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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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    There's lots. Dynamic marks (p, mp, mf, f, etc), cresc./dim., hairpins, accents... – MattPutnam Apr 23 '18 at 14:17
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    Just curious. Where are you seeing piano music which doesn’t include markings relating to volume? – AJFaraday Apr 23 '18 at 15:47
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    @GeneralNuisance That's because most of the instruments used in Bach's time had little capability of dynamic expression; recorders were the main woodwind instrument, and the harpsichord had not yet been replaced by the piano. – Chromatix Apr 24 '18 at 2:45
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    Sometimes it depends on the source of the sheet musics. For officially published classical piano books, I don't think I've ever seen a sheet without dynamics at all. But fan made sheet musics usually only care about notes, ignoring many things... including the dynamics. – Andrew T. Apr 24 '18 at 4:51
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    Would downvote if I could, this question shows to me a clear lack of research effort. – Pierre Arlaud Apr 24 '18 at 7:55
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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:

https://en.wikipedia.org/wiki/Dynamics_(music)

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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.

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    fff does not always mean “very very loud”. When written in e.g. a flute part, it's an instruction for the conductor to tell the trumpets that the f they have at that spot should maybe be only mf after all... – leftaroundabout Apr 23 '18 at 16:33
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    @leftaroundabout Sure, but it might be a matter of available players. Some composers wrote with orchestras of specific compositions, skill levels, and instrumentation in mind. If a composer may say something like "Ignore the written fff play mf at most" to a brass section, for example, it might be because the brass section is too numerous for the original design of the piece. It at the very least is influenced by the characteristic of the sections and also whether there is a soloist, and how loud their instrument is. – psosuna Apr 23 '18 at 18:51
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    Any trumpet player will tell you mf stands for megaforte. – RedSonja Apr 24 '18 at 10:32
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    @RedSonja brass players are a bunch of mfs in general... – topo morto Apr 24 '18 at 10:34
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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: https://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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  • Nitpick: the fortepiano was a less advanced precursor to the modern pianoforte. – Chromatix Apr 24 '18 at 2:47
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    even then composers may be delighted by interpretations radically different from their own: or not. Paul Hindemith once asked a conductor who invited him to the premiere of one of his works: “Do you think you could possibly play it any better than I hear it in my own head?” – aeismail Apr 24 '18 at 7:38
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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.

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    This doesn't seem to answer OP's question. – David Bowling Apr 24 '18 at 22:07

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