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Qin Tunings, Some Theoretical Concepts  /   Problems with just intontation tuning  /   mode  /   rhythm  /   HIP  /   glossary 首頁
Tuning a Qin 1 古琴定弦法

1. Introduction

Tuning a qin requires first setting it to standard tuning then modifying that to achieve any of the non-standard tunings. Today this is quite simple: almost all qin pieces use standard tuning, the main exceptions being two melodies that use ruibin tuning, in which one string is altered: the fifth string is raised a half tone. In constrast, early qin music had a great variety of different tunings, some requiring re-tuning as many as four of the strings. The most common non-standard tunings are given in the chart at the top of the page on mode.

It is important to remember that traditionally there was no absolute pitch in qin tuning. Standard modern Western concert tuning puts the pitch A at about 440 Hz (vib/sec),2 and Western influence in Chinese conservatories has led to pervasive claims nowadays that qin strings should follow that standard and be tuned so that the lowest string in standard tuning is tuned to the Western concert C.3 Traditionally, however, the relative tuning accorded with such factors as individual taste, the size of the instrument, the weather and other factors. On my silk string qin the first string is usually tuned to between the modern Western pitches of B and Bb, but there are old recordings of silk string qins with the bottom string tuned as low as G or has high as C sharp, the lowest string is at least as low as G or as high.4

When my teacher Sun Yuqin first taught me to tune my guqin there was no discussion of absolute pitch any more than there was of mathematics. On this site mathematical calculations are discussed either elsewhere or in the appendices below.

  1. For calculations based on relative pitch see Qin Tunings, Some Theoretical Concepts.
  2. For finger positions generally used see Appendix I, Theoretical Finger Position Charts.5
  3. For the resulting harmonics with do = 60 Hz, see Appendix II, Pitches available in harmonics.
  4. For considering actual pitch see Appendix III, Absolute pitch.

For actual tuning of the qin the general principle for pitch seemed to be to tighten the strings as much as possible without them breaking easily. As for the actual process, my teacher first showed his students how to do a general tuning using open strings and stopped sounds, then a fine tuning using harmonics. As with teaching in general the students simply mimicked him. The sequence was not always the same, but this did not affect the result. Here is a discussion of the process.

On the accompanying illustration note that qins have seven strings, numbered from the far side of the player, and 13 markers (hui) indicating harmonic nodes, but also used to indicate stopped-sound finger positions.

   

Standard Tuning:6 General Tuning

As a typical example for standard tuning, once the pitch of either the fourth string or the seventh string seems to be about right, you can start with the following six steps.

  1. Bring the 7th string in tune with the 4th string by having the open 7th string have the same sound as the 4th string stopped in the 9th position.
  2. Tune the 5th string by having the open 7th string have the same sound as the 5th string stopped in the 10th position.
  3. Tune the 6th string by having the open 6th string have the same sound as the 4th string stopped in the 10th position.
  4. Tune the 1st string by having the open 4th string have the same sound as the 1st string stopped in the 9th position.
  5. Tune the 2nd string by having the open 4th string have the same sound as the 2nd string stopped in the 10th position.
  6. Tune the 3rd string by having the open 3rd string have the same sound as the 1st string stopped in the 10th position.

Fine Tuning: Standard Tuning

Now use the following harmonic positions to make the tuning more precise. This tuning is more precise because with the stopped sounds it is almost impossible to put the left finger down in precisely the correct position, while the harmonic position must be precise or the note will not ring clearly.

(A footnote below describes how to set the fifth string to 202.5 Hz [the A one octave below 405 Hz on the chart below, that considers the open first string as having the pitch 60 Hz, between a modern concert B flat and B natural]. The following process can easily be adjusted so as to begin by setting the pitch for this fifth string, then adjusting the other strings accordingly.)

