Sstrhsrtj

I just recently learned about time signatures and the beat and I need to clearly understand the relations of these things, as for now I don't seem to do it. Please correct my thoughts on the following stuff.

As for the time signature 4/4 the first 4 tells that there are 4 beats in the measure. What exaclty is the measure? Is the measure the second 4 that tells us it is 1/4 of the duration of the beat?

I did some calculations so far, e.g. the duration in s of the beat which is 60/bpm. So for 90 bpm it would be 0,67s per beat.

Would it be then correct to say that a time signature of 4/4 with 90bpm would result in a single note duration of 0,17s and that there need to be at least 4 notes that equal 4 quarters?

If the time signature was 3/4 for the same bpm would the single note duration still be 0,17s?

The top number - in red for the image below - is how many beats are in a measure (or bar.)

The measure are indicated on the staff with vertical lines - measure are shown in the image below with a red bracket.

The bottom number is which note is used for the beat in this example the 4 means 1/4 (quarter) note. Notice that each quarter note is numbered 1, 2, 3... to show the counting of the beats. 3 beats for 3/4 and 4 beats for 4/4.

A nice PDF about meter is available from Toby Rush.

With that covered...

Is the measure the second 4 that tells us it is 1/4 of the duration of
the beat?

No. Now we know that there are 3 or 4 beats in the beats depending on the meter.

Would it be then correct to say that a time signature of 4/4 with
90bpm would result in a single note duration of 0,17s and that there
need to be at least 4 notes that equal 4 quarters?

No. 90 bpm / 60 secs = each beat is 0.66 seconds. 0.66 sec for quarter notes, 0.33 sec for eighth notes, etc. If you switch to 3/4 meter, these times per rhythmic note value will stay the same. But the feel of the phrases will shift from even 2's and 4' to 3's. Like the feel of a polka versus a waltz.

The measure is the part of the score between the two vertical lines.

The Bottom number tells you what note corresponds to one beat. So if that bottom number is a "4", then each beat is a quarter note (1/4 of a whole note). The top note tells you how many beats there are in the measure. If the top number is "4", then there are four beats per measure. So a signature of 4/4 means four quarter-notes per measure; 3/4 means three quarter-notes per measure.

Nothing in the time signature tells you tempo, the amount of time taken up by each beat or measure.^*. The tempo is indicated separately by a notation such as "60 bpm," or "Larghetto." The tempo notation is optional.

If the tempo is marked, then that, together with the time signature, tells you how long each measure will last. For example, if the tempo notation is "60 bpm" and the signature is 3/4, then each quarter note lasts a second, and there are three quarter notes per measure, so each measure lasts 3 seconds. If the tempo notation is "120 bpm," then each quarter notes lasts half a second, so a measure of three quarter-notes would be 1-1/2 seconds.

Would it be then correct to say that a time signature of 4/4 with 90bpm would result in a single note duration of 0,17s and that there need to be at least 4 notes that equal 4 quarters?

Each quarter note will be 1/90 of a minute, or 2/3 of a second. Since there are four quarter notes per measure, each measure will last 4 * 2/3 second, or 2-2/3 seconds.

^* While it is technically true that the signature does not tell you the tempo, there are conventions for certain kinds of music that do. For example, if the piece is Irish and it's in 6/8 time, it's probably a jig and it's played at around 110 bpm, with each beat being one triplet of eighth notes. When conventions like that are sufficient, the arranger may opt to not notate the tempo explicitly.