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Message: 11427 Date: Sat, 17 Jul 2004 07:13:20 Subject: Re: names and definitions: meantone From: monz thanks, Gene ... this is great! it looks to me like this tells the whole story ... but others out there will know better than i. can you make some like this for all of the other named temperaments? i'm in no hurry, but folks who are confused about the names might appreciate it. -monz --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote: > --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote: > > > family name: meantone > > period: 2:1 ratio > > generator: a flat fifth or sharp fourth > > wedge product: eh? > > 5-limit: 81/80 > mapping: [<1 2 4|, <0 -1 -4|] > poptimal generator: 34/81 > MOS: 5, 7, 12, 19, 31, 50 > > 7-limit: > > name: meantone, standard septimal meantone, 12&19 > wedgie: <1 4 10 4 13 12| > mapping: [<1 2 4 7|, <0 -1 -4 -10|] (fourth generaor) > 7&9 limit copoptimal generator: 5^(1/4) fifth (1/4 comma meantone) > 7 limit poptimal: 86/205 > 9 limit poptimal: 47/112 > TM basis: {81/80, 126/125} > MOS: 5, 7, 12, 19, 31, 50 > > name: dominant, dominant sevenths, 5&12 > wedgie: <1 4 -2 4 -6 -16| > mapping: [<1 2 4 2|, <0 -1 -4 2|] > 7&9 limit copoptimal generator: 29/70 > TM basis: {36/35, 64/63} > MOS: 5, 7, 12, 17, 29 > > name: flattone, 19&26 > wedgie: <1 4 -9 4 -17 -32| > mapping: [<1 2 4 -1|, <0 -1 -4 9|] > 7 limit poptimal: 46/109 > 9 limit poptimal: 27/64 > TM basis: {81/80, 525/512} > MOS: 5, 7, 12, 19, 26, 45 > > 11 limit > > name: meantone, meanpop, 31&19 > wedgie: <1 4 10 -13 4 13 -24 12 -44 -71| > mapping: [<1 2 4 7 -2|, <0 -1 -4 -10 13|] > poptimal generator: 47/112 > TM basis: {81/80, 126/125, 385/384} > MOS: 5, 7, 12, 19, 31, 50, 81 > > name: huygens, fokker, 31&12 > wedgie: <1 4 10 18 4 13 25 12 28 16| > mapping: [<1 2 4 7 11|, <0 -1 -4 -10 -18|] > poptimal generator: 13/31 > TM basis: {81/80, 126/125, 99/98} > MOS: 5, 7, 12, 19, 31, 43 > > name: meanertone > wedgie: <1 4 3 -1 4 2 -5 -4 -16 -13| > mapping: [<1 2 4 4 3|, <0 -1 -4 -3 1|] > poptimal generator: 13/31 > TM basis: {27/25, 21/20, 33/32} > MOS: 5, 7, 12, 19, 31, 43
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