Where is the cutoff for "narrow" dispersion speakers and "wide" dispersion speakers?

[Arindal]

Directivity between speakers in say 200-1000Hz band varies much more than in 1-10kHz band.

If there is no directivity forming by means of cancellation at play (such as dipole or cardioid or low-order x-over filter in that band), directivity below 1,000Hz vastly depends on geometry, i.e. baffle dimensions, shape, driver sizes and placement etc. Speakers of identical geometry and driver sizes perform astonishingly similar under 1K.

I would say that differences in directivity between different models are more pronounced and important above 1K, if we take the relative behavior to the band below 1K into consideration. Your coax example shows a step up in directivity index at 700Hz, further narrowing down towards higher frequencies, which is of course audible under normal circumstances.

As rule of thumb smoothly increasing DI towards treble is best for home audio.

Many people who support the concept of constant directivity, dispute that (and so am i). There is no psychoacoustical or technical reason why DI should increase. Constant directivity is ideal, at least in bands in which we are sensitive for distinguishing direct from indirect sound, as the result in the room should be identical tonal balance of direct sound and indirect sound.

My suspicion is that smoothly/ continuously increasing DI got accepted by many, for the reason it is much more simple to implement in a speaker concept. And it is at least capable of removing the most annoying flaws of uneven directivity by attenuating the typical ´harsh reflections´ in 2K+ bands. But under home conditions it does come at a cost of colorated in-room-response, with the resulting midrange-heavy, dull, detached reverb, making particularly recordings with natural reverb intolerable to listen to, in my understanding. I tried several speakers of that category, which had been highly praised here, at home, and had to send them all back.

 

[olieb]

If one is looking for a single number to characterise the "narrow-wide" impression/effect one probably should take into account the range 1-10kHz (or 0.5-10kHz) and use some kind of weighting factor to account for the (hitherto unknown?) impact of different frequency ranges for this impression?
Some sort of bell curve centred around 2...3kHz might be appropriate?

But maybe it is not only the DI averaged in this way that is important, but the average slope of DI (characterising how close to constant directivity the speaker is) is important too, as @Arindal argues.
Unfortunately, if we need multiple numbers, it's probably no easier than looking directly at the spinorama.
And what is the role of the smoothness of DI as compared to an uneven radiation with directivity "errors"?

There is no psychoacoustical or technical reason why DI should increase. Constant directivity is ideal, at least in bands in which we are sensitive for distinguishing direct from indirect sound, as the result in the room should be identical tonal balance of direct sound and indirect sound.

I do see a ("technical"?) reason for an increasing DI, as the overwhelming part of all recordings is mixed and mastered with speakers that have this characteristic. So a lot of decisions are made on this basis and is seems not too far fetched that a reproduction system with similar characteristics might have advantages. (Not the least being that the perceived sound gets a lot brighter if the DI is not increasing.) [Geddes reports that he had to tilt down on-axis FR as his CD speakers sound too bright otherwise.]
And what exactly makes CD "ideal"? Most sound sources have a directivity that is not constant (voice, violin, guitar, drum, trumpet, ...). So the reverb of nearly everything in a room sounds different compared to the direct sound, in nearly all cases the reverb is somewhat dull compared to direct. Not to mention that air and surfaces also change the sound of reflections by attenuating HF.
So a constant DI is not fundamentally different but more a reduction of the amount of treble attenuation in the reverb. And the impact of this depends, among other things, on the beam width of the radiation.
That said, I don't want to argue against CD, I am more or less agnostic here.

 

[Thomas_A]

If one is looking for a single number to characterise the "narrow-wide" impression/effect one probably should take into account the range 1-10kHz (or 0.5-10kHz) and use some kind of weighting factor to account for the (hitherto unknown?) impact of different frequency ranges for this impression?
Some sort of bell curve centred around 2...3kHz might be appropriate?

But maybe it is not only the DI averaged in this way that is important, but the average slope of DI (characterising how close to constant directivity the speaker is) is important too, as @Arindal argues.
Unfortunately, if we need multiple numbers, it's probably no easier than looking directly at the spinorama.
And what is the role of the smoothness of DI as compared to an uneven radiation with directivity "errors"?


