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Why this?

I was following pretty well until this:

"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."

Where did this mystery expression come from? Why n - 5e3 - 7e5? How did you derive that equation?

- mbattaglia1 September 26, 2011, 07:28:36 PM UTC-0700

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.

- genewardsmith September 27, 2011, 06:09:56 AM UTC-0700

Where did the val <3 5 7| come from?

- mbattaglia1 September 27, 2011, 09:11:43 AM UTC-0700

Apply the val <3 5 7| to |e2 e3 e7> and get 3e2+5e3+7e5.

how did you calculate this? Is there a source where I can learn it easily?

- xenwolf September 28, 2011, 12:02:51 AM UTC-0700

Xenwolf - check out my beginner's article to vals on this page:

Gene - still curious where <3 5 7| came from :)

- mbattaglia1 September 28, 2011, 07:46:54 AM UTC-0700

<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.

The patent vals for 3, 4, 5, and 7 are all quite useful for this tablet business in connection with JI tablets.

- genewardsmith September 28, 2011, 09:44:15 AM UTC-0700

Okay, so now the next step. Since u = n - 5e3 - 7e5, you derive this

if u mod 3 = 0, then

note(n, [r e3 e5]) = |u/3 e3 e5>

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

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.

- phjelmstad October 08, 2011, 02:30:05 PM UTC-0700

Is n just the note number in c? (1 3 5, or 1 2 3?)

- phjelmstad October 08, 2011, 02:32:09 PM UTC-0700

|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.

- genewardsmith October 08, 2011, 02:49:56 PM UTC-0700

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?)


- phjelmstad October 09, 2011, 02:23:16 PM UTC-0700