# Will a sound composed of the frequencies 450Hz, 650Hz 850Hz have a clearly defined musical pitch? Why?

According to my lecturer, the perceived pitch of a sound composed of the following harmonics: 750Hz, 1000Hz, 1250Hz is equal to the fundamental frequency which is the highest common factor of the harmonic frequencies; so 250Hz.

He also said that the harmonic frequencies 450Hz, 650Hz 850Hz do not have a clearly defined musical pitch.

How can this be true when the harmonic frequencies have a highest common factor and therefore a fundamental frequency of 50Hz?

The brain is quite good at filling in for a few missing harmonics. For example music still sounds reasonable on a smartphone speaker even though that speaker is incapable of creating low frequencies. This Wikipedia article explains the phenomenon (thanks to Glen for the link).

So it's possible that if you heard the 2nd, 3rd and 4th overtones of 250Hz your brain would fill in the blanks and it would still sound like a 250hz note. I use the qualifier possible because I'd want to try the experiment before committing myself - taking out both the fundamental and the first overtone seems quite a big change.

However for 450Hz, 650hz and 850Hz to sound like a 50Hz note you brain would have to fill in the fundamental and the first seven overtones. I suspect this would be a mental step too far, and this combination of frequencies would instead sound like a dischord.

There must be sound synthesis apps for PCs that could generate this combination of frequencies. It would be an interesting experiment to try.

• I'm sorry but your comment: "However for 450Hz, 650hz and 850Hz to sound like a 50Hz note you brain would have to fill in the fundamental and the first seven overtones." is pure speculation unless you have a citation. – Danny Rancher Mar 19 '14 at 19:12
• Just tried this experiment with 750&1000&1250 as well as added 500 Hz signals to them in Audacity and compared it with 250 Hz sound. Didn't find any similarity... – Ruslan Mar 19 '14 at 19:12
• @DannyRancher: it's true that a combination of 450Hz, 650hz and 850Hz would be the 8th, 12th and 14th overtones of a 50Hz note i.e. the note itself and the first 7 overtones would be missing. I wasn't saying anything more than that. – John Rennie Mar 19 '14 at 19:17
• @Ruslan: really what you'd need to do is take some immediately recognisable note, e.g. an A played on a guitar or trumpet, then filter out the fundamental and first overtone to see how this changed the note. The claim made in the question is that the filtering would leave the sound still recognisable as an A. I have to say I'm not sure about this. Maybe just taking out the fundamental wouldn't matter because a lot of the characteristic sound of instruments is due to the overtones. Taking out the fundamental and first overtone is a big change though. – John Rennie Mar 19 '14 at 19:21
• @JohnRennie: Even the third and fifth harmonics alone can be sufficient to create an illusion of a root frequency, especially if the listener has been cued into what to expect [e.g. if the root, third, and fifth are played together and the root decays to nothing, the root pitch will continue to be heard]; at that point, if the frequencies of the third and fifth were changed while maintaining the same ratio, the "virtual" root frequency would change as well. – supercat Jun 1 '14 at 21:31