Wednesday, 25 April 2012

The Sound of Music

Oscilloscopes and guitars are a wonderful combination :-)

This is what an open-E played on the 6th string of my Stratocaster knock-off looks like:-

The two vertical dashed lines measure that time between two consecutive peaks (12.19ms) and from this we can work out that the fundamental frequency is 82Hz (as it should be...E on the 6th string is supposed to be 82.4Hz).

The scope can also do spectrum analysis (showing the harmonic content).  Here's the same open-6th string:-

Unsurprisingly, you see a strong peak at 82.4Hz (the fundamental) with 1st harmonic (164Hz, one octave above), 2nd (247Hz, which is B on the 2nd string, nicely illustrating the relationship to the 5th note in a chord) and 3rd (329Hz, which is the E on the 1st string, two octaves above the fundamental) all strongly present.  Although there isn't much of it, 4th harmonic occurs at 412Hz (you can just barely see it).  This is G# played on the 1st string which illustrates the role of the major 3rd note in a chord.  I think its interesting to see how the notes of a major chord all occur as harmonics of the fundamental.

Another interesting thing to look at is how tuning using harmonics works.  This is the 6th string with me barely touching the string just above the 12th fret to damp the first harmonic:-

Two interesting things:  the strongest peak is at 164Hz (one octave above that open E, just as you would expect).  The fundamental frequency of that string is almost completely gone (because my finger prevents the string from moving at its centre point).  Also, there is very little other harmonic content.  Sure enough, if I graph the signal it is much closer to being a pure sine wave at 164Hz:-

If you play that with another (nearly) pure sine wave which is only slightly different (i.e. fractionally out of tune) they will interfere with each other, creating that "fading in and out" effect that we listen for when tuning using harmonics.  They will fade in and out at a rate equal to the frequency difference (which is why you can only hear it when you are very close...tuned to within a few Hz)

These graphs illustrate this pretty well.  Here are harmonics on two strings (6th string 5th fret and 5th string 7th fret) which are slightly out of tune:-

The "waviness" in the signal shows the interference between the two (at ~3Hz, measured with the vertical dashed lines) which I can hear as the characteristic fading in and out.  When I correct the tuning and repeat the test...

...the "waviness" is gone.  This video illustrates what is going on:-


Finally, it is interesting to see the harmonic content of the same note played on two different strings.  Here's the open 5th:-

And here's the same A played on the 5th fret of the 6th string:-

Note the much stronger fundamental (110Hz) compared to the 1st harmonic.

Saorview on the cheap

Irish readers who aren't living under a rock should know by now that the analogue terrestrial TV service will be switched off in October of this year (i.e. 2012).  If you haven't make some arrangements to receive digital TV by then you will be enjoying uninterrupted views of cosmic noise, left over from the big bang (otherwise known as "snow" or "static").

I came across plans for a homebrew antenna at  I just had to tried it and it worked beyond my wildest expectations.  Here it is, mounted in my attic, facing roughly in the direction of the Kippure transmitter:-

Signal strength...100%, bit-error rate...0%:-

The only part I had to buy was the 300Ω <-> 75Ω balun (part number FD78K from Maplin, about €3.50)


I have been running with this for over a year now and it works perfectly.  I have made a few more of them for family and friends with equal success, even in locations where analogue RTE service was poor.

If you really really can't pick up the Saorview terrestrial service, there is also the Saorsat satellite service.  You will need a Ka-band LNB (which is different to the normal type of LNB you would use for picking up Sky/Freesat etc. from Astra 2) and a dish aligned on 9oE.  I tried it with an ordinary cheap-and-cheerful satellite receiver and a dinky 40cm dish mounted in a bicycle-repair stand...

Saorsat dish

...and it works a treat.  You don't get TV3 or 3e at the moment but hopefully that will change.  I haven't tried it, but I understand that it is possible to use a slightly bigger dish and mount a normal LNB off-centre and you can pick up both Saorsat and Sky/Freesat etc. using a single dish. (where I bought the Ka-band LNB among other goodies) sell a mounting bracket sized for exactly this purpose (the positioning of the LNB is critical for this trick to work).  Its a great site with a great range of well-priced products.  They also make their own excellent tutorial videos.  Highly recommended.