Monday, January 9, 2017

The guqin "harmonic" markers - hui - their physics and history

Cents and Non-cents


Western music is fast because it's not in tune - Terry Riley

Before we get going we should define the term cents.   Here is the wikipedia cents definition. Informally if we are talking about notes in an octave we understand that an octave by definition represents a doubling in pitch.   So if note C is at 100 hertz,  note C(octave higher) is at 200 hertz. Cents refers to the idea that we can divide an octave up into 1200 equal divisions.  With equal temperament an octave is divided up into 12 half-steps of 100 cents a piece, 12 * 100 = 1200. Cents also allows us to compare different tuning systems so we can say something like the pythagorean tuning version of a major 3rd (4 half-steps) is at 408 cents and is thus slightly sharper than the equal temperament major 3rd which is 400 cents or the just intonation major third of 386 cents.   It further is useful in the measurement sense because octave ratios represent doubling so if I have an octave from 100 to 200 hertz, I also have an octave that is "bigger" going from 800 to 1600 hertz.   Using cents makes this doubling linear so there is 1200 cents in every octave and every octave and interval within an octave is now describable.   So for example I can say that if C1 = 0 cents and E1 is a just major third associated with it at 386 cents,  then we move to a higher octave like C4, the just major third in that octave (E4) is still 386 cents "up" from C4.   When we use cents we will primarily use it to compare intervals.   It is likely that few if any people can hear a 1 cent difference in pitch.   It is claimed that some can hear a 5 cents difference.   You might try tuning your qin to some note (say string 1 as C) and then with an electronic tuner that shows cents see if you can detect a 10 cent and/or less difference.

Guqin Hui and the Harmonic Series


So in this blog I'm going to discuss the 13 markers found on the guqin that in Chinese are called "hui" 徽.    This will include discussion of the acoustic theory from physics behind the hui and discussion of the known history of hui.  The hui are typically translated as "studs" which I think is a terrible translation because "studs" to me stick out.  Perhaps "markers" would be better and in fact closer to the original meaning.  However I will just stick to the Mandarin pronunciation as "hui" (if English speaker - pronounce as whey in curds and whey).  The hui are inlaid into the surface above string 1 (see guqin picture below) and are usually mother of pearl although other substances including jade and gold have been used.   One other thing - this discussion is free of traditional guqin scholar pitch pipe theory.  You can view it either as being based entirely on "maker" design (by unknown guqin makers or designers from the Han dynasty or before) and also based on the theory that those designers understood the integer math behind just intonation. 

The hui have two functions:  1. they mark harmonic positions and 2. they are used as part of an X, Y coordinate system in guqin tablature for helping players play notes.  The Y part of the system is the open strings from 1 to 7.  The hui are the long X axis part of the system to tell you where to press down notes or to play harmonics.  Note that by "harmonic" I mean overtone which is the conventional meaning of the term amongst musicians in the English language.   I do not mean the physics term that allows you to call an open string a "harmonic".   So when I say the first harmonic I mean the 1st overtone (at an octave), 2nd harmonic, the 2nd overtone (a perfect fifth) etc.  In terms of lengthwise left-hand fingering position, hui tell you where to put your left hand fingers to play a note. The left hand goes to a hui (or inter-hui) position and the right hand plucks one of the seven strings.   Here we are really only interested in the harmonics aspect and not in the notion of pressed notes on the gugin.    A hui we go.

To start with feel free to spend some time looking at: wikipedia on harmonic series

So go and twang string 1 on the guqin which we shall give its "modern" name of C2 at frequency 65.4 Hertz (HZ) assuming 440 HZ for "concert A" and that we are simply picking out C2 at 65.4 hertz because it is convenient.   Note that C2 on a piano is an absolute pitch name at this time and place because we can figure out a known number of vibrations to go with it (Hertz). However it may also be used in the same sense as a relative note name a la DO RE ME SO LA.  I will try and be careful about that if and when it matters.   It doesn't matter here because string 1 is assumed at this point to be all by itself - or put another way we are looking at notes generated by string 1 on string 1.  I am just going to proclaim that string 1 played open is "C" and if you have it tuned to Bb - no worries.  It would not matter if it was A1 for that matter or C at 65.2 HZ.  What will matter is interval degrees as for example string 1 hui 5 played as a harmonic is a perfect fifth.  This is because the harmonic played at that note is a "G" above the open string which is a "C".    So I will use note names a la C G etc.

When we talk about the notion of a harmonic series we are saying that string 1 as C when plucked may be viewed as a composite consisting of a  fundamental wave (for example C2) plus overtones at equal integer divisions of that fundamental at various ratios.   E.g., the 1st overtone (2nd partial) is at a 2 to 1 ratio (2:1) and can be viewed as being two wavelets half the size of the fundamental that are "waving" at the same time that the fundamental is vibrating.  The all important 2nd overtone is at a ratio of 3:1. This is the perfect 5th.  The third overtone is at a ratio of 4:1 and is a 2nd octave above the fundamental.  The 4th overtone is a major third.  The fifth overtone is a perfect fifth that is an octave higher than the 2nd overtone.   The sixth overtone is a minor 7th (not marked on the guqin).  The 7th overtone is yet another octave that is 3 octaves higher than the fundamental.   Overtones go on forever at an increasing integer ratio.   However in the real world they all have different strengths and some of the lower overtones are stronger than others.   After a while of course the higher overtones are too weak to register at all on the ear.

Note this nice picture (purloined from wikipedia).   It shows the 1st 8 "partials" (a partial is the fundamental and any other overtone related to it as generated when we twang our open string).  Our picture does not show the 8th partial (1/8) but just imagine one more wave cluster with 7 nodes and 8 wavelets at the bottom of the picture.   Note how the partials are increasing in frequency and note where the node points are as for example with the 1/2 specimen the node is at the halfway point.



Figure 1: Harmonic overtone series - nodes/wave patterns


So basically the first 8 partials (7 in the above picture) have the following integer ratios,  and interval values (Table 1 below).  We will assume string 1 is C so  we can even give them note names.   So for example if string 1 is C then the 1/5 ratio is a major 3rd and we can call it E.   If you are paying attention and have not fallen asleep, note that you cannot play this particular E on a normal piano using the keys (you can play it on a guqin).   Hopefully that statement has gotten your attention.  Also of course you may have figured out that the node positions in the harmonic overtone series picture  (barring 1/7)  mark hui positions on the guqin.
         
Table 1:  ratios and partial intervals and hui position

        1/1   unison (C2) (open string as fundamental of tone)
        1/2   first octave (1st overtone)  (C3)  (hui 7)
        1/3   fifth (octave+fifth actually)  (G3)  (hui 5 and hui 9)
        1/4   2nd higher octave  (C4)   (hui 4 and hui 10)
        1/5   major 3rd  (E4)  (hui 8, 6, 3, 11)
        1/6   fifth at 2 octaves higher (G4)  (hui 2 and hui 12)
        1/7   minor 7th (Bb4)  (not found as marker on guqin)
        1/8   3rd higher octave  (C5) (hui 1 and hui 13)

We can take the above list of partials and state that it applies to all the guqin strings.  So for example,  if we say string 2 is D, all the intervals are the same.   We would have the fundamental as D2, and then the first octave higher would be D3, the perfect fifth would be A, etc.  For string 6 since the fundamental is C3, all the note names would simply be an octave higher than string 1.
      
There are lots of things you can infer about this glimmer of physics from the acoustics of music. Different strengths of the overtones is what gives us "tone color" and so if string 1 is silk or string 1 is nylon-metal as a guqin string they don't sound the same.  Notes pressed at different places on the top even if the same pitch don't sound the same either (different wood excitation).  This is because their overtones have different strengths.    Of course if you played the same C on a piano it doesn't sound the same either.   Overtones are what gives us tone color.

Let's take a look at a rather common picture though in terms of guqin - which is some "random" (maybe not) guqin and its 13 mother of pearl markers aka hui.
    

   



So this is a picture of the famous Tang dynasty guqin named "Jiu Xiao Huan Pei" (I happen to own a fake copy of it - so this might be a picture of the fake).  Keep in mind that this guqin is on the order of 1300 years old (or 20 years old if it's a fake).   Now let's consider why there are 13 hui.

