The power of Repetitiveness

Talk about what you've discovered by using ETC-- and post your high ranks!
paulriley
Posts: 21
Joined: Fri Feb 22, 2008 5:36 am
Location: London

Postby paulriley » Tue Mar 25, 2008 3:45 pm

when you say average frequency, is that the actual frequency that is being produced out of the speaker? what happens when two live instruments are playing?

aruffo
Site Admin
Posts: 1694
Joined: Tue Dec 14, 2004 12:09 pm
Location: Evanston, IL

Postby aruffo » Tue Mar 25, 2008 4:08 pm

I was curious so I took C4 and C5 and combined em, then compared the resultant wave to a G4 (making sure they all had the same phase). Here's the result.

Image

djf
Posts: 33
Joined: Sun Oct 22, 2006 12:20 am
Contact:

Postby djf » Tue Mar 25, 2008 4:35 pm

That's exactly what I would expect. The 2:3 ratio is the same ratio as C4:G4, and the C5 waveform sort of gets "embedded" in the C4 waveform because that's a simple 2:1 ratio. The thing is, there's nothing about that waveform that suggests that the two tones shown are in any way "the same". The combination tone has an overall period that's the same as that of C4 because it's essentially a difference tone: C5 - C4 = C4 (using crazy music math).

gavriel
Posts: 101
Joined: Sat Jun 10, 2006 11:54 am

Postby gavriel » Tue Mar 25, 2008 4:49 pm

Niccceee.
There you have it.
The distances between the vertical red lines (between the "zeros") is the frequency. It is objectively the same.
The distances between the tops of each wave is the chroma. These are different.
On the upper sound you have the upper tops, the distance of which is the frequency of C4 and then the "mini tops" which add another mini top in between every two upper tops and thereby double the frequency (this is the C5).
The distances between the tops are greater on the upper sound than on the lower one. They are standing in a ratio of 2:3 (C4:G4) and 3:4 (G4:C5). Which makes perfect sense since:

C4 = 261.63Hz
and 261.63*3/2 ≈ 392 (which is a G4)

G4 = 392Hz
and 392*4/3 ≈ 523.25Hz (which is a C5)

So there you have it an objective representation of a sound with the chroma (top to top distances) of C notes (≈262Hz and 523Hz), but at the same time a distance of 392Hz from one zero level to the other (height of a primary G note).

These zero levels start a new major wave in the upper sound in sync with a major wave start in the lower sound once per three waves. That explains what I was writing before about "timbre and fractional height takes time" to be perceived. ...
More time than simple height and chroma.

First we perceive simple height/chroma (in that case we hear a compound C or a G)
Then we perceive fractional height (in that case we start hearing a sameness between the C and G)
and lastly we perceive timbral character.

In that sense one could describe AP as more "Patient" listening and RP as an "impatient" listening. Fractional height cannot be perceived right away, you need to allow many tops go by before you can recognize the fractional ratio between these tops and see if it repeats over at least three cycles before you can recognize fractionaly.


Edit: sorry corrected some mistakes above...
Last edited by gavriel on Tue Mar 25, 2008 5:51 pm, edited 1 time in total.

djf
Posts: 33
Joined: Sun Oct 22, 2006 12:20 am
Contact:

Postby djf » Tue Mar 25, 2008 5:22 pm

gavriel wrote:The distances between the vertical red lines (between the "zeros") is the frequency. It is objectively the same.

No, the distance between the vertical red lines is the frequency of G4 (the bottom one). If you compare those lines to the compound C on top, you'll see that it takes 3 periods of G4 to get 2 periods of the compound C, so the frequencies are in fact objectively not the same.

aruffo
Site Admin
Posts: 1694
Joined: Tue Dec 14, 2004 12:09 pm
Location: Evanston, IL

Postby aruffo » Tue Mar 25, 2008 9:39 pm

Yes, the distance between the vertical red lines is the G4 frequency.

I'd like to believe that you're both right in your assessment of this image-- that djf is correct to point out the 3:2 ratio, and that Gavriel is correct to note that a cycle matching the G is visibly present. My uncertainty in evaluating the equality arises from the fact that the visibly-matching cycle is an "odd symmetric" flip rather than an "even symmetric" wave that would have matched the G-cycle directly.

I'm currently in a Signal Processing class, which is where I got that jargon from.. I'll ask the prof and see if he has an opinion.

djf
Posts: 33
Joined: Sun Oct 22, 2006 12:20 am
Contact:

Postby djf » Tue Mar 25, 2008 10:22 pm

The thing is, the 3:2 ratio has nothing to do with the fact that the combination tone supposedly sounds like the same height as the G. It's simply because the frequency of the waveform of the combined tone is 2/3 the frequency of the G. You would get the same 3:2 ratio simply by comparing a pure C4 to a pure G4.

TS
Posts: 168
Joined: Sun May 07, 2006 4:58 am

Postby TS » Wed Mar 26, 2008 8:45 am

gavriel wrote:I find that one has to strictly separate psychoacoustics from physics.

If we listen to a C5 alone than it is at the same height no matter which velocity we play it in, right? Because there is no fractional height synthesis involved anyway = no clash/compounding of overtones of another tone involved.


If you decrease the volume of a sound, then at some point the lowest frequencies will disappear while the higher frequencies still remain. If the lowest frequencies disappear, then the average center frequency surely shifts, so C5 isn't necessarily the same height regardless of velocity. If you make a game that's based on height, then simply having your speakers at the wrong volume level can in the worst case screw everything up, like it did for me with the tritone paradox.

paulriley
Posts: 21
Joined: Fri Feb 22, 2008 5:36 am
Location: London

Postby paulriley » Wed Mar 26, 2008 2:22 pm

djf is right, all this seems to be showing is that there is a simple ratio between C4 and G4, adding C5 does not affect the time it takes to do one cycle, doesn't it?

