Moving from the near listening position to the "imaging compromise" position merely 6 inches back, now I can't hear much difference, if any, in the quantity bass. The differences seem to be more in the highs. The highs go from decidedly dull to bright and open (perhaps a tad too bright). But that also does seem to have an effect, not on the quantity of bass but the quality of bass instruments. When the sound is dull from high frequency rolloff, the bass instruments don't seem very distinct. Everything, including the bass, has a dull quality.
Underlying this, I had forgotten I had also angled the Acoustats for the new compromise position. So any listening position closer than that would be too far off axis for good response, since the speakers are angled just inwards from where the highs start to roll off abruptly.
It has long been observed by many that good high frequency reproduction is necessary to get the bass right. There is a rule (can't remember who named it) that even provides a formula. If you have bass response to 20Hz you must also have treble response to 20kHz. If you have bass response to 30Hz, you should have treble response to 15khz (and no higher). And so on. With the bass response to 15Hz that I achieve, I need corresponding high frequency response to 30kHz (!), according to the rule.
Anyway, ignoring that rule for the present, why should treble response affect the bass sound? I can think of several possible reasons.
1) It's in the mind, so to speak, a perceptual or psychoacoustic effect.
2) It's in the harmonics. You need the HF to get the bass harmonics.
3) It's in the sound physics.
4) It's the nature of the actual instruments.
I want to explore (3) a bit. A steady bass tone such as from an electronic oscillator is just bass. But any tone that starts and stops is a "transient". And transients, by their nature, have lots of frequencies. Assuming a bass tone were to abruptly start, at that very instant you would have the equivalent of a impulse or square wave, containing a range of harmonics up to infinity (depending on how abrupt the start really is).
That's my limited understanding anyway. Most discussions of frequency response, from a simplistic Fourier Analysis standpoint anyway, make lots of assumptions including waves that continue unchanged forever. Once you have changes, the steady state analysis no longer applies. And I'm not exactly sure what applies then. But I think the argument in the preceding paragraph are somewhat true. An actual mathematical analysis would be far more complex. You might consider that the bass tone is "modulated" by an underlying on-step and off-step, and then you have to consider the mathematical effects of that modulation.
And that's not even considering the nature of bass instruments and bass instrument players. Bass instruments can have "attack" sound (from a pluck, say) which truly is something like a step or impulse or short square wave. Failing to reproduce that "attack" sound correctly, which requires fully extended frequency response, will also result in dull sounding bass.
I'm not actually sure which of these effects is greater, though I suspect the reproducing (or not) the attack sound is really the most important, and the quasi-impulse character of all tones which start and stop is a less important, but non-negligible factor.
WRT the natural harmonics of steady bass tones from bass instruments, I suspect they trail off pretty quickly. So if you have a bass tone at 60Hz, by the time you get to 1200Hz (20th harmonic) there isn't much there anymore.
Underlying this, I had forgotten I had also angled the Acoustats for the new compromise position. So any listening position closer than that would be too far off axis for good response, since the speakers are angled just inwards from where the highs start to roll off abruptly.
It has long been observed by many that good high frequency reproduction is necessary to get the bass right. There is a rule (can't remember who named it) that even provides a formula. If you have bass response to 20Hz you must also have treble response to 20kHz. If you have bass response to 30Hz, you should have treble response to 15khz (and no higher). And so on. With the bass response to 15Hz that I achieve, I need corresponding high frequency response to 30kHz (!), according to the rule.
Anyway, ignoring that rule for the present, why should treble response affect the bass sound? I can think of several possible reasons.
1) It's in the mind, so to speak, a perceptual or psychoacoustic effect.
2) It's in the harmonics. You need the HF to get the bass harmonics.
3) It's in the sound physics.
4) It's the nature of the actual instruments.
I want to explore (3) a bit. A steady bass tone such as from an electronic oscillator is just bass. But any tone that starts and stops is a "transient". And transients, by their nature, have lots of frequencies. Assuming a bass tone were to abruptly start, at that very instant you would have the equivalent of a impulse or square wave, containing a range of harmonics up to infinity (depending on how abrupt the start really is).
That's my limited understanding anyway. Most discussions of frequency response, from a simplistic Fourier Analysis standpoint anyway, make lots of assumptions including waves that continue unchanged forever. Once you have changes, the steady state analysis no longer applies. And I'm not exactly sure what applies then. But I think the argument in the preceding paragraph are somewhat true. An actual mathematical analysis would be far more complex. You might consider that the bass tone is "modulated" by an underlying on-step and off-step, and then you have to consider the mathematical effects of that modulation.
And that's not even considering the nature of bass instruments and bass instrument players. Bass instruments can have "attack" sound (from a pluck, say) which truly is something like a step or impulse or short square wave. Failing to reproduce that "attack" sound correctly, which requires fully extended frequency response, will also result in dull sounding bass.
I'm not actually sure which of these effects is greater, though I suspect the reproducing (or not) the attack sound is really the most important, and the quasi-impulse character of all tones which start and stop is a less important, but non-negligible factor.
WRT the natural harmonics of steady bass tones from bass instruments, I suspect they trail off pretty quickly. So if you have a bass tone at 60Hz, by the time you get to 1200Hz (20th harmonic) there isn't much there anymore.
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