We do not fly to the moon because it is easy, Kennedy.
I am sorry that my post offended you. That will not happen again. And I had not especially you in mind. That was only a reaction that I see many times
on Threads like this that people do not have basic understanding. When that basic understanding is not there it is mostly impossible to discuss advanced issues.
I have simply tried to give an answer to your statement:
"It will somewhat resemble a square wave, but one where the fundamental frequency is the 45 Hz "
So if you take away the fundamental 15 Hz of your example the result clearly does not resemble a square wave.
You also said before:Okay, but I will say again that it was obvious that the resulting waveform won't be a square wave. Also, "resemble a square wave" isn't exactly the same thing as saying that you'll get another square wave. No matter. I'm still curious to know what you think the overall periodicity will be. If you answer this, you'll be answering a question as opposed to a statement.
My Sonarworks 4 correction has a button to select "linear phase". It adds 43msec to the processing time. It seems to have a subtle but real audible effect, slightly clarifying the image and transients. Is this what we are talking about? My room is treated for early reflections.Everyone is justly raving about the performance of the Kii3 and the D&D 8c.
The Toole school preaches that everything which matters is expressed in the frequency response measurements.
Yet there is a chance that the time-domain performance of these speakers may contribute to the overall results.
https://www.stereophile.com/content/dutch-dutch-8c-active-loudspeaker-system-measurements
https://www.stereophile.com/content/kii-audio-three-loudspeaker-measurements
Everyone is justly raving about the performance of the Kii3 and the D&D 8c.
The Toole school preaches that everything which matters is expressed in the frequency response measurements.
Yet there is a chance that the time-domain performance of these speakers may contribute to the overall results.
https://www.stereophile.com/content/dutch-dutch-8c-active-loudspeaker-system-measurements
https://www.stereophile.com/content/kii-audio-three-loudspeaker-measurements
In my opinion time coherence is subtle but important. That is one of the reasons I chose and still love my Thiel CS 3.7 speakers.
Current active speakers can switch this on and off to test. I have listened to a demonstration of a Goldmund system and it was noticeable. Even fixing it with convolution is worth it. After all it is still part of high fidelity to the source.
You also said before:
"What I was trying to say (and believe that I did say in an adequately clear manner) is that if the low-pass filter that is applied is sufficiently steep, that there will be no remnant of the original 15 Hz fundamental in the output waveform, and that the overall periodicity evident in the output waveform will be that of the 3rd harmonic (45 Hz)"
The square wave without the fundametal 15 Hz looks like
View attachment 73264
Indeed the signal still shows a periodicity of 15 Hz despite there is no 15 Hz sine wave in the signal. That's pretty funny. It may also explain why we perceive a fundamental frequency despite its total absence.
My Sonarworks 4 correction has a button to select "linear phase". It adds 43msec to the processing time. It seems to have a subtle but real audible effect, slightly clarifying the image and transients. Is this what we are talking about? My room is treated for early reflections.
To my ears, the "linear phase" button smears chocolate icing thickly on the cake.
Is it possible that the lack of early reflections from the Kii, DutchDutch, and my expensive room enable the audibility of the "linear phase"? If so, the measurements could include time numbers for those interested, even though they are not universally considered important.
Current active speakers can switch this on and off to test. I have listened to a demonstration of a Goldmund system and it was noticeable. Even fixing it with convolution is worth it. After all it is still part of high fidelity to the source.
Devialet SAM fixes the bass delay for time alignment, but also extends the bass response while limiting the max excursion to protect the drivers. So listening with/without SAM unfortunately is not time alignment alone, the added bass response will change the perception too.I auditioned Sonus Faber Guarneri evolution with and without the Devialet SAM, where the SAM supposedly is to do phase correction and some supposedly other types of magic. I think through the Devialet it works best with all the DSP processing turned off, I have no idea what that DSP stuff is doing in this situation but to me it clearly disrupts the musical flow and makes it all become unnatural to my ears
(Through this specific demo, at least)
So I wonder ... making everything look better and measure more nice can possibky kill the music
Devialet SAM fixes the bass delay for time alignment, but also extends the bass response while limiting the max excursion to protect the drivers. So listening with/without SAM unfortunately is not time alignment alone, the added bass response will change the perception too.
It's kind of weird that even though the periodicity is that of a 15 Hz sine wave, there is no spectral energy at that frequency.
The harmonic waves all have positive (and later negative) going zero crossings aligned at that 15Hz period. They are still adding to make the step up, and subtracting to make the step down, even without the 15hz wave.
Whats missing is a major support for the flat areas of the wave.
---
What's weirder to the eye vs the ear, is that even if the alignment of the harmonic waves is lost, the steady state sound heard is the same.
Square to F9
View attachment 73309
This because the waveform is still strictly symmetric. I did tests with a fundamental and a 2nd or 3rd harmonic with varying amounts of start phase offset in 22.5° increments. While the 3rd showed neglegible change of timbre vs. start phase (position of the harmonic on the fundamental) when stepping through the 360° range, the set with the 2rd harmonic shows a slightly wandering timbre.What's weirder to the eye vs the ear, is that even if the alignment of the harmonic waves is lost, the steady state sound heard is the same.
Because the former is the correct term to use - a transfer function can be expressed as a function of amplitude/magnitude and phase.Why would I mean amplitude instead of attenuation?
Now what on earth would motivate you to say, " ... math, which you seem shy of ..."
my math skills are much too rusty
All physical systems are bandwidth-limited - perfect square wave reproduction would require (impossibly) infinite bandwidth.why it isn't reasonable to expect audio components to reproduce square waves?