b-string – Traveling Guitarist

A common problem that people run into when they're playing their guitar is that sometimes, the B-string doesn't sound that great even though it's perfectly in tune. Explained in short, the reason why the B string always sounds out of tune is that we use the 12-tone Equal Temperament tuning system to tune the instrument, which is not 100% accurate in comparison to the way sounds occur in nature. In other words, the 12-Tone Equal Temperament tuning system is an imperfect way of tuning the guitar/piano in comparison to the way the correct notes actually sound. If we were to tune the guitar in such a way where the strings/frets were perfectly in tune with each other, it would make playing the instrument more difficult, because there would be way more frets on the guitar. In fact, people have created guitars where the strings are perfectly in tune with each other as well as the frets. And the guitar looks like a nightmare. Rather than having the guitar divided up into an equal number of frets laid out on the fretboard, the guitar looks like something you can see in the image below: Image from Unleashed.com The reason for this can be explained using the exploration of two different systems of tuning, the Equal Temperament tuning system, and Just Intonation. This is going to get a little complicated, but bear with me, I'm going to make sure that you understand by the end of this article because it took a long time for me to comprehend as well. Let's un-pack what both of these things mean. Equal Temperament explains a form of tuning in which every pair of notes are separated by the same ratio. Explained in another way, the ratio between the two frequencies of each note is the same. In Western Music, we use 12 Tone Equal Temperament, which separates the octave tone into 12 parts. So, 1/12 of the octave tone works out to be a semi-tone. A semi-tone is the difference between two frets on the guitar. Playing from the bottom open E string on the guitar, traveling up one fret by one fret all the way up until the 12th fret E on the bottom E string are all semi-tones. The twelve notes that make up the 12-note system in Western Music is divided up into 12 different semi-tones per octave. Technically, this system is "unnatural," and that's because it's not equal to the natural harmonic series. The natural harmonic series is the exact speed of the vibrations which make up the sound of each note. The main problem with the way in which we tune our pianos and guitars is the fact that the sounds they produce are not 100% equal to the natural harmonics. For instance, the 'A' right after the Middle 'C,' measured in hertz, is 440hz. Hertz measures the vibrations of the string, and each hertz is one cycle per second. Getting back to what I mentioned above, the idea of ratios explaining notes, this means that 880hz is the same note, but it's one octave higher. 880hz is also an 'A' note, but it's an octave higher than 440hz. It's a 2:1 ratio. The 2:1 ratio is an octave higher no matter the actual frequency. 220Hz is also 'A,' and 440Hz is also an 'A,' and 880Hz is also an 'A.' Using these ratios for the Hertz frequencies is what's called "Just Intonation," and it's a system of measuring sounds and it's actually 100% accurate. As I just explained, when using Just Intonation's measuring system, the 2:1 ratio for harmonic frequencies, is always communicating an Octave. And while this system is 100% right on the money, if we were to use this system to tune our instruments, it would be extremely difficult to play the instrument. Check out the image if the guitar image above and thank the fact some European guy came up with the 12-Tone Equal Temperament system. In case you didn't understand anything I just said above, let's talk about it a little more. Intervals are based on the ratios in comparison to one another, for instance, an octave is the ratio of 2:1, using the frequency in Herts to explain them. For instance, the frequency of the octave is 2x the frequency of the lower note. So if you play the A string, but then play it an octave higher, the octave higher version of it is vibrating twice as fast and because the string is vibrating twice as fast, that means that it sounds much higher. Using the ratios between intervals in this way is also known as "Just Intonation." Measuring the intervals in this way is the way that the intervals should actually be in order for them to be 100% correct. However, when we divide the octave tone into 12 different parts - semi-tones - then the ratios between the semi-tones end up being slightly imperfect. When using the Equal Temperament system of tuning, which we do in the Western World, in which the octave is divided by 12ths to create each note of the scale, every interval between each