41. Then, if we add all these convergent series, we'd get the harmonic series , a divergent one. 42. However, if we add all these fractions up, we will get a part of the harmonic series , which diverges. 43. Accomplished alphornists often command a range of nearly three octaves, consisting of the 2nd through the 16th notes of the harmonic series . 44. The "'escala nordestina "'( ) are a body of musical scales commonly used in the harmonic series . 45. The output of this stage is a set of virtual pitches that correspond approximately to the fundamentals of approximately harmonic series of pitches. 46. In terms of what one hears, each octave in the harmonic series is divided into increasingly " smaller " and more numerous intervals. 47. Of course, the above " equation " is not necessary because the harmonic series is known ( by other means ) to diverge. 48. He also proved that the harmonic series does not converge, and provided a proof that Wallis'product for \ pi is correct. 49. From B 1 down lies the " pedal range ", i . e ., the fundamentals of the instrument's harmonic series . 50. The addition of valves made it possible to play low in the harmonic series of the instrument and still have a complete selection of notes.
