Speaker directivity

     for enveloping

Speaker directivity should be decided before purchasing a speaker. Directivity depends solely on the speaker's construction and cannot be changed later. While placement and speaker direction can slightly adjust the direct sound and the proportion and direction of reflected sounds, the speaker's construction determines the core.

Directivity is crucial for achieving both sound clarity and a enveloping. Sound clarity is easy to achieve; listen to the sound with headphones, and every detail on the recording will reach your ears. Achieving enveloping is more complex. As F. E. Toole states it, the whole good sound image topic is a "circle of confusion." The basis of this confusion regarding enveloping is the realization that a true presence effect is provided by room reverberation, which lasts 1-2 seconds relative to the direct sound. In home spaces, such reverberation is more like 0.2-0.4 seconds. Since home room reverberation is negligible compared to a concert hall, it is considered good practice that room reverberation is part of the sound recording. And based on the spatial additions in music recordings, a spatial sound image should also arise when listening with headphones. Unfortunately, this doesn't work. Therefore, speakers are needed for presence, and practical experience shows that different speakers create a sense of presence to varying degrees.

Targeting

To understand this topic, we need to take a step back. If there is a singer with a guitar in the living room, accompanied by, for example, drums, then you can be sure that there is a presence effect. They are present, and the effect is both audible and visible. So, it's worth considering what the sound directivity profile of musical instruments and singers is. Fortunately, the Technical University of Berlin has measured the directivity profile of many musical instruments. Most musical instruments are invisible to bass sounds and are predominantly omnidirectional. This also corresponds to the directivity profile of bass sounds from a typical speaker. In terms of high frequencies, one might expect more directivity, but looking at the profiles, the sound of most instruments is also wide-angle there. The directivity index (Sound Directivity Index, or SDI) remains below 4 dB for most musical instruments, while speakers often have it up to 12 dB. The result seems natural, as most instruments are designed to be presented to the entire audience. Individual highly directional instruments are placed on the rear edge of the orchestra mostly, and the overall sound directivity profile is wide.

In total 22 instruments were measured by Technical University of Berlin. In picture there is selection of some more commonly used instruments sound directivity index and their average.

This is a good guide for choosing the best speaker directivity profile for the best spatial effect. If the speakers have a similar directivity profile to most musical instruments, there is some hope that the music will sound natural from the speakers, regardless of the recording. Next we can take closer look on the interaction of the room and the speaker. Let's start with the rarer and less frequently needed solutions.

Directivity

Narrow directivity speakers are needed for critical listening, when the goal is to assess the details of music playback. For this, as much direct sound as possible is very good, the sound is clear and evaluable. Another need for narrow profile speakers is when room reflections are very strong and they definitely need to be reduced for a good sound image. This need is either in very reflective rooms and/or in very large rooms where reverberation and reflections begin to dominate the sound image. Directional speakers are also helpful in a larger room cinema system. In such a situation, the use of many speakers together creates natural sound, and reflections from the wide sound profile can negatively affect sound clarity. Very directional speakers are rather rare and expensive, mostly solved with either very large setups or very dominant horn-like waveguides. Most often they are seen in everyday life in the context of world-class star concert tours, where truckloads of equipment are set up in concert venues. Smaller solutions on the same topic are in recording studios. So, for example, if studio speakers are offered at a bargain price, it is worth taking a look at the speakers and thinking about the directivity profile. Compared to the directivity profiles of musical instruments, conventional speakers are all narrow in the high-frequency range.

At the other extreme, also less frequently needed, are 360 degrees, or omnidirectional speakers. Some musical instruments also have this profile, but there are limitations here as well. This type of speaker is good to use in a room with few reflections to create your own music island, where there is no fixed listening position. For example, it is a good speaker for a meeting room, at a trade fair, outdoors, in L-shaped rooms, and rather for background music than for focused listening. In all such situations, the sound image is natural in every listening position. On opposite side in typical home room, reflections will start to swallow up sound details and the sound clarity will not be comparable to slightly more directional speakers, although the sense of presence is good.

So we get closer to speakers with an ideal directivity profile for enveloping. Let's take a closer look at the details of this ideal across different frequencies. 

Let's start with bass (20-300 Hz). Like musical instruments, most speakers are omnidirectional here (sound also spreads behind the speaker equally). Bass directivity can be set by using multiple sound sources together and timing the audio signal, the speaker's own size, shape or direction does not affect it. As a rule, controlled bass sounds better in a room, so it's worth using multiple bass speakers. The main concern, of course, is room resonances, and multiple bass speakers are also a good solution for managing them. Achieving a bass directivity profile is a science in itself and is not crucial for the entire sound image (although it improves the sound image, especially by better managing room resonances).

The midrange (300 - 1000 Hz) directivity profile of mid-sized speakers is very similar to average musical instrument directivity profile. Both have a directivity profile (SDI) that fluctuates around 3 - 4 dB in this range. Here you can also distinguish between horizontal and vertical directivity profiles. The vertical profile could be more directional and the horizontal wider. The ideal is then 4-5 inch midrange speakers. If there are several of them stacked, then the vertical profile is slightly more limited and although it may also lob slightly vertically, it is still a common solution for expensive speakers. In addition, playing midrange frequencies from multiple speakers reduces the ripples in the listening position sound profile caused by floor and ceiling reflections. So there is a small loss and a slightly bigger gain here. One 5-8 inch midrange speaker also works very well and authoritative sources claim that reducing floor and ceiling reflections has little impact on the perceived sound image.

