# Looking for a program that measures dissonance



## sammyooba

When one plays dissonant sounds, there is this "wobbly" sound. For example, A and A# played together creates this huge wobbly dissonant sound. Is there a program that can pick up this dissonant sound and measure it?


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## Argus

The 'wobbly' sounds are called beats. They occur when the waves move in and out of phase. Generally, faster beats equals more dissonance. You can calculate the beats quite simply if you know the frequencies of the two tones.

Mate, do yourself a favour and read Helmoltz On The Sensations of Tone or any decent acoustics book. It'll clue you in a lot on these matters.


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## sammyooba

I did a quick google search and found beat frequency. It says to just find the difference between 2 different frequencies. 

How does the number of beats in a second transition to the dissonance?

I know from from some of my previous experiments that when one raises or decreasing the frequency by about 1% isn't dissonant at all. It is like the eye of a storm. Raising/decreasing the frequency from that point starts to become very radical and dissonant, I think it was around 5-10% increase/decrease where it is most violent. After that point, it will become more and more stable at about 25% and 50%. Around 40%, it seems to become dissonant again. I believe musicians call this the devil sound in music. Trivial: 1 - .4 = .6 . Ugh oh, 666.

So Basically what I'm asking is -

Once I calculate my beats per second by subtracting, how do I translate this to dissonance? I know it can't be, 'the more beats per second, the more dissonance' Since subtracting a note an octave higher has no dissonant sound 

Nor can it be 'the least the beats per second, the more the dissonance' because of that 'eye of the storm' part.

Why i want to calculate this is because I was wanting to see if I can create a composition based on just adjusting ratios between varying degrees of non-dissonant sounding tones and varying degrees of dissonant sounding tones. I have a great idea of how this will work using some of my previous calculations, but I just need a way to measure dissonance now to be able to do this.
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I'll check out that book when I can. Thanks


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## Argus

The Helmoltz should explain a lot. The main problem with your question is when various psychoacoustics, and combination tones are taken into consideration. Plus, the subjectivity of the consonance-dissonance continuum.

Just remember all tones but sine tones are created with multiple soundwaves (partials) so the beats may not necessarily arise from the fundamental.


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## petrarch

sammyooba said:


> I did a quick google search and found beat frequency. It says to just find the difference between 2 different frequencies.
> 
> How does the number of beats in a second transition to the dissonance?


Yes, frequencies will beat with a frequency equal to their difference.

One thing to keep in mind is that only for values higher than ~15 Hz will the beat change from a variation in intensity to become audible itself.

When you mix two frequencies 1% apart, you have a difference of about 3 Hz around middle C. This is not heard as a tone, and therefore does not cause any "dissonance". The difference will have to be at least about 5% to become audible (5% of 300 Hz is 15 Hz).

Then it becomes an issue of common divisors and common multiples of the frequencies involved. If the difference is such that the ratio is made up of low integer numbers, it won't be dissonant. Dissonance starts creeping in when the ratios are made up of prime or co-prime numbers of around 5 and above.


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## petrarch

sammyooba said:


> Around 40%, it seems to become dissonant again. I believe musicians call this the devil sound in music. Trivial: 1 - .4 = .6 . Ugh oh, 666.


Not really. The diabolus in musica is the tritone, or augmented fourth, which corresponds to a ratio of 7/5. In equal temperament it divides the octave in half. 0.6 is the ratio of a minor third.


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## Philip

petrarch, 7/5 is the lesser septimal tritone, which is equal to 1.4, hence 40% above the root in terms of frequency.

sammyooba, the pulsation is calculated by subtracting the frequencies, not the ratios. Eg. in equal temperament, the pulsation heard between C4 and F#4/Gb4 is periodic at (369.9944227 Hz - 261.6255653 Hz) = 108.3688574 Hz.


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## Philip

In the same way, the "wobble" between A4 and A#4 is periodic at (440*1*2^(1/12) Hz - 440 Hz) = 26.16376152 Hz


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## petrarch

Philip said:


> petrarch, 7/5 is the lesser septimal tritone, which is equal to 1.4, hence 40% above the root in terms of frequency.


Correct, but Sammyooba was clearly decreasing the frequency by 40%, not increasing (thus the 1 - .4 = .6 little calculation).


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## Argus

petrarch said:


> Then it becomes an issue of common divisors and common multiples of the frequencies involved. If the difference is such that the ratio is made up of low integer numbers, it won't be dissonant. Dissonance starts creeping in when the ratios are made up of prime or co-prime numbers of around 5 and above.


The problem is that dissonance is a subjective term and depends on more than just the relationships of the fundamentals.

For instance, is a 45/32 tritone more dissonant than a 7/5 or 10/7 one. One is within the 5-limit but high numbers, the other is low numbers within the 7-limit. Plus, 45/32 relates better to other intervals that would be used in actual music i.e. it's a 5/4 above 9/8, a 3/2 above 15/8 etc whereas the the septimal tritones aren't. Also, 45/32 is a naturally occuring harmonic contained within partial rich tones (albeit a rather distant one).

Then there's the harmonic content of the tone. A church organ tends to sound more dissonant than a flute ensemble simply because of the overtone rich timbre. The dissonance level depends largely on the situation the intervals are used in.

So I'm unsure about the low prime number ratios = greater consonance always being the case, especially in actual music and not acoustical experiments. Same reason why the 7/4 harmonic seventh can sound a bit off in music, it's fine in relation to the unity but with other likely tones that are part of the scale it will probably clash. Then again La Monte Young's Well Tuned Piano is built around 7/4's and 3/2's and it works well.


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