It was found during the measurements, that with changing the physical dimensions of the tuning slot, not only the objective parameters of the sound spectra changed, but the pipe sounds were also quite different from a subjective point of view. In particular, by increasing the length above the tuning slotLS the number of strong harmonics in the sound decreased, which resulted in sounds with different characters. In order to justify the perceived quality of pipe sounds with different number of strong harmonics a subjective experiment was prepared.
Three times six sound recordings of pipe #1 were selected for a subjective comparison from the measurements presented in Section 6.3.3. As discussed there, three series of measurements were carried out with fixed slot heights (60 mm,45 mm, and30 mm) and twenty different lengths above the tuning slot. The width of the slot was unchanged (7.5 mm). Seven sound samples sound
samples
were selected for listening from the twenty recordings of each series: The sound of the pipe without an additional paper tube was selected as the reference sample, and six samples were selected with different number (7, 6, 5, 4, 3, and 2) of strong harmonics. The samples were prepared from the sounds recorded by the microphone near (at a distance of50±5 mm) the mouth of the pipe in all cases. Six-six pairs (i.e. six times the reference sample plus six selected samples) of samples were prepared from the three measurement series. The first sample was always the reference
6.6. SUMMARY 81 sample of the given series. The attack was removed by applying a one-second-long fade-in at the beginning of the sound samples.
Since the sound of single organ pipes is unfamiliar for common people, the listener should be familiar with the sound of organ pipes with tuning slots and should be able to distinguish different partials in the pipe sound. Therefore, two experienced voicers were asked to take part in the evaluation. Both voicers have listened to the prepared sample pairs in a random order and their opinions concerning the differences of the timbre and loudness between the reference sample and the second sample were noted and evaluated.6The results of the comparison carried out by the well-known voicers Konrad Mühleisen and Johannes Kirschmann are summarized as follows.
Both voicers recognized in all cases that the timbres of the reference sound and the following sound were different. They could also hear that the sound becomes more and more “round”
and “hollow” (i.e. more dominant fundamental tone in the recorded pipe sound) with decreas-ing number of strong harmonic components. The characteristics of the reference sound and the sample with seven strong partials were found a bit too sharp and harsh, while samples with six
and five partials optimal
harmonic content were assessed as nice pipe sounds with rich overtone content. Below five strong
partials the samples sounded more and more “round” and “hollow”, and the loudness gradually decreased. No significant difference was found between the three sample series with different slot heights. The dependency of the timbre on the additional length above the slot was the same.
However, sound samples with30 mmslot height sounded a bit “forced”; i.e., the octave was en-hanced in the sound. These pipes were close to overblowing. The most balanced sounds were found in samples of pipes with45 mmslot height.
The voicers were quite surprised when they learned that the best sounds were produced by pipes with2–3DPadditional length above the tuning slot since the traditional length above the slot is smaller or equal to the pipe diameter. The sounds of such pipes were assessed as too sharp in the subjective comparison. This result also indicates that in order to achieve a better perceived sound quality the traditional scaling rules should be revised in the case of labial organ pipes with tuning slots.
6.6 Summary
Detailed investigations of two labial organ pipes with adjustable tuning slots, which distinguish the sound of these pipes from the sound of common labial pipes (withtuning roll,tuning ringor clear cut endopening) have revealed properties that had not been known before. The presented
results of the experiments may allow the development of improved scaling rules improved scaling methods for
pipes equipped with tuning slots.
By choosing the effective length above the tuning slot appropriately the harmonic partials above a desired frequency limit can be suppressed and hence the timbre of the pipe can be de-signed. The applicability of this approach was confirmed by the subjective comparison presented in Section 6.5. Thus, the desired sound characteristics of the pipe can be achieved by the proper selection of the length above the slot and of the slot height. These two parameters have to be de-termined by the scaling procedure and kept constant during the voicing and tuning adjustments.
The pitch of the pipe can then be tuned by adjusting the width of the slot.
