1. For calculations based on relative pitch see Qin Tunings, Some Theoretical Concepts.
2. For a listing of pitches available in harmonics with do = 60 Hz, see a footnote below
3. For comments on absolute pitch see another footnote below

I eventually made a series of Theoretical Finger Position Charts, but all my teacher did was have me copy him. For tuning he showed me first how to do a general tuning using open strings and stopped sounds, then a fine tuning using harmonics. 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.

General Tuning (Standard)

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)

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.

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)

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.

 
Footnotes (Shorthand references are explained on a separate page)

1. 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)

 
Appendix I: Theoretical finger positions for standard tuning (正調 zheng diao, two versions)
I use charts such as the ones below when doing dapu. Capital letters indicate open strings and harmonics. Small letters show stopped sounds. (Top)

 
Appendix II: Pitches available in harmonics
This uses a do = 60 Hz (a slightly flat B about two octaves below modern concert middle C);
Note that with stopped sounds any pitch is available.

For the harmonics on the above illustration, listed below are possible vib/sec (Hertz, Hz) measurements based on the open first string tuned to 60 Hz (between A# and B). Note that the 13 hui form a mirror image from the middle (#7). Thus, a harmonic played at #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. (So [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 pitches on the above chart can be grouped as follows (the range of a qin is four octaves plus a whole tone):

	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	= 160, 320, 480
	fa# "just"	= 337.5, 675
	so	= 180, 360, 720
	la	= 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

Modern standard pitch is A above Middle C = 440 Hz (Hz [= vib/sec]). With this as the standard, here are the approximate values for a chromatic scale beginning one octave below this A:

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

On my qin the first string is usually tuned to about 60 hz, making it a slightly flatted B two octaves below middle C: if the first string is tuned up to the modern C (ca. 65 hz) it breaks too often. Tuning the first string exactly to B (ca. 62 hz) is usually not a problem for the qin, but it can still cause problems when playing with instruments inflexibly tuned to modern concert pitch but also 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.

The most natural solution to this 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).

Return to Top, to Analysis or go to the Guqin ToC.