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What is music?
Map of the fretboard
The Major Scale
The C Major scale
Generally speaking, chords change with the first beat of the bar, but again, this is strictly up to the composer. They can change anytime at all but to be able to be enjoyed by the masses, a certain regularity and even predictability must be included. Most people prefer to listen to music they can tap along to. Most of us seem to have a deep-rooted understanding of rhythm, something that goes way back. Strange time signatures thwart that foot-tapping. Symmetry seems to be the prerequisite for that to happen naturally.
An example of an asymmetrical rhythm is 5/4. I prefer to count that as "One Two Three One Two" ... same with 7/4. I would count that as "One Two Three Four One Two Three". I find it much easier to hear that time signature if I break it down into smaller groupings.
"Phrasing" is a word used to describe how time is manipulated. Singers and instrumentalists often "bend" perfect time as a way of adding emotion to their performance, which is an aspect of something even subtler known as "Feel". So, instead of keeping, for example, the melody line notes exactly synchronized with the underlying beats, the player or singer can either push the notes slightly ahead of the beat, or lag them slightly behind. Listen to any Frank Sinatra tune .. he was the master.
The main thing to remember is that underlying every piece of music is a steady regular pulse — that foot tapping thing — each unit being one beat.