At some point in your guitar-playing life, you’ll likely experience a faulty tuning key and need to replace it. Maybe your current tuners aren’t accurate enough, or seem to weigh your headstock down? Or maybe you just like the look of Kluson “green keys” instead of your Gotoh’s. Whatever the reason, it’s important to have at least somewhat of an understanding of what these things are and how they work before you spend money to replace them.

The first thing you’ll need to look at, of course, are the technical specs of the tuners you currently have to make sure you don’t cause yourself too much grief installing the next ones. The best case scenario would be you finding a set that will slip seamlessly into the peg-holes of your guitar without any modification. The next best would be the required installation of “adapter bushings”, which are basically just different thicknesses of metal used to, well, adapt to variations in diameter.

The last thing you want to end up doing is widen the peg holes. Sure, it might work – but if you’re doing this to a valuable guitar, you don’t want to be doing anything that is changing it from its original condition.
Most machine heads will show in-depth measurements of all of their components so there are no surprises when it comes time to install. A good example would be here on Stewmac’s site that shows basically everything you’d need to know as far as sizing goes.

Aside from the physical-size measurements of the peg, one of the first specs you’ll always see is a ratio such as “14:1”. This has nothing to do with the installation of the part, but rather its functionality. Now, let’s not forget the ultimate reason these things exist… to keep your guitar in tune! If you were having trouble tuning, or your tuner seemed to constantly “skip” over notes or pitches, this ratio is something you want to pay close attention to. Essentially, the higher the number, the finer the tuning you are able to do. The first number is the number of full turns it takes you to turn the peg before the inner gear completes one full cycle. Therefore, if you had something that was 1:1, you can imagine how hard it would be to zero in on any given pitch. If you feel like you want something that’s a little more precise, try to find a higher ratio tuning key. I’d recommend something 16:1 or higher.

A further method of helping keep your guitar in tune would be to invest in a set of locking tuners. They basically do what the name suggests – lock your strings in place. They help prevent string slippage without the string having to be wrapped around the peg-shaft “X” number of times, which makes for an easier re-string. At the end of the day, a string is going to go out of tune because something moved somewhere. Locking things in place is a good way of preventing that!
If you’ve ever held a really old guitar in your hands and tried to tune it, you may have seen plastic tuning pegs literally fall apart in your hands. Over time, and from lots of use, the plastic can come loose from the metal. At first this can cause tuning problems as it doesn’t properly grasp the mechanism when you turn it, and later, the piece can crumble and break. You can find high-quality keys made with plastic that will last longer than others, but if you really want something that will stand the test of time, metal is your best bet.

The last thing you might want to ask yourself when considering a new set of pegs is “will this change affect my tone?” You’ll get a different answer for this depending on who you ask.
First of all, of course a better set of pegs will be less prone to rattle, fall out of tune or break which are all things that I think we can all agree makes your guitar sound better. The only other thing that can really be argued for having an affect on your tone here would be the weight of the pegs. Different players and luthiers could argue for days over which is better – a heavier headstock or lighter. Some would say the heaviness would take away from the vibration of the neck, while others would say it adds sustain. Some would argue that it really doesn’t matter. One thing that we can be sure of, however, is that a heavier/lighter set of pegs might change how you play. A guitar that is heavier or lighter at the headstock will have a different balance, and will feel different in your hands and around your shoulders. Probably not by much, but it doesn’t take much for a guitar to feel different, and consequently make you play different. My advice would be to go with a set that doesn’t change the balance of your guitar too much.
Remember, the majority of your tone comes from your fingertips, which comes from you, which comes from your current state of mind, which can be affected by how comfortable or uncomfortable an instrument is in your hands!

Tips on Tones: Issue #21 – Machine Heads from MyRareGuitars.com

Music is Mathematics

There are two basic numbering systems in music. One has to do with the scale, the other with the key.

Let’s look at the numbers relating to the scale first.

There are seven notes in the scale. Simple enough. The order of intervals, or spaces, between these 7 notes is what makes it unique. The formula, as we should all know by now is Tone, Tone, semitone, Tone, Tone, Tone, semitone.

