In order to make some messages more easy to understand, fewer words (i,e. smaller or limited vocabulary) can be employed to structure the messages, so when somebody misunderstands one or more words, he can judge if the perceived one could or could not have been uttered in the middle of the other words that he actually understood (Sanders, p. 183), this is also helpful with large sentences in normal speech. Other way to guaranty easy understanding under harsh conditions is the use of so-called coded messages, as in the case of saying positive or negative instead of yes or no. This way of talking works well under any circumstance, but it is even better when speakers and listeners are aware of it.

Figure 3. Time response of the ‘example’ word, and frequency spectrum of an ‘a’ as in ‘bat’, showing over 25 harmonics accompanying the 100 Hz fundamental frequency.

Intelligibility of Speech

Intelligibility of speech is the term employed to specify the quality of a speech communication system in order to determine the possibility for an audience to understand a spoken signal and it is based on the analysis of different acoustical conditions. It can be estimated from several parameters developed by several researchers for this purpose, like the Articulation Index AI; the Preferred-Octave Speech Interference Level PSIL; the Preferred Noise Criteria PNC curves; the Speech to Noise ratio in dB (A); or the amount of time that the reverberation lasts in the place where any speech message will be presented to an audience. (Sanders p. 182).The communication system could direct (acoustical), or through electronic equipment (Electroacoustic).

AI is a easy but elaborate calculation that first requires some noise and speech level measurements in 1/3 octave bands, then the extraction of the level difference in each band, and the application of a different weighting values, according to its contribution to the understanding of the message, to each and every 1/3 octave band speech to noise difference in the range from 200 Hz to 4 kHz, before adding up all the individual resulting values in order to get a final value which will be between 0 and 1. Where 0 means no possibility at all to understand a word, while 1 represents the possibility to understand the whole message, but actually the real intelligibility of the spoken message is highly dependent on the message itself, the vocabulary employed, and the context of the message. Sentences of a known topic will approach 100 percent intelligibility with an AI of only 0.4, while simple words out of context require a larger value, so bellow 0.3 is considered as unacceptable, 0.3 to 0.5 as acceptable, 0.5 to 0.7 as good, and beyond that as excellent.

PSIL was developed as a simplified method to evaluate the same problem of intelligibility of speech in the presence of wide band noise, and it is determined by the arithmetic average of the octave noise levels at 500 Hz, 1 kHz and 2 kHz, which are considered the most important frequency bands for the intelligibility of speech, and then compared with the speech level. For instance, at normal voice level of 65 dB (A), a PSIL of 60 is considered satisfactory, i.e. only 5 dB bellow the normal speech level.

The Preferred Noise Criteria curves developed as reference noise levels that could be acceptable for many acoustical installations, represent sets of curves from 63 Hz to 8 kHz in octave bands, which should not be exceeded by the noise level according to the application given to different places or acoustic signals involved, as for instance in any sitting area of an auditorium, the noise level should be bellow the curve PNC 35 in order to allow full understanding of the spoken messages.

Another way to estimate the speech comprehension is by measuring the amount of acoustic noise present in the environment while talking and the speech level in dB (A). This parameter is commonly expressed in the Speech/Noise ratio (S/N), and it is represented by the dB difference between the speech and the noise sound levels. It is always desirable to be able to provide a positive and large S/N ratio, i.e. the voice level well over the noise level, and when this value is 15 dB or more, the voice message passes without any acoustical disturbance and then it is easily and completely understood, while S/N values in the range of 7 – 11 dB are good enough for most people to understand the full message. When the S/N value is further reduced, still the message can be fully understood, although the lower the value, it requires from little to a lot of attention and discipline from the audience side, and then the S/N could be as low as -10 dB (Harris, p. 16.6).

This means that if for instance, when the background noise level is in the order of 30 dB (A), which is a background noise level easily found in the open space without the presence of nowadays machinery, mechanical ground and air transportation and electronically amplified noises, normal speech can be very easily understood up to some 16 m. away from the speaker, because the speech level will be in the order of 41 dB, i.e. an Speech/Noise ratio of 11 dB. Some speakers can produce higher level voices, as high as 82 dB (A) without great effort for them (shouting they can reach some 88 dB (A)), which means that they can produce a S/N ratio of around 17 dB better than the average speaker, further increasing that distance, under the same general acoustical conditions, to a little more than 120 m., where the speech level will be in the order of 40 dB, provided there is not extra attenuation over the square distance law for the sound level, which indicates that the sound level is attenuated by 6 dB per doubling the distance from the sound source (Rossing, p. 115).

