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As I understand, the quarter note is a note that lasts for one beat.
the half note, is a note that lasts for two beats,
the full note, is a note that lasts for four beats,
now i get that, but what is the length of one beat? is it standard? does it differ from instrument to another ?
I'm using virtual piano http://virtualpiano.net to practice
The duration of the beat is set by the tempo marking, usually an italian word like lento, andante, vivace, etc. that you may have noticed at the beginning of musical scores.
These words correspond to an approximate setting of beats per minute (bpm), that you find for example in wikipedia and is usually also marked on the scales of metronomes. But the performer or conductor must make is own judgement as to the precise tempo to use.
So, for example, an andante tempo marking is considered to be somewhere between approximately 76 and 108 bpm. Taking 90 bpm as example, for a 4/4 time signature:
Now, something to keep in mind is, metronome scales and conventional bpm ranges for tempo markings do indeed assume a beat unit of a quarter note, but that's not always true. The time signature used for each piece defines, in its lower number, what rhythmic unit corresponds to a beat (many times a quarter note, yes, but also frequently an eighth and some times a half note, or other values).
For example, for a 3/8 time signature (not very frequent, but for the sake of example) and the same andante tempo marking:
This is important, as the beat unit defines the intended musical "pulse" of the piece, so it's not the same thing a "pulse" of 3 quarter or of 6 eight notes per measure, despite the overall measure duration resulting the same.
We should also refer the case of compound time signatures, where a beat is a dotted rythmic note. For a 6/8 time signature:
To avoid any confusion and provide more precise performance instructions, since the invention of the metronome some composers provide tempo markings in precise bpm.
One beat is as long as the composer says it will be. Usually signified at the beginning of a piece with 'bpm', This stands for beats per minute, so if it stated 60bpm, there would be one beat every second.A tune twice as fast would be 120bpm. No-one actually times abeats per se, but instead would use a metronome to set the speed of the piece.It's also very important that the composer states what that 'beat' actually is - it could be, and usually is, a crotchet, but could be a dotted crotche or quaver or minim. Dance tunes in particular will have a bpm that needs adhering to, whereas a lot of classical pieces will not have an exact metronome mark, but will say 'andante', 'presto', 'largo' instead. These are vague on purpose to give performers a margin in which nto work. With modern pop type music, in order to keep everyone in time, a cick track is used - it's a sort of metronome, and means that if recordings are done at different times (or even different countries!), the beat will remain constant.
The answers above are correct, but only with regards to post-baroque music, which is when tempo indications began to mean absolute tempo with regards to the time signature. In baroque music, on the other hand, oftentimes the time signature is not an indication of what the core rhythmic unit is. An example could be the first movement of Georg Philipp Telemann’s ‘Sonata for two Flutes in A major’; for this, the tempo is written as andante cantabile and then time signature set to 2⁄4, but playing the piece at this tempo would surely ruin it.
The general rule for baroque music and earlier, is that the tempo is indicated for the rhythmically most important unit; this is usually the bass line. Listen to this [http://tidal.com/track/61413470] (Georgiev–Goranova–Ivanova recording) for an example; it is at roughly 85 bpm by the quavers (eight notes).
Summary: For early music, the time signature does not necessarily indicatewhat should be counted by the tempo indication; rather it is an indication of what the feel of the music should be. Combine that with finding the most important rhythmical pattern and apply the tempo to that unit, whilst trying to maintain a pace giving the feel of the time signature. Also note that having an indication at all of the tempo, is a sign that the beat should be straight, as opposed to an inégalité performance, as Das wohltemperierte Klavier is a good indication of (where only a couple of all the pieces have tempo indication. For inégalité, please view the article on Britannica (https://www.britannica.com/art/inegalite).