  1. A harmonic played on the 7th position of the 7th string should have the same sound as a harmonic played on the 9th position of the 4th string.
  2. A harmonic played on the 7th position of the 6th string should have the same sound as a harmonic played on the 9th position of the 3rd string.
  3. A harmonic played on the 7th position of the 5th string should have the same sound as a harmonic played on the 9th position of the 2nd string.
  4. A harmonic played on the 7th position of the 4th string should have the same sound as a harmonic played on the 9th position of the 1st string.
  5. A harmonic played on the 9th position of the 7th string should have the same sound as a harmonic played on the 10th position of the 5th string.
  6. A harmonic played on the 9th position of the 6th string should have the same sound as a harmonic played on the 10th position of the 4th string.
    (Note: A harmonic on the 9th position of the 5th string will not have the same sound as a harmonic played on the 10th position of the 3rd string.)
  7. A harmonic played on the 9th position of the 4th string should have the same sound as a harmonic played on the 10th position of the 2nd string.
  8. A harmonic played on the 9th position of the 3rd string should have the same sound as a harmonic played on the 10th position of the 1st string.

The same results come from testing the harmonic positions at the player's right end of the qin, as follows.

  1. A harmonic played on the 7th position of the 7th string should have the same sound as a harmonic played on the 5th position of the 4th string.
  2. A harmonic played on the 7th position of the 6th string should have the same sound as a harmonic played on the 5th position of the 4th string.
  3. A harmonic played on the 7th position of the 5th string should have the same sound as a harmonic played on the 5th position of the 2nd string.
  4. A harmonic played on the 7th position of the 4th string should have the same sound as a harmonic played on the 5th position of the 1st string.
  5. A harmonic played on the 5th position of the 7th string should have the same sound as a harmonic played on the 4th position of the 5th string.
  6. A harmonic played on the 5th position of the 6th string should have the same sound as a harmonic played on the 4th position of the 4th string.
    (Note: A harmonic on the 5th position of the 5th string will not have the same sound as a harmonic played on the 4th position of the 3rd string.
  7. A harmonic played on the 5th position of the 4th string should have the same sound as a harmonic played on the 4th position of the 2nd string.
  8. A harmonic played on the 5th position of the 3rd string should have the same sound as a harmonic played on the 4th position of the 1st string.

During the above process, if one of the strings is found to be out of tune, you make the necessary adjustments then go through either the entire sequence again or, more commonly, only the harmonic sequence. In fact many people do their tuning using only the harmonic sequences, unless the qin has gone very badly out of tune.

Almost all melodies in the active repertoire (i.e., excluding melodies reconstructed from early tablature) use this standard tuning. With different tunings, the relationships are always given in terms of how they deviate from this standard tuning. For example the raised 5th string tuning (usually called ruibin diao in old handbooks but today other names may be used) is usually indicated as follows.

General Tuning (Ruibin)

To achieve this tuning, first do the standard tuning, as above. Then from standard tuning raise (tighten) the 5th string so that the open 7th string has the same sound as the 5th string stopped in the 11th position (newer handbooks may try to be more precise by saying position 10.8).

Fine Tuning (Ruibin)

The harmonic equivalents have now changed, as follows.

  1. A harmonic played on the 7th position of the 7th string should still have the same sound as a harmonic played on the 9th position of the 4th string.
  2. A harmonic played on the 7th position of the 6th string should still have the same sound as a harmonic played on the 9th position of the 3rd string.
    (Note: A harmonic on the 7th position of the 5th string   no longer   has the same sound as a harmonic played on the 9th position of the 2nd string.)
  3. A harmonic played on the 7th position of the 4th string should still have the same sound as a harmonic played on the 9th position of the 1st string.)
    (Note: A harmonic on the 9th position of the 7th string   no longer   has the same sound as a harmonic played on the 10th position of the 5th string.
  4. A harmonic played on the 9th position of the 6th string should still have the same sound as a harmonic played on the 10th position of the 4th string.
  5. A harmonic played on the 9th position of the 5th string should now have the same sound as a harmonic played on the 10th position of the 3rd string.
  6. A harmonic played on the 9th position of the 4th string should still have the same sound as a harmonic played on the 10th position of the 2nd string.
  7. A harmonic played on the 9th position of the 3rd string should still have the same sound as a harmonic played on the 10th position of the 1st string.

Similar sequences are followed to adjust for and check the accuracy of the various other tunings used for the qin. For further information on this see Qin Tunings, Some Theoretical Concepts or Modality in Early Ming Qin Tablature.

