How do you hear tones?, Find out inside Options

[Pio2001]

Here is the sonogram of the sample :



Every trial except the seventh one is made of harmonics with not only the
fundamental missing, but some early harmonics too. The highest is always at the
same frequency.

The harmonics go up or down, while the missing fundamental goes in the opposite
direction.

I got 4 times the fundamental answer, 5 times the harmonic one, and three times
I heard distinctly several notes playing together, some going up, while other go down. I'm quite the opposite of you, Carlos

This post has been edited by Pio2001: Jan 19 2006, 23:18

[QuantumKnot]

I got 100% exact answers to the table, so I guess I'm a fundamental tone listener. But I let some of my colleagues try the test, and for a good proportion of the samples, they made the opposite conclusion or were left guessing (ie. they couldn't hear the difference).

[Gecko]

I find it weird, that someone who thinks number 1 is decreasing, is a fundamentalist, while in fact the fundamental changes to a higher pitch. Same goes for the other samples.

P.S.: Please excuse the silly pun.

[benski]

Every sequence is basically a chord in the normal position, followed by another (different) chord in an inverted position. e.g. C-E-G (I), B-D-G (V). As others have pointed out, the "center of energy" has moved down, but the root has gone from C to G.

[mdmuir]

When I tried the test using my desktop speakers, I tested as a 0/12 (overtones). When I tried it again 10 hours later with my Sennheiser 850's, I tested 9/12 (more fundamental).

What is up with THAT?

[hawkeye_p]

JeanLuc pointed out an interesting fact:
I recall not being able to distinguish between my speakers in phase and out of phase (one pair of cables crossed).

This would correlate with my result.

Edit: Typo

This post has been edited by hawkeye_p: Jan 20 2006, 07:56

[Continuum]

I find it weird, that someone who thinks number 1 is decreasing, is a fundamentalist, while in fact the fundamental changes to a higher pitch.

It doesn't. The pitch of the (removed) fundamental is the same as the distance between two harmonics, so as they get closer the frequency decreases.

[hawkeye_p]

Continuum,

your interpretation is not completely right (at least as long benski's analysis is correct): The fundamental (base tone) is not removed but one octave higher.

[kjoonlee]

9/12 consistency with the table - mostly fundamentals then, if that's to be trusted.

This raises an interesting issue though - I am a competent musician, and I play well by ear, but I've often been fascinated by the fact that I can hear chords very clearly, but not the constituent notes. I can recognise progressions and subtle harmonic changes, and find them quickly on the piano, but I find it very difficult to pick the notes of a chord out in isolation (ie. sing them back). I hear the 'colour' of the chord as whole but not the individual notes very well.

Wonder how this relates to the topic under discussion.

C

You know, that reminds of how speech recognition works for vowel sounds. You measure the harmonics, and pick the harmonics that are louder than adjacent ones. The first of these is the first formant, and the second of these is the second formant. You call those harmonics "formant frequencies."

When you hear [i], [a], or [u], the main difference between the sounds is the difference between the formants. You can hear the distinct vowels very clearly, but not the individual constituent formants.

I wonder how *this* relates to the topic under discussion.

[QuantumKnot]

You know, that reminds of how speech recognition works for vowel sounds. You measure the harmonics, and pick the harmonics that are louder than adjacent ones. The first of these is the first formant, and the second of these is the second formant. You call those harmonics "formant frequencies."

When you hear [i], [a], or [u], the main difference between the sounds is the difference between the formants. You can hear the distinct vowels very clearly, but not the individual constituent formants.

I wonder how *this* relates to the topic under discussion.

The formants aren't really the individual harmonics. They are simply peaks in the power spectral envelope caused by the resonances in the vocal tract. The individual harmonics are related to the pitch and represent the glottal excitation (the vocal cords vibrating) that gets 'filtered' by the vocal trac.

One of the issues of speech recognition is to recognise words, sub-words, or phonemes, rather than the person speaking. It is known that pitch and related measures are often speaker-specific (and gender-specific, of course) so it is desirable to remove this information for speech recognition (called speaker normalisation). That is why LPCCs (linear prediction cepstral coefficients) were one of the earlier features used in speech recognition, since linear prediction separates the power spectral envelope from the underlying harmonic structure (contained in the residual). Also, MFCCs (Mel frequency-warped cepstral coeffs) which are now the most popular features used in speech recognition are calculated based on the output energies of triangular filterbanks warped on the Mel scale. Hence, nearly all of the harmonic structure has been removed (smoothed out by the filters) and only the envelope/shape is kept.

