View source for Talk:Preferred number

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== This article is in need of major rework ==

There are currently a number of basic issues with this article: 
# It contains a large amount of [[WP:OR]]. {{pslink|Semiconductor devices}} has already been marked as such seven months ago. Many other sections contain no references and could arguably be seen as OR, as well. 
# This article is about numbers, but out of 11 topical sections and subsections, only four (#1, 3, 4.1, and 7) actually deal with numbers proper, the other seven deal with [[physical quantities]] where the number part can not be separated from their unit. 
# It seems to have no structure; it seems a loose collection of topics about abstract number sequences interspersed with very specific practical applications. 
# Most of the article is dedicated to Renard numbers, which is not a problem in itself, but it leads to some coordination problems with other wikis who keep Renard numbers in a separate article, such as de:WP. It might be worth considering following their example. 

These problems are most obvious in the following sections:
# {{pslink|Semiconductor devices}}: OR has already been noted. As for the numbers, they are obviously not chosen to be compatible across the series, as evident from comparing across the 10-fold change of the scale, e.g. 3 µm - 350 nm - 32 nm. Therefore, this section does not belong in this article. 
# {{pslink|Rail gauges}} just [[WP:CHERRYPICK|CHERRYPICK]]s two values out of more than a dozen; the fact that one is half of the other hardly makes them a "series" or a "logarithmic scale", as described in the lede. If there is no series or sequence, then this section does not belong in this article. (The fact that 1600mm ≈ 63″ is an interesting coincidence, though. Maybe that could be mentioned under {{pslink|Renard numbers}} or a subsection.) 
# Section {{pslink|Music}} has many issues: Twelve-tone equal temperament is not defined by a sequence of numbers specifically chosen to be nice to do computations with, but simply by their frequency ratio. The sequence would be the same if you measured the frequency in beats per minute, or even the wavelength. The sequence of pitches is only indirectly connected with this article through the fact that it forms a [[geometric progression]], which also happens to be what preferred numbers approximate. This is therefore [[WP:OFFTOPIC]] here. If at all, such information therefore could be included in the article [[geometric progression]]. However, not in its present state, as it has several issues, such as questionable OR. (E.g. the statement "All the standard piano key frequencies are close ..." is at least misleading: The R40 values for D, F♯ and G have errors exceeding 17.5 cents, the largest error of the [[Equal temperament#Comparison to just intonation]]. (The fact that R40 also divides the octave in 12 steps is a coincidence that might be worth a mention under {{pslink|Renard numbers}}.) In addition, this section rambles about topics that have nothing to do with preferred numbers and are far better treated elsewhere, such as A440 or differences between musical instruments.  

In conclusion, I am planning to delete these three sections. I know that some editors put some effort into them, and I don't want to discourage people, which is why I'm bringing this up here first before doing so, and I'm asking for your understanding. I also would like to start a discussion about how to tackle the three issues listed in the first paragraph for the remaining article. &mdash; [[User:SebastianHelm|Sebastian]] 09:14, 31 January 2016 (UTC)

:On rail guages, I don't think that it is even an interesting coincidence that 1600mm ≈ 63″.  The fourth Renard number is 2.5 times the first, so the fourteenth is 25 times the first.  Because the scale is approximately logarithmic, 25 times any Renard number is either exactly or approximately another Renard number.  There are 25 mm to the inch, so ''any'' Renard number of inches is bound to be exactly or approximately a Remard number of mm.  That relationship between inches and mm might be worth mentioning though. {{interrupted|Spinningspark| 10:09, 31 January 2016}}
:: Actually, there are two different coincidences at different precision levels: The one is that, at a precision of 1.6%, 25mm ≈ 1″. That would be the ratio of 1600mm:64″. The other arises because 64 is not a preferred number, but 63 is. Now, the ratio 1600mm:63″ is much more precise, its error is only 0.012%. Interesting tidbit, but not sure if it's encyclopedic. &mdash; [[User:SebastianHelm|Sebastian]] 18:02, 31 January 2016 (UTC) 
:On semiconductors, I agree that the present section is off topic, but some semiconductors, such as Zener diodes, do genuinely follow the E12 series of values as a deliberate design. [[User:Spinningspark|<b style="background:#FAFAD2;color:#C08000">Spinning</b>]][[User talk:Spinningspark|<b style="color:#4840A0">Spark</b>]] 10:09, 31 January 2016 (UTC)
:: Yes, of course, the E series clearly belongs in this article! &mdash; [[User:SebastianHelm|Sebastian]] 18:02, 31 January 2016 (UTC)

I have now deleted the three sections. In addition, I merged the "Building" section into the new article [[ISO 2848]]. That standard does not consist of preferred numbers, since they do not repeat by multiplication with the basis (usually 10). &mdash; [[User:SebastianHelm|Sebastian]] 09:18, 15 February 2016 (UTC)

=== Structure and suggested further cleanup ===
Further elaborating on problems #2 and #3 noted above, the structure is currently a mix of numerical sections and application sections. Since this article is about numbers, I would like to arrange all sections by numeric criteria, that is, whether they are based on powers of 10 or 2. There are still more standards or quasi-standards that are not series of preferred numbers, since they do not repeat with any basis: 
# computer graphics aspect ratios
# retail packaging 
I suggest to remove these, or move them to appropriate articles. 

