I'm looking for a push in the right direction as to how to go about writing Super Mario type video game themes. What scales/modes work best, time signatures, etc...
Examples of where I'm trying to go:
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The Super Mario theme song is characterized by mode mixture and syncopated sixteenth note rhythms alternating with eighth note triplets.
Each note duration is very short, and each voice has a different rhythm. When the voices overlap, you hear the combination of all of the rhythms into a more constant stream of impulses. Each impulse has a different combination of voices and pitch content, and that's what gives the music its bouncy feel.
The melody is in a pretty simple C major scale, but the harmonies borrow from the parallel minor in some cases. This is called mode mixture.
If you would like to compose music in this style, you should transcribe it exactly so you can deconstruct and see/hear for yourself what makes it tick.
This notion may be apocryphal, but it does fit with what I remember of the Super Mario Brothers themes from NES.
I have at least heard that notes sounded on the early NES games had no capacity for duration (nor, presumably, timbral variations). So, you end up with each note being the same length. That limitation would tend to lead to a more rhythmic, perhaps contrapuntal style. I don't know how pitches would have been specified, so it is quite possible that pitches had to stay within the Western system of twelve tones, and presumably composers would remain within major and minor keys by choice. Other than that, though, I don't know that there are any "restrictions" on what you can write that would be similar in style to a particular video game.
I'm going to outsource my answer from this video, since it's pretty much exactly what you're asking for.
The Mario Franchise, when examined closely, draws a lot of influence from various jazz styles, more than people expect. Lots of chromaticism, and quickly-paced melodies. The Mario franchise's music in general, no matter who composes each piece, tends to have a lot of strong melodic material, an interesting/often-funky bassline, and never seems to take itself too seriously.