Could some do a graph with G4 compared with Db tones instead of C?

djf
Posts: 33
Joined: Sun Oct 22, 2006 12:20 am
Contact:

Postby djf » Wed Mar 26, 2008 3:04 pm

I just remembered something which might partially validate gavriel's position. When two sine waves with different frequencies are added together, one can apply trigonometric identities to change this sum of sines into a product of a sine and a cosine. The frequencies of the sine and cosine are (f1+f2)/2 and (f1-f2)/2, respectively. Depending on how close f1 and f2 are, two things can generally be heard: If the frequencies are close enough to be considered as practically the same note, but out of tune, what we hear is a tone with frequency (f1+f2)/2 (which is the average of the frequencies), and the amplitude acts as a sine wave with frequency (f1-f2). When the notes are farther apart, the (f1-f2) takes over and instead of acoustic beats, we hear it as a difference tone. We also no longer hear the average frequency very clearly as it is easier to hear the individual tones. However, the average frequency is still present in the mathematical representation, so it may be possible to hear it. The problem with applying this to anything else, though, is that in order for this analysis to hold, the original 2 sine waves must have the same amplitude. I haven't found any simple formulas for combining waves with different frequencies and amplitudes.

paulriley
Posts: 21
Joined: Fri Feb 22, 2008 5:36 am
Location: London

Postby paulriley » Thu Mar 27, 2008 8:16 am

it seems then that it may be a process that happens in the mind (as with those early experiments asking people to sing a tone after listening to a chord) rather than in the physical wave form doesn't it? Which brings back the problem of how to measure the tones loudness so that they are perceived as equal, because if one appears slightly louder then the perceived height shifts.

I played chord hopper without my headphones and used my computer speakers, the higher lower tones are much quieter and I was struck by how much higher the chords sounded.

gavriel
Posts: 101
Joined: Sat Jun 10, 2006 11:54 am

Postby gavriel » Sat Mar 29, 2008 6:56 pm

Hi all,

Here is an image explaining part of what I meant:

Image

Every two cycles of C4 (green)
Every four cycles if C5 (red)
and every three cycles of G4 (yellow)
Equal one compound cycle of C4+C5 (or of G4 with a C chroma)

At the beginning of every compound cycle the air pressure will be the biggest, since that is when all cycles have a "top" at the same time.
This compound top is what gives the sensation of fractional height.
At all other instances only one of the cycles experiences a top.

Study this chart carefully and you will see that the upper sound can only be a result of a compound C chromas with the height of a G. Objectively.
I am using the middle levels instead of the tops or bottoms because it is easier to draw the lines that way.

I have much more to say about this! but cannot type much right now since I am on tour... and have to work (on stage).
Will post more later.

TS
Posts: 168
Joined: Sun May 07, 2006 4:58 am

Postby TS » Sun Mar 30, 2008 2:40 am

gavriel wrote:At the beginning of every compound cycle the air pressure will be the biggest, since that is when all cycles have a "top" at the same time.
This compound top is what gives the sensation of fractional height.
At all other instances only one of the cycles experiences a top.


If you look at the part that says "One cycle of perceiving compound C4+C5" on the image, you can see that this cycle is three times slower than the G4 cycle, which means that the simultaneous "top" has a frequency of about 130 Hz, which is C3. So it seems that C4+C5 actually has the "height" of C3, not G4.

This doesn't really have much to do with height, it's all about the harmonic series and overtones. You can see it from this description:
gavriel wrote:Every two cycles of C4 (green)
Every four cycles if C5 (red)
and every three cycles of G4 (yellow)

C5 is four cycles and C4 is two cycles, so their relationship is 4/2, which is the octave, which is exactly right. G4 is three cycles, so the relationship between G4 and C4 is 3/2, which is the perfect fifth, and the relationship between G4 and C5 is 3/4, which is the perfect fourth.

If we start building the harmonic series from C3, we get C3, C4, G4, C5. So far these are the tones we have got. We could continue the series, so we get C3, C4, G4, C5, E5, G5, and the properties of these frequencies are that they all have a simultaneous maximum at
every 1 cycles of C3
every 2 cycles of C4
every 3 cycles of G4
every 4 cycles of C5
every 5 cycles of E5
every 6 cycles of G5
It's the harmonic series.

If height is a spectral phenomenon, then it's almost impossible to get any information of it by looking at drawings of waves.

paulriley
Posts: 21
Joined: Fri Feb 22, 2008 5:36 am
Location: London

Postby paulriley » Sun Mar 30, 2008 7:01 am

gavriel, surely you could draw the same lines when comparing c4 with g4. They would still share the same high and low point wouldn't they? because the c5 doesn't "change" the c4.

djf
Posts: 33
Joined: Sun Oct 22, 2006 12:20 am
Contact:

Postby djf » Sun Mar 30, 2008 10:58 am

gavriel - Cool picture, but TS and paulriley are saying the same things I've been saying. If you can, make a graph comparing A4 to the compound A# or G# that we determined from a previous post. The graph you have right now appears to support you because G and C are closely related pitches, but I suspect that if you use pitches either a semitone or a tritone apart, the relationship won't be so obvious.


Return to “Your observations”

Who is online

Users browsing this forum: No registered users and 1 guest