combination tones and the ear

“Relating frequency to pitch as perceived by the musician, two notes will “sound” similar if they are spaced apart in frequency by a factor of two, or octave. This means that the frequency interval between 100 and 200 hertz sounds the same as that between 1,000 and 2,000 hertz or between 5,000 and 10,000 hertz. In other words, the tuning of musical scales and musical intervals is associated with frequency ratios rather than absolute frequency differences in hertz.”

Ohm’s law of hearing is a statement of the fact that the perception of the tone of a sound is a function of the amplitudes of the harmonics and not of the phase relationships between them. This is consistent with the place theory of hearing, which correlates the observed pitch with the position along the basilar membrane of the inner ear that is stimulated by the corresponding frequency.


The ear is responsive to the periodicity of a wave, so that it will hear the frequency of a complex wave as that of the fundamental whether or not the fundamental is actually present as a component in the wave, although the wave will have a different timbre than it would were the fundamental actually present. This effect, known as the missing fundamental, subjective fundamental, or periodicity pitch, is used by the ear to create the fundamental in sound radiating from a small loudspeaker that is not capable of providing low frequencies.

If the intensity of a sound is sufficiently great, the wave shape will be distorted by the ear mechanism, owing to its nonlinearity. The spectral analysis of the sound will then include frequencies that are not present in the sound wave, causing a distorted perception of the sound. If two or more sounds of great intensity are presented to the ear, this effect will introduce what are called combination tones. Two pure tones of frequency f1 and f2will create a series of new pure tones: the sum tones,

and the difference tones,

(Here n and m are any two integers.) Sum tones are difficult to hear because they are masked by the higher-intensity tones creating them, but difference tones are often observed in musical performance. For example, if the two tones are adjacent members of the harmonic series, the fundamental of that series will be produced as a difference tone, enhancing the ability of the ear to identify the fundamental pitch.

the ear

combination tones and the ear

White Noise Production

Going through field recordings I made on a canoe trip over the summer. bits where the mic is resting just below the lip of the canoe and the wind seems to make strange harmonics, the mic held near the interior body of the canoe as we slowly drift through reeds which are scraping the sides of the boat.  I just moved and the first sounds of the new home the strange hums of a house – I recorded the strange hum in the bathroom.

I took small small clips from these recordings and copy and pasted and then merged them into one long clip screen-shot-2016-11-29-at-1-20-07-pm

Above you can see how I split the areas I find interesting through my initial 3-4 times listening to the clip then picked certain sections and dragged them away. from those smaller sections I listen several more times and take a really small segment from which to make a bigger clip out of. You can see the transformation bellow.


Then next step is a series of effects mostly Eq and compressors perhaps some noise reduction


Finally I have larger chunks to play with and begin to listen to them in relation to each other.

screen-shot-2016-11-29-at-1-21-23-pm the same two clips equalized differently

White Noise Production


Over the summer I skipped a midi keyboard. I stopped learning how to use it and operate Ableton when term started as I wasn’t sure how it could be relevant to a Fine Art practice/didn’t have a direct application for it. Although perhaps that is a backwards way of looking at a term aimed at experimentation.

I had the idea that I wanted to use the dials on the midi keyboard to modulate the tones/fq that I chose for the lowest fq (adapting pitch, volume, eq, tonality). By working Live with Ableton (apposed to Audition which is more structured and linear) I could create something which is not complete planned out  but is based on a loose set of tones which organically comes together based on feel, listening, and essentially my subjectivity.

With a friend, over the summer, we figured out how to map the midi to ableton and use the dials, how ever the modulations and effects we made with the dials were not recorded in when we recorded (only the notes were). So I used Lynda to familiarize myself with my ableton.

I realized that I am trying to use an Audio Clip with midi  which doesn’t work. I looked into converting the Audio Clip into a Midi Clip but all of the options to do so alter the clip in ways I don’t want – from my understanding.

another option may be to try an use midi to operate audio effects on an audio clip… don’t really know how any of it works it may be better to work in Audition.



Combination tones/Tartini pitch/the phantom fundamental psychoacoustic phenomena


sum tone – i.e. the first column
difference tones – the latter two

I came across this first in “Low End Theory” in the section on the history of organs. The principle was developed by the composer Tartini who used the theory in his composition and claimed that it had been “revealed to him in a dream by satan”. The theory much much later became the basis for developing sonic weaponry.

Sorge, author of ‘The Secretly Kept Art of Scaling Organ Pipes’ (1764) is also known for discovering the phenomena. Those who could not afford the massive organ pipes (the lower the pitch the bigger and heavier the pipe) could use the difference tones to produce the desired “phantom” pitch.

In considering my sound installation.. I’m interested in the relationship between the speakers/fq and what happens when the body – the ‘viewer’ is placed between these relationships. I will have no idea until the day of the exhibit what it actually feels like inside the installation. I’m working with guesses and hypothesis, which is a bit scary but also takes the pressure off in the sense that I can view the whole project as an experiment.

The spacial relationship between the speakers has been settled moving upwards from lowest fq to the highest – white noise.

I thought of it at first as one big chord which would modulate into periods of dissonance and harmony. I am now interested in using it to create low phantom fundamentals.. perhaps infrasonic.. I have only read around infrasound not sure what is known and unknown about it.

also the bass logic and the subwoofer boombox are the only two speakers capable of emitting real bass tones – and the logic not as much. I don’t know if I will be able to produce the volumes and intensities needed to stimulate the phenomena.



Combination tones/Tartini pitch/the phantom fundamental psychoacoustic phenomena


Went to Richard’s film screening and started listening to his soundcloud. we went to a contemporary coral concert a couple weeks ago and the piece below reminded me of the use of sine tones with acoustic compositions. There were four speakers facing the audience and the singers in the centre.