I do see a ("technical"?) reason for an increasing DI, as the overwhelming part of all recordings is mixed and mastered with speakers that have this characteristic. So a lot of decisions are made on this basis and is seems not too far fetched that a reproduction system with similar characteristics might have advantages. (Not the least being that the perceived sound gets a lot brighter if the DI is not increasing.) [Geddes reports that he had to tilt down on-axis FR as his CD speakers sound too bright otherwise.]
And what exactly makes CD "ideal"? Most sound sources have a directivity that is not constant (voice, violin, guitar, drum, trumpet, ...). So the reverb of nearly everything in a room sounds different compared to the direct sound, in nearly all cases the reverb is somewhat dull compared to direct. Not to mention that air and surfaces also change the sound of reflections by attenuating HF.
So a constant DI is not fundamentally different but more a reduction of the amount of treble attenuation in the reverb. And the impact of this depends, among other things, on the beam width of the radiation.
That said, I don't want to argue against CD, I am more or less agnostic here.

In the end it is a blend of the spectrun emitted by the speaker vs the spectrum of absorption of the room.

 

[Arindal]

Unfortunately, if we need multiple numbers, it's probably no easier than looking directly at the spinorama.

I am afraid even multiple numbers would not do. The issue of directivity and room reflections and the two interact, is too multi-dimensional to be described by a simplified model. Looking at spinorama is helpful to a degree one can understand which combinations might be compatible and which are rather likely to cause problems, but it does not allow a prediction and does not replace a proper listening test and some optimization in the room, IMHO.

I do see a ("technical"?) reason for an increasing DI, as the overwhelming part of all recordings is mixed and mastered with speakers that have this characteristic. So a lot of decisions are made on this basis and is seems not too far fetched that a reproduction system with similar characteristics might have advantages.

I do support the general approach of getting home listening conditions closer to average studio conditions, but I see two major issues in your assumptions here:

- i don´t see an overwhelming part of recordings being mastered on speakers with imbalanced off-axis behavior in the sense of overrepresented upper bass/lower midrange. Broad-radiating, constant directivity speakers are as common in mastering and main monitoring in studios, as are uneven ones. Having seen a lot of studios from inside, I don't recall a single example of such tonally imbalanced control room with midrange-dominated reverb. Some anecdotally existed in the old days when big Urei, Altec-Lansing or Tannoy monitors were popular, but these days are long gone.
- having speakers at home with similar characteristics compared to studio and mastering, alone does not help, as the room acoustics vastly differ. Indirect sound at home tends to dominate, compared to studio conditions, and studio control rooms are usually well or over-damped in the midrange. So even a speaker with overly low midrange directivity would not create a midrange-heavy reverb field as it would under home conditions. Particularly small speakers which are more or less omnidirectional below 800Hz, in studios are mainly used as nearfield monitors, which leads to quite the opposite mixture of direct and indirect sound compared to home conditions.

(Not the least being that the perceived sound gets a lot brighter if the DI is not increasing.)

That is kind of the litmus test other way ´round: If your theory would apply and a majority of studios would mix and master under midrange-dominant conditions, those recordings would all sound annoyingly treble-rich and bright under nearfield, overdamped room acoustics and tonally well-balanced conditions. But they don't!

And what exactly makes CD "ideal"?

From theoretical point: tonal pattern of the reverb on the recording and tonal pattern of the additional reverb in the listening are more or less identical, allowing them to blend and creating a ´natural´ soundfield enveloping the phantom sources of instruments and voices (in case of acoustic recordings). So classical and jazz recordings will not only retain their ´natural´ tonal balance, but also the ambience, depth-field and dynamics intended by the recording engineer.

from practical point: indirect soundfield in the listening room being tonally balanced, hence more similar to the studio conditions even if indirect sound is more pronounced in level.

Most sound sources have a directivity that is not constant (voice, violin, guitar, drum, trumpet, ...). So the reverb of nearly everything in a room sounds different compared to the direct sound, in nearly all cases the reverb is somewhat dull compared to direct.

The tonal pattern of the reverb caused by the natural directivity of instruments and voices, is inherently captured by the microphones in the concert hall already, so it is part of the recording, and under home listening conditions, part of the direct sound. If you want to hear this natural reverb in your listening room, you have to keep the additional reverb created by the speakers as tonally similar (and as diffuse) as possible. That's the idea of constant directivity and balanced room reflections.

If you add an extra filter of dullness to the reverb, well, it sounds even duller. That's why sent the KEFs and Neumanns back.

Not to mention that air and surfaces also change the sound of reflections by attenuating HF.

Attenuation of treble caused by the air itself and non-linear absorption grades of surfaces, is rather a matter of the highest treble region and mostly applicable to very long listening distances. Indeed a minor decrease in indirect sound level above 7K is to be expected and not perceived as dull. Tonal issues caused by directivity imbalance are mostly limited to the frequency range 400...7,000Hz, as these are the bands we are best in distinguishing direct and indirect sound.