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Does the time signature change affect the tempo ? Or atleast apparent or virtual tempo ?
First understand some background information :
Higher bpm means faster song. Here the "beat" refers to "real" beats.
A rhythm repeats after certain beats e.g. 4, 6 or 9 etc. We define bar = measure = Number of beats in bar. There is no confusion here.
A rhythm may have stronger emphasis after 2 or 3 or 4 beats interval.
Each beat may have inherent sub-beats (weaker) of 2 or 3 or 4. It is called by definition as == Meter == !!!
Often when we say, we have cycle of 9 beats repeatition, we really mean 3 beats repeatition with each beat subdivided into 3 (meter). Because you may want metronome at 3 beats boundary, not on all 9 beats !!! Compare this with 2 cycles music where you get alternative weak, strong beats.
We want a notation which is easy to write down and also express the meter/strong beats.
Time signature aids in this expression along with "metronome" marking.
Also we want to avoid writing triplet figure over every subdivided beat. Other than that there is no real significance for the denominator in time signature.
The bpm is usually referred as q = 60 bpm; Which implies 60 beats in minute with each beat annotated as "quarter" beat in sheet music. By default metronome is suggested one per quarter note duration.
For music of nature 6/8, we use denominator 8 for purely notational convenience and to avoid writing triplet figure over the notes in sheet music. Here we may expect a metronome strong beats at 1 (2 3), 4 (5 6). We mark the tempo in such cases like q. = 60 bpm; which hints that the overall speed of the beats/song is still same, but the weaker sub-beats are of divided by 3 in nature.
You may also come across tempo marking as e (eigth notes) = 60 bpm (suggesting faster song since metronome suggestion);
So one 6/8 song is not necessarily faster or slower than 4/4 song. It's meter is just different. The 4/4 songs typically divide the beats into sub weaker beats into 2 or 4 which often goes unnoticed.
Given same Midi file, if you change q = 60 bpm to q = 120 bpm, song will play twice faster. If you change the time signature from 4/4 to 2/4, nothing will change except, the bars will appear every 2 beats vs 4 beats and metronome will sound Tic-tac-Tic-tac vs Tic-tac-tac-tac.
If you change the time signature to 6/8, it will deduce 3 quarter note duration in measure.
It specifies the lowest number of beats where the rhythm pattern repeats itself.
Now -- the denominator specifies beat - note relationship. i.e. 4 means 1 beat is 1/4 note. (standard). 2 means 1/2 and 8 means 1/8 th.
Why would you typically want to have higher denominator like 8 or 16 ?
Instrs:Violin, range: B3-C#6; Cello, range: A2-C#5; Double Bass, range: A2-C#5