Kirk Newton | Acoustics

The acoustics of any hall, as perceived by a member of the audience, consist of three factors: volume, equalization, and reverberation (i.e., reflected sound). 

VOLUME

Volume, easily understood as the loudness of sound, needs clarification in relation to acoustics. Technically, volume is referred to as sound-pressure-level and is measured in units called decibels. Subjectively, one decibel is the smallest difference in loudness that the human ear is supposed to be able to perceive. Objectively, six decibels is the amount sound becomes louder or softer if the distance from the sound source is halved or doubled.

In a concert hall, the sound one hears consists of directly radiated sound and reflected sound.

1. Directly radiated sound, referred to as primary sound, is the sound that reaches the ear directly from the source.

1. Reflected sound is the sound that reaches the ear after being reflected off the various surfaces of the hall (walls, ceiling, etc.). It is usually confused with and mistakenly referred to as reverberation.

Although the sound one perceives consists of both primary sound and reflected sound, the primary sound determines the perceived volume level. This is appreciably louder because: 

1. sound becomes softer in proportion to the square of the distance traveled and the reflected sound travels a much longer distance, and

1. sound is partly absorbed and diffused by the reflecting surface. Therefore, reflected sound normally plays a negligible role in the actual perceived volume level.

Primary sound and reflected sound are essentially two separately arriving sounds of different volume levels. A characteristic of hearing is that the loudness of two sounds of different volume is not perceived as the sum of the two. The combined sounds are perceived as being only as loud as the louder of the two sound-sources. The louder sound determines the apparent volume level; the less loud sound does not add appreciably to the perceived volume level. This can be demonstrated in a room with four speakers, one in each corner. If the speakers play with unequal volume levels, the sound will always seem to be coming from the direction of the loudest speaker even with differences in volume as small as a few decibels. It only becomes obvious that the other speakers are playing if they are switched off.In everyday life, most sound-environments are full of sound-absorbing objects and materials and, because one is usually close to the sound source, reflecting surfaces are proportionally much farther away. Therefore, the ear is conditioned to hear a relationship of primary to reflected sound in which the volume of the reflected sound is so much lower than the primary sound that one is not aware of it. 
Because one is quieter, calmer, more relaxed, and more concentrated than usual during a concert, perception of subtleties is heightened. Therefore, for the sound to seem natural, the proportionate volume level of reflected sound relative to primary sound must be somewhat less than in real-life. 

EQUALIZATION
Equalization is essentially a further delineation of volume. Sound consists of vibrations (frequencies) of different speeds (cycles per second, or Hz), from approximately 20 Hz to 17,000 Hz, with most sounds lying within 40 Hz to 12,000 Hz. The equalization of sound is the volume of all the frequencies in relation to each other. If the equalization of a hall is correct, a sound from the stage in which all frequencies are equally loud will reach the audience in exactly that same volume relationship. If the volume level of some frequencies in relation to the others is changed when the sound reaches the audience, the hall is unequalized and does not radiate all frequencies correctly. In other words, the equalization of a hall is a function of volume in that it deals with whether the different frequencies reach the audience in their original volume relationship to each other, or whether the hall distorts that original balance, transmitting some frequencies more strongly than others.
How sounds radiate from their sources (their dispersion characteristics) differs over the frequency spectrum. Lower vibrations radiate almost equally in all directions, while higher frequencies radiate more directly in straight lines. Because strongly reflective surfaces usually change the frequency balance in favor of the more directly radiating higher frequencies, the reflecting surfaces of a hall have to be carefully designed to not change the equalization. That holds true for the directly-radiating surfaces of the stage as well as the reflecting surfaces of the hall.
Ideally, a concert hall should not favor the high frequencies, but should have a mellow, warm sound, i.e., it should slightly subdue the higher frequencies. The more mellow the sound, the more freedom the musicians have in the manner in which they can produce and articulate the sounds. The less the hall highlights the higher frequencies, the greater the range of dynamics (from triple-pianissimo to triple-fortissimo) and the more types of attack (from sweet dolce to vigorous, biting accents) the musician can make use of while retaining beauty of tone. But, in a bright hall, all hard accents and biting attacks sound overly harsh and stringent. The sound in loud passages has a harsh, biting edge. To compensate, the musicians have to avoid the more vigorous, biting attacks and accents, and the dynamics have to be kept down if the sound is to remain listenable. The strings, for example, cannot really "dig in" and play full out with plenty of bow-pressure and a big tone. If they do, the sound is hard, harsh, and edgy.
Equalization is the most important single factor in any acoustic, and, in fact, in sound itself. It is the factor that most obviously changes the quality of a sound. Anyone with a hi-fi system that includes an equalizer can easily find this out by observing the differences in the sound when the frequency balance is changed. But, for decades, people have been hearing grossly unequalized, distorted sound reproduction (recordings, live broadcasts, live sound reinforcement).¹ They have been conditioned to ignore the distortions of unequalized sound, have become used to them, and thus do not notice that, in a bad acoustic, the equalization is inevitably the worst factor.

