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| = ARCHIVED WIKISPACES DISCUSSION BELOW =
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| '''All discussion below is archived from the Wikispaces export in its original unaltered form.'''
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| == Why this? ==
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| I was following pretty well until this:
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| "If r is even, therefore, we will regard the 3-tuple [r e3 e5] as denoting a major triad, and if [n, [r e3 e5]] is the tablet we wish to define, we first calculate u = n - 5e3 - 7e5."
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| Where did this mystery expression come from? Why n - 5e3 - 7e5? How did you derive that equation?
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| - '''mbattaglia1''' September 26, 2011, 07:28:36 PM UTC-0700
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| Apply the val <3 5 7| to |e2 e3 e7> and get 3e2+5e3+7e5. We want to find a monzo which will make the result n, so we want n-3e2-5e3-7e5 to come to 0. So, we are going to need to pick a monzo such that n-5e3-7e5 is divisible by 3.
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| - '''genewardsmith''' September 27, 2011, 06:09:56 AM UTC-0700
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| Where did the val <3 5 7| come from?
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| - '''mbattaglia1''' September 27, 2011, 09:11:43 AM UTC-0700
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| <em>Apply the val <3 5 7| to |e2 e3 e7> and get 3e2+5e3+7e5.</em>
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| how did you calculate this? Is there a source where I can learn it easily?
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| - '''xenwolf''' September 28, 2011, 12:02:51 AM UTC-0700
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| Xenwolf - check out my beginner's article to vals on this page:
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| http://xenharmonic.wikispaces.com/General+Theory
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| Gene - still curious where <3 5 7| came from :)
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| - '''mbattaglia1''' September 28, 2011, 07:46:54 AM UTC-0700
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| <3 5 7| is a great val for representing the skeleton for 5-limit triads. It equates major and minor, and also augmented and diminished for that matter, but gives the general outline of note and chord relationships. That's what tablets are for. It makes commas out of 10/9, 16/15 and 25/24, so these typical voice-leading intervals tend to appear when you change the chord identifer but not the note number.
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| The patent vals for 3, 4, 5, and 7 are all quite useful for this tablet business in connection with JI tablets.
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| - '''genewardsmith''' September 28, 2011, 09:44:15 AM UTC-0700
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| Okay, so now the next step. Since u = n - 5e3 - 7e5, you derive this
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| if u mod 3 = 0, then
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| note(n, [r e3 e5]) = |u/3 e3 e5>
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| So the monzo is divisible by 3, I see that, and then the "note" is determined by n (a "note number") and c (a "chord identifier), I'm not sure exactly what the note and chord identifiers are, but I am completely lost as to what the final ket vector is, (the "note"), does
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| n determine the residue of mod 3 here? What do you do with the final vector? I thought I had gotten this but I seem to be going around a vicious loop with this. Thanks - pgh.
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| - '''phjelmstad''' October 08, 2011, 02:30:05 PM UTC-0700
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| Is n just the note number in c? (1 3 5, or 1 2 3?)
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| - '''phjelmstad''' October 08, 2011, 02:32:09 PM UTC-0700
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| |u/3 e3 e5> is a 5-limit monzo. It belongs to the chord identified by "c" as one of its constituent notes, and the 3et val maps it to "n". It is the unique 5-limit note belonging to the 5-limit triad denoted by c which maps to n.
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| - '''genewardsmith''' October 08, 2011, 02:49:56 PM UTC-0700
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| Thanks. I know I should just work a few more example problems (and I will), and I see how 3et val gives us the n, I would guess the modulus would determine which note in c you get (the 1st, 2nd or 3rd?)
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| pgh
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| - '''phjelmstad''' October 09, 2011, 02:23:16 PM UTC-0700
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