Talk:Relative errors of small EDOs

(WIP) Relative Errors of Small Edos

I did a change to the upper table to right-align the numbers, I hope that's okay. Here some (hopefully helpful) suggestions:

• leave out the repetitive /1 in the headings
• leave out the column for prime 2
• switch from permille with one decimal place to the more common percent with two decimal places

Best regards --Xenwolf (talk) 07:26, 14 May 2020 (UTC)

> right-align

Thx. No idea how you did it.

> leave out the repetitive /1 in the headings

> leave out the column for prime 2

Although this article is about edos, the method is valid for all rank-1 temperaments. For non-octave temperaments, the errors of, for example, 3/1 and 3/2 are different. Maybe I'll do ed3, ed5, etc. in the future. That's the reason why the /1 and prime 2 are there.

> percent

I'll do the switch after I fill it all up to see if it looks better. FloraC (talk) 15:15, 14 May 2020 (UTC)

Maybe I can help you with this, I'm a professional programmer who can automate this with Perl or Python. I'd also hand you the script for further adaption then ... Please tell me if this sounds right to you. --Xenwolf (talk) 18:49, 14 May 2020 (UTC)

Nice.

I don't suppose your script generates those values (cuz I did so in C), just doing with the table, right? FloraC (talk) 02:52, 15 May 2020 (UTC)

Such a script would also generate the values. --Xenwolf (talk) 05:50, 15 May 2020 (UTC)

Let's do it then. FloraC (talk) 12:04, 15 May 2020 (UTC)

permille vs. percent

Comparison of permille and percent formatting below. I restricted the tables to only a few columns and rows

Edo Relative Errors (in ‰) 3/1 5/1 7/1 11/1 13/1 9 -264.7 102.6 -266.2 -134.9 -304.0 10 150.4 -219.3 -73.5 405.7 -4.4 11 -434.6 458.8 119.1 -53.7 295.2 12 -19.6 136.9 311.7 486.8 -405.3 13 395.5 -185.1 -495.6 27.4 -105.7 14 -189.5 493.0 -303.0 -432.0 193.8

Edo Relative Errors (in %) 3/1 5/1 7/1 11/1 13/1 9 -26.47 10.26 -26.62 -13.49 -30.40 10 15.04 -21.93 -7.35 40.57 -0.44 11 -43.46 45.88 11.91 -5.37 29.52 12 -1.96 13.69 31.17 48.68 -40.53 13 39.55 -18.51 -49.56 2.74 -10.57 14 -18.95 49.30 -30.30 -43.20 19.38

To me the percent values look more familiar and the grouping is better (at maximum pairs of numbers) --Xenwolf (talk) 19:07, 15 May 2020 (UTC)

BTW: the Python script to produce the two tables above (except for the percent and permille symbols) is as follows:

import math

primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]

def rel_err(p, edo):
    v = math.log(p) / math.log(2) * edo
    t = round(v)
    e = (t-v)
    return e

def edo_primes(edo_min, edo_max, primes, unit):
    pot = unit[0]
    precision = 4-pot
    scale = 10 ** (pot)
    print('{| class="wikitable sortable mw-collapsible" style="text-align:right"')
    print('! rowspan="2" | Edo')
    print(f'! colspan="{len(primes)}" | Relative Errors (in {unit[1]})')
    print('|-')
    for p in primes:
        print(f'! {p:2}/1')
    for edo in range(edo_min, edo_max):
        print('|-')
        print(f'| {edo:2}')
        for p in primes:
            print (f'| {rel_err(p, edo)*scale:6.{precision}f}')
    print('|}')

edo_primes(9, 15, primes[1:6], (3, 'permille'))
edo_primes(9, 15, primes[1:6], (2, 'percent'))

--Xenwolf (talk) 20:48, 15 May 2020 (UTC)

Cool. A cent is really a cent in 12-edo. Why didn't I see that. And I get the idea of the program. I can do the other table on my own. FloraC (talk) 20:06, 16 May 2020 (UTC)

change from h1 to h2 headings in article body

I plead for the restriction to h2 headings in the article body, and reserve h2 headings for the article title. If you know this great feature in Wikipedia (it's currently not provided in this Wiki but probably will in future), you will know that - as a user - you can export a very book-like presentation of a handpicked collection of articles as PDF. --Xenwolf (talk) 19:22, 15 May 2020 (UTC)

But what about the table of contents? FloraC (talk) 20:06, 16 May 2020 (UTC)