The ear capacity for level and frequency is very large. It can detect sound levels from 0 up to 120 dB, representing the range from 20 μPa to 20 Pa of acoustic pressure, and frequencies from 20 Hz to 20 kHz, making nearly a ten octave range with the higher frequency 1000 times larger than the lower, which means that all the speech sounds in level and frequency are located in the very central part of these two extremely wide ranges, where the discrimination of sounds is much better than near the edges, Figure 4 shows the normal speech range in the central area of the ear capacity (Beyer, p. 109). This can be explained because speech was developed after the ear, people is borne with their full hearing capacity, but need to learn to speak, so groups of people formed their communication languages with sounds they could easily generate, and also were easy to discriminate from other sounds in order to avoid confusion. This also explains why there are very many languages in the whole world.

Reverberation time, represented by the length of time that the ear can still listen to and integrate to the original sound from the source, the sound reflections produced inside any room, and arriving to the ear with very short time delays. For proper intelligibility of speech within rooms, reverberation times from 0.4 to 1 second are appropriate, depending on the room size, and in general the shorter, the better. This is the main parameter that prevents understanding of speech sounds, for example, inside many churches, where reverberation times in the order of 2 to 5 seconds are common place.

Figure 4. Amplitude and frequency ranges of speech (dashed area), and hearing capabilities (between feeling and audition thresholds) of human beings.

Together with the S/N ratio, the meaning of the speech sounds, the context of the heard sentences and the topic being presented to the audience have a great influence in the possibility to understand the uttered message, for instance, in the presence of the same amount of noise (i.e. the same S/N ratio), when people have some knowledge of the presented topic, or it is within an already known context, they will be able to understand a lot more than when they are totally unfamiliar with it. This is the main reason to use an especial small set of words when understanding of the message is paramount (Sanders, p. 178), for example as in airplane to ground communications.

Directivity is another issue which can also drastically affect the intelligibility of speech, because as already mentioned, most of the voice energy goes away from the speaker directly in front of him within an angle of some 30 – 45 degrees at each side of the central axis, which is also dependent on the radiated frequencies (wider for low frequencies and narrower for high ones), and then usually the speaker moves his head continuously while talking, looking at different areas of his audience, and momentarily neglecting others, especially at the edges of the audience area.

In an open space, like in front of a Pyramid or a tall basement, some 15,000 to 20,000 standing people can be comfortably accommodated within a floor area of 100 x 100 mts., where the farthest person would be located at just little over 110 m. away from the speaker, considering him to be within at an angle of 30 degrees to either side from the main axis of the speaker voice radiation, so this is a kind of a crowd that a single person can address without the use of electronic amplification, provided there are no obstacles or intruding noise. And for music and drums shows, the distance and addressed audience could be a little larger, especially when supported by visual displays as dances or ritual activities, which were rather common in ceremonial sites.

By the times when pyramids and basements were built and frequently used, the main source of noise could have been the crowd itself and some other natural sounds such as wind, waterfalls and animals (there were no traffic or industrial noise).

Experience has proven that  most of the audience in the very last rows of large gatherings, as far as they could be very interested in the message, they also know that it will be difficult to understand everything that is spoken far away from him, especially with a crowd in the middle of the way.

The last element for a good communication system is the listener itself who can have advantages and disadvantages such as: 1. Familiarity with the kind or topic of message; 2. Known general vocabulary; 3. Interest he might have on the topic; 4. Attention given to the speaker; 5. Concentration he may set to try to understand the message, especially in difficult acoustical conditions; and 6. Good hearing capacity in both ears. So even a well uttered message, under excellent acoustical conditions and low background noise level will not be fully understood by the audience if the listeners lack one or more of the above mentioned and bellow described parameters.

1. Familiarity is related to the previous knowledge by the listener on the general topic being presented, which helps him to build up inside his head the small parts of the message that might disappear due to head movement of the speaker, a lack of articulation from the speaker, some short sudden noises, etc.

2. People who handle a larger vocabulary than others will understand more of a given message because it will be simpler for them to discriminate between similar words. Conversely, when the speaker uses a simplified vocabulary, and it is known by the audience, it will be much more simple to understand him.

3. Interest in the message is the real desire to get informed and/or updated in the topic presented. Interest promotes attention.

4. Attention is the willingness to listen to and to understand what is being presented. The message is easily lost if the audience is paying attention to something else.

5. Concentration allows people to fully understand spoken messages within harsh acoustical conditions, like in the middle of a party or in the within a crowd that has less interest in the same message.

