User talk:Aura/Aura's Diatonic Scales

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

Thanks! Fixed. --Aura (talk) 06:47, 7 September 2020 (UTC)
Great 🙂 I now also added a space after the *. 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? --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... --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. Mediant - 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. --Xenwolf (talk) 15:27, 21 December 2020 (UTC)

Right, I attempted to fix it with links in the style of Wikipedia:Mediant. --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? --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. --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. --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) --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. --Aura (talk) 22:59, 13 March 2021 (UTC)
Sorry for disturbing, after picking up on the comment (“fun fact”), I wanted to know more: (29/16)/(77/64) = 116/77 is about 709.4 cents in size. --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. --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? --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. --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? --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. --Aura (talk) 04:54, 17 March 2021 (UTC)