When you are a guqin maker and you go to install the hui you measure slightly outside the string path of the 1st string based on making integer divisions of the total string length between the inside of the longyin (on the left in the picture) which is like a guitar nut and the inside of the yueshan (right in picture) which is like a guitar bridge.  We can say the string path is the distance between the nut and the bridge.  So the 1st hui maker division can be considered to be hui 7 which is right in the middle. It's divide by 2 and is supposed to go at the halfway point.   The hui are numbered from 1 to 13 from right to left.  Hui 1 is closest to the bridge (yueshan).    You install hui at any position along that path that include integer divisions of 2/3/4/5/6/8.   If there is a hui in a position (like hui 7) and it is also included in divide by 4 and divide by 8 -- well you don't install it again. Once is plenty.   So let's have a nice hui installation table as follows (hui, integer division, interval value based on the fundamental):

hui 1 - divide by 8 - 3rd octave
hui 2 - divide by 6 - 2nd fifth
hui 3 - divide by 5 - major 3rd
hui 4 - divide by 4 - 2nd octave
hui 5 - divide by 3 - perfect 5th
hui 6 - divide by 5 - major 3rd
hui 7 - divide by 2 - octave
hui 8 - divide by 5 - major 3rd
hui 9 - divide by 6 - perfect 5th
hui 10 - divide by 4 - 2nd octave
hui 11 - divide by 5 - major 3rd
hui 12 - divide by 6 - 2nd fifth
hui 13 - divide by 8 - 3rd octave

One thing to point out about this is the hui are symmetrical from 1-7 and 7-13.   E.g. hui pairings like 1 and 13, 2 and 12, 3 and 11, etc. are the same note.  Now this symmetry and the number of hui and the position of where you play the harmonics are all implicit in the overtone wavelet picture in Figure 1.   For example hui 7 is placed at the node between the 2 wavelets.   When you lightly touch there you are canceling out the fundamental and our ears hear the 1st overtone (2:1 ratio) which is an octave higher.   Hui 3, 6, 8, and 11 which are based on divide by 5 are all placed at the 4 nodes between the 5 "wavelet" markers or put another way, at positions that are 1/5th of the way between nut and bridge.   These 4 notes are all major thirds.  They are all the same note because they are the same divide by 5 ratio.   On the other hand,  hui 13 (and 1) are the 3rd octave because they are a 1/8 ratio.   When you play one of those you have canceled out the divide by 2 and divide by 4 octaves. That note at the 1/8 ratio is not going to be the note at the 1/2 ratio (the 1st octave) because the first octave requires half of the string to vibrate.   So all the hui cancel some partials out.   A simple example is that divide by 5 is not going to allow divide by 2 to vibrate.

So let me point a few things out that are perhaps beginning to be understood at this point:

1. the hui on the guqin are basically positioned at 6/7 harmonic partial positions (neglecting the fundamental which is the open string).

2. Of the 1st 8 - the only partial that is skipped is divide by 7 which would add 6 more hui and produce a lot of minor 7ths that were of no interest to the designers of the guqin (or at least its hui).   It might have crowded things up a bit and made things confusing.

3. why are there 13?   Neglecting duplications the 2nd partial (1/2) gives us one hui, 1/3 gives us 2, 1/4 gives us 2, 1/5 gives us 4, 1/6 gives us 2, and 1/8 gives us 2.  1+2+2+4+2+2 = 13.   Of course if we put in the 1/7 partials we would have 19 hui but never mind.  If we left out the major 3rds we would have 9 hui.   Of course there is an entire cosmological aspect of this like the  notion that the 13 hui represent the lunar calendar months.   Perhaps this is a reason for including the 5th partial?   I will revisit this subject later.   The bottom line is that the 13 hui are pretty solidly embedded in both the top and in fundamental acoustical theory.

4. if you are sad that the 1/7 minor 7th didn't make the cut, you can always find them for yourself. For example there is one around hui 4.4 on the guqin.  There are 6 of them by definition.   Of more interest is the 1/5 division which gives us the major third.   It did make the cut.   The line had to be drawn somewhere.

5. A certain party has pointed out that the divide by 8 fractions of 3/8 and 5/8 do  not have hui.   This is true.   Perhaps this might be regarded as a clue that 13 hui was deemed enough or that putting hui in at 3/8 and 5/8 would have been "one (well two) too many".   If we explain all the possible divide by 8 hui notes then 2/8, 4/8, 6/8 are all lower octaves and are dealt with by divide by 4 and divide by 2 already.   1/8 and 7/8 (which have hui) give us octave notes that are 3 octaves higher than the fundamental.    One of these two notes (3/8 and 5/8) can be found about hui 5.7 or so which if you say play hui 1 first - you should be able to find it on your own.

So the hui on the guqin are based on a fundamental acoustical physics property - harmonic intervals.    We don't know when they were invented but we do know that this is a solid principle of acoustical physics.

Because the hui markers are placed at the harmonic interval junctions for pitches including the following intervals (based on the idea that the pitch and the fundamental make a two-tone interval):  octave, perfect fifth, major third,  we can make the assertion that


  all the harmonics found on the 7 strings therein are just intonation notes.   

And there are 13 * 7 of them for 91 in all.   91.    That is a lot of notes.    Of course an overall theme of why the guqin is designed the way it is seems to be to have a lot of notes that are the same note more or less but have different tone colors for contrasting "two notes - different timbre".    A great number of harmonics helps with this design notion.

Just intonation is defined as notes created by small integer ratios of the note in question and the fundamental.  Just intonation is merely another way of looking at the result of the harmonic overtone
series.  So one could make a scale out of notes produced by just intonation.  The set of harmonics on the guqin based on the 13 hui give us 3 notes (unison, perfect fifth, major third).    So before when we said we had a major third (4 of them actually) - these are just major thirds.   They are not equal temperament major thirds.   They are also not pythagorean major thirds either.  They are just major thirds.

 The wikipedia page on just intonation provides more information:  wikipedia: just intonation.   In fact there is a dynamite table on that page that shows just intonation ratios for a C scale that we will come back to later (in the next blog post about guqin tuning).

 One thing worth understanding is that just intonation is in some sense historically the dominant intonation idea for instruments and voices in most human cultures.   This is because the 2 overtones of octave and perfect fifth are fundamental in music and so often make up the idea of tonic and dominant in melody.  Equal temperament may have been invented in China by a Ming prince but it was used in European classical music (say more and more from roughly 1700 on)  to solve various tuning problems with keyed instruments like "spinets" and eventually pianos.  These "problems" more or less came out because of the use of triads (1/3/5) relationships in European classical music which from a global perspective is an aspect of European classical music from Renaissance times on. Of course it's an aspect of world music at this point given the ubiquity of equal temperament instruments like pianos and guitars.   On the other hand vocal music and violin players (and guqin players) don't have any frets to fret us in.  And even in classical music in Europe there was great resistance to ET for long periods of time especially by violin players.   Many felt that the just major 3rd sounds much better than the ET equivalent of it (386 cents versus 400 cents).


Harmonic note choices and the just major third


If we stop for a moment and think about the design choices for notes for the 13 hui, you observe that you have a grand total of 3 kinds of notes -- all just intonation by definition:

  1.  octaves of the fundamental including one octave above, 2 2 octaves higher, and 2 3 octaves higher. 
  2. perfect fifths, 2 at a perfect fifth above the octave, and 2 more an octave higher than that.
  3. 4 just major thirds.   

This reflects that there aren't a lot of choices in the lower partials.   Our guqin harmonics are basically dominated by octaves or perfect fifths.   And that gives us 9 of 13 hui per string.  It isn't that we don't have tonal variety because after all we have the lower five (fretless) strings that are pitched differently in the standard tuning (C D F G A).   And of course we have timbre variety because there are different octave positions and different perfect fifth positions.   Of course as we will see in the next blog on tuning the harmonic octave and perfect fifth hui are important there as well.   

But that leaves us with the 4 just intonation major 3rd hui (per string all the same note so for string 1 if C, then hui 8 is E).   We are told that the guqin represents some sort of stab at cosmology.   And in this case we have 13 hui because of this bald statement:  there are 13 hui because they represent the 13 months in the lunar calendar.    Except there are 12 months - so that statement has to be amended somewhat along the lines of -- well there are 13 if you count the leap month.   Best to not argue with this barring pointing out that there are 13 hui because the 4 perfect major 3rds might have been added for several other reasons all of which are less cosmological:  

1. they add a little tonal variety which tends to go unappreciated (back to this below).  
2. they mark out some important real estate in terms of pressed fingering positions (e.g., lot of notes used all the time between hui 7 and 8 - you may have noticed).   This is the other function of
the hui but it rather important.  On string 7 press the string down at 7.6 says our tablature and we players know that means -- assume there are 10 divisions between hui 7 and hui 8, and press the note down 6/10s of the way between the two hui (closer to 8).  
3. and of course they have a nice complete arithmetic feel because this gives us 7/8 partials. Installing the minor 7th with 6 more hui might be a bit much.   

