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I have a somewhat bizarre question, I don't really understand this musical concepts and I think that some Electrical engineering could help in this case, especially with the analytic phase.

Assuming that you are considering the music as an electric signal, and you have to define the properties and the values that this hypothetical electrical signals must offer :

  • what is an harmonics ? For example when you play a single note on a piano and you press 1 key, the other keys/strings around that key vibrate and create something that you hear as 1 single note but in reality it's something composed of multiple harmonics. What is the parallel that works in Electrical engineering ?
  • what is an Accordion ?
  • also if you have a note that is standardized and defined to be at X Hz, this means that you have X bandwidth ? What goes and fits in that bandwidth ? It means that if a note plays at 50Hz from a string I can get noise and additional harmonics from 0 to 50Hz only from that string ? This is like having an engine producing AC at 50Hz that can spike sometimes or that needs to "clean" its own output ?

According to my intentions I would like to compare this concepts to something practical and maybe some working components like a transformer, a resistance, a capacitor, use whatever you want that fits the explanation.

I would like to know how things look like, what properties are expressed and in case of diagrams and pictures what is the domain on the x axis and the domain on the y.

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closed as off-topic by Scott Seidman, Matt Young, Joe Hass, Leon Heller, Daniel Grillo Apr 8 at 2:47

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I'm assuming you have no background with the difference between the time and the frequency domain? –  horta Apr 8 at 0:57
    
@horta a recap is always a good thing –  user2485710 Apr 8 at 0:59
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This question appears to be off-topic because it is not about electrical engineering –  Scott Seidman Apr 8 at 0:59
    
accordion ac·cor·di·on [uh-kawr-dee-uhn] noun A horrific, ear piercing, portable wind instrument having a large bellows for forcing air through small metal reeds, a keyboard for the right hand, and buttons for sounding single bass notes or chords for the left hand. "A gentleman is a man who knows how to play the accordion, but doesn't." –  Matt Young Apr 8 at 0:59
    
@ScottSeidman How could it be ? I'm asking you to formulate an answer in engineer terms –  user2485710 Apr 8 at 1:01

3 Answers 3

up vote 2 down vote accepted

There's a lot of questions in this post. In very brief attempt to summarize this topic, a pure note would be a sine wave in the time domain. In the frequency domain, this is represented by a single spike at a point on the x-axis (now the frequency axis starting at 0 and usually going up logorithmically).

"A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency" http://en.wikipedia.org/wiki/Harmonic
So a harmonic is nothing more than frequency that's double or triple or quad etc. the original frequency. Most notes made by instruments aren't pure sine waves so you end up getting some kind of harmonics coming from it which can be seen somewhat here: http://www.dspguide.com/ch11/5.htm

Bandwidth is simply a measure of a range of frequencies. A note isn't a bandwidth. A note and its harmonics could be filtered with a well chosen resistor and capacitor to filter a certain bandwidth that allows the note and it's harmonics to pass. Hope I made the frequency world a little less foggy...

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I like to picture the frequency domain as the set of frequencies that are resulting from the FFT for a given wave. It's basically the internal look to the components of a wave from an analytical and numerical viewpoint. The point is, where do you find Harmonics or an equivalent concept in the EE ? –  user2485710 Apr 8 at 1:23
    
@user2485710: In non-sine waves, such as the odd harmonics of a square wave. –  Ignacio Vazquez-Abrams Apr 8 at 1:25
    
@IgnacioVazquez-Abrams could you elaborate more ? a picture maybe ? –  user2485710 Apr 8 at 1:38
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@IgnacioVazquez-Abrams so a square wave is suitable for something like digital communications ( 1 and 0 ) because even with some noise ( more harmonics ) the frequency domain clearly shows the Hz and the values from the original signal ? –  user2485710 Apr 8 at 1:46

A single note is what you get out of a [sine wave] oscillator. If your oscillator drifts a bit, the frequency out will change: variations like this are called "frequency jitter".

If you have a single 50Hz (Hetrz) oscillator, and it drifts by +/- 1 Hz, then you could say it has a "bandwidth" of 2 Hz (Fmax - Fmin).

If you add MORE oscillators, and each one is at some multiple of the original (100Hz, 150Hz, etc.) they are harmonics. If you add the original and the harmonics, the effect is to "distort" the original signal. The sum of all these sources no longer looks like a sine wave. It could be square, triangle, ramp... it depends on how many harmonics you add, which ones you add, and how big they are.

It's the harmonics that make a piano sound like a piano, instead of a violin.

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I would suggest you may also make progress by examining the mechanical (physics) and psycho-acoustic aspects of music.

The musical significance of sounds corresponds to how humans have become specialized to process sounds, which in turn is an adaptation to the mechanical/physics characteristics of objects that produce sounds, and that are important to us. Particular interest in the co-evolution of human voice apparatus, and ability to detect sound nuances.

So, we are good at 'note' (fundamental frequency), and 'timbre' (mix of harmonics). This particular relationship can be easily understood by observing the vibrartion of strings -- a guitar is an easy one to examine but it applies to piano etc. Especially if you can view with a strobe light.

The string, fretted for a particular note, can vibrate using its whole length (the fundamental frequency), or vibrate the two halves with the midpoint stationary (double the frequency -- first harmonic), or thirds of the length (second harmonic). The mix of fundamental and harmonics (along with the 'envelope' pattern: onset, sustain and decay of the loudness), gives the instrument its particular recognizable character (which can be somewhat varied by the skilled player). And we recognize those patterns of harmonics and loudness even if the instrument plays a different note.

Similar logic applies to air vibrated by some device (vocal cords; a reed), with fundamental frequency and harmonics encouraged or reduced by the shape of the cavities in the mouth and nose (or instrument's plumbing). Again, that's how we recognize a person or instrument even if they sing or play a different note.

Lots of objects that aren't intended to be musical nonetheless reveal their character through this interplay of "note" (fundamental frequency) and "timbre" (pattern of harmonic vibrations)... from tigers to motorbikes.

You can extend this exploration to what happens when multiple notes are played simultaneously and so on.

Summary: Yes, there are EE analogs to a number of these phenomena, but it's the mechanics of common objects, and psycho-acoustics, that get closer to an explanation of "why is it musical".

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