 
Appendix I: Theoretical finger position charts
When doing
dapu I use charts such as these to quickly know the pitches indicated in tablature. In the charts the words in capitals are the relative pitches of the open strings, letters in capitals show the harmonics, small letters show stopped sounds. The stopped positions are "theoretical" because the shape of individual instruments changes the actual positions played. (Top)

Standard tuning (正調 zheng diao, two versions)
In standard tuning the open first string is usually considered either as do or as so (traditionally there was no absolute pitch,
discussed below).

Non-Standard tunings (外調 wai diao, many variants)
In non-standard tuning one or more of the strings is lowered or raised from standard tuning. Any string might be considered as do. There are five qin tunings set to the standard Chinese pentatonic scale of 1 2 3 5 6 (do re mi so la). One of them is the standard tuning treated as 5 6 1 2 3 4 5, shown at the top of the chart directly above. There are five of these in all, as follows (links are to charts below):

1 2 3 5 6 1 2   manjiao (lower 3rd string)
2 3 5 6 1 2 3   ruibin (raise 5th string)
3 5 6 1 2 3 5   mangong (lower 1st, 3rd and 6th strings )
5 6 1 2 3 5 6   zhengdiao (standard)
6 1 2 3 5 6 1   guxian (tighten 2nd, 5th and 7th )

There are further variants; most include non-pentatonic notes. The two most common examples are as follows:

1 3 5 6 1 2 3   huangzhong (lower 1st, raise 5th strings)
2 4 5 6 1 2 3   qiliang (raise 2nd and 5th strings)
Once again, traditionally there was no absolute pitch, as discussed below..

Manjiao tuning (慢角調 manjiao diao)
From standard tuning lower the third string a half pitch. In this tuning the open first and sixth strings are do.

Ruibin tuning (蕤賓調 ruibin diao)
From standard tuning raise the fifth string a half pitch. In this tuning the open fifth string is do.

Mangong tuning (慢宮調 man gong diao)
From standard tuning lower the first, third and sixth strings (or raise the second, fourth, fifth and seventh strings) a half pitch. In this tuning the open fourth string is do. (Compare this alternate, in which the second string is do and so (as with the 1 2 4 5 6 1 2 version of zheng diao) one string is tuned to fa.

Guxian tuning (姑洗調 guxian diao)
From standard tuning raise the second, fifth and seventh strings (or lower the first, third, fourth and sixth) a half pitch. In this tuning the open second string is do.

Huangzhong tuning (黃鐘調 huangzhong diao)
From standard tuning lower the first string a whole pitch and raise the fifth string a half pitch. In this tuning the open fifth string is do.

Qiliang tuning (凄凉調 qiliang diao)
From standard tuning raise the fifth string a half pitch. In this tuning the open fifth string is do.

Similar charts are available for most other tunings.

 
Appendix II: Pitches available in harmonics
This uses standard tuning, with the open first string (considered as do) = 60 Hz
Note that with stopped sounds any pitch is available

For the harmonics in the above illustrations it is mathematically convenient to consider the open first string to be tuned to 60 vib/sec (Hertz, Hz).7 Although, based on a modern concert pitch of A=440 Hz, this 60 Hz first string is a slightly flat B, for baroque music C is often based on A=415, making this 60 Hz open first string a slightly flat C (in this system C is about 62 Hz). On my qin this is close to the pitch I generally use for the open first string. Listed below are possible measurements (in Hertz) based on the open first string being tuned to 60 Hz. Note that the 13 hui form a mirror image from the middle (#7). Thus, a harmonic played at hui #1 on the first string has the same pitch as at #13 on the same string, etc. (The "just intonation" pitches at positions 2, 6, 8 and 11 on each string also have identical pitch.)