[Insolent]

5/12 - I guess that edges me into the overtone category.

[rutra80]

I'm unable to pass this test consistently. When I took it the first time, I percepted it as chords and I couldn't really decide if given test is inc or dec (depends on which tone I focus on). Then I took it the second time and I tried to "sing" these sounds in my mind, then they got somehow more consistent but different than the first time.
So, the results seem to depend on how you come to this test - if you come to it technically, like trying to figure how would you play these sounds on some polyphonic instrument (or how does its spectrum look like), then the results will be different than if you come to it purely aesthetically, like you do while listening to the music.

[Continuum]

your interpretation is not completely right (at least as long benski's analysis is correct): The fundamental (base tone) is not removed but one octave higher.

There is a misunderstanding. I'm talking about the fundamental frequency in the harmonic series, benski talks about the root of a chord (apparently sometimes called fundamental as well).

[Wombat]

Cool thing. I am a fundamental tone hearer with a bug. Tone 7 is inverted to me!

[vinouz]

hawkeye : continuum's interpretation is correct.

In fact, what happens in the 12 sound couples present in this sample, is that they are made of the last N (N= 2, 3, 4, ...) harmonics of different fundamentals, up to the LCM of the two fundamentals. But they never include the fundamental harmonic.

So the lower frequency the fundamental, the lower the distance between its harmonics.

Because of this, as the LCM (the higher band on the spectrum view of both sounds) is the same, the frequency of the N harmonics just before LCM are higher for the lower frequency fundamental than for the higher frequency fundamentals.

So the sound which has the lower fundamental (the fundamental is the GCD of all the harmonics) has the higher N harmonics before the first common harmonic (which is LCM of the fundamentals of the two sounds).

(LCM = lowest common multiple, GCD=greatest common divider)

For example, take couple number 12.
(I used audacity, hence the screenshots are from it.)
Its spectrum is

The first sound (left) is made of two bands: the lower, around 1328 Hz, and the higher, around 1660 Hz. They are separated by 332Hz.
1328=4*332 and 1660 = 5*332, so these two bands are respectively the 4th and 5th harmonics of the fundamental 332Hz (332 is the GCD of 1428 and 1660). This corresponds almost to a E2 (E2=329,63Hz).
The second sound (right) is also made of two bands: the lower is around 1245 Hz,and the higher is around 1660Hz as for the first sound.
1245 = 3*415 and 1660 = 4*415. These two bands are respectively the 3rd and 4th harmonics of the fundamental 415Hz (415 is the GCD of 1245 and 1660). This corresponds almost to a G#2 (G#2=415,3Hz).

The harmonics of the fundamental of first sound (332Hz) and of the second sound (415Hz) join at 1660Hz, as 1660 is the LCM of 332 and 415.

A fundamental tone hearer interprets the first sound as the 4th and 5th harmonics of the fundamental at 332Hz, a somewhat detuned E2, and mentally reconstitutes the missing fundamental. Try hearing the first sound of the 12th couple and playing an E2 on an instrument.
After that the fundamental tone hearer interprets the second sound as the 3rd and 4th harmonics of the fundamental at 415Hz, an almost perfect G#2, and mentally reconstitutes the missing fundamental. Try hearing the second sound of the 12th couple and playing a G#2 on an instrument.
As you see the fundamental hearer hears the second sound higher than the first in the 12th couple.

An overtone hearer interprets the first sound as the combination of two sounds: a pure harmonic at 1328 Hz (a slightly higher E4) and another pure harmonic at 1660Hz (an almost perfect G#4).
After that the overtone hearer interprets the second sound as the combination of: a pure harmonic at 1245Hz (an almost perfect D#4) and the same almost perfect G#4 at 1660Hz.
As you can see the overtone hearer hears, in both sounds, two notes, one of which is lower in the second sound (the D#4) than in the first sound (the E4).


--- A second exercice: how to hear like an overtone hearer when you're fundamental tone hearer and vice versa ?

A) you're an overtone hearer and wanna understand.

Create a sound which implements all the harmonics of the fundamental, including the fundamental and, of course, the two that you hear as distinct sounds.

