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Author Topic: Harmonics and fundamentals  (Read 8660 times)

luis Markson

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Harmonics and fundamentals
« on: April 26, 2011, 07:50:11 am »

If it is possible for a single harmonic to have a louder amplitude than the fundamental in a complex waveform why don't we perceive the pitch to be  the frequency of the harmonic?

If we were able to remove the fundamental what would detemine the perceived pitch?

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John Roberts {JR}

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Re: Harmonics and fundamentals
« Reply #1 on: April 26, 2011, 10:24:59 am »

Psycho-acoustics... Effectively we have been trained by experience that harmonic overtones are just that, and the fundamental is the root note.

One pretty interesting example of this phenomenon is how tympani drums make perceived notes lower than their physical size would support. The tympani makes two closely spaced resonant notes (due to the physics of their closed curved back chamber), and our brain interprets the two pitches as both being overtones of a missing lower fundamental (equal to the difference between the two real pitches present).  So we hear a lower pitch that isn't really there.

In LF loudspeakers we can sometimes get distortion products louder than the fundamentals, when those fundamentals are well below the output capability of the speaker/box. 

JR
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luis Markson

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Re: Harmonics and fundamentals
« Reply #2 on: April 26, 2011, 09:56:35 pm »

Psycho-acoustics... Effectively we have been trained by experience that harmonic overtones are just that, and the fundamental is the root note.

One pretty interesting example of this phenomenon is how tympani drums make perceived notes lower than their physical size would support. The tympani makes two closely spaced resonant notes (due to the physics of their closed curved back chamber), and our brain interprets the two pitches as both being overtones of a missing lower fundamental (equal to the difference between the two real pitches present).  So we hear a lower pitch that isn't really there.

In LF loudspeakers we can sometimes get distortion products louder than the fundamentals, when those fundamentals are well below the output capability of the speaker/box. 

JR

So I'm guessing that this must be something both measurable and predictable? Are these principals the basis for sub-harmonic synthesis?




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Craig Walsh

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Re: Harmonics and fundamentals
« Reply #3 on: April 27, 2011, 12:46:29 am »

So I'm guessing that this must be something both measurable and predictable? Are these principals the basis for sub-harmonic synthesis?

Let's consider a sound with a strong output at 100 Hz. Is this a fundamental or an overtone?

Fundamental = 100, 1st harmonic = 200, 2nd = 300, 3rd = 400
Fundamental = 50, 1st harmonic = 100, 2nd = 150, 3rd = 200
Fundamental = 25, 1st harmonic = 50, 2nd = 75, 3rd = 100

The brain integrates the missing fundamental since the information regarding the pitch is present in the harmonic structure of the waveform. Most bass rigs cannot produce adequate output at 31 Hz, the fundamental for the B string on a 5 string bass. Yet, one can easily distinguish this low B from the B played an octave higher because of this processing in our brain. I won't even get into the typical bookshelf or computer speaker, but it is possible to "hear" the low B played even if the 1st harmonic is missing if so long as the rest of the harmonics are audible.

I am not aware if existing subharmonic generators are based on this principle. I think they just add in a waveform an octave below the most prominent low frequency. Indeed, if the name is correct, then they should be synthesizing sub-harmonics (e.g. 1/n, where n=the 1st, 2nd, 3rd etc. subharmonic). 
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Tim McCulloch

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Re: Harmonics and fundamentals
« Reply #4 on: April 27, 2011, 01:30:37 am »

So I'm guessing that this must be something both measurable and predictable? Are these principals the basis for sub-harmonic synthesis?

Predictable?  Yes.  It's about the ratio of the pitches.

In pipe organ building there is a type of pedal stop called "Resultant."  They fool you into thinking there is a lower fundamental than physical pipe lengths would suggest.

This more like Waves MAXbass than a sub-harmonic synth, which are basically octave dividers.  Somewhere in a rack I still own a dbx 500...
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luis Markson

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Re: Harmonics and fundamentals
« Reply #5 on: April 28, 2011, 08:22:06 am »

Let's consider a sound with a strong output at 100 Hz. Is this a fundamental or an overtone?

