ji.lua

-- some just intonation tables

local JI = {}

-----------------------------------------
--- 12-tone scales

-- small variation of ptolemaic 5-limit with closer minor 7th.
-- taking cue from jeff snyder and calling this "normal" since it is most commonly used.
-- also known as "Duodene" by Alexander Ellis (19th c.)
function JI.normal() 
   return { 
      {1, 1}, {16, 15}, {9, 8}, {6, 5}, {5, 4}, {4, 3}, {45, 32}, {3, 2}, {8, 5}, {5, 3}, {15, 9}, {15, 8}
   }
end


-- ptolemaic 12-tone (5-limit) - very similar except for kinda weird m7
function JI.ptolemy() 
   return { 
      {1, 1}, {16, 15}, {9, 8}, {6, 5}, {5, 4}, {4, 3}, {45, 32}, {3, 2}, {8, 5}, {5, 3}, {9, 5}, {15, 8}
   }
end

-- ben johnston's overtone scale
-- identical to jeff snyder's "otonal" scale
function JI.overtone() 
   return {
      {1, 1}, {17, 16}, {9, 8}, {19, 16}, {5, 4}, {21, 16}, {11, 8}, {3, 2}, {13, 8}, {27, 16}, {7, 4}, {15, 8}
   }
end

-- subharmonic mirror of the overtone scale
-- jeff calls this "utonal" after partch
function JI.undertone()
   return { 
      {1, 1}, {16, 15}, {8, 7}, {32, 27}, {16, 13}, {4, 3}, {16, 11}, {32, 21}, {8, 5}, {32, 19}, {16, 9}, {32, 17},
   }
end

-- lamonte young's 'well-tuned piano' (very eccentric)
function JI.lamonte() 
   return {
      {1, 1}, {567, 512}, {9, 8}, {147, 128}, {21, 16}, {1323, 1024}, {189, 128}, {3, 2}, {49, 32}, {7, 4}, {441, 256}, {63, 32}
   }
end

----------------------------------------------
-- higher-tone scales ,  gamuts

-- gioseffo zarlino's 16-tone (5-limit)
function JI.zarlino() 
   return {
      {1, 1}, {25, 24}, {10, 9}, {9, 8}, {32, 27}, {6, 5}, {5, 4}, {4, 3}, {25, 18}, {45, 32}, {3, 2}, {25, 16}, {5, 3}, {16, 9}, {9, 5}, {15, 8}
   }
end


-- harry partch 43-tone ({11-limit}, plus some)
function JI.partch() 
   return {
      {1, 1}, 
      {81, 80}, 
      {33, 32}, 
      {21, 20}, 
      {16, 15}, 
      {12, 11}, 
      {11, 10}, 
      {10, 9}, 
      {9, 8}, 
      {8, 7}, 
      {7, 6}, 
      {32, 27}, 
      {6, 5}, 
      {11, 9}, 
      {5, 4}, 
      {14, 11}, 
      {9, 7}, 
      {21, 16}, 
      {4, 3}, 
      {27, 20}, 
      {11, 8}, 
      {7, 5}, 
      {10, 7}, 
      {16, 11}, 
      {40, 27}, 
      {3, 2}, 
      {32, 21}, 
      {14, 9}, 
      {11, 7}, 
      {8, 5}, 
      {18, 11}, 
      {5, 3}, 
      {27, 16}, 
      {12, 7}, 
      {7, 4}, 
      {16, 9}, 
      {9, 5}, 
      {20, 11}, 
      {11, 6}, 
      {15, 8}, 
      {40, 21}, 
      {64, 33}, 
      {160, 81}
   }
end

-- finally, jeff snyder's full 168-tone gamut
-- see his disseration for reference:
-- http://scatter.server295.com/full-dissertation.pdf

function JI.gamut()
   return {
      {1, 1 },
      {256, 255},
      {96, 95},
      {81, 80},
      {65, 64},
      {64, 63},
      {45, 44},
      {40, 39},
      {33, 32},
      {25, 24},
      {21, 20},
      {20, 19},
      {256, 243},
      {135, 128},
      {19, 18},
      {18, 17},
      {17, 16},
      {16, 15},
      {15, 14},
      {13, 12},
      {12, 11},
      {35, 32},
      {128, 117},
      {11, 10},
      {10, 9},
      {285, 256},
      {64, 57},
      {9, 8},
      {96, 85},
      {17, 15},
      {256, 225},
      {585, 512},
      {8, 7},
      {55, 48},
      {15, 13},
      {64, 55},
      {7, 6},
      {75, 64},
      {20, 17},
      {45, 38},
      {32, 27},
      {1215, 1024},
      {19, 16},
      {153, 128},
      {6, 5},
      {40, 33},
      {39, 32},
      {128, 105},
      {11, 9},
      {315, 256},
      {16, 13},
      {5, 4},
      {64, 51},
      {24, 19},
      {512, 405},
      {81, 64},
      {19, 15},
      {80, 63},
      {51, 40},
      {32, 25},
      {9, 7},
      {165, 128},
      {128, 99},
      {13, 10},
      {21, 16},
      {256, 195},
      {675, 512},
      {45, 34},
      {85, 64},
      {4, 3},
      {171, 128},
      {128, 95},
      {27, 20},
      {65, 48},
      {256, 189},
      {15, 11},
      {48, 35},
      {11, 8},
      {18, 13},
      {25, 18},
      {7, 5},
      {80, 57},
      {45, 32},
      {24, 17},
      {17, 12},
      {64, 45},
      {57, 40},
      {10, 7},
      {36, 25},
      {13, 9},
      {16, 11},
      {35, 24},
      {22, 15},
      {189, 128},
      {96, 65},
      {40, 27},
      {95, 64},
      {765, 512},
      {256, 171},
      {3, 2},
      {128, 85},
      {195, 128},
      {32, 21},
      {20, 13},
      {99, 64},
      {256, 165},
      {14, 9},
      {25, 16},
      {80, 51},
      {63, 40},
      {30, 19},
      {128, 81},
      {405, 256},
      {19, 12},
      {51, 32},
      {8, 5},
      {45, 28},
      {13, 8},
      {512, 315},
      {18, 11},
      {105, 64},
      {64, 39},
      {33, 20},
      {5, 3},
      {855, 512},
      {256, 153},
      {32, 19},
      {27, 16},
      {17, 10},
      {128, 75},
      {12, 7},
      {55, 32},
      {45, 26},
      {26, 15},
      {96, 55},
      {7, 4},
      {225, 128},
      {30, 17},
      {85, 48},
      {16, 9},
      {57, 32},
      {512, 285},
      {9, 5},
      {20, 11},
      {117, 64},
      {64, 35},
      {11, 6},
      {945, 512},
      {24, 13},
      {28, 15},
      {15, 8},
      {32, 17},
      {17, 9},
      {36, 19},
      {256, 135},
      {243, 128},
      {19, 10},
      {40, 21},
      {48, 25},
      {495, 256},
      {64, 33},
      {39, 20},
      {63, 32},
      {128, 65},
      {160, 81},
      {2025, 1024},
      {95, 48},
      {255, 128}
   }
end

return JI