 | Hermann Ludwig F. von Helmholtz - 1875 - 900 páginas
...form just Thirds by just Filths, because it is impossible by multiplying any one of the numbers i! or £ or 2, each by itself, or one by the other, any...produce the same result as by multiplying any other one of these numbers by itself any number of times. Temptramcnt, however, consists essentially in replacing... | |
 | South Kensington Museum - 1876 - 458 páginas
...thirds by just fifths, because it is impossible by multiplying any one of the numbers £, or J, or $, each by itself, or one by the other any number of...produce the same result as by multiplying any other one of these numbers by itself any number of times." Thus, having this initial difficulty, how has... | |
 | 1876 - 434 páginas
...just 5ths, because it is impossible by multiplying any one of the numbers f , or | by two, or either by itself or one by the other any number of times,...produce the same result as by multiplying any other of those number? by itself any number of times." The ratios if you recollect, of the different notes of... | |
 | William Henry Stone - 1879 - 272 páginas
...by Mr. Ellis. " It is impossible," he says, in an appendix to his translation of Hehnholtz's work, " to form Octaves by just Fifths or just Thirds, or...produce the same result as by multiplying any other one of these numbers by itself any number of times." The physical fact may be otherwise stated by saying... | |
 | John Broadhouse - 1892 - 460 páginas
...gives the following list of vibration numbers, the upper line, as stated in the MUSICAL ACOUSTICS. paragraph just quoted, containing the " tempered '...circle. It is strange that Dr. Stone, while he says in c C| D n E F F} G G| A A» B 264 280296+ 3'4— 333— 352+ 373+ 395+ 419+ 444— 47°+ 498 + 264 297... | |
 | 1892 - 612 páginas
...scale, for it ia impossible, as Mr. Ellis pomta out, by multiplying any one of the numbers j, or j, or 2 each by itself, or one by the other, any number of times, te produce the same result aa by multiplying any other one of these numbers by ittelf any number of... | |
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It is impossible," he says, in an appendix to his translation of Helmholtz's work, " to form Octaves by just Fifths or just Thirds, or both combined, or to form just Thirds by just Fifths, because it is impossible by multiplying any one of the numbers... 