The Mathematics of Guitar Tuning

I have a few nuggets of basic music theory as they apply to the guitar.  This first one is about the difficulty of tuning guitars – and indeed any musical instrument – accurately, which I will show by looking at the mathematics of note frequencies.

In standard tuning, guitar strings are pitched either a perfect 4th (5 frets) or a major 3rd (4 frets) apart, and the ratios of frequencies are 4:3 (perfect 4th) and 5:4 (major 3rd). Therefore we multiply the frequency of each string’s open note by the appropriate ratio to get the frequency of the next string’s open note.

The bottom and top strings of a guitar are two octaves apart, which means doubling the frequency twice. The frequency of the low E on a guitar is actually 82.4 Hz, if we use A440 tuning, but we will use a notional base note of 100 Hz (it’s not so far out anyway, that’s about 3 or 4 semitones higher). Hence, doubling that twice, the top string should be at 400 Hz.

However, if we go up string by string, we get the following:
E – Pitch of lowest string = 100
A – Up a fourth (4/3) = 133.3
D – Up a fourth (4/3) = 177.8
G – Up a fourth (4/3) = 237.0
B – Up a third (5/4) = 296.3
E – Up a fourth (4/3) = 395.1

So we reach 395 Hz instead of 400 Hz, which is about a fifth of a semitone out. And that’s why you can’t tune your guitar! :)

PRS Periscope Guitar Wood Selection Videos

I’m a big fan of PRS guitars, and over the last few months they have released several videos on Periscope where they pick out the woods and design a private stock guitar, guided by voting from the live Periscope users.  One of the regular types of post on this site will be interesting videos that I’ve found on YouTube, whether old or new, and I’m kicking that off by linking to all of these Periscope wood selection videos so far.

I found these videos fascinating, to see the private stock wood library and the actual pieces of wood that they turn into beautiful and incredibly expensive guitars!

The original (unfortunately they committed the cardinal sin of holding the phone upright rather than on its side).  This is a Custom 24, and right now it’s actually up for sale secondhand at World Guitars for £7995.  More pictures can be found on the PRS Guitars blog entry about this guitar.

Number two, a semi-hollow McCarty – again, they made a blog entry for this one:

Number Three – this one is a Paul’s Guitar:

An interesting nugget of information from this video: most curly Maple trees don’t grow big enough to make one-piece tops.

Numbers 4 & 5 – they started to do them two at a time.  Interestingly, they show the finished second Periscope guitar at the start, and a fine instrument it looks too!  Here they did two Tremonti guitars.

Six and seven were done together again.  Fortunately, by now they’d figured out how to hold the camera the right way up!

And the latest one was eight and nine:

I’ll try to keep an eye out for more pictures of the finished guitars – some of them probably haven’t been finished yet, and PRS has only blogged about the first two, as I linked above.

Enjoy these videos!

Unboxing my new Marshall

Here’s the first link to one of my videos on YouTube!  I recently bought a Marshall Mini Silver Jubilee 2525H, and this was the first of several videos that I intend to make demonstrating this fine amplifier.

Until recently, I’d never played through a Marshall amplifier, and on a recent trip to England I took the opportunity to visit a shop where I was staying.  They had several Marshalls in stock, both new and secondhand, and I tried a number of them.  I was not looking at the handwired ranges as those are too expensive, and I really liked the sound and the flexibility of the DSL40C – an amp which is generally reckoned to be an excellent option in that price range.

However, the DSL40C is a combo and I really wanted a head, since I already have a 1×12 cab and I might buy a 2×12 cab in the future.  The DSL15 comes in both combo and head versions, but the DSL15H is poorly specced in comparison to the DSL40C, with neither reverb nor an FX loop.

A little while later I had some good news financially, and so I decided to celebrate by buying a Marshall.  Although I hadn’t had the opportunity to hear it, I decided to take a chance on the new Mini Silver Jubilee head.  It’s a 20W head, switchable to 5W in low power mode, and the circuit is based on the JCM800 with some modern tweaks.  It has an FX loop; no reverb but that’s not a problem as I can stick a pedal in the loop (it was the lack of both that really killed the DSL15H for me).  It’s a bit more expensive than the DSL amps but I’ve a feeling that this will be a modern classic for Marshall, and that it will be a worthy investment.

More about this amp in future posts!


Welcome to Gloopy Guitars! This website is currently under construction.

It will include news, blogs, articles, videos and links to information on electric guitars and related gear and other topics.

The site was created on 1 July 2016 and we hope to make some content available quickly, and then update the various sections on a regular basis.  Come back in a day or two to see our progress!