other is off by just a little bit and some more than others. For instance, a major fifth using the Just Intonation system is 2 cents flat from the Equal Temperament system, whereas Fourths are 2 cents sharp from the Equal Temperament, whereas Major Thirds, are 13 cents sharp. This is the point where it might start to make sense. If you take a look at the strings of the guitar, you'll notice that the guitar strings are usually a fourth apart from each other. Here are the tunings of each string on the guitar measured in hertz. E - 330 Hertz B - 247 Hertz G - 196 Hertz D - 147 Hertz A - 110 Hertz E - 82 Hertz Now, let's think of these harmonic frequencies using the ratios that I mentioned above. Notice the way that the Low E-String is 82Hz. The Low E-String is 82 Hz, and then an octave higher is 164 Hz, and then 328 Hz is an octave higher than 164Hz. However, notice that the high string is 330Hz. It's off by just 2 Hz. This is the compromise that I was talking about before. It's off by just a little bit, that way it can sound relatively in tune with the rest of the strings. I hope this is making more sense now. As I just mentioned above, each of the strings are separated by a fourth, ie, E to A, are four notes apart, A to D, are four notes apart, D to G, are four notes apart, but then G to B, is a third apart from each other, and then finally, B to E is a fourth apart from each other once again. This is why the B- string sounds out of tune. It's because the G string and B string are a major third different from each other, and in the Equal Temperament tuning system, the Major Third is 14 cents sharp in comparison to the Just Intonation system, which is 100% accurate. So, in other words, in certain key signatures, if the B string is slightly detuned by just 14 cents, then those two notes played together will sound just a little bit better. This is why if you tune the G and B strings by your ear, (which, if you do, you're innately using the Just Intonation system), the B-string will either sound like it's a bit flat, or the G will be a little bit sharp in comparison to the rest of the guitar that's tuned using the Equal Temperament system. This is a phenomenon that can be exemplified using the Red Hot Chili Peppers song, "Scar Tissue," and the YouTuber, Paul Davids, did a pretty good job of explaining this issue. The riff oscillates between two different notes, in the beginning, an F on the 8th fret of the 5th string, and an A on the 10th fret of the 2nd string, however, if your guitar is perfectly in tune, and you try and play this riff, you'll notice that it doesn't sound that great, and it certainly won't match the way the guitar player of the band, John Frusciante, played it on the record. It turns out that Mr. Frusciante actually had the B-string slightly detuned, which is something that other guitar players often do as well. A guitar has strings that are typically divided into 22 different frets, which means every time you're fretting the note, you're shortening the distance that the string has to vibrate, and therefore, slowing down or speeding up the vibration, which creates a different pitch of the sound. When tuning the guitar using harmonics, we are tuning the instrument based on precise ratios. In other words, if you're tuning the guitar into fourths, ie, E to A, A to D, D to G, and B to E using harmonics, in comparison to 3 frets up the string up to the 7th fret harmonic, then the one place where you'll hear that it doesn't sound right in comparison to equal temperament is from the G to the B. Explained in another way, using the "Just Intonation" and the "Equal Temperament" method will sound slightly different in certain keys than in others. There is a difference between G to B of 14%, also called 14 cents, which is the measurement we use to compare the two frequency ranges. When tuning the B string sharp or flat in standard tuning, you're making the decision to either be tuning closer to a Just Intonation Vs Equal Temperament system. Just Intonation will be more suited to some keys than others, while Equal Temperament tuning will sound weird in different keys. In conclusion, the Equal Temperament method is a way for players to shift between keys without each key sounding kind of different in terms of the ratio difference between each note. It's a compromise between the perfect tuning system and the imperfect tuning system. I hope this was helpful to you. If you need further explanation, I recommend checking out Paul David's video, "Why Didn't Frusciante Tune His Guitar?!" YouTube Video Tutorial https://www.youtube.com/watch?v=mW3YV543ll0&feature=youtu.be Conclusion I hope this article was helpful to you. Do me a favor and post this on your Facebook, Twitter, and Instagram, to help me out. Cheers and have a nice day.