The information how to reduce guitar tuning problems has been available for few years. As period in "nylon string guitar" history it can be considered as a rather recent development. Before that the builders have produced guitars in a traditional way and the players have used to the inaccuracies. One could think that the now when more information is available, the change from old to new is rapid. However now the time has passed and still few builders have adopted the changes. The shops are full guitars, which cannot be tuned well enough!
Causes of guitar intonation
There are many reasons why the guitar is out of tune, so before we go to the solutions, it is useful to remind the causes for guitar intonation.
Tuning errors, stretching of the string during playing, we see often an artist tuning the strings even during a performance!
Bad quality of the strings itself, thickness variations, aging and wearing of strings ,the normal tension and high-tension strings have different tuning properties.
Wearing of the frets, a flat fret is not giving the same vibrating distance as a round one Wrong height at the nut- or wrong action at the 12th fret cause errors. The tolerances of fret locations, not correct or more probably completely missing nut compensation cause errors.
The stiffness of the string itself causes tuning errors. It should bend close to the ends, but due to the stiffness of the material it cannot do it. In order to compensate the non-moving distance, the saddle has to be comensated by moving forwards.
Also the higher harmonics tend to go sharper due to stiffness, but the problem is smaller compared to other errors.
Then there are resonances caused by the guitar itself. The lowest resonance peak is normally from 90 -120 Hz depending of the size and form of the body. The soundboard and the bottom move to different directions, which causes air to pump in and out through the soundhole. At the next soundhole resonance the soundboard and the bottom move to the same direction. These resonances are in the area of 150-250 Hz. The next a bit higher resonance occurs when the soundboard and the bottom move to different directions, but the air goes to opposite direction compared to the 1st case. These and other resonances cause audible sound when plugging the string, it’s like hitting a small drum!
Another problem occur when the harmonics are close to body resonances. The harmonics are affected by the body resonances and the strings are not able to vibrate as well as normally. As a result certain harmonics are attenuated faster and the pitch can be shifted lower or higher. The changing of fret locations doesn’t help, because even if one would be able to put one harmonic to correct pitch, the rest harmonics would be then out of tune! The error has been up to 10 Hz in one "Hauser" model, but normally with other guitars the shifting has been about +/- 1-3 Hz at maximum. This effect can be reduced only with better soundboard construction and internal bracing. Still the biggest problem is to make a guitar in which all notes sound equally well. Many of the items above prohibit getting the perfect sound from the guitar. To most of the problems accurate construction will help, but for the two last there is no clear answer available. Here we try to concentrate to guitar tuning and especially to compensations. If they are set correctly, there is more room for other errors.
Guitar compensations
The author of the article in the "Guild of American Lutherie #47 - 1996" concerning "Classic guitar Intonation" was an exceptionally innovative Greg Byers. He then presented the calculations and experimental test results for classical guitar compensations. For those who don't know what compensation is, it is a measure with which the string has to be prolonged or shortened in order to produce correct pitch. The measures in the table below are in millimeters, for a typical guitar with 650mm scale-length using Augustine Regals with Blue Label Basses:
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The nut compensation guarantees that the 1st position gets correct pitch due to stretching of the string. Otherwise the all those notes will come sharp. Without nut compensation the frequency errors are always audible.
The saddle compensation takes part of both stretching and stiffness of the string. The stiffness changes during aging and the new strings are normally easier to tune.
The measures are for the guitar with a 650mm scale-length, if it is more, then the amount of compensation is different. The longer scale causes more tension to the strings and reduces the needed compensation caused by the stiffness of the strings.
The nut compensation
The nut compensation is possible to construct to new and to old guitars. The luthier can shorten the fretboard by 1,0 mm using a router and the new bridge-bone is adjusted so that the compensations are according to table 1 for each string:
The saddle compensation
The saddle compensation is more difficult to implement, because the saddle bone is straight and rather thin (2,5 mm) compared to the nut. If one sets the guitar so that the 1st and the 6th string get the exact compensation and the rest strings are more or less out of tune. The angle of the saddle affects much to the resulted compensations. The following table shows three typical variations, which all have been used for a classical guitar:
| | Compensation | a) straight saddle | Delta s | 1st, 6th correct | Delta s | 1st,4th correct | Delta s |
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- The straight variant has big errors for strings 3 and 6. The error is possible to compensate with a saddle that is fine-tuned separately for each string, but more than half of the bone has to be removed and this weakens the quality and power of the sound. The use of thicker saddle bone would be better.
