User talk:Aura/Aura's Diatonic Scales: Difference between revisions
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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) | 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 best tonal harmonies- at least in my thinking | : 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) | |||