A borderline case are the following sections: 
# Paper documents, envelopes, and drawing pens
# Photography

Mathematically, sequences such as 1, 2, 4... can indeed be seen as preferred numbers, but they are a [[Degeneracy (mathematics)|degenerate]] case, the case of just having one single simple number, 1, which reduces them to simple [[geometric sequence]]s. Just as we do with [[linear equation]]s in the article on [[quadratic equation]]s, such degenerate cases can be mentioned here, but they should not have their main home here. Their home should be the [[geometric sequence]] article. But the good mathematicians caring for the [[geometric sequence]] may not be happy if the pure math there gets contaminated by practical applications. Since that's a borderline case anyway, I am amenable to arguments for them to stay here. &mdash; [[User:SebastianHelm|Sebastian]] 09:18, 15 February 2016 (UTC)

== Replace lists with tables? ==

I like the colorful table at [[:de:Renard-Serie#Werte]] and wanted to copy it here, but then I realized that they don't have the R80 series. Adding a whole column for all R80 values would obviously double the length of the table, which would be ugly. However, since the even-numbered values don't change, we could insert a column just for the additional values, like the blue column below. I just don't know what headline to give that column. (I'm using the symbol "\" to denote a [[Complement (set theory)|complement]], but that's probably not well enough understood by most readers.) &mdash; [[User:SebastianHelm|Sebastian]] 09:37, 31 January 2016 (UTC) 

{| class="toptextcells" style="margin:auto;"
|
{| class="wikitable" style="text-align:center;"
|-
!colspan = 5 |least rounded
|-
! bgcolor="#e2e2e2"| R5
! bgcolor="#ffe2e2"| R10
! bgcolor="#ffffe2"| R20
! bgcolor="#e2ffe2"| R40
! bgcolor="#e2ffe2"| R80\R40
|- valign=top
| rowspan="8" bgcolor="#e2e2e2"| 1.00
| rowspan="4" bgcolor="#ffe2e2"| 1.00
| rowspan="2" bgcolor="#ffffe2"| 1.00
| bgcolor="#e2ffe2"| 1.00
| bgcolor="#cce2ff"| 1.03
|-
| bgcolor="#e2ffe2"| 1.06
| bgcolor="#cce2ff"| 1.09
|- valign=top
| rowspan="2" bgcolor="#ffffe2"| 1.12
| bgcolor="#e2ffe2"| 1.12
| bgcolor="#cce2ff"| 1.15
|-
| bgcolor="#e2ffe2"| 1.18
| bgcolor="#cce2ff"| 1.22
|- valign=top
| rowspan="4" bgcolor="#ffe2e2"| 1.25
| rowspan="2" bgcolor="#ffffe2"| 1.25
| bgcolor="#e2ffe2"| 1.25
| bgcolor="#cce2ff"| 1.28
|-
| bgcolor="#e2ffe2"| 1.32
| bgcolor="#cce2ff"| 1.36
|- valign=top
| rowspan="2" bgcolor="#ffffe2"| 1.40
| bgcolor="#e2ffe2"| 1.40
| bgcolor="#cce2ff"| 1.45
|}
|
{| class="wikitable" style="text-align:center;"
|-
!colspan = 3 |medium rounded
|-
! bgcolor="#ffe2e2"| R'10
! bgcolor="#ffffe2"| R'20
! bgcolor="#e2ffe2"| R'40
|- valign=top
| rowspan="4" bgcolor="#ffe2e2"| 1.00
| rowspan="2" bgcolor="#ffffe2"| 1.00
| bgcolor="#e2ffe2"| 1.00
|-
| bgcolor="#e2ffe2"| 1.05
|- valign=top
| rowspan="2" bgcolor="#ffffe2"| 1.12
| bgcolor="#e2ffe2"| 1.12
|-
| bgcolor="#e2ffe2"| 1.20
|- valign=top
| rowspan="4" bgcolor="#ffe2e2"| 1.25
| rowspan="2" bgcolor="#ffffe2"| 1.25
| bgcolor="#e2ffe2"| 1.25
|-
| bgcolor="#e2ffe2"| 1.30
|- valign=top
| rowspan="2" bgcolor="#ffffe2"| 1.40
| bgcolor="#e2ffe2"| 1.40
|}
|
{| class="wikitable" style="text-align:center;"
|-
!colspan = 4 |most rounded
|-
! bgcolor="#e2e2e2"| R&prime;&prime;5
! bgcolor="#ffe2e2"| R&prime;&prime;10
! bgcolor="#ffffe2"| R&prime;&prime;20
! bgcolor="#e2ffe2"| ---
|- valign=top
| rowspan="8" bgcolor="#e2e2e2"| 1.0
| rowspan="4" bgcolor="#ffe2e2"| 1.0
| rowspan="2" bgcolor="#ffffe2"| 1.0
| bgcolor="#e2ffe2"| ---
|-
| bgcolor="#e2ffe2"| ---
|- valign=top
| rowspan="2" bgcolor="#ffffe2"| 1.1
| bgcolor="#e2ffe2"| ---
|-
| bgcolor="#e2ffe2"| ---
|- valign=top
| rowspan="4" bgcolor="#ffe2e2"| 1.2
| rowspan="2" bgcolor="#ffffe2"| 1.2
| bgcolor="#e2ffe2"| ---
|-
| bgcolor="#e2ffe2"| ---
|- valign=top
| rowspan="2" bgcolor="#ffffe2"| 1.4
| bgcolor="#e2ffe2"| ---
|}
|}
:I'm not sure that I like the table.  To my mind the plain text was more compact and easier to read.  I especially don't like the way the R80 series has been handled, which I think is confusing. [[User:Spinningspark|<b style="background:#FAFAD2;color:#C08000">Spinning</b>]][[User talk:Spinningspark|<b style="color:#4840A0">Spark</b>]] 19:08, 15 February 2016 (UTC)
:: [[User:Spinningspark| ]] You make some good points, it is less compact now, and it requires some explanation for the "R80 add'l" part. But allow me to say that I'm disappointed that you're only saying this now. I burnt the midnight oil to implement this and only did so after waiting two weeks, which I thought was ample time to provide feedback. You could have saved me a lot of time if you had related your impression sooner. So let's make the best of it: Maybe we can keep both, and fold the table, so that it doesn't take up as much space? Part of what motivated me was that I didn't like about the original tables was their naked look. Maybe we could replace the code formatting with an interlaced table, so that we can keep the concept of different colors for the different series. What do you think? &mdash; [[User:SebastianHelm|Sebastian]] 05:37, 16 February 2016 (UTC)
::: Sorry for not metioning it sooner.  I was dubious about your table when you proposed it, but did not feel strongly enough to post until I saw the effect of the full table in the article.  Going across horizontally might be better, for however many columns seems sensible, then, at the series that will not fit, start going down for the interstitial entries.  Why don't you open an RFC or ask at the Wikiproject for more comments.  If other people like your table then I'll shut up. [[User:Spinningspark|<b style="background:#FAFAD2;color:#C08000">Spinning</b>]][[User talk:Spinningspark|<b style="color:#4840A0">Spark</b>]] 07:29, 16 February 2016 (UTC)
:::: Which Wikiproject? &mdash; [[User:SebastianHelm|Sebastian]] 17:18, 16 February 2016 (UTC)
:::::The one at the top of the page that says this article belongs to it. [[User:Spinningspark|<b style="background:#FAFAD2;color:#C08000">Spinning</b>]][[User talk:Spinningspark|<b style="color:#4840A0">Spark</b>]] 18:36, 16 February 2016 (UTC)
:::::: Alerted the WP. &mdash; [[User:SebastianHelm|Sebastian]] 20:31, 16 February 2016 (UTC)

