Why is there no indication of relative loudness on sheet music?
When I'm playing on a piano I can read which keys I should press and when. But there seems to be no indication how loud each sound should be in relation to another. Why?
It seems to me that this important information is lost and it's open to interpretation. As a result the music played can be very different from what the author intended because loudness is a whole dimension of expression. There would me much less interpretation if loudness was indicated at least relatively. I do so for my own purposes, I draw a rising and falling line over notes. Am I missing something?
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Another aspect is the audience and acoustics. Is this for a family in the living room or for a large audience in a sound amplifying concert hall? The strength and overall volume one plays will be different.
For speaking (speeches), you "speak to the person at the back of the room." Same here. Everyone in the targeted audience should be able to hear the music. From that beginning point, ppp to fff (crescendo, >>>, or simply soft as I've seen written) accordingly.
There are actually many markings in music notation that have to do with dynamics. Whether it is setting the overall level, such as Piano (p = quiet) or fortissimo(ff = loud), or a crescendo (<) or decrescendo (>).
Maybe you just haven't come across these yet. If there are no markings on a piece of music it is up to the performer to interpret the music accordingly.
A more complete list of dynamic markings can be found on Wikipedia:
en.wikipedia.org/wiki/Dynamics_(music)
There are lots of indications -
explicit loudness markings (from ppp, pianississimo - very very soft - to fff - fortississimo - very very loud).
crescendo and diminuendo marks (which can be textual - 'cresc', 'dim' - or be in the form of the 'hairpin' symbols)
dynamic accents, showing that a particular note should be louder in volume - which can be marked with symbols, or textually (e.g. sfz)
The time signature, which gives an indication as to which beats of the bar should be stressed more (answers here and here, as well as elsewhere, have further details)
textual directions as to the general feel with which the music can be played ('con brio') or applying more specifically to the level of vigor ('smorzando', 'incalzando')
However, when you say...
Seems to me that this important information is ...open to interpretation
You're right! Almost everything on a standard score - rhythm, pitch, timbre, volume - is somewhat open to interpretation. That's part of the beauty of it -it opens the door to the artistry of the performer.
Since you are a relative newcomer to written music I assume, here are some thing you should note.
First, for graphical crescendo and diminuendo marks, use hairpins, as described in the already linked Wikipedia article: en.wikipedia.org/wiki/Dynamics_(music)#Changes
Second, much of the keyboard music we know and love was originally written for the harpsichord and the organ, which were incapable of any dynamic variations. Modern organs may have a global "volume knob" (expression pedal) and loudness settings for each register, but historical organs were on and off, and harpsichords still are, by design. The piano (originally called fortepiano) was invented much later and as you can guess from its name, dynamic variation capability was its primary "selling point".
Therefore, any dynamic markings in keyboard music written before some mid 1700's is an invention of the arranger.
Which brings are to the third point: exact intentions of a composer cannot be known unless you can just go and ask the composer, and even then composers may be delighted by interpretations radically different from their own.
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