Category Archives: Sound spectrum

Cicadas

Early summer days in this part of Australia ring with sound of cicadas:

These extraordinary little creatures spend years underground before popping up to find a mate  by climbing into the nearest tree. (Good David Attenborough dialogue, don’t you think?)

It’s the males that call – the females are silent but respond to a male by flicking their wings. For such a small critter the noise level they produce is incredible – over 100dB from around a metre away from just one insect.

I decided to record the sound and analyse it. To my surprise, this is what the spectrum looked like:

Cicada sound spectrum

Cicada sound spectrum

What’s surprising is that no natural oscillator I have ever seen has a gap in the spectrum, as you see here (between 600 and 800Hz). The only conclusion possible is that there there are two quite different species calling at the same time, most likely a bigger one in the lower frequency and a smaller one in the higher.

The two likely types are what are commonly called greengrocers and black princes. I have no idea which call is which…

This is a black prince:

BLACK PRINCE

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Getting comfortable with charts – the difference between noise and music

I know there’ll be some of you who turn off when faced with graphs and charts. Because they’re so useful, though, I’d like you to persevere with them. You can get a lot from them once you can relate them to something real – that’s what I’d like to try and do here.

We can all tell the difference between noise and music (although where the boundaries lie can be a matter of opinion and circumstance). First an example of noise – the sound of surf on a beach:

And next the musical sound of a singing wineglass:

Now here are the sound spectra charts of each one for comparison, beach first:

Beach noise

Beach noise

Singing wineglass

Singing wineglass

The horizontal axis of the graph shows frequency (pitch, in everyday terms), and the vertical axis shows loudness at each frequency.

The difference between the two sounds is very clear to the ear, and you can see it is also very clear from their sound spectra. Noise blasts out fairly evenly across a wide part of the sound spectrum, where a musical note has a series of well-defined peaks, often evenly spaced as in the wineglass example.

The value of the charts is that you can actually read off the frequencies of the main frequency peaks, and so compare different sounds more analytically than listening allows.

Here is another example: the noise of an electric kitchen mixer compared to the sound of a tubular gong of the sort you’ll find in wind chimes.

Here’s how the two look when you analyse them, the kitchen mixer in blue and the chime in red (I’ll leave you to imagine the sounds):

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The chart shows the sound level put out by each. One is a maddening noise, the other is a pleasant ring (unless small children get hold of it), and the chart makes the difference as clear visually as it is to your ears.

The chime produces its loudest tones at well-defined frequencies, where the mixer blasts it out right across the spectrum, with one peak at around 400Hz which could well be related to the speed of the motor. We could all hum a note to match the gong, and maybe with the mixer too, probably somewhere between G and G#, which is at the 400Hz peak.

One interesting aspect of the gong signature is that each peak is double. That’s because the gong has a split along it at the bottom, giving it two fundamental frequencies instead of just one.

Charts like this can help a lot in understanding music. The singing wineglass is one of the purest sounds you’re likely to hear (this is a different wineglass than before with a different fundamental frequency, but the same type of spectrum):

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This shows that the singing glass puts out sound strongly at some very well-defined frequencies: 709Hz, 1664Hz,1816Hz, and 2496Hz. These correspond reasonably closely to the scale notes F5, G#6, A6, and D#7 (the number refers to which octave each note belongs to). Notice that even a “pure” sound contains more than one musical note.

Thoughtlessly, the makers of the glass didn’t take the time to tune the glass to the standard musical pitches.

By contrast, I tuned the 2nd string of my Jumbo 6 guitar to the note B3 at 246.9Hz:

Here’s the analysis of the note:

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The peak frequencies in order are:

  1. 246.1Hz    (B3 is 246.9Hz)
  2. 492.2Hz    (an octave above, B4 is 493.9Hz – double 246.6Hz)
  3. 738.3Hz    (F#5 is 739.9Hz)
  4. 990.2Hz    (B5 is 987.8Hz)
  5. 1236.3Hz  (D#6 is 1318.5Hz)
  6. 1482.4Hz  (F#6 is1480.0Hz)
  7. 1728.5Hz  (somewhere between G# and A6)
  8. 1980.4Hz  (B6 is 1975.5Hz)
  9. 2226.6Hz  (C#7 is2217.5Hz)
  10. 2478.5Hz  (D#7 is 2489.0Hz)
  11. 2724.6Hz  (somewhere between E and F7)

Those with a music theory background will recognise B, C#, D#, E, and F# as notes in the B Major scale. This is what’s known as a harmonic series – more about these in another blog entry. 