The lower part of the high frequencies (1-7 kHz) is still covered with notes and a very important range for interpreting the sound image. Unlike speakers, more commonly used musical instruments have a wide profile here. For example, the singer's voice SDI is 4.6 on average and 6 dB at its maximum, the guitar SDI is 2.2 on average and 4.6 dB at its maximum. A well-executed conventional speaker has an SDI of 5 - 8 dB on average here. Obviously, this is where you can do something to widen the directivity profile and with it increase the sense of presence. The first and easiest solution is a phase plug - in the middle of the high-frequency speaker there is a small plate, cone or some other stationary obstacle, the purpose of which is to diffuse high frequencies. It works, but in a typical implementation, rather at the higher end of the high frequency. Another possible approach is a separate high-frequency diffusing waveguide (for example, like TiFi Elf), but this is very difficult to implement on a conventional speaker. However, it works very well in the frequency range under consideration. The fourth option is the so-called supertweeter. It is advertised with the idea that it reproduces sound up to 30-40 kHz, but the real benefit is different. With a very small diaphragm mostly, its directivity profile can be wider for high frequencies than a conventional two-inch tweeter The same is possible with a small throat diameter high-frequency compression driver, which, together with a suitable waveguide, can also have a wide directivity profile. And as a last resort, you can do something with waveguides (i.e. a horn-like formation around the high-frequency speaker), but they usually only affect the lower end of the high frequency on a conventional tweeter and do not solve a task like the one described here.

The upper part of the high frequencies (7-20 kHz) is also surprisingly wide in sound profile on musical instruments and is narrow only on very directional musical instruments (e.g. tuba). Here, the sound pressure level is very low on most musical instruments. So it is useful for the speaker's direct sound to cover the necessary listening positions, but there are little arguments to spread  these more widely. This width can be achieved with a small phase plug (for example, such a high-frequency phase plug is on the TiFi Helios and a more exciting version of it is on the KEF Meta), or a slightly modified profile of the high-frequency diaphragm. It is possible that there is also a benefit from a wide sound profile here, because it would help to keep the timbre consistent in comparison to reflected and direct sound, but solving this task can negatively affect sound clarity and purity, because by expanding the directivity profile here, we reach the problems of an omnidirectional speaker. So here, the sound profile is usually limited to consistency and covering listening positions.

TiFi different type of speakers compared to musical instruments average SDI. TiFi Helios is closest to conventional speaker, still with lower than usual SDI, TiFi Elf is totally different design with diffusing waveguide in front of tweeter and TiFi Poseidon is omnidirectional speaker.

Suggestions

Returning to the music played from the speakers and the usual listening room, some hypotheses can be offered from the above (some of which are proven, but not all)
- On average, a speaker with a wide directivity profile is better at creating a sense of presence than a speaker with a narrow directivity profile.
- Wide directivity profile of the speaker is especially important in the frequency range of 1-7(10) kHz
- Based on the previous hypothesis, high-frequency sound absorbers on the sides of the room can reduce the sense of presence.
- Turning the speakers in or out of the direction of the listening position affects the sense of presence and allows for some compensation for the narrow directivity profile of the high frequency. 

Outside of this post discussions, but according to common assessments:
- It is easier to achieve a sense of presence if the speakers are further away from the wall behind them (rather in the middle of the room than near the back wall)
- Listening to the speakers closer can also help to achieve a sense of presence. (When listening closer, the reflected sound lags slightly more and the sound image becomes more spatial.)

The above corresponds mostly to F. E. Toole's conclusion that the best sense of presence is created by speakers with a wide sound profile, where the direct sound and the primary reflected sound have a similar profile, and where the primary reflections in the listening room spread without altering their frequency distribution. Interestingly in their tests, the sense of presence was better also when the speaker with a wider directivity profile had more irregularities in its sound profile compared to more homogeneous narrow directivity profile speaker.

Predicting a speaker's directivity profile based solely on its appearance is quite difficult; one can only make assumptions. Indicators of a wider than usual directivity profile in the midrange include: a narrow speaker cabinet and the use of smaller drivers; for the high-frequency driver: small size, phase plug, compression driver, rapidly expanding waveguide, and a separate enclosure. The best tool for making assumptions is to search for speakers with a similar appearance on the website www.spinorama.org and check their directivity profiles there. Unfortunately, even such educated assumptions may not yield very good answers regarding high frequencies, as the details that determine high frequencies are mostly small. However, this is better than buying a speaker blindly. A somewhat more reliable option is to purchase a speaker for which a spinorama is available, measured and presented either by the manufacturer or by independent enthusiasts.

My preference aligns with the described profile, which narrows as frequency increases, but slower than in an average home speaker.

The largest difference from a typical speaker's SpDI is around 5-7 kHz. Within this profile, it is additionally helpful if the direct sound and primary reflections have similar graphs, preferably as straight as possible.

Musical instruments average SDI is quite close to TiFi Elf SDI. Closest to any other measured speaker I have encountered. This explains a lot why it considered most enveloping among others.

Notes

This is not a proven recommendation, but a hypothesis derived from measurements, listening, and scientific references, which can also be achieved when building a speaker. Of course, this is more of an average expectation, and a different directivity profile may be better in a specific room. There are also alternative design speakers that cannot be treated with a typical directivity profile, but can sound spatial.

Looking through all the promising speaker directivity profiles on www.spinorama.org, it must be acknowledged that a uniformly wide directivity profile in high frequencies is a true rarity. There were only a few where either the lower or upper end of the high frequency had a wider profile. All the rest, by estimation about 98%, were such that the SpDI exceeded 5 dB at 1-2 kHz and increased with frequency. In the context of the speaker world, these are not yet "directional speakers," but they create enveloping less than needed.