6. People with limited hearing capacity due to some sort of sickness or direct damage to the ear will need much better acoustical conditions and louder voices in order to properly understand messages. This problem is highly dependent on the amount of hearing loss and the frequencies actually affected.

Atmospheric effects

In open spaces, there are several atmospheric phenomena that might affect the propagation of sound, increasing or decreasing the sound propagation speed, add some extra voice level attenuation, or even by filling some areas with sound that otherwise will not receive enough. Among the main aspects are the effects of soil, due to its porosity, and that of the audience, both of them can introduce attenuation and delays, due to friction and thermal variations; the wind and the air temperature (Rossing, p. 114). These factors could reduce the sound level by some 15 dB more than the square low states, but usually it is actually more noticed beyond 100 m. from the sound source, which means that some of these effects are usually small within the expected distance.

There could also be interference by the same signal, which could be either, constructive or destructive, due to reflection from soil or walls, with changes in amplitude and phase. In general nearby wall help to increase the average voice level, a single stone wall located a short distance behind the speaker, will increase his sound level by some 2 – 3 dB. Instead, distant walls may produce echoes that could disturb the message.

Although actual attenuation frequently sticks to the square law process only within the mentioned distance, with some little gaining’s by reflection on nearby hard surfaces, and sometimes with the help of the environmental conditions such as wind and temperature gradient, all together will allow for a convenient communication, provided there are low environmental and crowd noises.

Beyond some 100 - 150 m. understanding is more dependent on the atmospheric conditions, which can help to improve it, or further deteriorate the message.

Addressing the people

When a priest or governor of a given culture had to stand on top of a pyramid or a high basement in order to utter a message to his people, most of them had to pay attention, because there was no way to increase the voice level beyond the natural capacity of the speaker, plus the acoustic conditions of the site.

Speech intelligibility is dependent on the speech level, and the noise level (Rossing, p. 311). So the main reason for not understanding by the audience was that the very crowd was not willing to be quiet enough while the speaker sent his message.

In some rituals, many people are not so much interested in the message itself, word by word, as they are in the significance of the rite itself, so in many cases, understanding each and every word was not absolutely crucial.

Most of the Mexican and American pyramids were employed as ceremonial sites, where people used to join to celebrate many different festivities, but also to receive information from the higher ranked people, messages about war situations, community safety, agricultural activities, religious rites, etc., that is why it can be assumed that the crowd used to pay attention to the speakers while in front of the pyramid or basement.

Level, distance and perception

The sole attenuation by distance according to the square of distance law is in the order of 6 dB per doubling the distance, so as explained before; a reasonable voice level can reach the audience in the lower flat bellow the basement. When one or more stone surfaces reflect the speaker voice within a few milliseconds (i.e. a few meters away from the speaker), an increase of 3 to 5 dB can be easily obtained, and clarity is also reinforced by these few first reflections, conveying the voice message to a larger distance from the speaker. With the use of other sound sources as implemented by antique groups, the event could have been noticed up to well beyond half a kilometer, for example with some single studied noise sources from those times, which generate 95 – 98 dB at 1 m. they can be heard well above the background noise that far away.

This also explains why church or public buildings, bell towers, carillons, sirens, people conveying voice messages and other sound systems are frequently located in high positions as towers, hills, etc.

The Ball game court in Chichen-Itza is an example where normal level voice can be easily understood over a very long distance, in the basements of this court located one before the other, across the longer axis of the court, because it is supported by several hard surfaces reflections in soil and walls, as well as free of obstacles between source and listener.

Every space has its unique sound, which depends on size, materials, form, which affect reflection, dispersion, absorption, refraction, etc. (Blesser, Salter, p. 12), all the mentioned factors, plus the activity and the attention given will influence, the level, the perception, and understanding of the emitted sounds in those spaces.

Some measurements

Figure 5 presents a drawing of a basement similar to the one measured for the preparation of this paper, except for the construction located above it. (lost-civilizations),

Figure 5. A basement similar to the one studied. The main difference is there were no extra buildings on top of it.

The basement is a flat surface 2.3 m. high over the flat area for the crowd, with 14 steps to get on top of it, so the speaker mouth would be about 3.8 m. above the ground level. Many sound level measurements in octave bands and in dB (A) were performed in the top of the basement, and on the flat hard floor area in front of the basement, which is an open space, with no less than 60 m. before any obstacle could be found. There was no wind present at the time of the measurements, and the temperature was also stable by mid-day.