String/rel. pitch/fraction of do     \ hui:
open
13
12
11
10
9
8
7
6
5
4
3
2
1
1. (Do [1]) = 3/4 (48/64)
60 Hz.
480
360
300
240
180
300
120
 
so'
do"
mi"
 
 
2. (Re [2]) = 27/32 (54/64)
67.5
540
405
337.5
270
202.5
337.5
135
 
la'
re"
fa#"
 
 
3. (Fa [4]) = 1 (64/64)
80
640
480
400
320
240
160
160
 
do"
fa"
la"
 
 
4. (sol [5]) = 9/8 (72/64)
90
720
540
450
360
270
450
180
 
re"
so"
ti"
 
 
5. (la [6]) = 81/64 (81/64)
101
810
608
506
405
304
506
202.5
 
mi"
la"
do#'"
 
 
6. (do [1]) = 3/2 (96/64)
120
960
720
600
480
360
600
240
 
so"
do'"
mi'"
 
 
7. (re [2]) = 27/16 (108/64)
135
1080
810
675
540
405
675
270
 
la"
re'"
fa#'"
 
 

The open string and harmonic pitches on the above chart can be grouped as follows (the range of a qin is four octaves plus a whole tone; the open first string is considered as do):

  Name    Pitch (Hz)
  do = 60, 120, 240, 480, 960
  do# "just" = 506
  re = 67.5, 135, 270, 540, 1080
  mi = 300 , 600
  mi "just" = 304, 608
  fa = 80, 160, 320, 480
  fa# "just" = 337.5, 675
  sol = 90, 180, 360, 720
  la = 101, 202.5, 405, 910
  la "just" = 400
  ti "just" = 450

As for the justified intonation ("just") notes, do# and fa# almost never occur (ti may occur slightly more often). In early tablature the justified mi and la do sometimes occur in the same pieces as the Pythagorean mi and la. This has led some people to try to retune the qin to avoid these "dissonances". I believe that qin players of antiquity appreciated the special colors brought by the occasional justaposition of such pitches. My argument is presented in Qin Tunings, Some Theoretical Concepts and Problems with Just Intonation Tuning.

 
Appendix III: Absolute Pitch

The Western modern standard pitch makes A above Middle C = 440 Hz (Hz = vib/sec). With this as the standard, here are the values (rounded off to the closest Hz) for an equal tempered chromatic scale beginning with the A two pitches below Middle C (to transpose any pitch down an octave divide it by two; to go down two octaves divide it by 4):

Name A A# B C C# D D# E F F# G G# A
Pitch (Hz) 220 233 247 262 277 294 311 330 349 370 392 415 440

As explained above, on my qin the first string is usually tuned to about 60 hz, putting it between the 58.27 Hz A#/Bb and the 61.735 Hz B♮ two octaves below middle C, as calculated from the above chart. (If the first string is tuned up to the modern concert C [ca. 65 hz] it breaks too often; if tuned exactly to a "baroque C" [modern B: ca. 62 hz] it is usually not a problem.) Thus there can be problems for the qin to play with instruments inflexibly tuned to modern concert pitch and awkward for playing accidentals. With stopped sounds any note can in theory be played on a qin, but harmonics and open strings are very important, and these are inflexible. Plus, I know of no one who can take a qin melody and transpose it up or down without retuning.

Thus when playing together with instruments using modern Western pitch, the most natural solution is using one of the non-standard qin tunings that lowers the pitch of the first string half a tone. The following shows the absolute modern pitch of standard tuning as well as of the three tunings which lower the first string half a tone. As can be seen, with huangzhong there still are several accidentals. These are avoided, however, with guxian and mangong.

  Tuning   \         String 1 2 3 4 5 6 7  
  Standard B C# E F# G# b c#  
  Huangzhong A C# E F# a b c#  
  Guxian A C D E G a c  
  Mangong A C D F G a c  

Unfortunately there are not many melodies that use guxian and mangong tunings (follow the links above to see listing).

 
Footnotes (Shorthand references are explained on a separate page)

1. Tuning a qin
To understand why the tuning methods (定弦法子) described on this page result in the desired relative tunings (相對定音) please study the mathematical relationships between positions on the seven qin strings as described under Qin tunings: some theoretical concepts.
(Return)

2. Pitch
Musical pitch is measured scientifically in terms of vibrations per second (Hertz/Hz). The higher number of vibrations per second, the higher the pitch. The precise mathematical relationships (e.g., doubling the number of vibrations per second makes the pitch go up an octave). In the Western during earlier periods the "standard" pitch was generally either lower or there was no absolute standard. In fact, although it is not certain when people first realized that pitch was related to the number of vibrations, it was not until the 1830s that we began to be able to measure these vibrations (proaudioencyclopedia.com).
(Return)

