View source for User talk:Aura/Aura's Diatonic Scales

== Lists ==

... are normally done by starting a line with an <code>*</code> for each item (no surplus blank lines are needed then). --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 06:30, 7 September 2020 (UTC)

: Thanks!  Fixed. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 06:47, 7 September 2020 (UTC)

:: Great 🙂 [https://en.xen.wiki/index.php?title=User%3AAura%2FAura%27s_Diatonic_Scales&type=revision&diff=48738&oldid=48726 I now also added a space after the <code>*</code>]. This is maybe a matter of taste, but from my experience this makes it easier to distinguish content and form. I hope this is okay for you. BTW: What about adding links to interval pages? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 09:48, 7 September 2020 (UTC)

::: It's definitely okay.  As for adding links to interval pages, feel free to go ahead and do that.  I would do it myself, but I'm not entirely sure where to place those links... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 13:02, 7 September 2020 (UTC)

== Link text ==

In my opinion, "Wikipedia article" is probably the worst text to chose for a link if there are more than one article you refer to. Imagine you only read/only copy/only print the text, all information where to look will be lost (Wikipedia has lots of articles). The easiest option to do better is using an interwiki-style link (i.e. ''see [[Wikipedia:Mediant]]'' or ''see [[Wikipedia: Mediant]]''), another option is copy the original HTML title and URL (i.e. [https://en.wikipedia.org/wiki/Mediant Mediant &#45; Wikipedia]) - maybe your browser has a plugin for that. At the risk of repeating myself: I really don't like these A/B links. They complicate the reading without bringing any advantage. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 15:27, 21 December 2020 (UTC)

: Right, I attempted to fix it with links in the style of [[Wikipedia:Mediant]]. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:38, 21 December 2020 (UTC)

== About minor thirds ==

Why do you prefer 77/64 over 6/5? Is it mainly used for melodic or harmonic reasons in your scales? --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 20:28, 13 March 2021 (UTC)

: It's more for harmonic reasons, especially the fact that the scales with the best tonal harmonies- at least in my thinking- have all their notes as either overtones or undertones of the Tonic, while 6/5 doesn't meet either of those criteria when used as an interval between the Tonic and another note in the scale.  That said, since 6/5 is a harmonic entropy minimum, it pays to try and find a ratio that's close by, and 77/64 is one of the simpler among such ratios, not to mention that 77/64 has connections to both 7-based and 11-based harmony, which I seem to use a lot, especially since it turns out that harmony based on 11/8 and 16/11 is hugely underrated. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:45, 13 March 2021 (UTC)

: I should mention, however, that while I think I've presented what are probably the best tunings for Ionian and Lydian, I'm more open to changing the tunings for Dorian, Phrygian, Mixolydian, Aeolian and Locrian- provided that the new tunings not only demonstrate Rothenberg propriety, but still have all notes in the scale as either harmonics or subharmonics of the Tonic. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:51, 13 March 2021 (UTC)

:: I think 77/64 is fine as it is. I was just curious about your reasoning. (Fun fact, I really like the interval 29/16, which is approximately a perfect fifth above 77/64. I'm not really sure if that fact is useful for your diatonic scales, but I thought that that was a nice coincidence) --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 21:59, 13 March 2021 (UTC)

::: Well, if I ever get to 29-limit material, you've at least given me a good cause to look at it beyond the expected reasons.  Still, I'm thinking that I perhaps need tweak some of my scales a little bit somehow- just to make it so that there are once again only three step sizes in the scale instead of like four or five. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:59, 13 March 2021 (UTC)

::: Sorry for disturbing, after picking up on the comment (''“fun fact”''), I wanted to know more: <code>([[29/16]])/([[77/64]]) = [[116/77]]</code> is about 709.4 cents in size. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 09:02, 16 March 2021 (UTC)

:::: If 116/77 is 709.4 cents, then it is so sharp as to be considered an entire step apart in my book.  Thanks for finding that information Xenwolf. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:03, 16 March 2021 (UTC)

::::: Taking this discussion even further, 116/77 is extremely close to the fifth of 22edo. Since 7edo has a very accurate 29/16, this means that 22*7 = 154edo has a very accurate 77/64. In addition, the difference between 116/77 and 3/2 is the 29 limit comma 232/231, which is similar in size to the marvel comma of 225/224. Any thoughts about this? --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 22:55, 16 March 2021 (UTC)

:::::: Considering that 159edo is my favorite EDO, and since the 232/231 comma maps to a single step in 159edo, I'd say that 116/77 maps to about 94 steps in 159edo, and this puts 116/77 on roughly the same level as 128/85 in my book. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 01:29, 17 March 2021 (UTC)

::::::: I'm not exactly sure what you mean, since I don't know what exactly you use 128/85 for. Do you think you'll try get into 29 limit stuff based on the relationship between 116/77 and 128/85? --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 02:08, 17 March 2021 (UTC)

:::::::: I will say that 128/85 is useful as an alternate fifth in certain contexts, even though resolutions using it are not as complete as those offered by 3/2.  Oh, and a good chunk of what determines when I'll get to 29-limit stuff proper is the pace at which I end up working out a few necessary things in lower limits. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:54, 17 March 2021 (UTC)

== Why 77/64? ==

Both the pythagorean 32/27 and 19/16 are simpler. Maybe for a smaller prime limit? It contains no simple ratios to other notes, so I don't understand the meaning for a smaller prime limit. (Sorry that English is not my native language, maybe my words are not proper)--[[User:Zhenlige|Zhenlige]] ([[User talk:Zhenlige|talk]]) 12:35, 12 December 2024 (UTC)

: I do indeed use Pythagorean 32/27 already, but in a different capacity, since it's not close enough to be substituted for 6/5.  For an interval to be a proper substitute for 6/5, I do indeed need a smaller prime limit than 19, but more than that, I also need something that has a power of two in either the numerator or the denominator.  As for simple ratios to other notes, 77/64 does indeed have a few, namely, it relates to 11/8 by 8/7 and it also relates to 7/4 by 16/11- granted, these are paradiatonic notes rather than diatonic notes, but all the same. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:26, 13 December 2024 (UTC)
:: So you want a near 6/5 but not exactly, that is, using a JI interval to approximate another? --[[User:Zhenlige|Zhenlige]] ([[User talk:Zhenlige|talk]]) 08:20, 14 December 2024 (UTC)
::: Yes, exactly. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:09, 14 December 2024 (UTC)