 4||, <<3 0 -7||<br /> <15 24 35|: <<3 0 -7||, <<3 5 1||<br /> <17 27 39|: <<2 1 -3||, <<1 9 12||<br /> <17 27 40|: <<1 4 4||, <<4 -1 -11||<br /> <19 30 44|: <<1 4 4||, <<5 1 -10||<br /> <22 35 51|: <<3 5 1||, <<2 -4 -11||<br /> <31 49 72|: <<1 4 4||, <<8 1 -17||<br /> <34 54 79|: <<2 -4 -11||, <<6 5 -6||<br /> <41 65 95|: <<5 1 -10||, <<4 9 5||<br /> <46 73 107|: <<2 -4 -11||, <<7 9 -2||<br /> <53 84 123|: <<6 5 -6||, <<1 -8 -15||<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="x7-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->7-limit</h1> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x7-limit-Temperaments"></a><!-- ws:end:WikiTextHeadingRule:4 -->Temperaments</h2> <br /> ammonite7: <<9 15 19 3 5 2||<br /> augene7: <<3 0 -6 -7 -18 -14||<br /> august7: <<3 0 6 -7 1 14||<br /> beatles7: <<2 -9 -4 -19 -12 16||<br /> blacksmith7: <<0 5 0 8 0 -14||<br /> dichotic7: <<2 1 -4 -3 -12 -12||<br /> dominant7: <<1 4 -2 4 -6 -16||<br /> flattone7: <<1 4 -9 4 -17 -32||<br /> garibaldi7: <<1 -8 -14 -15 -25 -10||<br /> godzilla7: <<2 8 1 8 -4 -20||<br /> immunity7: <<2 13 1 16 -4 -34||<br /> inflated7: <<3 0 9 -7 6 21||<br /> injera7: <<2 8 8 8 7 -4||<br /> keemun7: <<6 5 3 -6 -12 -7||<br /> lemba7: <<6 -2 -2 -17 -20 1||<br /> magic7: <<5 1 12 -10 5 25||<br /> meantone7: <<1 4 10 4 13 12||<br /> mothra7: <<3 12 -1 12 -10 -36||<br /> nautilus7: <<6 10 3 2 -12 -21||<br /> negri7: <<4 -3 2 -14 -8 13||<br /> orwell7: <<7 -3 8 -21 -7 27||<br /> pajara7: <<2 -4 -4 -11 -12 2||<br /> porcupine7: <<3 5 -6 1 -18 -28||<br /> progress7: <<3 -5 -6 -15 -18 0||<br /> progression7: <<5 3 7 -7 -3 8||<br /> schism7: <<1 -8 -2 -15 -6 18||<br /> sensi7: <<7 9 13 -2 1 5||<br /> sidi7: <<4 2 9 -6 3 15||<br /> superpyth7: <<1 9 -2 12 -6 -30||<br /> wollemia7: <<4 9 19 5 19 19||<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x7-limit-Bases"></a><!-- ws:end:WikiTextHeadingRule:6 -->Bases</h2> <br /> <12 19 28 34|: august7, dominant7, pajara7<br /> <15 24 35 42|: blacksmith7, inflated7, keemun7<br /> <17 27 39 48|: dichotic7, sidi7, schism7<br /> <17 27 40 48|: dominant7, progression7, progress7<br /> <19 30 44 53: godzilla7, meantone7, keemun7<br /> <22 35 51 62|: pajara7, magic7, porcupine7<br /> <26 41 60 73|: injera7, lemba7, flattone7<br /> <27 43 63 76|: augene7, superpyth7, sensi7<br /> <29 46 67 81|: negri7, nautilus7, garibaldi7<br /> <31 49 72 87|: meantone7, mothra7, orwell7<br /> <34 54 79 95|: keemun7, immunity7, wollemia7<br /> <37 59 86 104|: porcupine7, beatles7, ammonite7</body></html>