- This variant has the 1st and the 6th string set correctly and is also common. The problems come with the strings 4 and 5 that are much over compensated and cannot be corrected with fine- tuning.
- The 3rd variant has strings 1 and 4 set correctly. The errors can be corrected with fine-tuning, but the problem of narrowing the saddle still remains, but is slightly smaller than in the 1st variant.
When one saddle is not so good, let’s divide it into two parts and adjust the angles separately. As a result the strings can get very good compensations. The proposed solution and its errors are shown in the following table:
| | Compensation | Two part saddle | Delta s |
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The error with the two-part saddle is small enough that it is doesn’t especially need fine-tuning. I put an article about this to the "Helsinki Guitar Society Magazine 2-1999". The other of my guitars was taken to repair to Kauko Liikanen, who one of the most respected luthiers in Finland. The change was done by filling the old saddle-track with rosewood and then cutting two separate tracks with a router. The implementation is shown in the picture:
Picture 2. Two part Saddle
The tuning results were rather accurate when measured with an electronic tuner. Now the first series of the guitars with a two-part saddle construction are in sale.
Excel calculations
In order to estimate the amount of frequency error at all positions along the fretboard, an Excel spreadsheet was made. The calculations were based to Greg's model for fretting the string and othervise to a book called "Die Gitarre und ihr bau". When comparing the nut compensations to Greg's experimental values, the values from the tool are very close. The following picture tries to show the problematic 3rd string, with the following variations:
- With correct nut compensation; saddle compensation set to 0,14 mm short
- With correct nut compensation; one-part saddle compensation set to 1,8 mm short
- Without nut compensation; one-part saddle compensation set to 1,8 mm short
Picture 3. Different compensations with G-string
The picture shows that the guitar with the exact nut and two-part saddle compensation is superior to the others. With the two-part saddle the accuracy remains good along the whole scale. The one part saddle with or without nut compensation goes more and more out of tune when the position gets higher. The other strings have naturally better accuracy.
The real life is not as bright, even if we know how to set the compensations, there are places to make small errors during construction. The next picture tries to show that effect when frets and saddle are set at the accuracy of +/- 0,2 mm.
Picture 4. The effect of tolerances
The tuning accuracy is immediately worse, when the tolerances are brought in. The fret locations and the nut compensations should be done at least with the accuracy of +/- 0,2 mm. The amount of nut compensation can be measured easily with a micrometer in order to guarantee exact result. In order to make perfect tuning, the saddle could be even fine-tuned after completion of the guitar.
Practical measurement results
In order to prove the advantage of the better compensations different guitars were measured. Two guitars were from Liikanen, two others were my own prototypes. All guitars used nut compensation; three had a two-part saddle and one guitar was with one part saddle. The measurement accuracy in the "SpectraPro" spectrum analyzer was 0,336 Hz with the used settings (sample rate 44,1 KHz, FFT size 32 768 K, Decimation ratio 4). The measurement results when the open string is tuned correctly are shown in the following table for the 1st and the 12th position:
| Model Hauser, 1-Saddle | Model Lens, 2-Saddles | Alhambra, 2-Saddles | Landola, 2-Saddles | |||||
| String | 1st | 12th | 1st | 12th | 1st | 12th | 1st | 12th |
| 1 | 0,8 | 0,5 | 0,2 | 1,6 | 0,5 | -2,6 | 0,3 | -2,2 |
| 2 | 1,1 | -1,0 | -0,7 | -1,1 | -0,2 | -1,8 | 0,1 | -3,4 |
| 3 | 1,5 | 3,0 | 0,8 | 0,4 | -0,5 | 1,2 | 0,1 | -1,5 |
| 4 | -0,2 | -0,5 | -0,4 | 0,7 | -0,1 | -0,9 | -0,1 | -0,5 |
| 5 | -0,4 | -0,6 | 0,3 | 1,3 | 0,5 | -0,7 | 0,2 | 1,8 |
| 6 | 1,0 | -0,5 | -0,7 | 0,8 | -0,1 | -0,5 | 0.0 | 0,0 |
As expected the Liikanen model Lens with the new 2-part saddle was the best. The Model "Hauser" with a 1-part saddle was good, but the 3rd string is 3 Hz out of tune. In this guitar the saddle bone had been fine-tuned by cutting part of it allowing slightly better compensation.
The 2-part saddle looks better than the 1-part saddle, the listening tests show that the voice quality is better than the measurement results. The accords seem to stay and the typical modulation results are not present.
