Category Archives: Sounds / Effects

Lateral Music Theory #2: Tension, Instability

Continuing on from the earlier discussion on dissonance, there is another couple of numeric quantities that can help describe how chords are perceived. These are Tension and Instability. Instability matches the empirical perception of 3 note chords.

Tension is a word used to describe the ambiguity of how a chord seems to want to resolve. It is calculated from the relative size of the intervals of a three note combination. Specifically, from all the combinations of 3 tones from all the partials of the 3 fundamental tones.



ν is the product of the relative amplitudes of the three tones (0.0 to 1.0),

x and y are the interval sizes of the lower and upper intervals defined in semitones

α = 0.6 determines the steepness of the fall from maximal tension.

Total Instability is (I) is calculated from Tension (T) and Dissonance (D)

I = D + δT

where δ = 0.2

When all the partial combination D and T effects are summed in this way, the scores rank the sonority in a similar order to the empirically determined order.

You can calculate your own dissonance, tension, and instability for chords at a web page I wrote a while ago: here.

Lateral Music Theory #1: Dissonance

Dissonance is word used to describe how unpleasant something sounds; particularly in psycho-acoustic studies. In one article I read by Normal Cook, in the Music Perception Journal, it can be calculated numerically from the magnitude of tones that make up a sound.

The formula for calculating dissonance (D) from tones is



  • ν = the product of the relative amplitudes of the two tones (0.0 to 1.0),
  • x = the interval size defined in semitones.
  • β= -0.8 is the interval of maximum dissonance
  • β= -1.6 is the steepness of the fall from maximal dissonance
  • β= 4.0

When we plot this for 2 pure tones we get a nice little plot like this:

However, real instruments do not produce pure tones. They produce harmonics, that is, lots of extra tones that are roughly integer multiples of the frequency of the lowest tone. Interestingly, if you add up all the dissonances from all the pairs of tones between 2 “notes”, the plot starts looking a lot more interesting.

There are tantalising dips at important musical intervals; like the 5th, 4th, and octave.

I did my own plot, using the first 8 harmonics with similar magnitudes as a piano sound and got this plot:

This graph has some very interesting features. I have plotted the equal temperment semitone points with small grey lines. These miss the kinks in the dissonance plot slightly. But, when I plot the Just Intonation semitone points [1, 16/15, 9/8, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 7/4, 15/8, 2] in red, they match the troughs and kinks almost perfectly.

I wonder what this graph looks like if we extend it into the next octave?

Interestingly, this calculation can be extended to cover any combination of any number of notes and is an interesting way to compare chords of any kind. The part that appeals to me is that a simple relationship between tones and their perception can generate parts of music theory, without requiring “the edifice of music theory”. This is Lateral Music Theory.

You can calculate your own dissonance for chords at a web page I wrote a while ago: here.


Nature Sounds and the Windy Nemesis

I’m on holidays and have been reading a really interesting book by Bernie Krause called The Great Animal Orchestra.


Bernie has spent decades recording natural soundscapes and reading his book has inspired me to pay attention to the sounds of nature and make some of my own recordings here at the Novotel Twin Waters Resort near Maroochydore in Queensland.

I woke up just before dawn (5am!) and walked around to find a good spot to record. I enjoyed listening to the bird sounds but found, to my dismay, that the small amount of wind ruined most of my recordings.

Experimenting back at our apartment, I found that enclosing the Zoom H1 Handy Recorder in a baby sock helped a little, but there was still a little bit of wind noise near the lagoon and in the bush.

So did some research, and you can buy windshields for my sound recorder, or make one from fur, but I had no access to fake fur and wanted a slightly better solution than my trusty baby sock, so my ever thoughtful wife bought some wool from the supermarket and I improvised this fluffy beast using some wool and the tip of a baby sock.


I tried it out this morning at the lagoon, with some good results.

FuzzyBeastRocksRefelectiveLagoon One of the cool aspects of listening to natural soundscapes is seeing how the different animals find their own niche in time and frequency to make their voice heard. You can see this in the spectrogram of a portion of the sound here:

SpectrogramLagoonTime is on the horizontal axis, frequency is on the vertical axis. The low frequencies are the distant sounds of the surf. The high frequency sounds are of various birds that live around the lagoon.

I may still buy a proper wind screen for my sound recorder, but this improvised solution seems ok for the light breezes at dawn at the moment.


Music Creation Apps for the iPad

I’m currently digging around the internet for apps that I can create music with on the iPad. It is nice to be able to use the iPad for making things. I’ve had a really good experience with Procreate and Inkpad, so I thought I’d re-examine what’s out there for making music and make a list of things to check out. I’ve got the Animoog app for iPhone, which I’m contemplating upgrading to the iPad version, but I thought I’d see what’s out there first.

Here’s a list. Now to cherry pick it…

  • Wizdom Music Morphwiz – looks a little like an idea I had for making an app…
  • iceGear cassini – cheap, technical synth app
  • iceGear argon – even cheaper mono synth
  • 4Pockets Aurora sound studio – grid based sequencer, might be interesting
  • Yamaha TNR-I – a grid thing, might interesting to look into a bit more
  • Retronyms Tabletop (free) – have to check it out since it’s free
  • BeepStreet Impaktor – percussion synth, might be useful
  • Korg iElectribe – another percussion synth 4 track
  • Korg IMS-20 – analog synth with cables everywhere
  • Apple Garage Band – might check out, it’s cheap. I think my laptop has a version built in.
  • Animoog, of course.

An interesting app that lets apps interact in Audiobus. I don’t need it yet, but it is good to know it exists.

Another list.

  • Figure looks very interesting for knocking out ideas.
  • Animoog and Korg got another mention

Since, my immediate use for this kind of thing is knocking out some ideas, I might start with Figure; it’s a whole dollar.

Yet another list.

  • Impacktor, again. Looks like it samples whatever surface you sit the device on. Interesting
  • CP 1919 looks interesting too, some fluid physics involved.
  • Garage Band, and Figure got mentioned again

Another list mentioned Scape, by Brian Eno et. al. it looks like you make an image and that is converted to music.

I should also check out NOTION, a notation app for the iPad. It might be easier to use on the iPad than the mobile website version of Noteflight.

Coffee Cup Bass

I wrote a song that needed an upright bass.

I was quite pleased with it. I didn’t have an expensive sample library with the Upright Bass sound in it, so I grabbed a coffee cup, a pencil, a paperclip, some sticky tape, a rubber band, and a pocket knife.

After calculating the correct hole size using a formula related to a helmholtz resonator and cutting it out with the pocket knife, I had the instrument I needed.

Here is a picture.

Unfortunately, the Coffee Cup Bass is almost impossible to play. So I sampled it and played through a MIDI keyboard.

Cosmic Radiation Sound Effect Construction

I had the idea to write a theme for The Great A’Tuin, the turtle that supports the four elephants which support Discworld from the novels of Terry Pratchett. As part of this I was after a kind of “cosmic noise” effect in the background which kind sounds like a bunch of pops of static as if cosmic rays were bombarding the recording equipment. Something like the effect in the music for this awesome timelapse taken from the International Space Station is what I was after.

White and Gausian noise sounds terrible.

This article about the colours of noise is particularly interesting.

I tried Gausian noise taken to the power of 3, hoping that the effect exagerate some rare peaks as pops. But no.

After playing with some of the built in effects in Reaper, I settled on using a pink noise generator and passing the noise through a noise gate so that only very large values pass through. The attack and decay times were set short and produced the kind of sound that is good enough.

I didn’t even have to crank up SciLab to generate my own from scratch.

I used the cosmic noise in the background to this tune.