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To convert inches to millimeters, multiply inches by 25.40 and to convert millimeters to inches, multiply millimeters by 0.039370. However, because many flute dimensions are much smaller than resonator dimensions, we will use millimeter measurements throughout this chapter. A similar advantage also applies to flute construction. Recall that in Chapter 7, Section 12, we discussed the great convenience of centimeter measurements for cutting resonator lengths. Knowledge of longitudinal pressure waves and end correction terminology is essential for an understanding of flute acoustics. In preparation for Chapter 8, the reader should read, study, and absorb Chapter 7. Finally, L A replaces L S when, in predicting the frequencies of an existing flute, we cannot determine L S, which represents an exact acoustic half-wavelength in this context, we must calculate L A, which represents an approximate acoustic half-wavelength. Furthermore, the List of Flute Symbols below gives seven symbols that do not appear in Nederveen’s book: effective length L B(h) replaces λ H effective length L B(e) replaces λ E correction Δ l E replaces L B(e) in the context of flute length calculations corrections Δ l H and Δ l T, and length l T, represent simplifications. Since most of these symbols appear only in this chapter, they are not included in the List of Symbols at the beginning of this book.
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#Armstrong flute 104 serial number 4 6243 full
Because a full description of flute acoustics requires many different variables, this discussion begins with a list of symbols originally defined by Nederveen. Numerous tables of woodwind instrument dimensions are included at the end of the book. In his book entitled Acoustical Aspects of Woodwind Instruments, Nederveen carefully defines all the mathematical variables needed for a thorough investigation into woodwind acoustics. In writing this chapter, I am indebted to Cornelis J.
#Armstrong flute 104 serial number 4 6243 how to
Finally, Part III gives some suggestions on how to make very inexpensive yet highly accurate simple flutes. Since Part II is unintelligible without a thorough understanding of Part I, the reader should study this chapter from beginning to end. Part I investigates equations for the placement of tone holes, and Part II, mathematical procedures required to analyze existing flutes. Because these two variables exist beyond the realm of mathematical predictability, they depend exclusively on the skill of the performer.ĭue to the overall complexity of flutes, this chapter is divided into three parts. The intonation of a flute is also governed by the strength of the airstream, and by the amount the lips cover the embouchure hole. The mathematics of flute tubes, embouchure holes, and tone holes does not necessarily produce an accurate sounding instrument. From a mathematical perspective, these two approaches are distinctly different and require separate discussions.Īs all experienced flute players know, the intonation of a transverse flute - with either a very simple or a very complex embouchure hole - depends not only on the precision of instrument construction, but also on the performer. On the other hand, we may realize a given tuning by making a flute according to another sequence of equations. This method provides convenient solutions when a flute is extremely fragile and cannot be played, or is simply not available for playing. We may predict the tuning of an existing instrument by first measuring various flute bore, embouchure hole, and tone hole dimensions, and then substituting these data into a sequence of equations. It is possible to approach the subject of flute tunings from two different perspectives. In a work entitled The Greek Aulos, Kathleen Schlesinger (1862–1953) attempted to reconstruct Greek music theory by analyzing the remains of ancient reed flutes. Wind instruments are unique, however, because they alone embody the physical dimensions of scales and tunings. Part I: Equations for the Placement of Tone Holes on Concert Flutes and Simple Flutesįlutes, harps, and drums are the oldest musical instruments created by man. ON THE ART AND SCIENCE OF ACOUSTIC INSTRUMENTS