Wow - big question for a post on a forum to answer.
I think the simplest way to answer this is to think of an octave, and think of it split into 12 semitones.
In Western music we most onften hear two journies through these 12 semitones
- the major scale (where the gaps between the sequential notes of the scale are Tone Tone Semitone Tone Tone Tone Semitone)
- the minor scale (where the gaps between the sequential notes of the scale are Tone Semitone Tone Tone Tone Tone Semitone)
But you could make other sequences of notes too, that have a different journey path up through the octave.
These are the modes.
Why are they intereting?
Because all notes are related to each other (look at the circle of 5ths and "modes explained" on google and you will see a the beautiful interelation of music and harmony).
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