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I have been wondering how loud seem instruments to musicians that play them. Let's say that you put an instrument in a room with average acoustics and measure loudness that musician hears and loudness in front of a musician (where it is the largest). How big would be the difference between those two values for instrument of each instrument family (strings, woodwind, brass, percussion)? In case of which instrument is that difference the largest in which the smallest etc.?

My partial and most possibly wrong estimated guesses:

percussion - loudest in both cases -> smallest difference
strings - the most quiet to audience, quite loud to musician -> big difference
woodwind, brass - louder to audience than musician -> biggest difference

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    @Todd Wilcox: The positions of the musicians will likely affect which instruments they think are loudest vs. which instruments the audience thinks are loudest. The extreme example is me playing bass clarinet on stage with the concert band and thinking that my bass clarinet is loudest and the clarinettists in front of me are the second loudest. – Dekkadeci Mar 7 '18 at 20:49
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    This isn't a simple question. For example, take the triangle. It does not produce the most acoustic energy, but it is the instrument that is most easily heard and distinguished over a full orchestra. Does that make it the loudest? – John Wu Mar 7 '18 at 22:06
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    @ToddWilcox - a trombone, for example, will sound louder to someone standing in front of the bell than it would to the person blowing into the mouthpiece. And amplified guitars will sound very different to the player who's standing beside or behind the cab, compared to someone who's directly in line with the speaker in the auditorium. It may be loud on stage, but that's not the OP's point. – Tim Mar 7 '18 at 22:32
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    This is a very broad question: Way too many variables at play to give a clear answer: Instruments in question, size and acoustics of the performance space, layout of the ensemble, how loudness is determined... – Stinkfoot Mar 8 '18 at 2:54
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    @Stinkfoot - a mic and vu meter on a simple recorder will do the job quite just fine. The instruments in question - well, that is the question. – Tim Mar 8 '18 at 5:48
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I've played them all so I'll give my thoughts.

Percussion: Definitely the loudest, at least to the player. It's hard to play drums for a long time without any kind of ear protection and not feel it. This is most pronounced in cymbals, as they're very easy to play extremely loudly. Hard sticks or mallets will sound the loudest but even soft mallets with a strong roll can pierce the ears. The next would be the snare drum, followed by timpani, bass/tenor/toms, keyboard mallets, and finally auxiliary percussion. I've never felt the triangle to be that loud, sad to say. Since percussion instruments project outward from their whole body it only depends on how close you are as to how loud it sounds, which is why they are situated in the back (along with being huge and hard to move). The most directional percussion instrument would probably be the bass drum, since it's usually put on its side and hit on one side, thus projecting away from the player. But since it's so low and takes rather strong hits to excite it's not too loud, not like a timpani. Marching bass drums are extremely focused though.

Brass: As you guessed, loud to the audience compared to the player, also situated in the back. This depends on the instrument. Trumpets and Trombones point straight ahead so they lose the most to the player, while Horns point more toward the player and Tubas and Euphoniums point straight up. They are loud by design so it's not too hard to play louder than strings or woodwinds, and since they are directional and have a distinct sound percussion doesn't phase them. Brass + percussion is a popular combination for bombastic pieces. Sousaphone is one of the loudest instruments ever invented, and since the bell points straight forward it shields the player while delivering its full blast to the audience. I don't think I've heard anything not electrically amplified that's as loud as a Sousaphone player.

Woodwind: Quieter than brass, but can still be pushed to loud. A woodwind works by interrupting a stream of air through a tube at various lengths from a source of vibration, namely a reed excited to vibrate through exhalation. Since the sound comes from the holes that are open the sound one hears is based on which note in particular is being played and can sound from very loud and commanding (Low Bb on a saxophone) to timid and stifled (throat Bb on a clarinet). Bassoon is the strangest of all since the sound goes in a big loop that's almost as tall as a person, and sound can come from all over the place. When it comes to loudness, the heirarchy goes piccolo, alto sax, tenor sax, bari sax, flute, oboe, clarinet, bass clarinet, bassoon. Piccolos are dreadful little things and easily the loudest to a player since the whole instrument is right in front of your face. Saxophones have the loudest overall sound while bassoons are the quietest.

Strings: Strings are interesting in that the have both an excited membrane (string) and a sounding box that projects the sound. They are quiet overall and can only be pushed so hard before the string just keeps hitting the finger board. They're more consistent with volume compared to woodwinds, so no matter what note you play you'll generally get a similar volume, though low notes and body resonating notes will sound the loudest. Cello would be the loudest due to it's range compared to its size, with Bass and Viola being too small compared to how low they're tuned, and violins simply being too small. There's a reason you need twice as many violins in an orchestra. For players the violin and viola are louder since, again they're right in your face whereas cello and bass are situated lower compared to your ears.

One thing to consider is the stage and audience location. The proximity effect is important, with bass frequencies traveling further than higher ones, so from a distance a really loudly played tuba will be clearer than a trumpet. Number of players also plays a factor, and it's often that a band will have twice as many trumpet players as tuba players, making the trumpets louder. Focus of sound is important as well, which is why in marching band the percussion is up front since in an outdoor environment the unfocused sound of percussions bleeds into the open air, while in a small room a single snare can be deafening.

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