Matching frequencies to scale notes

When I analyse tap tones, I work in the unit for frequency – the Hertz (Hz). Frequency tells you how many times something vibrates in one second. With sound, that means the number of times in a second the particles of air near your ear push against your eardrum. The higher the frequency, the higher the pitch of the sound.

Musicians, naturally enough, don’t care nearly as much about this as guitar makers do. They know that if you go up an octave you’re hearing a frequency double that of where you started, and they know that the notes of the Western musical scale are at particular frequencies defined by a mathematical series known as 12 tone equal temperament.

Even if you aren’t a musician, you know that as well because you’ve listened to lots of music during your life. That’s what your ear has come to expect, especially if you’re from a Western culture.

Interestingly enough, guitars and other fretted stringed instruments aren’t very good at producing exactly the right frequencies to make a major scale sound perfect. If you have an electronic tuner, you can see this if you tune a string to its correct fundamental (eg the A to 440Hz) and then work your way up the fretboard fret by fret. Notice how cranky your tuner gets?

The frets aren’t right! That is one way to see it, but the explanation is actually to do with the physics of how real strings vibrate.

The reasons are something for another time, but musicians with really good ears – especially those who play fretless instruments like violins – are often driven crazy by what’s called the inharmonicity of a guitar. Fretless players can use subtle fingering adjustments to make their notes true.

The rest of us take it as it comes and put it down to being part of the sound of the guitar. Guitar makers pull their hats down over their eyes and quietly leave the room before they’re noticed.

So anyway, here’s a chart showing the notes in the diatonic major scale.

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The chart begins at 27.5Hz because the human ear doesn’t really hear anything much below that as a continuous sound (20Hz is considered the cutoff) . It ends rather arbitrarily at 7040Hz because most instruments don’t produce much sound at those high frequencies (but mainly because guitar makers don’t care about anything much over 5000Hz).

The standard tuning of guitar strings is shaded blue for your viewing convenience.

The octave number helps identify which note you mean: the B string on a guitar is tuned to B3 at 246.9Hz. Notice the doubling of frequency from one note to its octave above.

The little gradations on your guitar tuners that show how far above or below the string is are cents. The interval between any two notes is divided up into 100 parts, but as you can probably guess that isn’t simple because the frequency interval between two notes gets ever larger the higher you go.

Driving a guitar top

I have made the point that the reason behind my Yolande shape is that I want to drive the guitar top from the centre to achieve a particular sound. But where’s the evidence?

One way to show the difference between driving the top at the centre compared to the edge is to analyse the tap tones you get from doing just that.

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 In this chart the blue line shows the response of my Jumbo 6 being tapped just behind the bridge, near the centre of the lower bout. The red line shows the response when tapped right at the edge. There are two main differences:

  1. the peak at just below 100Hz is very much lower for the edge tap, as is the next peak at about 130Hz;
  2. the treble response from about 400 to 1000Hz is stronger for the edge tap.

The first peak is the low, boomy air body response. If you do this test on your own guitar – even if you don’t analyse it the way I have – you’ll be able to hear the difference. The edge will give you a slightly higher, thinner tone compared to the boomier centre tap.

So that sets the stage for an answer to why I design the way I do.

The next chart compares the response of one of my Parlour 6 guitars with a similarly-sized Martin 000-18 which has the bridge in the usual position for a dreadnought-shaped body, closer to the soundhole. The one on the right is the Martin, a lovely guitar.

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I tapped them each on the bridge where the strings cross the saddle. Keep in mind that this is not the best one-to-one comparison because of the other differences between the guitars (different top bracing, different-sized soundhole etc). I tried to make the taps as equal as possible.

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What’s remarkable is firstly the similarity of form between the two signatures – that’s because they’re both guitars.

It’s the differences that are interesting, though. The first peak – the airbody resonance – is slightly better for the Parlour 6, as well as occurring at a higher frequency because the airbody is a bit smaller than the Martin’s. From about 220Hz upwards, the Martin’s response is consistently stronger, and this corresponds to a very bright but slightly thinner sound. The Parlour’s tone is, for want of a better way to describe it, more like a smooth red wine compared to the Martin’s cheeky white. Both tasty, but definitely different.

You can see how the strength of the tap is important for this kind of comparison. Had I tapped the Martin less strongly, the form of the response would be the same but it might fall lower than the Parlour – or vice versa.