Spectral analysis of silk string qin sound

Spectral analysis or sound spectrum analysis are precise terms for the process of breaking down a complex sound wave into its individual frequency components (the full spectrum of the sound).³ Scientific measurements of these components of the sound of individual notes played on a silk string guqin, including their pitches, relative strength and decay speed, can show clearly the distinctive tonal qualities ("timbre", "color") of that note as well as the sonic capabilities of that particular musical instrument.⁴

Musical colors can be defined most scientifically in terms of the musical overtones of the pitches being played. A musical pitch is usually defined in terms of the frequency of that pitch. Thus the modern concert A is usually defined as 440 hertz, i.e., 440 vibrations per second. However, the pure pitch 440 hz is a generally perceived as unattractive. What gives beauty to the sound are the overtones that can be produced when playing this pitch on a musical instrument. These overtones are essentially multiples of the fundamental (e.g., 440, 880, 1320, 1760...), but they also include "inharmonic partials" and perhaps "noise". When the ear hears what the brain interprets as a pitch of 440 hz, what it actually is hearing is a whole series of overtones that it instinctively combines and interprets as 440 hz. These overtones combined may give a stronger sound than the fundamental, but they then usually fade away much more quickly.

As yet, to my knowledge the only sound spectrum testing of how this applies to the qin has been the one supervised in 1998 by Andrew Horner and Lydia Ayers of the computer science department at the Hong Kong University of Science and Technology.⁵ Andrew and Lydia had previously measured the overtones produced by several other stringed instruments. By analyzing these overtones they were then trying to duplicate them so as to be able to synthesize notes played by various stringed instruments such as guitar, piano, guzheng and so forth.

After discussing the issue with me, they had one of their students carry out a project trying to measure all the overtones from single notes played on a silk string guqin. They recorded the sound using what I understand was some sort of spectrum analyzer⁶ that could measure the component parts of a resonating sound wave, in particular breaking down individual musical notes (sound waves) into their various components (differing overtones) and showing how the separate overtones were fading over time in comparison with the fundamental pitch. For this I played open, stopped and harmonic tones, but only single notes at a time and with no slides or other ornaments.

The most noticeable result from measuring the notes and their overtones was their richness. The fourth harmonic was particularly strong, but over time the overtones decayed much more slowly than they did on instruments using metal or nylon strings. On other instruments (none with silk strings) the overtones would decay so fast that within about one second the fundamental was stronger than the overtones combined. However, on the qin with silk strings the overtones would remain stronger than the fundamental for five seconds or more. As they faded, different overtones would also decay at different speeds, and the way these separate overtones periodically came together tended to make the overall sound have a complexity that actually seemed somewhat unstable, sometimes going a bit higher, sometimes a bit lower.

Unfortunately, although our tests confirmed the richness of the overtones produced by silk strings, since we did not make comparable measurements on a similar instrument having nylon/metal strings, any conclusions must be considered preliminary. (See more under instability of pitch.)

It also must be emphasized that this test did not go through the rigorous protocals necessary to make from it a scientific report. But it did suggest that this would be a very much worthwhile project if carried out properly.

Footnotes (Numbers refer to entries in Zhongwen Dacidian)

1. Spectral analysis: analyzing the full spectrum of notes played on a qin
Follows on research originally done in Hong Kong in 1998.

Spectral analysis or sound spectrum analysis of musical notes is distinctive from acoustic analysis or sound analysis. Acoustic analysis usually refers to studying the sound waves as a whole (including sound level, waveform and vibration), while both spectrum analysis and acoustic analysis are types of sound analysis.

對絲弦古琴所發音符的全頻譜進行分析，以顯示其獨特的音響特質。
「頻譜分析」或「聲譜分析」是嚴格的術語，指將一個複雜的聲波分解為其各個獨立頻率成分（即聲音的完整頻譜）的過程。對絲弦古琴單個音符進行科學測量，包括其基音與泛音的音高、相對強度及衰減速度，可以清楚地展現該音符獨特的音色特質，以及該件樂器本身的音響表現力。
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2. Sample sound spectrum" (currently just a mockup, not from an actual test)
An actual chart for qin string sound, which might be called "A spectrogram-derived graph showing frequency and amplitude decay over time", is not yet ready. Note that the highest harmonic frequency shown here is 910 Hz with the highest inharmonic 1570. Sum of harmonics is higher, but what would it take to get up to a measurable 20,000 Hz, which is what good professional mics claim as their top range?

Because the actual notes have not yet been properly analyzed, the above is just a mockup giving an idea of what it might look like. In this mockup, each overtone was drawn with the same starting amplitude (1.0). The black line represents their sum. It begins at time zero, but is hidden under the other lines until the curves separate; in a real measurement, the overtones would have different starting strengths, so the sum line would be distinct from the beginning.
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3. Full spectrum
It may be interesting to try to compare timbre, also known as sound "color", with visual color. With the latter the spectrum of a "primary color" consists only of that color, but most colors are a mixture of a primary color or colors with secondary colors (a mixture of two primary colors) and tertiary colors (a mixture of primary and secondary colors). As for sound, there are fundamental frequencies (e.g., a pure 440 Hz sound wave), but most individual sounds are a mixture of the fundamental tone with its various overtones (partials). In other words, this may have a measurable frequency but it is in fact a combination of sounds that overall may be perceived as having that frequency but in fact consists of a variety of frequencies that may be changing at differing rates - constituent parts that when taken overall give the note its tonal colar. To put it another way, a color can be primary color (e.g. red), but more likely it will be some form of a blend; this by itself does not change but the color can appear different according to the light in which the color is seen. As for sound, at any particular moment a musical note could in theory be a pure fundamental frequency, but this is rare and hardly considered "musical": almost invariably, even if it is coming from a single source, the note will be a the mixture of the frequencies of its component sound waves, constantly changing, if only in a small way, as the component frequencies decay, perhaps at different rates. In this sense there actually are no "primary tones", only categories of "recognizable" tones, such as "violin tone", "speaking voice tone" and so forth.
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4. Tonal color
For example, the sound of a good violin is notable for the richness of its tones throughout the sound spectrum while that of a flute may be more focused on the upper spectrum.
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5. First test, with Andrew Horner and Lydia Ayers at HKUST, 1998
According to Andrew (HKUST page), he was working with "the WIN32 version of SNDAN (Sound Analysis toolkit), specifically, monan (monophonic analysis) on individual sustained tones; harmonic and overtone were used similarly" (see further).
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6. Sound spectrum analysis
Sound spectrum analysis can be done today using, for example, an Apple computer with Logic Pro to record the sound, and then analysis software such as Sonic Visualiser. Sonic Visualiser, when used together with an appropriate Vamp plugin (a type of plugin designed for this framework), can produce graphs showing frequency and amplitude over time. These tools allow you to track the fundamental frequency and automatically generate annotation layers that mark the fundamental and its overtones. The frequencies and their amplitudes can then be plotted visually on graphs.

An appropriate Vamp plugin would be the QM Vamp plugin Harmonic Peaks.

Explanatory notes:
Sonic Visualiser is a free, open source program built as a research tool by the Centre for Digital Music, Queen Mary University of London (QM). By comparison a program such as iZotope RZ 11 will analyze the sound and produce visual images but not graphs. However, Sonic Visualizer was explicitly designed to work with Vamp plugins — which are little analysis modules (for harmonic tracking, onset detection, chroma features, etc.). Annotation layers are transparent, stackable displays over the waveform or spectrogram.
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Return to the Guqin ToC or to miscellanea.