Background

1. Introduction

1.1. Background

Since 1960, everything has been evolving so drastically that the world envisioned by Dr.

Feynman in his famous speech [1] is now our reality. From vacuum tube to integrated circuits, things are breaking through the limitation of scale and blending into our lives in different forms and shapes. Musical instruments, as being important inventions in human culture, are also impacted by these major changes. For instance, synthesizers and electronic musical instruments are becoming more and more popular for their expansibility and playability in sounds; Digital forms of conventional musical instruments are being created as apps¹ in many mobile devicesfor their convenience and mobility; Various innovate musical instrument are being crafted, allowing more creativity and possibility of sound to be implemented. All of these not only symbolize the great advance of modern technology, but also the power of digital signal processing (DSP).

As the development of digital signal processing continues to thrive, many sound synthesis algorithms have been proposed. With the help of the increased computational power, more accurate and complex synthesis models can now be achieved with high efficiency and low cost, and more virtual instruments can be thus constructed systematically[2][3][4]. A well-developed sound synthesis model for a conventional musical instrument will not only serve as a digital copy of it, but also a starting point for creating imaginary sounds based on

1 Referring to software designed specifically for mobile operating systems such as iOS or Android.

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its original acoustical properties. That is to say, the gap between retrospective and futuristic sounds of a musical instrument could be bridged through the understanding of acoustics and development of sound synthesis models.

Therefore, it is meaningful to study the nature of traditional musical instruments and reinterpret them as computational models for better control over sounds. In the following sections, more lights will be shed on the Chinese instrument called the Chinese Chime-bells (or the Chinese two tone bells) and model-based sound synthesis.

1.1.1. Chinese Chime-Bells

The Chinese Chime-bell is one of the ancient percussion instrument from China, and it is also one of the most important inventions in Chinese history [5]. Generally, the Chinese Chime-bell is oval in shape, which is different from Western bells. The most famous set of the Chime-bells of all time is probably the one discovered in the tomb of Marquis Yi of Zeng in 1978 [6]. Those bells had soon been identified as cultural legacies that could date back to 433 B.C.

As shown in Fig. 1.1, the whole set is consisted of 65 bells of different pitches and sizes, and the primary material of the bells is bronze. There are three racks of bells, each rack has three levels, and the bells are placed on each level in order. Having a total weight of over 4400 kg, the complete bell set is a collection of bells with significant disparity. For example, the smallest bell is about 20 cm in height and 2.4 kg in weight, and the largest bell is about 150 cm in height and 203 kg in weight. Such great differences also reflected on their sounds.

The complete set of Chime-bells has a scale of over 5.5 octaves, which is comparable to

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modern instruments. Most of the bells are engraved with delicate symbols and have inscription on the surface, demonstrating the polished crafting skills of the ancient civilization.

In short, the Chinese Chime-bell is an incredible creation even from the perspective of modern technology.

The most important acoustical feature of the Chime-bells is its capability of producing two pitches from one single bell. As shown in Fig. 1.2, when the bell is struck at the Sui point and the Gu point, two different tones will be emitted. Normally, the interval between these two tones is major or minor third. According to previous studies [7], this feature was formed unintentionally in the early stage of ancient Chou dynasty because marks of tuning were still missing. In the late stage of ancient Chou dynasty, tuning marks on the inner walls of the bells could be easily found, and the sounds were all well tuned.

Other acoustical properties, such as having a wide range of scale and short decay time, also contributed to the uniqueness of this instrument. However, its physical size and high cost of manufacturing makes it a rare instrument and limits the possibilities for people to play it or even enjoy the sounds from it.

Figure 1.1. A replicated set of Marquis Yi of Zeng’s Chime-bells in Zhongshan hall, Taipei.

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Figure 1.2. Two strike points on the bell for emitting two pitches.

1.1.2. Model-based Sound Synthesis

Digital sound synthesis has been under its way for more than fifty years [8], and a myriad of synthesis techniques have been presented. Early synthetic techniques such as additive synthesis [9], wavetable synthesis, AM and FM synthesis [10] are simple and efficient methods for synthesizing sounds. However, to mimic the sounds of certain musical instruments and control the sounds according to their physical descriptions, more complex models based on acoustics of the musical instruments are needed. Such models, which can be referred as physical models, are the core of virtual instruments [3][11][12].

There are two general goals of physical modeling synthesis, one is to fully understand the sound-producing mechanism of traditional instruments in order to generate realistic sounds, and the other is to create imaginary sounds based on the acoustics of the instrument.

Many approaches, such as solving wave equation of vibrating objects [13], mass-spring paradigm [14], modal synthesis [15], or digital waveguides (DWG) synthesis [3], [16], have been proposed to create intricate models of musical instrument. However, most of the approaches share one common drawback of being computational demanding. The degree of authenticity of a sound is normally highly proportional to the computation load, and this could

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potentially increase the difficulty of real-time implementation. Fortunately, this issue has lessened due to the rapid growth of computational power lately.

Recently, more and more commercial electronic musical instruments such as Yamaha VL1 and Korg Wavedrum are integrating physical modeling synthesis into their systems for qualitative sounds and high interactivity, showing its potential in realizing virtual instruments.