If you put the treble and bass staff together in a grand staff (what you read playing piano), the G marked by the treble clef is the second line up from the bottom of the treble staff. The F marked by the bass clef is the second line from the top of the bass staff.
Middle C sits one ledger line below treble clef (or a fifth – five notes – below the second line G). It also happens to be one ledger line above the bass staff F (or a fifth – five notes – above the second line F). If you put both of your thumbs on middle C, your right pinky lands on the G marked by the treble staff; and your left pinky lands on the F marked by the bass staff.
Basically, it’s like we have one giant staff with 11 lines and the middle line is middle C. To make it easier to read, we took out the middle line, making it looks like we have two separate 5-line staves. It shows a huge range of the notes available to both hands simultaneously.
If you play a monophonic (one note at a time) instrument like in band or orchestra, you only need one staff, which makes the concept of two different clefs seem totally ridiculous. Conceiving of them as two parts of the same whole, connected by middle C, it makes it make a little more sense.
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