Acoustical Effects of a Membrane Hole

The effect of the membrane hole on the resonance frequency was already explained on the basis of the perturbation theory in the previous subsection. However, the tension, density, and quality of the membrane material as well as the size and location of the membrane hole will affect the instrument sounds. Therefore, an analytic model incorporating these parameters is desired. Samejima [48] and Ide [49,50] proposed a vibro-acoustical model of theflute with a membrane hole. Their numerical method is based on the coupling between the membrane vibration and the surrounding soundfield. Since its description is too complicated to the readers of this book, a brief explanation of the membrane tension effect on a modeled tube is given below.

A tube model is 250 mm long and 40 mm in diameter. Both ends are open. An open hole (18 mm in diameter) is perforated at the position of 140 mm from the top (left) open end. A piece of bamboo paper, whose aerial density is assumed to be 0.00374 (kg/m2) from the measurement, is glued over this hole. This model tube was used in acoustical measurements [49,50]. However, it was needed to setup the flat membrane surface for the calculation based on the finite element method, and then the model tube was approximated by a hexagonal column. Numerical calcu- lation on this column with a membrane hole was carried out by changing the membrane tension from 15 to 50 (N/m) stepwise. It should be noted that this applied tension is very low compared with the timpani head to which the tension of 4000–5000 (N/m) is usually applied.

The calculated result is illustrated in Fig.33, where the dashed line gives the result when the membrane is rigid or when the membrane hole is completely closed [48, 49]. The ordinate, relative SPL (sound pressure level), corresponds to the frequency response function (giving the resonance characteristics) defined by the ratio of the sound pressure at a receiving point (located at the center of the bottom end) to that at the sound-source point (located at the upper side of the top end). It is normalized by the value at the response peak.

Although the model tube with a rigid membrane hole indicates almost harmonic structure as shown by the dashed line (the peak frequencies are 628, 1268, 1892, 2546, 3180, 3808, and 4496 Hz in sequence), the model tube with a vibrating membrane causes appreciably inharmonic structure as shown by the solid line in

each frame of Fig.33. However, this inharmonicity seems to be diminished as the membrane tension T is increased. Frame (d) for T = 50 N/m shows the harmonic second mode.

The fundamental frequency f1in each frame of Fig.33approaches to that when

the membrane hole is completely closed. The f1for T = 15 and 25 N/m is 564 and

592 Hz, respectively; f1for T =∞ is 628 Hz. This result qualitatively corresponds

to the sound example shown in Fig.32, where f1for thefinite T is 912.5 Hz and f1

for the infinite T is 925.9 Hz. Probably it may be assumed that the tension of 15– 25 N/m is a little too weak in comparison with the actual case.

It is interesting that the resonance peaks on the dashed line split into two due to the membrane vibration. It is very appreciable in Fig.33a, where the second, fourth, and sixth resonance peaks on the dashed line split into two. This peak splitting might be interpreted as follows: If the membrane tension is quite weak, the membrane hole can be like an open hole. As a result, the resonance peaks of the upper tube (140 mm long) above the membrane hole and the lower tube (110 mm long) below the membrane hole might be produced. The second peak frequency on the dashed line is 1268 Hz; the corresponding splitting two peak frequencies in Fig.33a are 1188 and 1440 Hz, respectively. If the end correction is assumed to be 10 mm, thefirst-mode resonance frequency of the upper and lower tubes is calculated as 1147 and 1433 Hz, respectively. On the other hand, another interpretation might be allowed: Fig. 33 Calculated effects of the membrane tension T on the frequency response function of a simplified model consisting of a hexagonal column with open ends and a membrane hole [48,49]. a T= 15 N/m; b T = 20 N/m; c T = 25 N/m; d T = 50 N/m. The dashed line in each frame indicates the result when the membrane hole is completely closed

One of two splitting peaks might be derived from the modal frequency of the circular membrane that is considerably lowered by the surrounding air loading [49]. For example, the small third peak (1516 Hz) on the solid line in Fig.33c is considered as an original (0, 1) mode (4477 Hz) of the membrane vibration in Ref. [49]. More detailed calculation and experiment are necessary to judge which hypothesis is valid. Also, the variation of the third peak in Fig.33 should be paid attention. The frequency of the third peak appreciably higher than that on the dashed line and ascents (from 1968 to 2012 Hz) as the membrane tension increases from 15 to 25 N/m. However, that frequency for T = 50 N/m is significantly lower than that on the dashed line as shown in Fig.33d. The reasonable cause of this inversion is unknown. The interaction between the air-column resonance and the membrane vibration, particularly in actual shinobue with tone holes, is an intricate and intriguing topic in musical acoustics, which is hopefully solved in the near future by incorporating the blowing mechanism.