One contrarian thing to say about them is that they (just 3rds on string 1) are NOT regarded as the right match for tuning string 3.   In other words there is an age-old question about the design of the guqin which is this: in standard tuning why are the strings tuned to C D F G A c d as opposed to C D E G A c d?  Which is vexing (for some) when you understand that in the old times (Song and before but still findable in early Ming qin manuscripts) that the string names are Gong, Shang, Jiao, Zhi, Yu for the lower five strings, which should roughly be Do Re Me So La.   However the "jiao" string seems to be a 4th as opposed to the presumed jiao meaning of "me" (a 3rd).   Of course this problem was solved by leaving the open string tuning *alone* and changing the string names to numbers.   Jiao became 3! Problem solved!   

We'll come back to this question in the next blog.  However the notion of tuning string 3 to an E to match say string 1/hui 8 (just E) is not on.   Normally if we want string 3 down to E we compare it to the A string as a basis and play A/string 5, hui 5 which is a perfect fifth E courtesy of string A and then lower string 3 by playing it at hui 4 until it matches the hui 5 note on the A string.  We have lowered string 3 from F to E.  Overall (next blog!) you can say that the tuning for guqin strings is pythagorean and is based on the cycle of fifths therein.  The cents comparison of a just major 3rd at 386 cents to the pythagorean major third at 408 cents is a bit much.  Or put another way if you tune string 3 to match the just major 3rd as opposed to the pythagorean 3rd (compared to string 1), then you get to tune string 5 to match it.   This way leads to perdition.   String 3 is tuned in theory to the pythagorean E.   In summary the major 3rd harmonics as just harmonics are not deemed useful in terms of the pythagorean cycle of fifths nature of open and pressed string positions.   Mostly ...  

I expect the really compelling reason is #2 above - the 4 extra hui are there to help as a guide of where to push the open strings down (按) to the top.   However we should also consider the notion of the musical function of the harmonics available.   For the most part we know from comparing early Ming guqin tablature (say Shenqimipu and the like) to later qinpu - that the frequency of the use of those just major 3rd notes in pieces drops off.   Apparently they fell out of favor in the last 500 years or so (along with other pressed notes that were often a half-step off of some other note - which are common indeed in the oldest qinpu).   

Three little guqin harmonic exercises to consider though:

exercise #1. go play as harmonics, 3 notes in this order:

  1.  string 4/hui 7, 
  2.  string 1/hui 8, 
  3.  string 6/hui 7.   

You just sounded out a major triad that is basically G E C (an inverted C major chord).   It should sound pretty good. This is a pretty western thing to do because it's a 3-note triad broken chord.   It's not a very guqin/Chinese melody sort of thing.   But it's a western music thing of 1700 or so because of the just major 3rd, and the just perfect fifth.   You cannot play that chord on a piano tuned via equal temperament.   Many classical western musicians were and are still in love with the just major 3rd and hopefully it sounds good to you.   No worries - I probably haven't ruined your ears for equal temperament music.   

exercise #2. now play

  1. string 1/hui 8, and 
  2. string 5/hui 9.  

So the first one is a just major 3rd at 386 cents,and the second is a perfect 5th that in theory is around 408 cents when paired with string 1 to become a major 3rd.   Ironically they are both Es.   Welcome to just intonation (or perhaps the pythagorean extension of just intonation).   Just intonation is a wonderful place where G# and Ab are not necessarily the same note.   In Equal temperament they ARE the same note.   To some extent I have to wonder if our ears are brainwashed in this regard by ET and we have a hard time as a result with this sort of thing.   Lighten up.   When you listen to these 2 notes you can note that they are NOT the same note, but yet they would fall in similar places in a scale setting.   I suspect but of course cannot prove that to someone like the 13th century Song guqin master Mao Minzong (毛敏中) -- he would feel that the diversity therein was a good thing.  And he never had any ET tuning in his ears ever.   

exercise #3. speaking of Maestro Mao - in his piece (alleged piece but it may very well be his),  Lieziyufeng (Liezi Rides the Wind) in Shenqimipu (published in 1425) there is a passage of interest that uses the dayuan (striking the circle/打園) technique.  To play this technique you play two notes (often harmonics) and pluck the first note and then the 2nd note as a pair and the pairs are played several times in a row - ta DA, ta DA, ta DA.  Usually the pairs are the same harmonic notes found on two different strings as e.g., (string 2/hui 10 - string 4/hui 9).   Both these notes are D and we are invited to enjoy slightly different tone colors.   However in Mao's piece there is a passage whereby you are invited to enjoy (string 3/hui 8 and string 5/hui 7).   Yes these are both A notes but the 1st is a just major 3rd at 386 cents on the F string and the second is an A that is the just octave on the A string. They are on the order of 22 cents apart.   One might say that the composer is doing this because he wishes to heighten the strange atmosphere of Liezi (a Daoist Sage) riding the wind.   This may be true.    However similar juxtapositions may be found elsewhere in truly old pieces.   So whether this is to be perceived as normal in 1250 AD (or 250 AD?) or is meant to add a certain spice to the piece is hard for moderns to fathom.  

What we know about the design of hui in the guqin

So somehow artisans in China in the BCE era had some very good empirical knowledge of a fundamental music acoustics principle.  And some of them took that principle and applied it to the guqin -- marking out 6 of the 1st seven partials in the harmonic series is truly remarkable and was not an accident.

We can define the modern guqin (modern since the end of the Han dynasty at least) as having 3 characteristics:  1. there are 7 open strings that are tuned in a cycle of fifths fashion (we will come back to this in the next blog post)  2. there are 91 harmonic notes marked by 13 inlaid marks (hui).   and 3. the surface is flat enough that you can make "pressed notes" with all kinds of glissandi (sliding around, or just vibrato in various forms).   In addition, having all the harmonics and pressed note positions gives us a lot of the same note (or notes at a fifth relationship).   This gives us the ability to end phrases with matched open/pressed or open/harmonic note pairings.

So of course we can ask questions like the most basic of all:  just when did this kind of qin appear?  or what were the stages in its development?  Or the question we shall attempt to address in this section which is just when do we seem to have any documentation or pictures of hui as harmonic markers?  A good starting answer to those questions is this:  unfortunately nobody knows precisely.

We do however have some written statements that can shed some light on the matter. Joseph Needham in Science and Civilization of China, Volume 4-1 Physics and Physical Technology (Cambridge, 1961) has a long and interesting section on early acoustics in China.  He points out a couple of things that are salient to our discussion.   His main thesis is that in the Middle East in general and in Babylonia in particular ideas of the fundamental ratios for octaves, perfect fifths, and perfect fourths were invented and then transmitted outward both to Greece and to China.   In China the idea of generating a 12 tone "gamut" based on the cycle of fifths was developed from the notion of generating the next perfect fifth via a measurement system that involved taking a length of bamboo (a silk string works and is in fact easier to use) and multiplying it by 2/3rds or 4/3rds to get the next fifth.  This is in fact one way to do so-called pythagorean cycle of fifths - we'll explain it more in the next blog.   You can get the same result via frequencies by multiplying a fundamental by a 3/2 ratio or you can do it with measurement with ratios based on thirds.  This is known as the pythagorean cycle of fifths or if we are talking about a scale based on it, pythagorean tuning. Knowledge of the just perfect fifth is necessary as a precursor for the pythagorean cycle.   The book known as the Lushichunqiu  (呂氏春秋 is a text of approximately of 239 BCE.   It clearly defines how to do the pythagorean cycle of fifths generation for a gamut of 12 pitches (yellow bell generates forest bell etc., etc.).   So this gives us a hard date for knowledge of just intonation and its application to the pythagorean cycle.   Of course the original knowledge of these ideas came before - and possibly long before.

To some extent this question of "when for hui" is made more complex by our complete lack of knowledge about the origin of the guqin.