Later analysis showed that the Alhambra had some rounding at the nut at the 1st position. This can have happened after adjusting of the height at the nut or just wearing of the nut. After small filing the trouble was moved and the result better. Here I must say that the edges of the saddle are sharp and sometimes (not often) the string will brake.
More practical measurements!
In overall the error is more than expected! In order to get better view of the strings behaviour a new measurement was made for all strings. Each string was measured up to the 12th position and the spectrum was analysed up to the 5th harmonic. The results showed that many harmoniscs were often shifted from the correct pitch. For intance the string 6 ( E ) had shifts between A - A#, where the lowest 113 Hz body resonance is located. The string 4 (D) or the same notes on string 3 (G) had bigger -1,5--+1,5 Hz shifts between A#- H, where the flatter 231 Hz and the 253 Hz body resonances appear.
Picture 5. Frequency errors around the body resonances
Both pictures show that the harmonic frequencies are shifted on both sides of the resonances. The shifting is depending of the construction of the guitar, in this example the Alhambra has been measured. .The higher harmonics are affected as well, so the guitar sound is a compose of harmonics, which are slightly out of tune! Another example of the effect to the higher harmonics is shown below:
Picture 6. Harmonic errors for string E
Allmost all harmonics have shifts and probably the amount of those is even quite typical. But as it was mentioned, up to10 Hz deviation has been measured, when the pitch of the 1st harmonic was changed from G to G#! There are of course some notes between which are not troubled and all problems are not audible.
Origin of the Wolf Tones
The reasons for these so called wolf tones has been studied in many publications. One good source of information is the "ACUSTICA" magazine Volume 49 (1981), which explains how the effective lenght of string is changed close to the body resonances. When the string resonance is at lower frequency than that of the coupled structural resonance, the bridge moves in the same phase as the forces acting on it; the effective lenght of the string is increased and the resonant frequency is therefore decreased. For a string resonance above the resonant frequency of the coupled resonance, the bridge moves in opposite phase to that of the forces acting on it, so that the effective lenght of the string is decreased; its resonant frequency is therefore increased. For relatively weakly coupled string resonances the maximum damping occurs when the frequency of the string resonance coincides with the structural resonance.
According to the theory the effect can be controlled by reducing the Q-value of the body resonances or by increasing the effective mass at the bridge support. Probably the new soundboard designs have been improved in this sense. There is information in the New Millennium Guitar Magazine articles like the interview of Jim Redgate of his Lattice Braced Guitar and the one of the Dutch Jeroen Hillhorst. The Hillhorst soundboard design is not revealed, but it certainly contains interesting solutions, not ot mention the lifted fretboard and a bouble back. The Finnish Jaakko Liikanen has the "Lens resonance system" where the area around the bridge has been build to very stiff. There is no traditional bracing the saddle- and two-part bridge are well compensated. Could it be that once again we are facing a revolution in guitar construction?
Conclusions
The original purpose of this paper was to show how easy it is to build a guitar which goes well in tune. Many practical measurements were made during writing, some at home, once at the lutherists workshop. The spectrum analyzer results were compared with each other and to the 3D views, which showed the attenuation of harmonics along the time. The original purpose was not completely ashieved, but about the accurate nut and saddle compensations we can state the following:
The accurate nut and two-part saddle compensations are definitely needed, it gives more space for other errors!
All strings should go rather well in tune, if the tolerances are minimized!
The guitar sound comes softer; you will hear the difference and you'll play better!
There are still problematic notes that are slightly out of tune due to guitars own resonances. Development work is still needed to correft these problems.
The PC based spectrum analyzer "SpectraPro" was enough accurate tool, when analyzing the problem areas.
The studies continue by measuring advanced guitars and the wolf notes if any, probably more measurements of different string sets
References
[1] Guild of American Lutheries issue 47-1996, Classic Guitar Intonation - Greg Byers "Classic Guitar Intonation" by Greg Byers Finding perfect intonation through deep math and jiggling the string length at both ends. For some luthiers the quest for perfection knows no bounds. The rest of us are just jealous.