3. Absolute pitch?
The idea that qin should be tuned based on the modern Western concert standard of A=440 clearly has no foundation in Chinese tradition. The fact is that Chinese music conservatories are so imbued with Western aesthetic (or more specifically the aesthetic of Russian conservatories in the Soviet period) that even today in China "music" means "Western music" while "Chinese music" is considered "ethnic". The main reason for tuning a qin to Western concert pitch is that this allows the qin to play together with other instruments that use the same standard. It also allows the qin to be played louder, and the emphasis in the conservatories is performance, not self-cultivation.

This attitude is also completely bound up with the development of nylon metal strings during the Cultural Revolution, usggesting that it was, at least in part, another result of this Western influence; it is thus not surprising that this standard has been applied to the metal qin strings. It is more difficult to apply these pitch standards to silk strings, as such a high tuning on a standard size instrument leads to more string breakage. Unfortunately, instead of accepting this as an essential part of the qin tradition the conservatories try to use this as evidence that there is something wrong with the qin tradition.
(Return)

4. Actual pitches on a qin
This Bb is 9 notes below middle C. The actual pitch, though, is determined by such factors as individual taste (the higher the pitch the clearer and louder the sound, the lower the pitch the mellower the sound), the quality and size of the instrument, the weather (changing humidity requires lower pitch to keep the strings from breaking). My own tendency is to tune the strings up as high as they can go without causing them to break very often. What is "often"? The highest string (#7) is the one most likely to break (hence most sets include an extra 7th string); in a climate controlled room with regular play I expect the 7th string to go at least six months without breaking - often longer, certainly longer if tuned lower, shorter if not climate controlled.
(Return)

5. Theoretical Finger Position Charts
These are of particular use when reconstructing early music directly from tablature.
(Return)

6. Standard Tuning (正調 zhengdiao)
In Chinese this tuning literally means "correct" or correctly regulated. Non-standard tunings (外調 wai diao, literally "outside tunings") are described by how standard tuning must be changed to achieve them. There was no standard pitch (designated absolute pitch) in early qin tunings, so they are best described not by Western pitch names (A B C, etc.) but by relative pitch names (do re mi... or, in the Chinese number system, 1 2 3...).

Traditional tunings all emphasize the fact the qin music was basically pentatonic though, especially with the earlier surviving repertoire, there are many non-pentatonic notes. This led to an idiom which makes it difficult to play diatonic music on the qin using any of the traditional tunings.

There was a traditional disagreement in Chinese writing about whether the main pitch in standard tuning should be on the first or the third string. The choices are:

Standard tuning,  first string as 1 (do):   1 2 4 5 6 1 2
Standard tuning, third string as 1 (do):   5 6 1 2 3 5 6

Once again, in pitch these two tunings are identical: the difference has to do with which pitch is (or should be) the most important one.

It is somewhat puzzling, especially given the fact the the lower five strings are named gong shang jiao zhi yu, i.e., do re me sol la, why 1 2 3 5 6 1 2 did not become the main tuning. Instead it is generally called "lowered third" (manjiao) tuning, and at least since the Ming dynasty it has never been very popular. The answer to this probably concerns practical use of the tuning; there is some mention of this in the following arguments.

The arguments on the topic of standard tuning generally seem to concern music theory as opposed to practical use.

Although my transcriptions are all written in Western staff notation, this is treated like the Chinese number system, so that "A" has nothing to do with the modern A=440 Hz; instead it means la (further details).

The next footnote has an example of setting the actual pitch when tuning a qin.
(Return)

7. Tuning a qin so that the open first string is 60 Hz
To do this I use a Korg Orchestral Tuner OT-120. I calibrate "A" to be 405 Hz (compare "la" on the chart above), then pluck the open fifth string, tuning it so that when the meter centers it reads "A 2". Then, by going through the tuning process described in detail above, I bring the other strings in tune with this. Now when I play a harmonic on the 7th node of the first string (the open first string, one octave lower, seems to be a problem for the Korg) the meter should center and read "C 3".
(Return)

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