Pythagoras ratios for guitar

Understanding the notes

So our first little bit of math is to understand that from the TWELVE notes of the chromatic scale — all the notes — the scale uses SEVEN, spaced out as described. If there were six notes in the scale, you could imagine them evenly spaced a tone away from each other. But there are seven, so there have to be a couple of semitones thrown in.

(These seven notes by the way, weren’t simply chosen by someone long ago to be the ones we’d all use. They also come from mathematics, from fractions. For example, a vibrating string tuned to A440, when halved will produce another A note, but vibrating at 880 cycles / second, an octave up. That same string doubled in length will vibrate at 220 cycle / second, yet another A an octave down. That same string cut in 3 will produce E notes, and if you cut it into quarters and make 3/4 of it ring, you’ll be listening to a D note. Try it out on your guitar, you’ll hear for yourself. By the way, the halfway mark of guitar strings is the twelfth fret, the one third mark is the seventh fret, the one quarter mark is at the fifth fret.)

Back to the seven scale notes. Chords are made by combining alternate notes from the scale. The simplest chord of all is the triad. It uses three alternate scale notes. The old one-three-five.

You can add other scale notes to those to make an extended chord. The next alternate note is the seven. So a One-Three-Five-Seven combination is called a major seventh.

Mathematics Quote from Oswald Veblen (1924)

You can add a ‘Two’ note to the chord, but it has be added on the treble side of the grouping, so you’re actually using the ‘Two’ from the next octave up. Since the root (One) note of that octave can be seen as the eighth note of the scale, a ‘Two’ note is the next one up, the ‘Nine’.

You can use the ‘Four’ note if you want, but since it’s only one semitone away from the ‘Three’, it actually replaces the ‘Three’. This chord is called ‘Sus Four’. It begs to be brought back to the Three.

If you add not the Seven note that is in the scale but the next note down, the ‘minor Seven’ it’s sometimes called, you wind up with a Seventh chord, as distinct from the major seventh. They’re also referred to as ‘dominant’.

‘Elevens’ are ‘Fours’, ‘Thirteens’ are ‘Sixes’. (Simply subtract seven from those big numbers to find out which note is being called for). And so on and so. It’s pretty straight forward really: the numbers refer to the the seven notes by their order. Just remember that the One-Three-Five are taken for granted as being present.

The next set of numbers refers to the chords within the key. Each of the seven scale notes qualifies as a starting note to build a chord using the alternate note rule. These chords are often written as Roman numerals.

I — II — III — IV — V — VI — VII

Sometimes, you’ll see them written like this:

I — ii — iii — IV — V — vi — vii

This is a good way of doing it because it shows the major / minor quality of the chords. As I’ve been trying to impress upon you, it’s really important to instantly know what all those chords are for any key. Remember The Music Building I wrote about recently.

Let’s say you see a chord written as V7. What does that mean? It means it’s the Five chord from whatever key you’re in, and it’s the Dominant Seventh version. So if you’re in C, you’re looking at a G7. Or a vi7? That would be Am7.

Record producers often write tunes out simply using the numbers. If they’re unsure of the singer’s range, they will choose a suitable the key in the studio. Only then will the numbers become actual chords, mentally converted by the players. Nashville is famous for this kind of notation.

Of course, time signatures and tempo are also related to mathematics. In fact the method we use to crank up a song is for someone to yell out ONE – TWO, A ONE – TWO – THREE – FOUR. The whole of music is one seething mass of numbers when it comes down to it. Lucky for us it sounds and feels so good to make listen back to, otherwise who would bother trying to figure it out?

I hope this article hasn’t put anyone off. The fact is, all these numbers simply become music when you do put a bit of effort into practising it. The layers of music become distinct and workable. Then the fun begins…

Kirk Lorange is one of Australia’s best know slide guitarists. He is also the author of PlaneTalk guitar method. Check out his sites: www.KirkLorange.com and www.ThatllTeachYou.com

Music is Mathematics from MyRareGuitars.com