Equal temperament- the Chinese invented it, rejected it and readopted it

The study of tuning and temperament is a different task since there was no one single method, and case by case there are various of them on different occasions and instrumentations. The worst case, loss in tradition, also happened in China due to wars and invasions.

The most popular pentatonic system is based on the ratio of 4/3, multiplies the previous result of 2/3, multiplies the previous result 4/3, and so on. (link for the calculation detail.) Using this method we get the pentatonic scale and can be further expanded to 12 keys. At the same time, we still met the Pythegroen comma. Based on the backbone of pentatonic, notes can be added between mi-sol and la-do. (see pic) The added notes are in parentheses to form heptatonic (7-note) scales. Chinese opera and small instrumental ensemble trend to use heptatonic scales.

3 common heptatonic scales in the key of C.

In theory, these scales can be transposed to all 12 keys, but the Pythegroen comma is in the way. Many Chinese theorists tried different approaches and the most iconic one is the invention of equal temperament by Chu-Tsaiyu in 1584. However, this discovery did not favor by the musicians in China. These are some reasons:
  1. Vocal music is dominant- the pure P5 is easy for tuning by ears by singers. (Yang, 2015)
  2. No keyboard instrument like harpsichord, most of the Chinese instruments are agile to tune or a set of instruments with different sizes like Dizi. (Fisher, 1973)(The stone or bronze chime in court music is an exemption. But court music tradition had lost throughout history, I would not discuss today.)
  3. Tunes prefer changing mode (same note-set but in different tonal center) rather than changing key.
  4. Hetrophonic texture (when stacking third in Pyth. tuning, the third is noticeable out of tune).
  5. Small ensemble setting, echoing 2. that everyone can adjust with each other.
  6. Favor in just intonation sectionally in guqin music, playing harmonics also an important tone color and requires simple ratios in the length of the strings.

However, in the 19th century, the opium war (1839) marked the decay of Chinese culture. Intellectuals studied abroad and hoped to contribute what they had learned back to China, make the country powerful again. One thing particular in music is the symphonic orchestra setting for the west, such a big ensemble had not existed before. In order to put different folk instruments, ET is a handy scheme. The ET was reintroduced back to China. 



Yang, Y. et al. (2015) Tuning Features of Chinese Folk Song Singing: A Case Study of Hua’er Music. Journal of voice. [Online] 29 (4), 426–432.

Fisher, F. (1973) The Yellow Bell of China and the Endless Search. Music educators journal. [Online] 59 (8), 30–98.

Mok, R. T. (1966) Heterophony in Chinese Folk Music. Journal of the International Folk Music Council. [Online] 1814–23.

Comments

Post a Comment

Popular posts from this blog

Post-spectralism influence on tuning

According to Helmholtz (2011), a musical note is due to the fundamental frequency and the quality of a musical sound is due to the presence of upper partials. For traditional western music, pitch perception is mainly fundamental, rather than the frequencies in the spectrum which Teodorescu-Ciocanea (2003) describes as a “note proper” tradition. The spectralism composers shifted the domain from absolute pitches, intervals and chords to the spectrum. Spectral music is a complex approach to timbre, Teodorescu-Ciocanea (2003) classified 9 tendencies and their possibilities in spectral music. To conclude the techniques, tuning the frequencies according to the harmonic series is the major approach; while working with noise, generated digitally and/or extended techniques on instruments, is a sort of timbral dissonance which dilutes the pitch perception of a musical sound. Teodorescu-Ciocanea describes inharmonicity as the combination of frequencies that are not integral multiples of the funda
Read more

Haba's field shifting - and the expansion of traditional functional harmony

Image
Hába characterizes the quarter-tone gamut as separated into two fields, one half comprising the twelve conventional pitches, and the other half, shifting all the twelve notes by a quarter-tone, the twelve quarter-tone pitches. In harmony, Passages occur in which chords composed purely of conventional pitches alternate with chords composed purely of quarter-tone pitches. Two fields are not always rejecting each other when he equally divided a perfect 4th (5 semitones)into 2 equal intervals, equal 2.5 for each, the 0.5 quartertones always step into the other field. Sometimes, this fourth interval can be further divided into 2.5+2+0.5 or other permutations. This kind of splitting a fourth can be traced to ancient greek tetrachord, a scale of four notes, bounded by the interval of a perfect fourth. A chord across both fields, the chord spell like a flatter dominant 7th chord. the 7th harmonic on harmonic series is quite flat (-31cents). This chord combines both fields sounds better accordi
Read more

Temperament, Tuning, and Timbre -- the underrated trinity in music

 The trinity here is not about the Christianity faith, but similar to the idea of the Christian doctrine of it defines God as being one God existing in three coequal, the core and fundamental definition, temperament, tuning, and timbre (TTT) are the basic building blocks of music, yet, underrated and even neglected in our music education system. TTT correlates with each other. A note is played, it carries out a series of frequencies, the harmonic series. The series multiples from the fundamental frequency with a series of integers (1f 2f 3f 4f 5f 6f 7f 8f 9f 10f 11f 12f 13f...). The loudness of individual particles, and different patterns, creates different timbres. View the series in a different way, the combination of the integers creates intervals. The combination of the beginning of the series sounds more harmonious and vice versa; simple ratios sound pure and vice versa. The pure perfect 5th interval is based on the ratio of 2:3 (2nd and 3rd harmonics at the same time), Pytheogoro
Read more