Answers To A Student’s Questions About The Harmonic Series.

Questions People Have About The Harmonic Series.

These questions came from my close friend and guitar student Pascal, after he read my blog about the harmonic series, which you can read here:

The Harmonic Series & Its Implications on Composition.

I wanted to post these questions here for anybody else who is interested in learning about the nature of sound.
I believe it makes you a deeper musician if you understand the core of how magically structured sound is in nature.

Is a wave of ONE “pure harmonic” (Contained in the string vibration that produces a C note for example) the same type of Harmonic as the “natural harmonics” that is produced when you place a finger on top of the string? Or does that “natural harmonic” contain more “sub harmonics” than a pure Harmonic?

Ok, first off: there is no such thing as “subharmonics”.
A harmonic already is a simple, single vibration. You can’t have less than that one simple vibration, or you’d have complete silence.
There is also no such thing as a “pure harmonic”.
A harmonic always is “pure”, assuming that “pure” in this case means “one single vibration”.

So it already makes things easier to understand if we know that all the names “natural harmonic”, “pure harmonic”, or “sub harmonic” are either non-existing terms or are all different names for exactly the same thing: simply, “a harmonic”.

Yes: the natural harmonic that you produce when you pick a string while very gently touching it on the 5th, 7th or 12th fret, is one of the harmonics that make up the complete vibration/sound of that open string.

The reason why it is called “natural harmonic” in this case is purely and only a specific guitar technical term. This specific nomenclature doesn’t having anything to do with the theory of the harmonic series.
This is just the name we give to the technique of playing a harmonic that specific way on a guitar, as opposed to a “pinch harmonic” or “tap harmonic”.

When you hit harmonics on those frets on an E string, you are isolating those particular harmonics to vibrate independently from the rest of the harmonics in the series that that make up that E note.
In other words: when you hit a natural harmonic on the 5th, 7th, or 12th fret, only that one harmonic in the series vibrates, and none of the other harmonics in the series vibrate.
So your string only vibrates partially, only producing 1 single vibration.

Since there is no C string on a guitar, to play harmonics that are part of the harmonic series of C, you would have to finger a C note and then pick that string while touching it 5, 7 or 12 frets above the fingered C note.

Every vibration creates sound.
A harmonic is a sound, created by a pure, simple vibration.

A harmonic is THE MOST simple vibration.
It is a single vibration, that stands on itself, and that does not contain any other vibrations but just that one vibration that it is.
So there are no such things as “subharmonics”

Every note you play on your guitar, consists of a whole series of such simple/single vibrations that are all mathematically related to one another.
Meaning: one vibration moves twice as quickly as the first harmonic (octave), another vibration moves 3 times as quickly as the first harmonic (5th).
In other words: all vibrations are mathematical integers, mathematically related to the first harmonic in the series.

I think I found a video which gives a good view of harmonics in string vibration? What do you think?

That is exactly how it works and how it looks like!
Great video.

The complexity of the string vibration as shown in that video, is the result of all the embedded vibrations all interacting with one another.
This adds up to a complex looking string motion.

If however you play one single harmonic: the string moves much less.
As a matter of fact: the string vibration then looks like a sine wave.

This is a good site too:
Guitar String Vibration

I don’t see a minor 3rd between E and G and between G and Bb. Why ?

Because the string does not vibrate that way.

It’s really all physics and math.
Any object that vibrates in nature, vibrates in natural divisions of the entire length of that object.
Meaning: a string would never vibrate in for example 13/11ths of its full length because that is an unnatural division.
Diving by 2, by 3, by 4 etc. are natural, simple divisions.
“Natural” in this case means “not random”.

IF a string’s harmonics would vibrate at weird divisions like 12/7ths or 11/13ths of the length of a string, I think you would have dissonant odd bell like sounds.
I think you would have sounds that you can no longer sing, like for example the sound of a clang-y bell, where there are so many random harmonics that you can no longer discern a clearly visible pitch.

However; what makes up the highness or lowness (pitch) of a sound is an evenly reoccurring number of cycles per second.
This is called the “frequency”.
The higher the number of repetitions of that cycle per second, the higher the pitch.

What is that cycle?
Well it is basically the whole string vibration from the beginning of the string motion till where the vibration starts it’s motion over again.
When a string vibrates 440 times in a second, we are hearing an A note.
When the string vibrates 445 times in a second, we are hearing an A note that sounds slightly sharp.

This means that you get a naturally reoccurring wave (vibration) that keeps repeating over and over again for a set number of times per second.
This is why our ear can detect a recognizable note that we can actually sing.

It is because the wave keeps repeating without any change to that wave’s motion, that we hear a recognizable pitch.

When that set wave, vibrates 440 times in a 2nd, we hear an A and we can discern and sing that pitch.
If however: the first cycle would not repeat itself but change its motion (the shape of its vibration) with every repetition, our ear would be confused and would not be able to follow the sound.
After all: that would mean that every repetition of the cycle would be made up of a number of constantly changing harmonics.

You can’t discern a singable, recognizable pitch, if the harmonics that make up the fabric of that pitch, keep randomly dropping in and out and changing every time the vibrations cycle starts over again.

It would be like listing to a plethora of randomly occurring pitches all at one.
This would be a bit like listening to 10 people all talking at the same time, or listening to 4 songs simultaneously, or the sound of everybody in the orchestra all tuning their instruments all at once.

The actual sound of 1 wave is too short for our ear to be able to detect that sound.
It needs to repeat a certain amount of times for a certain length before our ear knows that that was an A.

