Mike's lecture on vector spaces and dual spaces: Difference between revisions

(4 intermediate revisions by 2 users not shown)

Line 1:

__FORCETOC__

= <u>EPISODE 1: Vector Spaces and Dual Spaces</u> =

If you haven't seen monzos or vals before and are totally confused, please read the pages on [[monzos|Monzos]] and [[Vals|Vals]] first!

Line 63:

Line 62:

# First you go down 4 octaves, at a rate of 12 steps per octave, putting you underwater at −48 steps.

# Then, you go up 4 tritaves, times 19 steps per tritave, giving you 76 steps. This lands you at a net of {{nowrap|−48 + 76 {{=}} 28}} steps.

~~<nowiki />~~# Finally, you go down one 5/1, times 28 steps per 5/1, putting you down 28 more steps. This lands you at a net of {{nowrap|28 − 28 steps {{=}} 0}}.

# Finally, you go down one 5/1, times 28 steps per 5/1, putting you down 28 more steps. This lands you at a net of {{nowrap|28 − 28 steps {{=}} 0}}.

So, if you mechanically work out the way that you'd compute how many steps 81/80 is in 12-EDO, you get 0 steps, meaning you're back at 1/1 and hence tempered out. No surprise there.

@@ Line 1: / Line 1: @@
-{{breadcrumb|Mike's lectures on regular temperament theory}}
+{{Main|Mike's lectures on regular temperament theory}}
 {{texmap}}
 __FORCETOC__
 = <u>EPISODE 1: Vector Spaces and Dual Spaces</u> =
 If you haven't seen monzos or vals before and are totally confused, please read the pages on [[monzos|Monzos]] and [[Vals|Vals]] first!
@@ Line 63: / Line 62: @@
 # First you go down 4 octaves, at a rate of 12 steps per octave, putting you underwater at &minus;48 steps.
 # Then, you go up 4 tritaves, times 19 steps per tritave, giving you 76 steps. This lands you at a net of {{nowrap|&minus;48 + 76 {{=}} 28}} steps.
-<nowiki /># Finally, you go down one 5/1, times 28 steps per 5/1, putting you down 28 more steps. This lands you at a net of {{nowrap|28 &minus; 28 steps {{=}} 0}}.
+# Finally, you go down one 5/1, times 28 steps per 5/1, putting you down 28 more steps. This lands you at a net of {{nowrap|28 &minus; 28 steps {{=}} 0}}.
 So, if you mechanically work out the way that you'd compute how many steps 81/80 is in 12-EDO, you get 0 steps, meaning you're back at 1/1 and hence tempered out. No surprise there.