Acoustics of baroque, classical and modern flutes - impedance
spectra, sound spectra, sounds and fingerings
Joe Wolfe, John Smith, John Tann and Neville H. Fletcher
We report studies on flutes that are variants on two basic geometries (Figure 1). The body of the modern or Boehm flute is nearly cylindrical, but the head joint is tapered towards the embouchure end. The flutes of the seventeenth, eighteenth and early nineteenth centuries (the baroque and classical flutes) are approximately conical over much of their length, with a cylindrical head-joint. The constraints of manufacturing the varying tapers means that all flutes are usually made in sections. The head joint includes the embouchure hole and has no keys. In the modern flute, the body is a long joint that has most of the holes and/or keys.
In the classical flute studied here, the 'body' comprised two sections, one with the holes operated by the left hand, and the other with all or most of the holes operated by the right.
Various different foot joints are used on different flutes. On the modern flute, the C foot has three tone holes (all operated by the right little finger) and permits a lowest note of C4. The longer B foot has an extra tone hole and allows B3 to be played. This change produces substantial acoustical differences, especially at the extremes of the range. The classical flute is and was much less standardised. It may have a short foot stopping at D4, or a longer foot that may descend to C4. The geometry of the foot may continue the cone of the body, or may flare out slightly at the end.
The modern flutes studied here are production-line models, which are widely available at relatively modest price. This choice was made to facilitate comparisons by other researchers. There are no production line classical flutes. Further, the original instruments of that period, usually made of wood, have changed their geometry over time. The instrument we studied was made by a local maker. It is pitched at A4 = 440 Hz, as are the modern flutes, which facilitates comparison with them. It has three interchangeable feet, examples of the three mentioned above.
Figure 1 shows a schematic diagram of the modern and classical flutes, a simplified acoustical schematic of each, and fingering diagrams that would be immediately familiar to a flutist. The example chosen is the fingering used to play either F4 or F5 (different jet lengths and speeds are used to play the two notes). The fingering diagram shows a player how to finger these notes: three fingers and the thumb of the left hand depress their home keys, as do the first and fourth fingers of the right hand. This can be readily related to the sketch of the flute, indicating which keys are touched on the instrument, and also to a simplified acoustic schematic of the instrument. For the note F4, the first six holes most remote from the embouchure hole are open, because F4 is six semitones above the lowest note (B3) on this instrument. Eleven holes are closed: this is possible because one finger key may close more than one hole, and because some holes are opened by keys rather than closed.
All tone holes on the instrument are approximately the same diameter, as shown in the acoustic schematic, except for the three holes closest to the embouchure hole. The two closest are the smallest holes, and are used as register holes for some of the highest notes, or for trills (rapid alternations of two notes) which would otherwise cross the 'break' between the first register (fundamental) and second register (second harmonic). The third small hole is used as a register hole for several notes (D5, D6, D#5, A6) and also as a tone hole for the transition between C5 and C#5, or between C6 and C#6. This double use requires that it be further up the tube than the expected place for such a tone hole, and this in turn requires it to be small so as to have a large end effect. Most of the holes are approximately in line, those off line are shown as ellipses. In one case there are two keys at the same distance from the embouchure hole: these are alternates: they are very rarely opened together (one fingering for C#7 is an exception), and exist mainly as an historical accident. The trill keys, the home key for the left fourth finger and the home key for the right fourth finger are closed when not touched.
In the modern flute, the body is cylindrical and the head has a slight conical taper. An adjustable cork in the head makes the acoustic length rather shorter than the length of the instrument, as shown. In contrast, the classical and baroque flutes (shown below) have bodies with conical tapers.
The fingering diagrams (again for F4/5) show that three fingers of the left hand cover the holes assigned to them. In the classical flute, the first two fingers of the right hand close their holes. The third finger has two jobs: it can either cover a hole or can depress the 'F' key. Here it does the latter, as indicated by the black shaded key on the fingering diagram. On the classical flute studied, this is the only key, and it opens a hole when depressed, so the ellipse at the end of the 'F' key is shown white for this fingering. On the baroque flute, F4/5 involves a cross fingering: i.e. one or more tone holes are closed downstream from the first open hole, here the hole below the 2nd finger of the right hand.
Figure 1. Fingering and acoustic schematic diagram for the modern and classical flutes. From the top are shown a fingering diagram for the modern flute, a sketch of the modern flute and an acoustic schematic of that instrument. Next is a fingering diagram and schematic for the classical flute. A similar legend is used for all the fingerings and notes in the data base. The example chosen here is the fingering for the notes F4 and F5.
The radical change in the flute in the nineteenth century was much larger and more abrupt than that of the other woodwind instruments. This was due to the flutist and flute maker Theobold Boehm, who aimed to make the flute louder, its timbre more homogeneous from note to note, and its tuning more in accord with that of other instruments .
In the classical flute, successive opening of the finger holes produces a diatonic scale (D major). Some of the remaining notes are produced by opening an extra tone hole, which is normally closed by a key. Others are produced by 'cross fingering', i.e. closing one or more holes downstream of the first open hole. This gives different timbre to adjacent notes.
Boehm's first innovation was the introduction of larger holes on the conical-bore flute, which made the instrument louder, and key rings and a coupling mechanism to avoid cross-fingering, which made the timbre more homogeneous. This system allowed the notes of the chromatic scale over most of the range to be played with all of the holes downstream of a particular point open. In search of a still bigger sound, he redesigned the bore: a cylindrical body and a tapered head profile, which he (inaccurately) called 'parabolic'. The cylindrical bore of the modern Boehm flute is larger (19 mm diameter) than that of the classical flute everywhere except near the embouchure hole, where it tapers to about 17 mm. This larger bore reduces energy losses near the walls. More importantly, the tone holes are considerably larger (about 13 mm diameter) and almost uniform in size, and so radiate more strongly. They also produce a brighter sound, as discussed later. Boehm developed a new system of coupled keys to cover these tone holes, now much too large for the unaided fingers. Thus most of the ordinary notes of the instrument require no cross fingering and this, together with the large tone holes, makes the downstream bore more nearly approximate a truncated pipe. This produces a more homogeneous timbre.
The changes to the flute since Boehm have been relatively minor. Boehm's revolutionary changes to the flute influenced the design of the saxophone, and were also imitated (to a lesser extent) on the clarinet. (The oboe and bassoon remain much more like their ancestors, having small tone holes and, particularly on the bassoon, less rational key systems.)