So anser to that question: you don’t have any other harmonics than the ones described in the harmonic series, because IF there WERE other harmonics besides these ones, then those harmonics would not longer be simple mathematical multiplications/divisions of one another.
They would be much more complex mathematical ratios.
This would produce complex/dissonant sounds that are not useful for creating music.

Think “pulling your nails over a chalkboard”, or “scratching with your fork into your plate really hard”.
Not very useful sounds in a music setting.

I suppose that all the series of harmonics (even we don’t hear them) vibrate immediately at the same time right? Or Is there a first harmonic that sounds first followed by another one, etc.?

To make sure, there is only ONE harmonic series.
That harmonic series is exactly the same for every note you can play on every instrument.

It’s a bit like for example a major scale.
There is only 1 major scale. “Major scale”, just like every scale, is the name of a certain intervallic order of distances between notes.
That intervallic order is: 2 whole steps, half step, 3 whole steps, half step.
You can start this from any of the 12 notes that exist in our music.

By the same token: the notes that make up the harmonic series are always exactly the same order for every note as well.

Root harmonic (in relationship to the note you are playing), followed by root again up an octave from harmonic number 1, followed by the 5th, then root again an octave above harmonic number 2, etc.
For reference, check The Harmonic Series & Its Implications on Composition.

Looking at it that way: the harmonic series literally really is a scale. It is a scale that consists of harmonics only.
It is a scale that is embedded in every note we can play on every instrument.
Really cool to look at it that way.

Yes, all harmonics in the whole series all vibrate/sound simultaneously when you hit a note on your guitar, exactly like in that video.
All harmonics are mini vibrations that are all parts of the greater whole: the big string vibration you are seeing with your eyes.

The vibration you are seeing with your eyes, is predominantly the first harmonic btw in the harmonic series.
The first harmonic is the strongest vibration. It has the most energy.
The harmonics get weaker the further they are in the series.

In your blog, I don’t see C2 on the chart. When you write “the next node, at 1/3 is close to G2 etc.”, what does that mean “close to G2”. (Does it mean that the first G in the Harmonic series should be G1?)

No that harmonic in that graphic in the blog is correctly labeled as G2, because G1 would be the G harmonic between the first 2 C’s in the series.
There is no vibration that produces a G note after the first harmonic when you hit a C on your guitar.
The next faster vibration after the first harmonic, is a C again an octave above the first C harmonic.

The numbers represents octaves.

C in the first octave would be C1
The the note 5 steps higher than that C in the same octave, would be G1 (which is non existent in the harmonic series of the note C)
Then C in the next octave, would be octave number 2 would be C2 (which is harmonic number 2 in the series of C, and the G that comes 5 notes higher from there would be G2 (which is the 3rd harmonic in the series of C), etc.

In recap:

So in the harmonic series for a C note, the first 4 harmonics are: C – C – G – C

  1. The first C would be called C1,
  2. then there is no G,
  3. the next harnonic is C again, which would be C2 (2nd octave after the first C which was C1).
  4. This means that the first G, the next harmonic, following after C2, is going to to be G2 because that G note is in the 2nd octave, as it follows after the 2nd C.
  5. etc.

If C is the note I’m playing, the First Harmonic is C2 ( ratio 2:1), which is a Perfect Octave, then I have G1 the Third Harmonic which is the Perfect 5th

No, the numbering of the harmonics their octaves is not in relationship to the C note you are playing, but in relationship to the very first vibration in the harmonic series of that C note.
All octaves are counted starting the first C harmonic in the series of harmonics.

This ties in to the above.
The numbers are not numbers of where the harnonic is in the harmonic series: the number represents octaves starting from the very first harmonic.
“3” does not mean “3rd note in the series”.
“3” means that that note is in the 3rd octave.

The first harmonic is the start of the first octave.
That starts on a C note.

This system is taken from the map out of a piano keyboard.

C1 is the start of the first 7 white and 5 black keys on a piano.
C2 is the start of the next octave. So any letter that is accompanied by the number 1, is a note that falls in between C1 and C2.
D4 for example: is the D note that falls in the 4th octave of the piano, in between C3 and C5.

Translating that to the order of the notes in the harmonic series, we get:

  1. The first C is C1
  2. The next one is C2
  3. The first G is G2 because it follows after C2 (same octave)
  4. the next harmonic is C3
  5. The next harmonic, E is E3 (same octave as the previous C)
  6. the G that follows is G3 (as it is in the same octave as the previous C and E harmonics)
  7. then Bb3
  8. then the D that follows is going to be D4, because it is up a 3rd from the previous Bb, which means that it passed over the next C (C4) octave.
  9. etc.

Why is there no harmonic F note… a Perfect 4th?

This ties in to a previous answer.
A string simple does not vibrate that way: it vibrates at even divisions of its full length.

If there would be such an odd vibration that produces an F, you would get a very hard to sing sound or a sound that has no identifiable pitch.
Like again for example the sound you get when you scratch your fork into your plate.
You cannot sing that sound that then gets produced. There is no clear pitch.

Conclusion

Though I believe this knowledge makes you a better, deeper, more well-rounded musician, I know this info isn’t for everyone.
Sound designers and recording engineers love these topics. 🙂
The above info is easier to digest if you’ve read the original blog post on the harmonic series first.

If you have any questions yourself about this or other music topics: you can hit me up in the comments section below.
If you like this blog: give it a rating and feel free to also give me any feedback.
I believe everything can always be improved. I’d gladly implement your suggestions and ideas in this blog or the next.

Be on the look out for more blogs about everything guitar, music, songwriting and music education.


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