Fundamental = 100, 1st harmonic = 200, 2nd = 300, 3rd = 400
Fundamental = 50, 1st harmonic = 100, 2nd = 150, 3rd = 200
Fundamental = 25, 1st harmonic = 50, 2nd = 75, 3rd = 100

The brain integrates the missing fundamental since the information regarding the pitch is present in the harmonic structure of the waveform. Most bass rigs cannot produce adequate output at 31 Hz, the fundamental for the B string on a 5 string bass. Yet, one can easily distinguish this low B from the B played an octave higher because of this processing in our brain. I won't even get into the typical bookshelf or computer speaker, but it is possible to "hear" the low B played even if the 1st harmonic is missing if so long as the rest of the harmonics are audible.

I am not aware if existing subharmonic generators are based on this principle. I think they just add in a waveform an octave below the most prominent low frequency. Indeed, if the name is correct, then they should be synthesizing sub-harmonics (e.g. 1/n, where n=the 1st, 2nd, 3rd etc. subharmonic).

So if I was to simultaneously generate 4 sine waves at 400Hz, 475Hz, 550Hz & 625Hz would we perceive the pitch to be 75Hz?

The intervals between the frequencies are the same as the harmonics for a 75Hz fundamental but occur at frequencies that are 25Hz out from the order of those harmonics.

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John Roberts {JR}

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Re: Harmonics and fundamentals
« Reply #6 on: April 28, 2011, 09:09:24 am »


So if I was to simultaneously generate 4 sine waves at 400Hz, 475Hz, 550Hz & 625Hz would we perceive the pitch to be 75Hz?

The intervals between the frequencies are the same as the harmonics for a 75Hz fundamental but occur at frequencies that are 25Hz out from the order of those harmonics.

The virtual pitch or phantom fundamental is based on a valid series of harmonics, with the fundamental weak or missing. Your example with 75Hz difference, does not map down to a 75 Hz fundamental.

In the tympani example I offered the partials are actually 1.5x, 1.99x, and 2.44, with a common term of .5x that also is a valid fundamental pitch for those specific partials. For a little more background on this, 1.5x is the most prevalent pitch perceived when that drum is played, but .5x can be heard if the drum is struck a certain way, so the relative strength and duration of these partials also influences the perception of phantom fundamental. 

JR
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thomas jones

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Re: Harmonics and fundamentals
« Reply #7 on: April 28, 2011, 10:14:58 am »

In tuning an instrument by ear to a tuning fork, for example, the subject tone is tuned below that of the fork (flat) then brought up to match the frequency of the fork. The deciding factor is a phenomenon called "beats" which lessen in frequency as the subject tunes up closer to the fork. These same beats are present in the interaction of overtones both octaves and 3rds, 4ths, 5ths and 7ths and can be of the missing fundamental that you speak of.
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luis Markson

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Re: Harmonics and fundamentals
« Reply #8 on: April 30, 2011, 02:53:13 am »

Can a harmonic be produced that is lower than the perceived pitch (fundamental)?
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Charlie Zureki

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Re: Harmonics and fundamentals
« Reply #9 on: April 30, 2011, 06:23:58 am »

Can a harmonic be produced that is lower than the perceived pitch (fundamental)?

  Sure... a subharmonic

  Hammer
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luis Markson

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Re: Harmonics and fundamentals
« Reply #10 on: April 30, 2011, 07:01:42 am »

  Sure... a subharmonic

  Hammer

I was under the impression that "subharmonic" meant a perceived pitch below a series of synthesised harmonics.
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Charlie Zureki

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Re: Harmonics and fundamentals
« Reply #11 on: April 30, 2011, 07:49:22 am »

  Sure... a subharmonic

  Hammer

I was under the impression that "subharmonic" meant a perceived pitch below a series of synthesised harmonics.

  Hello Luis,

   In regards to one of your previous posts .... A perceived pitch and a fundimental can be be the same, or, two separate things. (reread JR.'s post on his explanation)

   What do you mean by "synthesised harmonics"?