Contrary to traditional scaling rules, the length of the pipe section above the tuning slot has to be related to the effective length of the pipe and not to its diameter. The results of the experiments and listenings have shown that long slots are ineffective (i.e. when the slot is large, changing its size by rolling the material in and out does not provide enough control over the pitch), while pipes with short slots show a tendency of overblowing. Best results have been obtained by slot heights comparable to the diameter of the pipe.
6The voicers’ opinions were noted and evaluated by Judit Angster and András Miklós, co-authors of the paper [J3].
These findings need for an
improved acoustic model
are also supported by the simple one-dimensional model of the resonator;
however, this model is not explicit enough for applying it in the development of a new, improved scaling method for organ pipes with tuning slots. Therefore, an improved version of the acoustic model presented in Section 6.3.2 is needed, which allows a precise calculation of all dimensions of the pipes in the scaling process. This acoustic model also provides the possibility of a direct quantitative comparison of measured and simulated characteristics of tuning slot pipes. The improved acoustic model of labial organ pipes with tuning slots is presented in the next chapter.
Chapter 7
Modeling the tuning slots of labial organ pipes
A suitable acoustic model for the characterization of tuning slots of labial organ pipes is presented in this chapter. Since the tuning slot arrangement is similar—but not identical—to that of tone-holes in woodwind instruments, the adaptability of the well-established tonehole model for the specific problem is examined. A numerical model utilizing the finite element (FE) and perfectly matched layer (PML) techniques is set up for the simulation of tuning slots with design parame-ters varying over a wide range. Analytical tonehole models and the proposed numerical tuning slot model are both combined with analytical one-dimensional waveguide models to predict the acoustic behavior of tuning slot pipes. Comparison to measurements carried out on experimen-tal pipes proves that the hybrid waveguide/finite element model can predict the most important acoustical properties of the tuning slot pipe with good accuracy. The FEM also overcomes the limitations of traditional tonehole models relying on the equivalent T-circuit approximation. By means of the FE model the eigenfrequency-structure and its impact on the character of the sound can be foretold in the design phase, by which a more efficient scaling of tuning slot pipes can be achieved. This chapter is a revised and extended version of the paper [J4].
7.1 Introduction
In the previous chapter experimental examination of tuning slots of labial organ pipes was
re-ported. It was shown results of
experi-ments that the design parameters of the slot have a great influence on the sound
characteristics and the perceived sound quality of the pipe. It was also proven that currently applied design traditions do not provide sufficient control over the timbre. The conclusions of the previous chapter were that the acoustic effects of changing the slot parameters can be qual-itatively understood, although, to be able to predict the influence of the slot geometry on the acoustic parameters of the pipe precisely, a reliable acoustic model of a pipe resonator with tun-ing slot is required. Therefore, this chapter focuses on the acoustic model.
Since the musically relevant frequency range of the pipe sound is under the cut-on frequency of transversal acoustic modes inside the resonator, it is useful and common to represent the res-onator by means of a one-dimensional acoustic model. To the best knowledge of the author no established acoustic model exists for the specific problem of treatment of tuning slots. Neverthe-less, the rectangular tuning slot is a symmetric discontinuity in the cylindrical pipe body, which
is similar to the arrangement of toneholes of woodwind instruments. The latter topic tonehole research has already
been investigated by a number of researchers and various models have been published based on analytical [24, 83] and numerical [53, 91, 92] calculations and experimental results [45, 82,
83
Mouth Tonehole Open end
Mouth part
Tone-hole model Waveguide #1
Wave-guide
#2
Radiation impedance
Figure 7.1.Schematic and one-dimensional model a simplified woodwind instrument with one tonehole
108]. These models can be used for the approximate characterization of the tuning slot, however, due to geometrical dissimilarities their applicability is limited and therefore should be examined.
This topic is addressed in Section 7.3.
The main objective
objective of this chapter is to find a suitable acoustic model for the simulation of the tuning slot. Therefore, woodwind tonehole models and a numerical approach based on the finite element and perfectly matched layer methods are examined and compared to measurement results. The aim of the simulations is to achieve a reliable prediction of the behavior of the tuning slot, by which the timbre of the pipe can be controlled in the design phase.