Negative Evidence


You might read John Thompson's web page on guqin origins or at least look at the nice picture in the top at the right on that page.  See:   John Thompson on Qin Origins.    So archaeology has been kind enough to pull several instruments out of tombs that date roughly from the 5th to 3rd centuries BCE.   These graves are in regions associated with the Chu State 楚國 of Warring States times.   Note from the pictures that there are no hui and actually it looks like you couldn't press the strings down to the surface to play a note either.   If these instruments are qin, then they are qin ancestors or possibly cousins.   They could also be some sort of zither that died out or a Chu state instrument about which we do not know much.  In any case since we can't be sure that they are qin, we can't cite them as authoritative in terms of just when hui appear (or do not appear).

The Huainanzi

There is a book called the Huainanzi presented to the Han Emperor Liu Che better known as Han Wudi in 139 BCE by his cousin Liu An.  So that date can be presumed to be a rough "publication" date although it may be that the good news was that the presentation managed to get the book into the Han Imperial Library (therefore it survived).   Liu An is presumed to be the editor of the book.  It is quite a long book and is more or less a Daoist manual of how to run the state.    It has quite recently been translated in full into English as The Huainanzi - A Guide to the Theory and Practice of Government in Early Han China,   Columbia University,  2010,  translated by John S. Major, Sarah A Queen, and others.  Some think that the title basically means "Master of Huainan" (Liu An) because Huainan is a place name, and Liu An was its King at the time.  This would make the title similar to other books like Mengzi (Master Meng) and Zhuangzi (Master Zhuang).

The 19th section is called 脩務訓 (translated by Major as Cultivating Effort) and in overview is supposed to be on the subject of why the ruler must put necessary effort into his work and how to argue or refute a point during an oral debate.   The passage that is of interest to us is as follows:


今夫盲者目不能別晝夜,分白黑,然而搏琴撫弦,參彈複,攫援摽拂,手若蔑蒙,不失一弦。使未嘗鼓瑟者,雖有離朱之明,攫掇之捷,猶不能屈伸其指。何則?服習積貫之所致。故弓待檠而後能調,劍待砥而後能利。


The translation on p.778-779: 

Now in the case of a blind person, his eyes cannot distinguish day from night or differentiate white from black; nevertheless when he grasps the qin and plucks the strings, triply plucking and double pressing (footnote 38), touching and plucking, pulling and releasing, his hands are like a blur, and he never misses a string.   If we tried to get someone who had never played the qin to do this, though possessing the clear sight of Li Zhu or the nimble fingers of Jue Duo, it would be as if he could neither contract nor extend a finger.   What is the reason for this?  Such things are made possible only through repeated practice so they become habitual.

Our footnote (38) is devoted to the four character phrase in the middle of this section - 參彈複which literally means "3 plays (plucks), back to the hui".   Here is the text:  Cantan, triply plucking (the strings) and fuhui, doubly pressing (the frets) refer to the movements of the player's right and left hands, respectively.   We are grateful to Bo Lawergren and Yuan Jung-ping (private communication) for their help with the technical terminology of the passage.   

Kudos to the Sinologists for asking Qin people about this.   Kudos to the Qin people for helping out.

Some have doubted that hui in the above passage is referring to our beloved 13 harmonic series markers.   There is a dictionary definition for hui of "threads/tassels" as well as "beauty" and  "marks/badges/logos".    I would observe that in general one has to be careful of dictionary definitions with old texts simply because context is so important in Classical Chinese.   Old dictionaries don't necessarily have all the meanings of a term.  And context may be of crucial importance sometimes in helping you to explicate a word.  One old meaning of this term is more or less "badge" which can be understood to mean "mark".   13 marks is quite reasonable.  

More to the point the entire chapter and this passage in particular are about "striving" in the sense that you have to practice your art to get it right.   In this case we have the obvious contrast of the blind qin player who is a total master and is more or less  "shredding his qin" (to put it in up-to-date lingo).   His hands are like a blur and he never misses a string.   I don't see how in the middle of this episode told as an object lesson it would make sense for the blind master to muck with the tassels underneath the qin (if there are any).   Also the 4 character phrase can be interpreted as referring to both the right hand (3 plucks) and to the left hand "back to the hui" as a nice balanced phrase.   One can take "hui" to be referring to the left hand playing positions on a qin after all as that is a major function.   

So it seems highly likely that hui here are referring to the 13 markers and we have at least a date of 140 BCE to go on.   

Xi Kang and his Qin Fu poem:

Another early mention of hui is in Xi Kang's  Qin Fu (琴賦)poem.   Xi Kang of course was one of the Seven Sages of the Bamboo Grove, a qin player,  the reputed composer of at least the early stages of the guqin piece:  Guanglingsan (廣陵散) and a Daoist philosopher.   He lived in the Three Kingdom period post the Han Dynasty and his dates are said to be 223-262 CE.   Fu poems were popular in the Han period and were often long (for poems) and written in praise of some topic, place, or things with lots of detail and  different points of view.   Xi Kang's Qin Fu thus might be translated as a "Rhapsody on the Qin".

 One source of the poem is the Zhao Ming Wen Xuan 昭明文選 compiled by the Liang Prince Xiao Tong in the early 500s CE.  The Wen Xuan is a poetry collection which covers poetry from 250 BCE to about 500 CE and is an important source for pre-Tang poetry.   I have consulted the two translations of Qin Fu in English and an additional translation courtesy of a dual language edition (Classical Chinese,  colloquial Chinese) of the Wen Xuan from Taiwan.
The two English translations are:  1.   Hsi K'ang and his Poetical Essay on the Lute by R. H. Van Gulik,  published in Japan in 1969, and 2.  David Knechtges'(truth in advertising - took a class from him long ago) monumental stab at translating all of the Wen Xuan, in this case Wen Xuan or Selections of Refined Literature, Volume III pp. 279-303.   So having consulted three translations - it turns out that they all agree on "studs" - that is, in the two instances in the text where hui seem to mean those MOP (mother of pearl) markers on the top of a guqin.   In total there are three uses of the character 徽 in Xi Kang's poem.   One of them is clearly not the marker meaning and we will ignore it.   That leaves us with two candidates which show up in some fairly simple text.



1.  
絃以園客之絲,以鍾山之玉


Literally this means:  strings take Yuanke's silk,   hui take Zhong Mountain's jade.
Knechtges on p. 287 translates this as:  The strings are made of Yuan Ke's silk, for the studs they use Mount Zhong jade.   A footnote points out that Yuan Ke was a silk growing savant and Mount Zhong refers (maybe) to the Kunlun mountains.   Unlikely that tassels were made of jade.



2. 
絃長故鳴  

Literally this phrase is:  strings long, therefore hui cry.   Van Gulik on p. 114 translates this (a bit strangely) as:  As the strings are long, each can give the entire scale.    His sense agrees with Knechtges p. 299 though who says:  The strings are long and thus the studs can be used to sound the notes.  Although of course this is a poem and thus either or both of the two functions of the hui (position for pressed notes or as harmonics) might apply.    The Taiwan translation interestingly declared that the hui cry sub-phrase refers to the idea of making the harmonics sing out.   

Pictures at an Exhibition

As far as I know the first art we have that shows guqin hui are the well known tomb reliefs from the Nanjing area. The earliest of which are dated roughly around 400 CE or a little later.    The originals include two groups of four men apiece and a number of trees.   Seven of the figures are the Seven Sages of the Bamboo Grove and all are labeled with a name.   There are two figures playing qin - we see Xi Kang below.   This picture is a cleaned up version from the original brick relief to help make things easier to see.

Although we can't say that the hui are shown in anything like their true mathematical nature - at least one can observe them in the picture.

Xi Kang playing qin

Summary


So in summary we can say that the 13 hui are placed according to the harmonic overtone series.   Each of the 7 strings  has 13 clearly marked harmonics that based on the open string as fundamental are just intonation pitches including octaves, perfect fifths, and just major thirds.

Historically we cannot be sure when hui appeared but we do know that the idea of the harmonic overtone series must have appeared in China before the algorithm expressed in the Lushiqunqiu around 250 BCE that explains how to create a 12 tone gamut based on using just perfect fifths.   You have to have a perfect fifth before you can spin it out 12 times.  This notion was based on measurement (length) as opposed to frequency which of course is the same scheme that a qin maker would use to install the hui markers.   Our first mention of hui seems to be in the Huainanzi of about 150 BCE and later on in Xi Kang's Qin Fu poem.   Our first pictorial rendition seems to be from a brick relief in a tomb around the 4th Century CE.    If there are earlier candidates I would love to hear about them.   

In the next blog outing we will discuss the guqin tuning system.    

Thursday, November 17, 2016

Discussion of a Couple Aspects of String Making and Physics!