   Also, We can always measure the Fundimental  and related harmonics , but, we cannot measure "perceived harmonics", but, they can be modeled.

   Hammer
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luis Markson

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Re: Harmonics and fundamentals
« Reply #12 on: April 30, 2011, 08:44:54 am »

I was under the impression that "subharmonic" meant a perceived pitch below a series of synthesised harmonics.


  Hello Luis,

   In regards to one of your previous posts .... A perceived pitch and a fundimental can be be the same, or,   
   two separate things. (reread JR.'s post on his explanation)

Yep, I should have just said fundamental

   What do you mean by "synthesised harmonics"?

The process that plugins like Waves MAXbass use?

   Hammer


One pretty interesting example of this phenomenon is how tympani drums make perceived notes lower than their physical size would support. The tympani makes two closely spaced resonant notes (due to the physics of their closed curved back chamber), and our brain interprets the two pitches as both being overtones of a missing lower fundamental (equal to the difference between the two real pitches present).  So we hear a lower pitch that isn't really there.
JR
....

When you say " two closely spaced resonant notes" does this mean two separate sets of harmonics or two separate frequencies?


In the tympani example I offered the partials are actually 1.5x, 1.99x, and 2.44, with a common term of .5x that also is a valid fundamental pitch for those specific partials. For a little more background on this, 1.5x is the most prevalent pitch perceived when that drum is played, but .5x can be heard if the drum is struck a certain way, so the relative strength and duration of these partials also influences the perception of phantom fundamental. 


So in this example "1" is the fundamental? I am assuming 1.5x means one point five times...

So...

1 = fundamental
1.5x= perceived pitch
.5x = alternative perceived pitch (from performance style)

So here we have an example of a perceived pitch higher than the fundamental and at times lower. Or is there a fundamental at all?
« Last Edit: April 30, 2011, 08:47:18 am by luis Markson »
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John Roberts {JR}

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Re: Harmonics and fundamentals
« Reply #13 on: April 30, 2011, 10:06:39 am »




One pretty interesting example of this phenomenon is how tympani drums make perceived notes lower than their physical size would support. The tympani makes two closely spaced resonant notes (due to the physics of their closed curved back chamber), and our brain interprets the two pitches as both being overtones of a missing lower fundamental (equal to the difference between the two real pitches present).  So we hear a lower pitch that isn't really there.
JR
....

When you say " two closely spaced resonant notes" does this mean two separate sets of harmonics or two separate frequencies?
Two separate single notes with individual pitches. Drums do not make "sets of harmonics" like typical musical instruments because of their physical shape. Because the resonance waveform travels several different paths around and across the round membrane, there are pi terms in the ratios, and other obscure stuff. It gets even more complex with two headed drums, since the two heads couple together loosely and differently for different resonant series. Drums don't make overtones on integer harmonics but on non-musical ratios.   
Quote

In the tympani example I offered the partials are actually 1.5x, 1.99x, and 2.44, with a common term of .5x that also is a valid fundamental pitch for those specific partials. For a little more background on this, 1.5x is the most prevalent pitch perceived when that drum is played, but .5x can be heard if the drum is struck a certain way, so the relative strength and duration of these partials also influences the perception of phantom fundamental. 


So in this example "1" is the fundamental? I am assuming 1.5x means one point five times...

So...

1 = fundamental
1.5x= perceived pitch
.5x = alternative perceived pitch (from performance style)

So here we have an example of a perceived pitch higher than the fundamental and at times lower. Or is there a fundamental at all?


There is no, or only a very weak 1x fundamental. In a tympani the closed back severely damps the fundamental note, which would be the whole drumhead moving like a piston up and down as one. Since this fundamental would compress and rarify the air inside the drum. Overtones are moving up and down at different parts of the drumhead, so not damped by air pressure in back chamber. 

One minor terminology point,,, the physics guys call these phantom notes "virtual" notes, since they aren't really there, just like in some loudspeakers with severely attenuated fundamental, that fundamental note is virtual, not really present, while our mind fills in the missing information.

JR
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Re: Harmonics and fundamentals
« Reply #13 on: April 30, 2011, 10:06:39 am »


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