A pink noise sound source was located near the edge of the floor on top of the basement, and the first measuring point was chosen at 1 m. just in front of the source, in the radiation axis, to set a reference level.

Table 1 presents a few measurements of sound pressure level from the sound source location (1), which was emitting wide band pink noise with frequency response according to the speaker system used, it also shows the sound levels at three points at an angle of 30 degrees from the radiation axis, points 2 through 4, and distances of 10, 20 and 40 m. away from the sound source. Measured values on axis are also shown in points 5 and 6 located 10 and 40 m. away from the sound source, for comparison. Background noise level in octave bands and dB (A) is also shown in the last row if the table.

Table 1

The above Table only shows a selection of the measurements. 1 Sound source at 1 m., in the radiation axis, 2, 3, 4 at 30 degrees from the radiation axis, and at 10, 20 and 40 m. from the sound source. Points 5 and 6 show values measured at 10 and 40 m. on axis. Figures rounded to the nearest full dB value.

Figure 6 bellow shows a profile of these measurements locations. All measurements were performed at 1.5 m. above ground level, which is the measuring height recommended by most noise measurement standards.

Figure 6. Showing (not in scale) the basement, plus the sound source and some of the measuring points locations.

Results or comments

Measurements were performed without a crowd, so measured values indicate only the direct sound attenuation which proved to be as expected by the square distance law, but with a real crowd, there would be a little extra attenuation by people heads, and it would be noticeable special by the point 4 area and beyond, due to almost grassing incidence at that distance from such a low height basement, areas around points 2 and 3 will not be affected at all by this condition because they receive the direct sound from the sound source without any obstacles from a bigger angle. Even with the expected limitations by the presence of the audience, the voice uttered from the top of the basement will be easily understood in the studied area, and ceremonial rites would be clearly appreciated by anyone standing in the flat area bellow the basement.

The higher the basement, as for example from the top of a pyramid, the spoken sounds will clearly reach to a larger distance and a larger audience also, because the sound will be perceived by all the crowd in the distance from a bigger angle than in this case, thus reaching the crowd completely free from any obstacles, directly from the sound source to the audience, and then the sound level reduction will only be affected by the square distance law.

According to the articulation index definition (AI) and considering the background noise actually measured, although only in octave bands, taking these values as if they were 1/3 octave ones, which gives some extra safety margin in the results, plus the estimated voice level at the longest distance of 60 m. in the studied plaza before the basement, the AI could easily each a value in the vicinity of 0.83, which is actually considered as excellent.

With regard to the preferred speech interference level PSIL approach, with the octave noise level measured at the three frequency bands from 500 to 2000 Hz, a PSIL of 20 dB is obtained and it is considered very quiet, meaning that a loud voice uttered in the studied conditions can be easily understood in the mentioned area. It can be concluded that the higher the platform, the longer the useful distance, up to a practical maximum of some 120 m. due to the effects of atmospheric conditions above explained, and noise.

Intelligibility over longer distances can only be achieved with the support of some strong reflections from nearby large walls, as in the case of the Chichen-Itza Ball game. The walls have to be near in order to avoid echo formation, or sound could be amplified as it is done nowadays, with the help of electronic amplification.

The octave band background noise measured corresponds to PNC curve of 20 dB, which is considered as very good for large auditoriums, theatres and churches in order to allow for full intelligibility of speech (Sanders, p. 187). This means that the only noise that could have easily affected the speech intelligibility in the studied site, would have been the one produced by the crowd itself.

With regard to the Signal to Noise ratio approach to the speech intelligibility, it also confirms full understanding of messages within the distance studied and atmospheric conditions and noise present during the measurements.

Reverberation in this case is not an issue because it is an open space where reverberation is not produced.

All the main pyramids, and many of the small ones, in the ceremonial sites in Mesoamerica are much taller than this studied basement. Confirmation of the above statements has been obtained by the author without any test equipment in several archaeological sites. Further research will be performed in several other basements and pyramids, together with other acoustical studies, in order to complement this one.

Conclusions

Pyramids and basements can be conveniently used for speech messages, and probably it was in the past a common use of these constructions.

Speech communications might not have been the main reason to build pyramids or basements, as rituals and other festivities could be the first purpose, but definitely they can be used to convey voice messages.

Nowadays, some of these kinds of sites are employed from time to time to represent dances, theatrical plays or musical performances to very large gatherings, making good opportunities for people to get to know this interesting heritage.

Bibliography

Beyer, R. T. Sounds of our times, Two hundred years of acoustics.1999. Springer, USA.