So I have two things I wish to discuss:  1.   on the subject of string gauge and what if anything physics might have to say about this, and 2.   the curious phenomenon of string intonation or the match up of harmonics and pressed sounds at guqin hui positions.  

String gauge:

Here are two exhibits that you might spend a moment or two looking at (or longer ...)

1. Charles Tsua has been nice enough to gather information about various kinds of guqin string "gauges" (thickness) and put it together in a table on the web.   There is information here about several kinds of guqin strings including nylon-metal, and silk string brands and several other kinds of newly designed strings.   Note that silk strings might come in various different gauge sets (as with Wong Shuchee's Taigu strings) or the recently introduced Yuesheng nylon-metal strings that seem to have 3 gauges that are so close that perhaps they aren't all that different? 

https://en.wikipedia.org/wiki/User:CharlieHuang/Guqin#String_gauges

2. The 2nd exhibit is a Wikipedia page: 
https://en.wikipedia.org/wiki/Mersenne%27s_laws
and this equation in particular:

frequency = 1/(2 * Length) * the square root of (Force/Mass).

We can simplify the equation by ignoring length because we are talking about the fixed inside length of the string in the playing area (from inner nut to outer bridge).   That leaves us with Force and Mass.  Force is basically tension (how much did you twist the little tuning knobs or how tight did you wrap the string around the wild duck feet?).   Mass of course is how much does the string itself weigh although aspects of string construction are of course important but neglected in the equation.  There are also several assumptions that can be seen in the equation.   If you increase the mass of the string the frequency will go down (inverse square root of mass is proportional to frequency).   If you increase the tension the frequency will go up a bit (square root of tension is proportional to frequency).   We know and observe that fat strings are at a lower frequency than thin strings.  Fat/heavier strings are at a lower tension than lighter strings.  So if string 1 is tuned to a low C and string 6 is tuned to a C one octave higher we can deduce that there is higher tension needed to get string 6 to the desired frequency.  Be aware that with silk strings traditionally the highest string (#7) is the most likely to break and this is because it has the most tension on it (in order to be higher) and conversely the least mass.  

So there are a number of questions one might ask about string gauges (probably more than I can think of).  These might include:

1. Why given a kind of string (say silk) do we have different gauges in the 1st place?  The tradition for this with silk strings is quite old.   According to the Yuguzhai Qinpu (1860) there are 3 gauges of silk strings (which more or less go from skinny overall to "medium" to fatter).   The Yuguzhai calls these gauges  taigu, zhongqing, and jiazhong (太古,中清,加重 ).

2. Given the same kind of string, what might  happen if we replace a lighter gauge with a heavier gauge?   

3. Why might we want a lighter gauge?   

I'm going to focus on question #2 as to some extent the answers to these questions may be aesthetic and/or have to do with differences in construction of guqin (or strings).   Possibly you want lighter gauge strings because they are easier on sensitive fingers.  Possibly you want lighter strings because it is easier to do the infamous "gui" kneel without chopping off the end of your finger.    Let's stick with question 2.

First of all a certain trick exists which is like so: - with a given set of strings, and a given guqin -- try raising the pitch of all the strings 1/2 step.   You may end up with an improved sound.  The reason (if this happened) is presumably because since you raised the frequency but left the mass alone - you raised the tension too.   You tightened the strings to get a higher frequency.   This means when you play you are transmitting more energy via the strings to the yueshan/bridge to the qin top/etc.  And hopefully you got a better sound.   This can work.  It might be that you got a better sound because the heavier strings are doing a better job of "seating" the yueshan possibly because it wasn't glued in correctly or it doesn't fit correctly.  There are two negative trade offs though 1.  if you raise the tension the qin may be more difficult to play (the famous blues guitarist Stevie Ray Vaughn was well known to tune his electric guitar down 1/2 step in order to make strings easier to bend) and 2. if you do so your silk string 7 may explode.   

The traditional point of view for tuning a guqin with silk strings goes like this:  tune string 1 up as high as you can without causing string 7 to break.   Tuning string 1 to C is a recent innovation and (at least at first) was based on the idea of using nylon-metal strings.   I know of at least one guqin player who tunes his guqin with n-m strings down to B.  He does this for the same reason that SRV tuned his guitars down 1/2 step.  He feels it makes the qin easier to play.  It is useful to have a tuning standard (for n-m strings) but even if you are using n-m strings you don't need to follow it if you are comfortable with the sound and/or the playability of your tuning setup.  

So one obvious reason for a heavy or heavier string gauge may be simply that given the same desired frequencies - you will need to tighten the strings a bit to produce the same string frequencies compared to less heavy strings.   This might improve the sound of the qin by improving the overall energy transmission of strings to yueshan to qin body.   So overall we might end up with a little ore resonance due to a little more "shaking" because the yueshan wiggles a little more (or does a better job of it).   I have heard a few people remark that so and so a qin needed the heavier gauge string.   Presumably this is not to make the qin less resonant and physics suggests that this is not what is going to happen anyway.   It *might* make it more resonant in a good way without having to resort to tuning the strings higher.    At some point the yueshan might fly out or the wild geese feet may get pulled out (or silk #7 will explode).   You should stop before that point.   Certainly your mileage may vary.  

 The Low String Intonation Mismatch Problem:

Picture #1 - Guitar bridge
Picture 2: Low E guitar string
The easiest way for me to describe this is to first of all explain what happens with lower guitar strings on an electric guitar.   See picture #1  and #2 but see #1 first.    All guitars actually have this situation as a side effect of being a fretted instrument.   The frets decree note positions which are based on equal temperament.   If string 1 is tuned to low E, then fret 1 is F in terms of equal temperament and that is the end of it.   Unless you switch to a fretless guitar you cannot change the situation (or you switch to theorbo or oud but never mind).   Harmonics are based on division of string lengths by even numbers as for example divide by 2 gets you the same note one octave higher which on guitars is at the 12th fret (as far as I know ...).  On guqin this is the 7th hui marker.   This represents the half-way position between the guitar nut and the guitar "bridge" (where there are a number of different architectures).   On the guqin it is half way between the inside edge of the yueshan (bridge) and the longyin (nut).  Note that a major difference between guitars with fretted fingerboards and guqin which are fretless instruments is that note positions for fretted notes are *fixed* and with fretless instruments they are not fixed.  I am not going to explain just intonation, mean intonation and the like to say nothing of equal temperament but I will say this.   As before harmonics which represent overtones of the fundamental open string will provide higher octaves (divide by two) or as found on the guqin - pure fifths and/or pure major thirds (which are *not* the same as the major third you might find in equal temperament).  So keep in mind that the guitar is *fretted* and the layout of frets is based on the mathematics of equal temperament.   Now let's explain pictures 1 and 2.

In Picture 1, you are looking at the "bridge" for a telecaster electric guitar.   The low E string (which is wrapped) is to the left and the high E string is the 6th string to the right.   The low E is closest to the player.  These two open strings are 2 octaves apart.    The functional bits for the bridge consist of the bridge pickup at top (never mind) and the various "saddles" (which are really the bridge in terms of string function) at the bottom.   Each string has its own saddle.  Each saddle has two sets of screws for changing position horizontally or vertically with respect to the bridge and the fretboard.   We care here about lengthwise which means the screws  with the springs that are sticking out the bottom of the bridge metal slab.   Assuming you use a small screwdriver you can change the overall length (the string path) of an individual string.   Now assume this guitar is setup correctly (which by definition is probably technically impossible to be 100% correct because equal temperament means everything is slightly wrong - but I want to avoid that issue).   You can assume that the nut way at the other end of the fretboard is in alignment with the top of the bridge slab (or put another way the strings are at 90 degrees to the top of the bridge slab).   So note that the low E string and its saddle is roughly on a slant compared to the high E string.   The low E string path is *longer* than the string path of the high E string.   Why?   

But first how ...   in order to set an approximately correct string path for strings on an electric guitar, what you do is get out the correct size screwdriver and then play the harmonic at the 12 fret and match it up with the pressed note at the 12th fret.   If they don't match you use the screwdriver to move the saddle for the string out.   This is a needed adjustment (lengthwise) for getting a guitar to be more "in tune" and is one of a number of steps needed in this process at least for electric guitars.
If you have an acoustic guitar you may note that the bridge is simply slanted to make a low E string have a longer string path than the high E.  Acoustic guitars are "hardwired" in this way.   Ironically you could claim that different gauge strings on a guitar need a different setup.   And do it if you change strings to a different maker or different gauge.  People usually don't usually bother with this.   So we still have the question though - why?  

