ARITHMETICAL PROGRESSION
\ˌaɹɪθmˈɛtɪkə͡l pɹəɡɹˈɛʃən], \ˌaɹɪθmˈɛtɪkəl pɹəɡɹˈɛʃən], \ˌa_ɹ_ɪ_θ_m_ˈɛ_t_ɪ_k_əl p_ɹ_ə_ɡ_ɹ_ˈɛ_ʃ_ə_n]\
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A series of numbers are in Arithmetical progression when each is greater (or less) than the one before it by a constant difference ; as 7, 10, 13, 16, etc. ; in Geometrical P. when each is obtained from the one before it by multiplying it by a constant number (or fraction) ; as 5, 15, 45, 135, etc. ; in Harmonical P. when any three consecutive numbers are such that the first has to the third the same ratio as the excess of the first above the second has to that of the second above the third ; as 6/5, I, 6/7, 3/4, etc. When strings, in other respects alike, have their lengths in harmonic P. , the frequencies of their vibrationson which the pitches of their tones dependare in arithmetical P.
By Henry Percy Smith
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