Relationship between overtones and harmonics definition

What's the difference between overtones and harmonics? - Music: Practice & Theory Stack Exchange

relationship between overtones and harmonics definition

The term harmonic has a precise meaning - that of an integer (whole number) multiple of the fundamental frequency of a vibrating object. The term overtone is. Harmonics obey the Bullard Laws of Harmonics, which is a new discovery that I made while researching harmonics. You can find this list in Wikipedia, minus the . Look up overtone in Wiktionary, the free dictionary. Overtones, partials and harmonics from fundamental frequency.

It turns out that when the string is thick, its ends are comparatively stiff which shortens the effective string length.


And the bendier the whole shape is, the more it is effectively shortened. So the overtones of thick strings tend to have a higher frequency than the proper harmonics would have.

So the various modes and thus the overtones of the string are approximately harmonics but not perfectly so. An interesting other case are free reeds like in a harmonica or accordion.

Difference Between Harmonics and Overtones

The reed travels through a reed plate with slots, a metal reed basically a rectangular strip of metal blocking the slot is mounted on one side and sort of punches hard holes into the air stream when bending back and forth through the slot. Since the punching-holes-in-the-air-stream act is periodic, the resulting overtone-rich sound does not have any disharmonicity.

However, the reed action itself has higher modes: Now free reeds are not just flat but are profiled in a manner where bending the reeds stronger will still result in the same frequency accordion or will result in bent pitches harmonica.

relationship between overtones and harmonics definition

Because of that profile, the metal overtones are usually so far away from the harmonics that they don't get excited. However, when tuning such reeds, one scratches or files the reed in different places depending on whether it needs to go up or down in pitch. In the process of tuning it may happen that one of the vibrating modes comes close to an actual harmonic.

An Introduction to Overtones and Harmonics

In that case, it will get excited and interfere with the air harmonics from the "punching a hole in the airstream" act. Most importantly, bar makers may reshape the bar in ways that alter the relationships between the frequencies of the different modes, bringing some of the most prominent ones into harmonic relationships. In some ways bells are similar to the gongs discussed earlier: Makers of large bells go to great ends to manage the relationships between these modes, with the idea of tuning the most prominent among them to relationships that will make musical sense to the ear and help the listener to focus on the frequency of one mode in particular as the defining pitch.

Nonetheless, you may have had the experience of listening to a melody played on a set of carillon bells, and at some point realizing that your ears were tracking some unintended mode in the bell sound as the defining pitch.

Difference Between Harmonics and Overtones

Interestingly, the mode that is intended and usually heard as the defining pitch is not the lowest of the frequencies present. There is quieter but still audible lower frequency within the carillon bell tone known as the hum tone. The mode that gives the bell its defining pitch, meanwhile, is variously known as the strike tone, the prime, or sometimes, confusingly, as the fundamental. I have found this bell terminology to be useful in other contexts.

Recently I made a set of disk gongs in which I managed to adjust the inharmonic relationships between three of the most prominent modes to where they aligned in much more coherent relationships.

Overtone - Wikipedia

Specifically, I got them pretty close to octave relationships. I did this through a combination of careful sizing of the gongs and careful hammering of the nipple at the center. You can read about it here. Like the big bells, these tuned gongs have a clear defining pitch.

Borrowing the carillon terminology, this pitch can be called the strike tone or prime. And of course there are a lot of other frequencies present. Together these reinforce very nicely the sense of pitch, while additional quieter inharmonics add a bit of color. Aside from specialized cases such as strings, carefully designed wind instruments, and the artificial timbres of many electronic instruments, most physical vibrating bodies are not well described by saying they have a single fundamental followed by a series of harmonics.

In some other cases, as just discussed, it seems useful to borrow terminology from the carillon bells. Those are cases where we can speak of a prime tone as the defining pitch, without implying that that defining pitch is the lowest tone present, nor that it is the fundamental tone of a single overtone series.

These are the cases in which many modes of vibration are present with all of their corresponding audible frequencies, and the effect on the ear tends to be ambiguous as to which of them, if any, is most naturally heard as a defining pitch.

What is the difference between an overtone and a harmonic?

One can simply think of the vibrating body as having multiple modes of vibration producing different frequencies. Then try to be realistic and open-minded which modes are most audible, what the relationships between them happen to be, and how the ear makes sense of the blend.

Words like fundamental, overtone, harmonic and inharmonic become less important in such cases.

relationship between overtones and harmonics definition