Note the high skinny E string back in picture #1 and now note the closeup of the fatty string in picture 2.  Long ago various worthies who we shall call string engineers - be they in China or in Europe were pondering why string instrument strings when they become dense enough (say string 1 on a guitar or the fattest string on an oud, or theorbo lute) seemed to suck (that means sounds bad) when you just added mass to the string by adding more lengthwise threads.   String 7 on your guqin sounded good even though because of all the tension needed it might break at the bridge (such is life).  So the situation was string 1 not as good as string 7.   Why?  String 1 just made a  "thumpity thump" sound and did not sound so good.  So added lengthwise thread to make a lower string doesn't seem to produce the desired quality.   So what did these geniuses do?   Why they made an engineering tradeoff.   They traded off the exact alignment of harmonics with pressed (fretted for the theorbo and guitar) pitches FOR a better sound for low strings.   So one or more parties invented the idea of putting a horizonal wrap of a certain density on low strings which improves their tensile "flappiness" and certainly does improve their sound.  This is a very positive side effect.  Now string 1 and string 7 are equally good.   Of course there is a negative side effect for doing this.  Hopefully in picture 2 you can see the outside metal wound wrapping on string 1.   The high E string is not wrapped.  The low string is wrapped.   

By the way this doesn't matter if your guqin strings are silk or nylon-metal or whatever.   Physics applies in both cases.   At some point fat strings with lengthwise threads are not going to sound as good as strings with equal (or possibly less?) density than strings with an outer wrapping.   We know that silk strings in China have had wrapped silk strings 1-3 since at least the Song dynasty.  And at some point string 4 was wrapped too.   String 4 represents an engineering trade off  point between wrapped and unwrapped.  Maybe it needs to be and maybe it doesn't   However I can guarantee that string 1 needs to be wrapped.   

So a guitar is in some sense a monumental set of fudged tradeoffs in terms of an equal temperament fretboard combined with the string intonation bridge adjustment I just outlined.   One can claim that all guitars are "out of tune".   And that equal temperament allows us to transpose between the keys of E and E flat and that sort of thing (beyond my scope here).   The difference in the length of strings due to lengthwise bridge saddle adjustment is certainly necessary and certainly noticeable.   

A gugin on the other side is a fretless instrument and like all fretless string instruments (say including violins, string basses, and cellos) the instrument designers have chosen to not care about this issue.  In other words the yueshan and the strings should more or less be at 90 degrees (especially string 4 as it is down the center of the guqin).   So assuming you have wrapped strings for say string 1 you can try the following experiment on your guqin.   Get an electronic tuner that shows cents and play the harmonic at string 1, hui 7.   This is the halfway point and assuming your hui is at the correct position (which on terrible guqin may not be true),  you should for example be producing a C one octave higher than the open string C.   Now play the note with your thumb at string 1 hui 7, pressed note.   You should notice that said note is a bit sharp if your pressed point is actually in the middle of the hui.  I just tried it and found the correct note was more or less at the left edge of the hui.   Of course this depends on the size of the hui and hui 7 is usually the biggest one. 

So here's a fact to be aware of:  if your qin notation says play pressed note such and such on string 1 at position X (say hui 7) this is an engineering compromise.   If you by some chance have guqin strings that are not wrapped you would find that hui 7 string 1 is strictly accurate.   If  you have strings that are wrapped, the correct note position is slightly to the left.   The discrepancy between pressed note and harmonic gets worse according to theory as you get closer to the yueshan/bridge.  

The bottom line here is that guqin players have to use their ears as well as their eyes to correctly "fret" their pressed notes especially on their lowest strings.  This is the same with a cello as with a guqin.   Theorbos are interesting because they have *moveable frets* but never mind.   

I suspect that this is one reason we guqin players may take advantage of sliding up or down into a note.   We use our ears possibly more than our eyes sometimes to reach positions that sound right.  
You could also argue (and violin players do this as a matter of course) that you need the small "yin" vibratto because it helps fool people into thinking that you hit the right note. Apparently if you play part of the correct position in the yin vibratto people will hear what they perceive at the right pitch.   

One last thought:  traditional tuning for a guqin circa 700 AD might go like this (note there are no batteries but you might have a handy xiao that you made all by yourself for a reference pitch).  

1.   go thru and do some harmonic based tuning say by matching up string 7, hui 7, to string 4,  hui 4, and repeat across 4 sets of strings.   Then refine it a bit with matching up string 7 hui 5, and string 5 hui 4.  This is harmonic based tuning.   Exactly how you do it might vary a bit but assume you did it
and you believe your guqin is in tune.

2. by doing this you have automatically tuned the open strings.   

3. you MIGHT worry a bit about pressed notes but in point of fact the low strings won't match up perfectly so my advice is to not worry about it.   You might play 1 and 6 and 2 and 7 open but that's open ...  

However the thing that guqin music does in this regard is interesting which is that musical phrases often end with a so-called "yun" (韻)or rhyme which means a matchup (often) of a open string and pressed string.      The pressed string is the one that needs to match the open string (or a harmonic) and your left hand and brain need to somehow make that happen.   That problem is on you and not on the string or instrument maker.   Fretless instruments are heartless like that!  

Guitars on the other hand are a different matter.   I would happily claim that they are out of tune by definition because equal temperament is out of tune by definition.  Ironically the majority of guitars are used for playing 3 chord country and western dittys or power rock solos (with 3 chords - maybe 4).  Guitar players often tune their instruments to a chord (song is in key of C so I'll play a C chord and tweak things a bit to make that sound right to my ear).   They are trying to get the fudge out of a monumental engineering fudge and I know from experience that tuning to the major dominant chord for a song is somewhat helpful.   

Happy intonation.  


Sunday, March 29, 2015

Making a Guqin - Web Book - Table of Contents

An Introduction and Table of Contents

I have decided to organize some of my blog posts into what you might call a "blog book" - in other words a set of postings that cover how to make a guqin from start to finish.   Unlike ordinary books though I will be able to modify, change, and or insert and delete material at any time.   This book is also "free".   There is a sequential order to the postings so the links below present a table of contents.

In order to make a guqin I would suggest that you read my translation "Abiding with Antiquity" which has one volume on guqin making a la 1850 in Fujian province in China.   It's a translation from Classical Chinese.  You can find it on Amazon here:  Abiding With Antiquity.   Of course this isn't a modern explanation and in fact I think the overview presented in that book is too simplistic.   For example, the method for rounding the top is much too simple and no one would be satisfied with its outcome.

So an obvious question is that if you wanted to make a guqin - what skills would you need? 1. you need woodworking skills however gained.   Often community colleges in the US might have such a course or you might take a course in guitar making.   2.  you need to have some guqin knowledge that I am not going to provide here.   You should be able to play some simple pieces as e.g., the piece Wine Crazy which includes the "gui" kneeling technique.   Wine crazy is a good piece for checking out how a guqin is doing in terms of its playability in a quick and dirty fashion.  Certainly playing other pieces would be a good idea and one can point out that guqin makers such as Zeng Chengwei are guqin master players as well.  3.  General knowledge of the guqin won't hurt.   There are several books in English including Robert Van Gulik's famous book "Lore of the Lute".   You might be able to find it in a library and it has been republished recently from Thailand.   Juni Yeung has published a book on guqin playing in English called Standards of the Guqin which is findable on lulu.com.  John Thompson has extensive writings up about the guqin including translations at his website:  www.silkqin.com.    Of course learning Chinese and living in China or Taibei or Hong Kong or possibly Singapore for awhile wouldn't hurt.

So more or less with some deviations the blog postings will be following a multi-year trail of an attempt to build two guqin.   One in theory was to be made from Paulownia (top) and Padouk (bottom).  Unfortunately the Padouk warped (I was deceived by beauty and violated my rule of  forcing the plank to first spend a few years on the wood pile).   So at this time said guqin will consist of Paulownia and maple (dyed a bit to go with the Paulownia).   A second guqin that at the time of writing is in what I call "intermediate test stage" has been made of spruce and maple and it will show up from time to time.

One deviation in the usual norm of brushing on lacquer from the lacquer tree is that for 5 years or so now I've been attempting to use clear finishes to show off the wood grain.   I have used traditional lacquer in the past and will discuss how to do so.   I should point out that spruce is actually a fairly hard wood.   Paulownia is not however and an attempt to do a clear finish of some sort on Paulownia is by definition a learning process (which is still underway).  Nevertheless I've made guqin with the traditional lacquer processes and will present that as the primary finishing methodology.