5

Conclusions

Distinctive characteristics of Japanese (or Asian) flutes (fue) and their music are recognized in (1) wind noise as an essential part of the instrument tone, (2) timbre-oriented music rather than octave-oriented or harmonic-oriented music, and (3) high-frequency emphasis suitable for the performing environment (partic- ularly, for the outdoors). If there is no wind noise, the shakuhachi and nohkan cannot create their own sounds. The nohkan has been pursuing very solid and hard timbre and has definitely upset the octave expected when overblown by inserting a kind of obstacle, the throat (called nodo) between the embouchure hole and the top tone hole. The classical (komuso) shakuhachi traditionally prefers personal deeper introspection to musical performance itself. The nohkan used to be played in out- doors and produce very high and penetrating sounds. In matsuri (Japanese folk festival) procession, the shinobue with a membrane hole perforated between the embouchure hole and the top tone hole can create the decisive effect of the high-frequency emphasis due to the membrane vibration.

The classical (komuso) shakuhachi has been played in religious environments and appreciated natural bamboo structure. Its original construction had no ground- pastefinish as seen in the modern shakuhachi but had very thin urushi coating over the inner bore surface. The diaphragms were not completely removed and small ridges were retained on the inside bamboo nodes. These remaining diaphragms might affect the intonation and timbre, although their effects are not satisfactorily elucidated yet. The essential difference between classical and modern shakuhachis is in the difference of the inner bore shape with or without the remaining dia- phragms. The calculation of the input admittance is very effective to make the difference clear.

The wind noise is dominant between about 1.5–3 kHz when the classical sha- kuhachi is blown by muraiki (a rough and strong blow) during the starting transient.

The definite contrast between noisy, rough sound by muraiki and clear, almost noiseless sound by smooth blowing is the essence in shakuhachi sounds.

Also, crossfingerings in the shakuhachi playing, which yield subtle timbre taste, are investigated through the measurement and calculation of the internal standing-wave patterns and the calculation of the input admittance. Crossfingerings in the shakuhachi often causes pitch sharpening (called intonation anomaly in this chapter) instead of conventional pitch flattening. This is mainly due to only five tone holes in the shakuhachi. The intonation anomaly is generated if the resonance in the upper bore above the top open tone hole or in the lower bore below the top open tone hole leads the resonance of the whole bore. In other words, the complete coupling between the upper and lower bores through an open top open tone hole is derived when both bores give very close resonance frequencies in the fundamental or higher harmonic modes. The intonation anomaly strongly depends on the position of the top open tone hole. This intonation anomaly has beenfirst quanti- tatively described through the shakuhachi acoustics.

A special tube device (about 80 mm long), the throat (nodo), is intentionally inserted between the embouchure hole and the top tone hole in the nohkan. As a result, the nohkan bore becomes narrowest near the middle of the throat, and then the octave relation between thefirst and second registers is upset. This throat shape in the nohkan is a great contrast to the cylindrical headjoint in the piccolo that yields the correct octave, although the both have a reverse (convergent) conical bore below the throat and the headjoint, respectively. Acoustical effects of the throat are investigated on the bore with or without the throat and on the bores with different throat shapes through the calculations of the input admittance and the internal pressure distribution for several fingerings. The throat makes the notes of the second octave increasingly flat to the lower octave as the scale is ascent. This octave shrink is generally carried out by the major increase in thefirst-mode res- onance frequency and the minor decrease in the second-mode resonance frequency. The calculated result shows good agreement with the conventional measured result if the fact that the nohkan has no standard length and no consistent pitch is con- sidered. Also, the admittance suggests that the throat does not operate to play easier the hishigi tone, the powerful piecing altissimo tone. Moreover, a comparison between the nohkan and the piccolo on a crossfingering with two extremely distant open tone holes reveals that the upper tone hole operates as an octave hole.