Here, I created a sawtooth signal of frequency 332 Hz (E2), followed by the first sound in the couple 12 of the test, then a sawtooth signal of frequency 415Hz (G#2), followed by the second sound in couple 12.

Sorry, no flac, just a mono WAV file.
The spectrum is as follows


You have the kind of signal that a fundamental tone hearer reconstitutes (timber excepted), down to the fundamental tone (lowest bar in the "ladder").

B) you're a fundamental tone hearer, you wanna understand (as me)

Create a sound separating the two components of the sound couple 12.

Here is a sine signal of frequency 1328Hz (the E4), followed by a sine of frequency 1660Hz (the G#4), followed by the first sound of couple 12, which is their combination.
Then, a sine of frequency 1245Hz (the D#4), followed by the same G#4 at 1660Hz, followed by the second sound of couple 12, which also is their combination.

Here again, no flac, just a mono WAV file.
The spectrum is as follows


You have the decomposition that an overtone hearer gets.

Amusingly, when performing that second experience, I had difficulty returning back to my 'fundamental tone hearer mode' on the sample ! (talk me about rewiring the brain)

Note : as I'm a fundamental tone hearer (12/12), I'm not sure the example sound in A is well suited for overtone hearers. I myself don't hear the different sounds composing the harmonics. But I can, with exercice B. One of my coworkers heard the distinct frequencies, and still managed to get 12/12 when I asked him to search the fundamental tone. Great !

Hope it helps a little. All in all, I lost a nice day .

Vincent

This post has been edited by vinouz: Jan 20 2006, 18:52

[marq_]

If your an fundamental tone hearer and want "hear" it like an overtone hearer, concentrate on the tests long enough, and you'll soon get the "overtones only". (It's like that 3d cube thing - it can be a cube or a corner).

[vinouz]

Wombat : note that the 7th couple, on which you fall, is exactly the one having a difference in that the harmonics of sound having the lowest fundamental are taken at LCM and LCM+1*fundamental instead of LCM and LCM-1*fundamental. This raises the energy in higher frequencies, and thus confuses more the listenner.

[Pio2001]

JeanLuc pointed out an interesting fact:
I recall not being able to distinguish between my speakers in phase and out of phase (one pair of cables crossed).

It must be because you were not exactly at the same distance of both. In a shop, I did not noticed it until I moved in front of the listeners in order to have the speakers positionned symetrically before me. The inversion is then obvious.

[JeanLuc]

JeanLuc pointed out an interesting fact:
I recall not being able to distinguish between my speakers in phase and out of phase (one pair of cables crossed).

It must be because you were not exactly at the same distance of both. In a shop, I did not noticed it until I moved in front of the listeners in order to have the speakers positionned symetrically before me. The inversion is then obvious.

I did not make myself clear enough I guess ...

So-called 'Fundamentals' are believed to be very sensible to phase shifting of a kind that is e.g. caused by steep crossover networks in the crossover frequency range ... that's why these people might prefer 2-way speakers with a simple 6dB/octave crossover.

An inverted phase of one channel will most likely lead to unknown interferences and frequency band cancellations (especially in the low-end beneath 200 Hz) which would be a rather tonal issue - a plain lack of bass ...

[Gecko]

Thanks everyone who helped me understand. Especially vinouz for the detailed explanation.

[zombiewerewolf]

Well, it seem I'm a 100% fundamental tone hearer which probably true because I prefer piano to cello.

[Wombat]

Since some people hear differences with speakers or headphones i tried it also and can´t repeat it. I always have the same scores and tone 7 is still inverted of course.
Maybe i drunk something away on the left part of my brain

Edit: Brain parts

This post has been edited by Wombat: Jan 21 2006, 04:32

[gameplaya15143]

same as the table except for #5 (11/12)
apparently I'm a fundamental tone hearer

I just find it interesting how different people hear things differently (or interpret what is heard differently)

[Hollunder]

looks like I'm a fundamental one too

nr. 5 is more a guess for me, I do hear a difference but I can hardly say if it's going up or down. Well, my ears aren't trained at all, so this might be the problem here. Nr.7 is inverted of course, everything else is as in the Table.

[breez]

0/12 so according to this I'm a pure overtone hearer. The notion of the preferred instruments though, is only somewhat correct. On few of the samples I wasn't sure and I made the choice based on the first impression. On those samples I could easily think that it was the opposite really.

This post has been edited by breez: Feb 6 2006, 15:55