ProSoundWeb Community

Please login or register.

Login with username, password and session length
Advanced search  

Pages: [1] 2  All   Go Down

Author Topic: Harmonics and fundamentals  (Read 2672 times)

luis Markson

  • Sr. Member
  • ****
  • Offline Offline
  • Posts: 295
  • Just keep going....
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?

Logged

John Roberts {JR}

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 13337
  • Hickory, Mississippi, USA
    • Resotune
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
Logged
Tune it or don't play it... please

luis Markson

  • Sr. Member
  • ****
  • Offline Offline
  • Posts: 295
  • Just keep going....
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?




Logged

Craig Walsh

  • Newbie
  • *
  • Offline Offline
  • Posts: 1
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). 
Logged

Tim McCulloch

  • SR Forums
  • Hero Member
  • *
  • Offline Offline
  • Posts: 13311
  • Wichita, Kansas USA
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...
Logged
Chewing through your wimpy dreams
They eat without a sound,
Digesting England by the pound.

luis Markson

  • Sr. Member
  • ****
  • Offline Offline
  • Posts: 295
  • Just keep going....
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.

Logged

John Roberts {JR}

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 13337
  • Hickory, Mississippi, USA
    • Resotune
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
Logged
Tune it or don't play it... please

thomas jones

  • Newbie
  • *
  • Offline Offline
  • Posts: 21
  • NE WI
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.
Logged
I came late but I made up for it by leaving early.

luis Markson

  • Sr. Member
  • ****
  • Offline Offline
  • Posts: 295
  • Just keep going....
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)?
Logged

Charlie Zureki

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 1206
  • South Eastern Michigan (near Windsor)
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
Logged
Do it the right way....don't be a Dino!
Pages: [1] 2  All   Go Up
 


Page created in 0.18 seconds with 23 queries.