== 1-2-5 and USD/CAD currency ==

The statement on US/Canadian currency is at best confusing, more likely misleading.  Both currencies follow a (1¢)-5¢-10¢-25¢-(50¢)-$1-($2)-$5-$10-$20-$50-$100 progression in current issuance, with some denominations obsolete or rare in either country or both.  The implication of the current text is that $2 should be $2.50 which it is not in either country, although the $2 bill is not commonly used in the U.S. while the $2 coin ("Toonie") is in very common use in Canada.  $2.50 coins and $25 bills have historically existed, but so have many other odd denominations, e.g. $3.
[[User:HPA|HPA]] ([[User talk:HPA|talk]]) 07:05, 9 August 2016 (UTC)
:Seems the section discussed above has been deleted. I can't say if it was too poor quality or if it simply didn't belong here (or if the deletion was a mistake), but I actually came here looking for information on preferred denominations of [[legal tender]] around the World. Is that to be found anywhere on wikipedia or elsewhere?--[[User:Nø|Nø]] ([[User talk:Nø|talk]]) 17:42, 25 February 2017 (UTC)

== Related stuff ==

There are a number of examples of preferred numbers not mentioned in the article - perhaps because they are not commonly ''called'' preferred numbers, while they are the same thing, or very nearly so:

* The [[Modulor]] by [[Le Corbusier]]
* Denomination or [[face value]] of [[coin]]s, [[paper money]], [[postage stamp]]s, [[casino chip]]s, etc. Well, it this is mentioned in relation to the 1-2-5 series, but that dis far from all that could be said (especially if we look back in time).

I'm not sure how (or if) to include this. Perhaps as See also link to [[Modular]] would be fine, there, I have found no obvious target for a link about face values. E.g., the article [[face value]] does not discuss the preferred numbers involved. Perhaps wikipedia is missing an article here - or a section on this somewhere? (Random fact: When I visited the [[Soviet Union]] in 1989, there were coins with face value of 3 and 15 [[kopeck]] -- numbers ''not'' preferred in most currencies. The 3 kopecks were needed in phone boxes, and in short supply, and thus worth a good deal more than the face value.) [[User:Nø|Nø]] ([[User talk:Nø|talk]]) 11:16, 8 March 2025 (UTC)