[2] Helsinki Guitar Society, Kitaristi 1-1999, Kitaran sävelpuhtauden ongelma - Kauko Liikanen
[3] Helsinki Guitar Society, Kitaristi 2-1999, Vanhan kitaran sävelpuhtaus - Rauli Parkkali
[4] Die Gitarre und ihr bau, Verlag Edwin Bochinsky
[5] AUDIBILITY OF INHARMONITY IN STRING INSTRUMENT SOUNDS, AND IMPLICATIONS TO DIGITAL SOUND SYNTHESIS Hanna Järveläinen, Vesa Välimäki and Matti Karjalainen Helsinki University of Technology
[6] Modelling of Tension Modulation Nonlinearity in Plucked strings, Tero Tolonen, Vesa Välimäki, Matti Karjalainen IEE TRANSACTIONS ON SPEECH AND AUDIO PROCESSING, VOL 8, NO3, 2000
[7] Kitaran akustiikasta ja sen mittaamisesta, Matti Stenroos Teknillinen korkeakoulu 1999
[8] Theory of String Resonances on Musical Instruments, C.E. Gough, ACUSTICA" magazine Vol 49 (1981
Probably the hardest niche to fill in the classical guitar is that beginner’s guitar. Teaching for the last 35 years I have encountered abominations in wood destined to drive a poor guitar student into oboe.
The Martinez Classical guitar, imported by The Hill Guitar Company of Felton, CA from China is the guitar I’d suggest in $695 to $795 range. So far there is no guitar under this price that I could recommend and a few above this price that you’d be best staying away from.
As a lot of cheap guitars don’t have solid tops there is little tone to be had therefore little tone is developed by the student. The Martinez is full of tone and has a wide pallet of tone color with ample volume. It is quite surprising how even and loud these guitars are and I took one dozen of them, the ones I considered the best at Hill’s Felton shop. All of these guitars were set up at the Hill shop so they’re guaranteed to play as well as any of the Hill guitars.
Honestly this guitar surpasses all of the student guitars from some major companies. New Millennium Guitar will only deal superior instruments so you can be assured that this is the finest in sound and playability in this student category.
I have made some final determinations concerning woods and arrived at spruce and Indian rosewood as my preferred combination; have also looked back to the 7-fan brace top construction as probably the most tonally responsive setup. The lattice-braced guitars lacks the width of tonal color of the 7-fan but is sufficient to broadcast my music being punchier and louder. Two of my favorite luthiers, Greg Byers and Kenny Hill have recently made guitars with lattice-bracing so I am confirmed by their ears that it is sufficiently robust in transmitting good tone since both luthiers are dedicated to this cause.
And what are we talking about here? The new Angella Americana, a guitar I named and screamed for its existence. Randy, with his last guitar that I reviewed instantly turned out to be my favorite builder these days so I asked for something in line with my sound sensibilities and visual aesthetics. With German spruce and Indian rosewood this guitar was made in line with my tonal thinking and even compositional needs for a full and robust sound that has a tremendously beautiful sustain and musical decay. Musical decay is a term I learned from Randy.
The Angella is a 9-braced top in German spruce so this is the starting point towards the tight braced guitar forwarded by Ignacio Fleta in the 1950’s. Fleta was a cello maker and repairer who kept running the cello of Pablo Casals. It is no wonder that his basic building technique was to make the guitar like a violin with the body and neck made separately and joined by a dovetail. Fleta also used a 9-fan bracing pattern that made his guitars so large and so mysterious sounding that Segovia and John Williams used them for performance and recording. I contend that it is really the first modern guitar since Torres was just a culmination of building trends; Fleta stepped away from prevailing building trends and did something totally different.
I will say right off the bat in assessing the sound of this guitar is that it is the best sounding guitar I have heard in seven or so years. It is remarkable in its ability to be crystalline and in the same piece of music, be absolutely sweet depending on the right hand’s disposition. This is so hard to achieve, usually a guitar has one of the other, but never the two in abundance! I believe my choice of Indian rosewood made the difference because this is a guitar more to my tastes than the same guitar with Brazilian rosewood that I reviewed earlier.
More than likely it is the tighter bracing that makes this kind of speaking possible although I haven’t heard a lattice guitar that has such a present “g” string that will speak open, and at any fret and even above the 12th fret. Another aspect of this tight bracing is the guitar is able to speak at low volumes and it does not “crap” out at high volumes and this to me is the worst characteristic of looser braced guitars.
Being a firm American in all ways that characterize the national personality, and old fashioned type of American that is extremely proud of being such, a composer that is involved in Americanisms and searching for a national aesthetic in a classical guitar, I almost despise Moorish rosettes. I am not a Spaniard and I don’t perform or compose Spanish music. The beauty of the Moorish rosette and Spanish guitar music is undeniable but I would rather have no rosette than a Moorish one so I asked Randy to “Americanize” a rosette and to look towards our great Native American heritage without copying. After all Native America IS America and most of us are but transports to this country by our ancestors. The rosette is only the finishing touch to a guitar that is an American one, made by a bold explorer in the American spirit of experimentation, another firm American that has found an American sound and visual identity.
