## The power of Repetitiveness

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...

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.

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.

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.

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.

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.

Here is an image explaining part of what I meant:

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.

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.

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