Chinese Musicology:1/3 Method

Pentatonic scale v.

12-tone scale

1/3 Method• Perfect 5th at higher pitch

Cut 1/3: forward arrow x 3/2• Perfect 4th at lower pitch

Patch 1/3: backward arrow x 3/4

F1 G1 A1 B1C D E F G A B

F1 G1 A1 B1C D E F G A B

F1 CG1

A1B1

C#

DE

F#

G#

A#D#

F1 G1 A1 B1C D E F G A B 1 1.06787

=(3/2)3

(3/4)41.125

=(3/2)(3/4)

1.201355=

(3/2)4(3/4)5

1.265625=

(3/2)2(3/4)2

1.333333=

(3/4)-11.423828

=(3/2)3

(3/4)31.5

=(3/2)

1.601807=

(3/2)4(3/4)4

1.6875=

(3/2)2(3/4)

1.8020225=

(3/2)5(3/4)5

1.8984375=

(3/2)3(3/4)2

=(3/2)-1

=(3/2)2

(3/4)

Pipa– the lute

6 xiangs

24 pings

Total30 frets

TuningADEa

Pipa History

• Pipa – meaning plucking back and forth• Appeared in Chinese written texts of the

second century BC• North-South Dynasty (420-589 AD), pipa with

a crooked neck was introduced from Middle Asia.

• The two styles were combined and evolved into the present day pipa.

Pipa– the lute

Finger-Plucking Techniques:彈 : forward挑 : backward摭 : inward分 : outward滾 : long inward輪 : long outward掃 : inward swash拂 : outward swash推 : push

The bold strings rattled like splatters of sudden rain, The fine strings hummed like lovers' whispers. Chattering and pattering, pattering and chattering, As pearls, large and small, on a jade plate fall.

Pipa

Erhu – the spiked fiddle

Erhu HistoryErhu dates back at least a thousand years. Different names appear at different times and places. It is called 胡弓 in Japan, Dan Nhi in Vietnam. At its early age in China, it was 嵇琴 . Mongolians have a similar instrument called morin-huur. A more descriptive term is spiked fiddle. Its timbre is closer to human voice than other string instruments. Its key part is a snake skin-covered sound box. A gauge is used to replace the finger board and nut. The bow is captured between two strings. These quaint features make the playing hard to perfect and yet it is these features that give charm in the music of erhu.

Erhu: Comparing with Violin

• Longer strings• Same finger position for two strings• No fingerboard: more flexibility• No peg box or nut• Sound box: drum-like• Bow captured between two strings

Erhu Ergonomics: Comparing with Violin

• Easier on fingering: up-down motionsame stop for both stringseasier for fiddling

• Harder on bowing:capturedhorizontal

Erhu

•The article “Why is the violin so hard to play?” applies

to erhu too.http://plus.maths.org/issue31/features/woodhouse/index.html

• Since there is no fingerboard, finger pressure is a critical part of the erhu technique. The instrument is thus capable of tremendous tonal flexibility and expressiveness.

Why is the violin so hard to play? by J Woodhouse and PM Galluzzo

When you pluck a note on a guitar string, there isn't very much that can go wrong. You may not play the right note at the right time, of course, but a single note will always come out at the expected pitch, and sounding reasonably musical. When a beginner tries to play a violin, things are much more difficult. When a bow is drawn across a string, the result might be a musical note at the desired pitch, but on the other hand it might be an undesirable whistle, screech or graunch. This difference stems from a fundamental distinction between the physics of plucked and bowed strings. Linear versus nonlinear: plucked versus bowedA plucked string, like that on a guitar, can be described by linear systems theory. The essential feature of a linear system is that if you can find two different solutions to the governing equations, then the sum of the two is also a solution. In the context of vibration, this idea has a direct physical application. A vibrating object like a stretched string has certain resonance frequencies, each associated with a particular pattern of vibration called a vibration mode. The corresponding resonance frequencies are the "fundamental" and "harmonics" of the note to which the string is tuned. If the string is set into vibration in the shape of one of these modes it will continue to vibrate in this shape at the corresponding resonance frequency, with an amplitude which gradually dies away as the energy is dissipated into sound and heat.

Now if the string is vibrated in a way that involves several of the mode shapes at once, then the principle of linearity comes into play. Each mode simply goes its own way, vibrating at its particular resonance frequency, and the total sound is the sum of the contributions from these separate modes (you can read more about adding harmonics in Music of the Primes in Issue 28). The guitar player can vary the mixture of amplitudes of the various modes, by plucking at different points on the string or using a different plectrum, but the set of resonance frequencies is always the same. In musical terms, the pitch of the note is always the same but the tonal quality can be adjusted. A bowed string is different. A note on a violin can be sustained for as long as your bow-stroke lasts, with a steady amplitude. Although energy is being dissipated into sound and heat, somehow the bow is supplying additional energy at exactly the right rate to compensate. This is one identifying sign of a non-linear system, for which the idea of adding contributions from different vibration modes cannot be applied in the simple way described above. The theory of such systems is always more intricate, and there is scope for very complicated outcomes and chaotic behaviour (read more about chaos in Issue 26). The range of good and bad noises which can be made on a violin string are examples of these complicated outcomes. The same general comments apply equally well to other musical instrument capable of a sustained tone such as the woodwind and brass instruments…….

Why is the violin so hard to play? by J Woodhouse and PM Galluzzo

Dizi- flute

Dizi

membrane

Dizi History

• Flute: Likely the oldest musical instrument of human kind

• Varieties include qudi ( 曲笛): more mellow and lyrical soundbangdi ( 梆笛 ): more bright and vigorous sound

• The first written record of the membrane (dimo) dates from the 12th century.

orhttp://www.im.tv/VLOG/Personal/485269/1010915

Demo at 山青水秀 611kdFBdje20110915.flv

Guzeng- zither

Guzeng - zither

koto (Japanese)gayageum (Korean)

đàn tranh (Vietnamese)• 15-34 (normally 21) Strings• Pentatonic Tuning

… D E F# a b …• No frets

Guzeng History

• 2500 years• Recently, half-tone strings are added.

Guzeng - zither

Left hand: vibrato, halftone and slidingRight hand: similar to pipa, creating sounds that

can evoke the sense of a cascading waterfall, thunder, horses' hooves, and even the scenic countryside