Making a guqin is in some sense a multi-year process.   In the world of instrument making (and in traditional thinking about the guqin in China) one encounters a notion that an instrument needs to be played before it can reach its sound potential.   I believe this to be true.  So for better or worse - patience in making an instrument is perhaps the #1 requirement.   Once you finish it - you have to get it played and this may take a year or more.   The other side of this notion is that by making a guqin you will learn how to repair a guqin (or possibly your coffee table).   So for example, having the bottom warp on you is an extreme example of repair.    But "two steps forward, one step back" is not unusual in a task of this nature.

A story:  maybe a decade or so ago when I decided to start (again) and try to make guqin the first thing I did was "destroy" one.   I took apart an old crappy guqin I had purchased in Taiwan in the 1970s just to see what made it tick.  For the most part this involved a big screwdriver and a dremel.  The dremel was used to sand off all of the lacquer all the way around the two sides and the screwdriver was used to pry it apart as carefully as I could do (multiple screwdrivers actually - as some wedging had to be done to slowly convince the top and bottom to separate).   This guqin was probably built by a furniture maker from a piece of Paulownia and a piece of catalpa.  It was warped lengthwise and more or less had a hump "up" in the middle.  When I took it apart finally it turned out that the bottom catalpa board was warped and the top reverted to being straight!  I made a new bottom for the qin from poplar as an exercise and this was my first "recent" attempt to start making a guqin.   I gave the guqin to a friend as it was now playable.   One of the things to do I would recommend for a novice guqin maker is to find a crappy guqin (something cheap on ebay is in this case exactly where one might look but your mileage may vary) and disassemble it.   In fact,  try to repair it.  The point is that once you have it open you can see what was going on.   And perhaps you can try to put it together again like I did.  I even managed to improve it although all I did was give it an unwarped bottom - which made the top playable again.

Table of Contents

Finding Wood
Roughing Out the Top and Bottom Boards
Smoothing the Sides and Making the Nut Slot
Top and Bottom (Board) Measurements
The Earth is Flat - Working on the Bottom
Wild Geese Feet
Peg Protectors
The Top is Round Like Heaven
Finishing Theory and Some Practice
Hollowing Out the Top
Cracking the Nut - Making the Dragon Gums
Making the Bridge - or Yueshan
Making the Chenglu - Bridge Accessory
The Hui - Mother of Pearl Markers
Intermediate Test Phase
Completing the Guqin


Completing the Guqin

In this section I am going to discuss what is necessary based on the process so far (especially the intermediate test blog post) to finish up your guqin.   Roughly you need to do the following:

1.  do any remaining work on the inside including optional installation of the heavenly and earthly pillars.   (see below).  

2.  glue up the sides and clamp them together

3. use some form of "bamboo nail" system (optional) post glue up to hold the two halves together

4. finish top and bottom with finish lacquer if you didn't already do so.

5. finish the sides with huitai and finish lacquer.   This may take awhile as there are 4 sides -- although sometimes it seems like there are more sides (there are 6 sides total!).

6. play it for some period of time.   You may need to achieve immortality in order to play it long enough (I understand there may be difficulties here).

Let me make some specific remarks about "glue" in this section.   Traditionally in China
glue will turn out be lacquer (nothing wrong with finish lacquer although more precisely 生漆 or raw lacquer would be used) that is more or less 大漆.

As I learn more I tend to be in favor of things that can be easily removed which means hide glue.
Hide glue can be removed with some combination of water (hot water is better) and or a heat gun (cheap).   This means that if you make a mistake along the lines of getting the glue where you don't want it or you want to "unglue" something to fix a possible misalignment (or simply take something off to perform an upgrade or experiment) then hide glue is what you are after.   It doesn't need to be the fancy powder kind either - Titebond hide glue is fine.     So e.g., if you are putting in the wild geese feet and you want to do it in such a way that someone can replace them later BUT you want them glued in so they don't fall out - then hide glue is your friend.   Superglue can be useful for gluing something fast but you must do your very best to avoid getting it in unwanted places as it is hard to get off (sanding and/or acetone but by definition either might damage a finish).   Epoxy can have its uses too and sometimes it is useful to have something strong that might take awhile to harden - thus giving you time to move something about a bit before you clamp it.   When I say "glue" - you will have to decide what you want to do.   However a glue-up of the sides would call for either hide glue (me) or "qi" lacquer - from the tree (China).

Heaven and Earth Pillars

We should first discuss what the pillars may be for in terms of function.   The Yuguzhai Qinpu says they are installed in order to help prevent warping.   Warping is a factor if the wood (especially the bottom piece) is not dry to begin with although if you take a dry guqin into a wet climate there could be problems eventually.   Typically warping would occur lengthwise due to the relatively long nature of the wood (as opposed to widthwise).   I fail to see how pillars would help much with anti-warpage since there are only two of them although perhaps they can add a bit of structural rigidity.   However it is possible that a guqin bottom might choose to warp width-wise (cupping) and in that case one could see how the top might provide some stability.   Some woods (maple as an example) are very good at absorbing moisture and expanding no matter how dry they might be.   In that case the inside of the bottom board may need to be treated with some agent to keep out the wet.   Walnut oil is a possibility.  

The Yuguzhai says nothing about whether or not the pillars might have an acoustic function.   I would expect that their overall acoustic function might be negative as they would tend to damp the movement of the top board as opposed to transmit vibration from the top to the bottom.   I have personally witnessed the "earth" pillar (between the two sound holes) more or less make worse the pressed note sound over where it was installed.   However this is not the last word in terms of acoustic functioning and if you can somehow figure out some way to install them and possibly move them around a bit (before sealing up the guqin) you might stumble over some improved acoustic
functionality of some sort.

Note that both pillars are traditionally installed on the center line position (4th string position on the inside).   A friend has relayed a question to and from a Taiwan guqin maker and he said that the earth pillar in particular may (or may not) help in terms of glissandi sounds (say 上 下) or on the other hand they might hurt the resonance in a particular spot. So caution should be exercised on the exact placement for the earth pillar vis-a-vis the string 4 notes.  Do not install it where a note might be played (at last in terms of the standard tuning).

I have installed them although I tend to not do so -- and will outline how to do it.  Traditionally
one pillar is round (heaven) and one is square (earth) but I suspect this may not be too important.  I just use some sort of hardwood dowel at 3/8s of an inch thick.   This thickness should not be taken
as the last word - thinner might be reasonable.  A little thicker might be good for experimenting with sound function (can't fall over).

Zeng Chengwei is a very traditional guqin maker and his guqin have heaven and earth pillars.  They are also made out of Paulownia and catalpa (his qin - not his pillars).   His pillars are on the order of 3/8th of an inch thick.He places the heaven pillar (which is between the big sound hole and the bridge) more or less at the shoulder (5 1/2 inches towards the bridge from the bridge-side of the big sound hole.   He places the earth pillar (which is between the two sound holes closer to the smaller sound hole) measuring out towards the nut from the edge of the big sound hole closest to the nut about 5 3/4 inches out from the left hand edge of the big sound hole.   It is fairly clear that if pillars are deployed - exactly where seems to vary from maker to maker.   Do not take the positions stated here as the last word on this.

The sound pillars need to be glued to the top and bottom although if there is truly a tight fit you might not need to glue one end (say the top).   I use a 3/8s inch forstner bit to drill a small but flat hole in the top board (which after all is curved).  Measure the dowel so that it is more or less the exact correct height for getting from the top (small depression) to the bottom.   If it is too tall you won't be able to close up the guqin.   Once you get around to closing it up (final glue up - see below) make sure you don't knock the pillar over.   If your big sound hole nayin is not too tall (assuming it sticks up from the inside bottom of the top board (or I should say sticks down towards the hole in the bottom board) - you might be able to move a pillar around post glue-up of the two boards and finish work on the sides.  This might be a good experiment for looking for an acoustic "sweet spot".   I haven't tried it as my nayin tend to be "too tall".

Glue Top and Bottom Together

Once you decide the time has come for glue up of the sides, use some sort of mechanism like either a stick or a brush (or rag) to spread glue carefully on the inner rim of the top.   This is a relatively easy thing to do.   I would certainly use a glue that will take awhile to dry as you are going to need to 1:  somehow position the guqin top and bottom so that they are in correct alignment and 2. clean off any excess glue (perhaps more than once) that is squeezed out between the boards and 3.  clamp the top and bottom together.

