τετρακτύς

Noun

 * 1) the sum of the first four numbers, i.e. 10 (= 1+2+3+4)
 * 2) The four terms (6:8:9:12) of the proportion corresponding to the chief musical intervals; also their sum +1 (= 36); the sum of the first 8 numbers. (6:12::1:2::diapason, 6:9::2:3::diapente, 6:8::3:4::diatessaron; 1:2, 2:3, 3:4 being the ratios of neighboring terms in the sum of the previous definition. 8:9::tonus as a bonus. A diatonic scale may be derived from this; semitonus can be derived to be 243:256 by fitting tonus as many times as possible into a diatessaron and finding out what ratio remains. Tonus times tonus times semitonus equals diatessaron: do–re–mi–fa (6:8). Fa to sol is tonus (8:9). Sol to do’ is another diatessaron: sol–la–si–do’ = tonus times tonus times semitonus = do–re–mi–fa transposed to sol (9:12). 384:432:486:512:576:648:729:786::do:re:mi:fa:sol:la:si:do’.)
 * 1) The four terms (6:8:9:12) of the proportion corresponding to the chief musical intervals; also their sum +1 (= 36); the sum of the first 8 numbers. (6:12::1:2::diapason, 6:9::2:3::diapente, 6:8::3:4::diatessaron; 1:2, 2:3, 3:4 being the ratios of neighboring terms in the sum of the previous definition. 8:9::tonus as a bonus. A diatonic scale may be derived from this; semitonus can be derived to be 243:256 by fitting tonus as many times as possible into a diatessaron and finding out what ratio remains. Tonus times tonus times semitonus equals diatessaron: do–re–mi–fa (6:8). Fa to sol is tonus (8:9). Sol to do’ is another diatessaron: sol–la–si–do’ = tonus times tonus times semitonus = do–re–mi–fa transposed to sol (9:12). 384:432:486:512:576:648:729:786::do:re:mi:fa:sol:la:si:do’.)
 * 1) The four terms (6:8:9:12) of the proportion corresponding to the chief musical intervals; also their sum +1 (= 36); the sum of the first 8 numbers. (6:12::1:2::diapason, 6:9::2:3::diapente, 6:8::3:4::diatessaron; 1:2, 2:3, 3:4 being the ratios of neighboring terms in the sum of the previous definition. 8:9::tonus as a bonus. A diatonic scale may be derived from this; semitonus can be derived to be 243:256 by fitting tonus as many times as possible into a diatessaron and finding out what ratio remains. Tonus times tonus times semitonus equals diatessaron: do–re–mi–fa (6:8). Fa to sol is tonus (8:9). Sol to do’ is another diatessaron: sol–la–si–do’ = tonus times tonus times semitonus = do–re–mi–fa transposed to sol (9:12). 384:432:486:512:576:648:729:786::do:re:mi:fa:sol:la:si:do’.)
 * 1) The four terms (6:8:9:12) of the proportion corresponding to the chief musical intervals; also their sum +1 (= 36); the sum of the first 8 numbers. (6:12::1:2::diapason, 6:9::2:3::diapente, 6:8::3:4::diatessaron; 1:2, 2:3, 3:4 being the ratios of neighboring terms in the sum of the previous definition. 8:9::tonus as a bonus. A diatonic scale may be derived from this; semitonus can be derived to be 243:256 by fitting tonus as many times as possible into a diatessaron and finding out what ratio remains. Tonus times tonus times semitonus equals diatessaron: do–re–mi–fa (6:8). Fa to sol is tonus (8:9). Sol to do’ is another diatessaron: sol–la–si–do’ = tonus times tonus times semitonus = do–re–mi–fa transposed to sol (9:12). 384:432:486:512:576:648:729:786::do:re:mi:fa:sol:la:si:do’.)
 * 1) The four terms (6:8:9:12) of the proportion corresponding to the chief musical intervals; also their sum +1 (= 36); the sum of the first 8 numbers. (6:12::1:2::diapason, 6:9::2:3::diapente, 6:8::3:4::diatessaron; 1:2, 2:3, 3:4 being the ratios of neighboring terms in the sum of the previous definition. 8:9::tonus as a bonus. A diatonic scale may be derived from this; semitonus can be derived to be 243:256 by fitting tonus as many times as possible into a diatessaron and finding out what ratio remains. Tonus times tonus times semitonus equals diatessaron: do–re–mi–fa (6:8). Fa to sol is tonus (8:9). Sol to do’ is another diatessaron: sol–la–si–do’ = tonus times tonus times semitonus = do–re–mi–fa transposed to sol (9:12). 384:432:486:512:576:648:729:786::do:re:mi:fa:sol:la:si:do’.)
 * 1) The four terms (6:8:9:12) of the proportion corresponding to the chief musical intervals; also their sum +1 (= 36); the sum of the first 8 numbers. (6:12::1:2::diapason, 6:9::2:3::diapente, 6:8::3:4::diatessaron; 1:2, 2:3, 3:4 being the ratios of neighboring terms in the sum of the previous definition. 8:9::tonus as a bonus. A diatonic scale may be derived from this; semitonus can be derived to be 243:256 by fitting tonus as many times as possible into a diatessaron and finding out what ratio remains. Tonus times tonus times semitonus equals diatessaron: do–re–mi–fa (6:8). Fa to sol is tonus (8:9). Sol to do’ is another diatessaron: sol–la–si–do’ = tonus times tonus times semitonus = do–re–mi–fa transposed to sol (9:12). 384:432:486:512:576:648:729:786::do:re:mi:fa:sol:la:si:do’.)