REVERBERATION and REFLECTED SOUND 

Reverberation is the most misunderstood and least important of the factors. Reverberation is the process of the reflected sound bouncing back and forth off all reflecting surfaces until it stops. The word "reverberation" is the wrong term to describe what is actually heard. The sound quality that is heard and called reverberation is actually the result of only the first-arriving reflected sound. These sound effects, wrongly referred to as reverberation, are understood and discussed only in terms of reverberation time, but actually consist of two other factors: volume and reflection time.
The more important of these factors is the volume. If the reflected sound is so soft as to be covered (masked) by the primary sound, it will obviously not make the slightest difference except in the pauses. The time factor only plays a role when the volume of the measured reverberated sound is loud enough to be perceived, however subtly, by the listener. In a concert hall, the important point to remember is that the volume of reflected sound should not be loud enough to be consciously heard, even when the tensions of the body have relaxed and the listener is hearing very loudly.²
The characteristics of primary sound do not change. Therefore, the first-arriving reflections determine the character of a hall's acoustic because they are the only reflected sounds loud enough to affect the sound's characteristics.
The simple mathematical difference between the arrival-time of the primary and reflected sound is the pertinent time-factor in acoustics: reflected-sound-time minus primary-sound-time equals reflection time. This interval is purely a function of the size and shape of a hall. Reflected sound can also be measured from the source, in which case it becomes simply the time it takes for the sound to travel to the reflecting surface and back to the source. This measurement indicates how the performers, not the audience, experience the sound.
The concept of "reverberation time" as a meaningful acoustical measurement is wrong. It does not represent actual listening experience. In actual listening, there is no one single time for reflected sound to reach a listener. All sounds continue reverberating back and forth off all surfaces until they die down to absolutely nothing. But we can only perceive the reverberating sound while it is still loud enough to be heard. The misunderstanding stems from the measuring technique.
The value stated as the reverberation time is an arbitrarily chosen value that is supposed to represent the point at which the reverberating sound has died down to a volume level so weak that it essentially is no longer present (1/1,000,000th of the original volume). In a hall with a measured one second reverberation time, the sound would actually lose approximately 75% of its loudness in the first 1/lOth of a second. It would be almost instantly covered by the continuing sounds of the music and, in pauses, will be covered by the room's natural noise level (ambient sound) long before it becomes 1/l,OOO,OOOth of its original volume. The measuring instrument registers the first-arriving (direct) sound and then records the length of time it takes for that sound to die down (decay) to that irrelevant, insignificant volume level. But this measurement is worthless because it neither tells the actual time it takes for the reverberations to stop nor does it tell anything about the really important, bearable sound events that happen in between. Any effect the reflected sound would have on the acoustic qualities of that room would happen long before the measurement was reached.
Although no instrumental measurements can duplicate the way the reflected sound is actually perceived, they can provide helpful information. A more difficult, but more meaningful measurement for acoustical evaluation would be to measure the time-interval between the first arrival (direct sound) and the very next few arrivals (the first-arriving reflections) along with their volume-levels. Careful tabulation of that information for a large number of concert halls would probably lead to insights into the real differences between good and bad halls.
The first-arriving sound reflections are necessarily the loudest. But it is impossible to establish a single reflection time. The reflecting surfaces are at differing distances from the listener. Sound reflected off the ceiling, the side-walls, the back wall, and the wall behind the performer will reach the listener at different time intervals since each of these surfaces (even each segment of the surface) is at a different distance from the performer and the listener. Also, a measuring instrument has no way of telling whether the sound reaching it is a first arrival from a far wall or a second, third or fiftieth arrival from a near wall. Since all of the bearable reflections arrive so quickly, they amount to a steady sound made up of the many arrivals of reflected sound which are so close together that they cannot be registered separately.
There is a prevalent misunderstanding that reverberation is something beneficial that can be added to sounds at will within a wide range of parameters. Reverberation is really a PROBLEM that has to be controlled, and not a benefit for which it is only a matter of finding the ideal amount, and the more the merrier.
What reverberation amounts to is repetitions of progressively more and more distorted reflected sound because no surface reflects all frequencies equally. When loud enough to be heard, the effect of these reflections is similar to the effect of reprinting the same picture a number of times on top of itself, with each reprint shifted slightly and the color-values changed. The result on paper is a blur, and conically the result of repeated, bearable reflections is also a blur. The prevalent idea that a long "reverberation time" can be excellent for a Mahler symphony but wrong for the speaking voice (because speech would be rendered unintelligible) is not valid. If the reflections blur speech, they will also blur the Mahler symphony. The problem in recognizing this fact is that, in the Mahler symphony, it is the most subtle nuances, which are the most difficult-to-hear aspects of sound, that are blurred. We are seldom able to be aware of all the subtleties of nuance in fine music. It is therefore difficult to know that those nuances have been eradicated, and a regular audience quickly becomes used to music without them.
At the Church of Saint John the Divine in New York City, the reflection times are so long and the reflections so loud that one can hear a distinct echo along with the many arrivals. Anyone familiar with the acoustic of such a room will understand that reverberation should be treated as a basically undesirable element to be held to low limits, and not as a toy to be played with for various effects, as is often the case with reverberation devices in sound-reproduction.

This apparent relationship between the volume of direct and reflected sound must be preserved if the sound in a concert hall is to seem natural. 

^Found this here. Great outline.