For clamping I have just used a number of ordinary woodshop bar-clamps.   Usually you need more and this is a good excuse for obtaining a lot of them.   One must exercise caution and use some sort of padding - felt pads,  clean cloth rags, or what-have-you to make sure
that the clamp parts don't hurt the finish.   Possibly a longer piece of wood under a clamp with felt on the underside of it might help to make sure that the clamp will not put a dent in a soft wood top made of Paulownia.   I remember seeing a video of a guqin maker in China who just used pieces of cloth and tied the guqin together!   Certainly a more complex clamping jig could be made and I may do this sooner or later (or try it).   For example if you had a number of curved pieces to fit the curve of the top (which sooner or later you will start making the same way time after time after doing your first few initial guqin) - you could take these and give them longer ends that would stick out past the sides. Then you could clamp these top pieces to straight bottom pieces that would go under the flat bottom of the guqin.  

Once the guqin has been successfully clamped together - give the glue enough drying time.  This depends on the glue in question.   Lacquer would need a few days at least and possibly longer.   Hide glue would be done the next day.   (And it can be undone rather easily for that matter).   In Figure 1 below we have a picture of a glue up taking place - the guqin has been fastened together at both ends (to keep the wood from moving) and clamps have been put in the middle.  
Figure 1 - glue up of paulownia/maple guqin

Bamboo Nails

"Bamboo nails" is the term that the Yuguzhai qinpu uses to describe what is more or less a doweling system that has been used by some people (but not all) in more or less firmly putting the top and bottom together.   I have no idea if "bamboo" is involved or not.   You can however see the depressions at points in the bottom of a Zeng Chengwei guqin.   They measure about 8 mm in diameter.   I personally use a system (actually two possible systems but only one per qin) that is more or less a functional equivalent but I do not do this sort of thing exactly.

If the side of your guqin (the top) is on the order of 1/2 thick and you used dowel pins of some hardwood on the order of 1/4 to 3/8s inch thick,  you would proceed to drill holes from the bottom roughly half-way thru the side of the top.  Then you would cut your dowel pins to the proper size and then use a wood mallet to drive the dowel pins in from the bottom.  One should be careful to not drill thru to the top or put the dowel pin in too far.   It is common to use a wooden block between any sort of hammer and dowel pin to cushion the hammer blows.   Dowel pins (according to the bottom's architecture) might be installed as pairs on both sides near the peg pool, at the shoulder, at hui 7, near the wild geese feet, and near the nut (on the sides of course).

Once the dowel pins are installed you would use lacquer cement (huitai) to cover them up and then could proceed to either do the final finish work (or repair the damaged finish work) on the bottom of the guqin.

Now having given the dear reader some idea of what the traditional approach here may be (and doing nothing other than a glue up is one possibility),  I shall explain what I have actually tried doing.  This consists of two approaches:

1. putting dowels on the inside.   This doesn't do anything much for holding the top and bottom boards together but it is great for aligning them.   I tend to use rather skinny dowels and then drill out holes for them in the top.   Of course - here we come to one of the great mysteries of woodworking - which is given two pieces just how do you get a dowel (or its hole) to align in two separate pieces of wood?  The answer of course is you use a dowel center (say 4 to 10 of them depending on just how many side pairings you want).   A dowel center is basically a round piece of metal that has a little rim so it can't fall in your drilled hole (on one side) and a sharp sticky pin in the center.   This allows you to carefully press the boards together with the dowel centers installed.   The result is holes in the other board that shows you where to drill the paired holes.

2. another possibility that I am rather fond of (someone will find this horrible but I've been doing it for awhile and it has no adverse effects on the sound) is using wood screws from the bottom up as opposed to dowels.   This allows me to screw the bottom and top together and then unscrew it to muck with the inside etc. and etc. over and over again as desired.   Holes are drilled initially through the bottom with an ordinary bit (top up so any splitting is around the inside of the bottom) and then I use a forstner bit  for countersinking the holes  so I can seat the screw top below the level of the bottom wood.   One is told that other woodworkers use countersink bits first and then drill the remainder of the hole in (not me).   It should be pointed out that the goal here is to actually screw the top to the bottom so that the exact width of the bottom hole (other than larger) is not crucial in terms of the screw.   Screws are screwed in manually.   Anymore I tend to do this early on - more or less when the top is hollowed out so that I sand the top and bottom edges level and then go ahead with the intermediate testing.   This also alleviates any worries about stringing during intermediate testing causing a Paulownia top to bulge out in the middle.  See Figure 1 below for a very recent photo of the bright shiny new maple bottom joined with the Paulownia top.   I haven't even drilled the holes through the chenglu for pegs and strings or dealt with much at that end yet so this is actually going on before I reach "intermediate test stage".

This is an area where your mileage may certainly vary and I would encourage anyone doing it to try out different methods as time goes by.   Of course one method per guqin would be a good idea.  Or you could just skip it and stick with the final glue-up.

Figure 1.  "dowels" (screws) holding maple bottom to Paulownia top

Finish Work

At some point you have to "finish" the finish.   We have already discussed all aspects of finishing in a previous blog post so I won't go into too much detail here.   However at this point we have got the bottom and top together in some fashion (I hope you didn't use nails).   So as a reward you get to finish four sides now including the bridge "back" side (past the "forehead"),  the nut side,  and the two long sides proper including curvy bits depending on your overall guqin design.

There is an interesting question here and my answer is that I tend to slow down and do this finish work on a side at a time.   The question is:  do I finish the sides with the guqin in the usual horizontal position or do I do it so that the guqin side in question is facing up?   I prefer doing it with the side in question facing up but this will tend to slow you down.  If you can do it with the qin horizontal you may be able to do 3 (or even 4) sides at once on a given finish pass.   However this can lead to drips - so in either case be sure and check for finish drippage in unwanted places and wipe it off while it is still wet.   You will make mistakes but part of the art of doing this sort of thing is learning how to be patient with yourself and how to minimize mistakes.


Final Remarks

Once the guqin is finished you should string it and play it.  In theory this is what you were waiting for (although it may be that the process was what you wanted to do anyway).   I have two general notions to present here:  1.   consider what you did right or wrong and mentally note what you might do to improve in the future.   I keep notes on past operations but I suspect my notes are not comprehensive enough about what happened.   However they are comprehensive enough to tell me what measurements need to be used in a particular work phase.  2.  there is a general question in the land of wooden acoustic stringed instruments (which includes guqin) and it goes like this:  "do instruments improve as we play them?".   The conventional answer for the guqin from centuries of tradition is that of course a guqin CAN improve over time.   We say "the guqin opens up".   Guqin players may not know that people say that about classical guitars, violins, and Fender electric guitars for that matter.  Some claim that "opening up" is a myth.   I've made a guqin that opened up over several years of playing and prize it highly at this point.   So I fear I have to say:  "it happened to me".   Let's assume for the sake of argument that "opening up" is not a mental psychosis of some sort and consider the problem for a moment.

If you need to practice a guqin and you are making two a year or four a year - and the guqin need to open up there are many questions in this regard about what you might do.   If you start selling them, perhaps you are going to need to push this process off onto the consumer.   If you make 4 a year and need to practice on each one 1 hour a day for a year -- well that's just not reasonable.   Heaven help you if you made two a month (which is what Zeng Chengwei told me - although he has help).

So I should point out that there exist ways of automating this process.   E.g, in the guitar luthier world, it is known that one can deploy a "tonerite" (see amazon.com for more info) to automate this process.   In general what you are doing is deploying something along the lines of a resonance speaker system to turn the instrument in question into a speaker system - and then you shake it with music.   If you could do this 24 hours a day you can more or less play something "an hour a day for a year".   If this system actually works you can get a year of "play-in" in about 2 weeks.

Final Pictures

Here are recent pictures of the two guqin mentioned in these blog posts - and their current states.  The spruce/maple guqin is more or less done.  The Paulownia/maple guqin is just past intermediate test stage and still needs a lot of finish work overall.

The first 3 pictures show the spruce/maple guqin and the last one shows the Paulownia/maple guqin  The bridge height on the maple/spruce guqin is on the order of 5 mm at hui 7.   The bridge height for the Paulownia guqin is on the order of 6 mm per string.   Both are easy to play.   Both sound good but are very very different in terms of their sound.  It is reasonable to assume that neither of them has opened up yet.