The spectra of the first-register tones in the nohkan usually show indefinite harmonic structure. The lower harmonics are seemingly masked by wind noise from about 1 to 2.5 kHz (a little lower than that in the shakuhachi). However, higher harmonics can be usually recognized in the second-register tones of the low-pitched fingerings. On the other hand, the second-register and third-register tones (above 2 kHz) of the high-pitched crossfingerings produce almost sinusoidal waveforms. These tonal differences in the registers andfingerings are very characteristic in the nohkan. Through this tonal tendency and construction method based on the urushi coating, the nohkan has been always pursued very solid and hard timbre for the high-pitched tones.

The shinobue has been played by common people in various occasions, par- ticularly in local festivals, matsuri. The pitch, intonation, and tone itself of the shinobue largely depend on the locality. The shinobue played in the north Kyushu has been kept the original one traditionally played in China and Korea. It has a membrane hole just halfway between the embouchure hole and the top tone hole. The membrane vibration, which is affected by the hole position, membrane mate- rial, membrane tension, and so on, produces characteristic high-frequency emphasis, which should be very effective in matsuri procession. This phe- nomenon is common to the stringed instruments with the sawari (gentle touch) mechanism against the string vibration. Therefore, the high-frequency emphasis seems to be the tonal taste common to musical instruments in East Asia.

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Author Biography

Shigeru YoshikawaAfter graduating from Physics Department of Nagoya University in 1974, Shigeru Yoshikawa started acoustical research on organ pipes. He worked for Technical R&D Institute of Defense Ministry from 1980 and investigated underwater organ pipes while personally studying musical acoustics. He was a professor of musical instrument acoustics at Graduate School of Design, Kyushu University from 1998 and was retired in 2015.

Chris Waltham, Kimi Coaldrake, Evert Koster and Yang Lan

Abstract The qin (guqin, chi’in) is a seven-string zither with long roots that run deep into Chinese history. The instrument occupies a central place in Chinese musical culture, one that may be compared to that of the violin in Western music; both instruments are deemed to have attained some level of perfection. The qin’s history is intertwined with philosophy and folklore and its construction is replete with symbolism. While much has been written on the evolution, organology and playing practice of the qin, little has been published about its acoustics. This chapter explores the qin’s background and summarizes the few acoustical studies that have been published to date. Many questions remain, and prospects for future research are discussed.

1

Introduction

The qin (in pinyin, otherwise chin or ch’in in the Wade-Giles romanization) is an instrument that occupies an ancient and central place in the musical and philo- sophical culture of China [1]. It is a plucked seven-string zither and is often referred to as the guqin, with the prefix “gu” indicating its great antiquity. Like an old Italian violin, a fine qin is considered an objet d’art as well as a musical instrument.

C. Waltham (&)
E. Koster
Y. Lan

Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada e-mail: [email protected] E. Koster e-mail: [email protected] Y. Lan e-mail: [email protected] K. Coaldrake

Elder Conservatorium of Music, University of Adelaide, Adelaide, SA 5005, Australia

e-mail: [email protected] © Springer International Publishing AG 2017

A. Schneider (ed.), Studies in Musical Acoustics and Psychoacoustics, Current Research in Systematic Musicology 4,

DOI 10.1007/978-3-319-47292-8_2

The four arts that every Imperial Chinese scholar-gentleman was expected to master were qin, qi, shu and hua (i.e. music, the game of go, calligraphy and painting), of which the qin camefirst. Failing mastery, scholar-gentlemen needed at least to own a qin, even if it had no strings [2].

The very name of the qin is linked via homonyms to concepts of rectitude and restraint. Thus the Book of Rites, Liji, which records social norms of the Zhou Dynasty (c.1046–256 BCE) states: “Lute1means restraining. With this instrument licentiousness and falsehood are restrained, and the human heart is rectified” (p. 41 in Ref. [3]). The names of each part of the instrument are replete with symbolism and lore.

In the course of this chapter we review two recent publications on qin acoustics. One is a published thesis in Chinese by Yang [4,5] who did extensive work on finite-element modelling of the qin soundbox (without any fluid coupling) and also the mechanical properties of the strings. The second is a study of radiation and significant radiating modes conducted by three of the present authors [6].