Talk:159edo

Okay... I have a list of the approximate errors in cents for 159edo's approximations of certain prime intervals:

• 3: -0.068
• 5: -1.408
• 7: -2.788
• 11: -0.374
• 13: -2.792
• 17: +0.705
• 19: -3.173
• 23: -1.859
• 29: -3.162
• 31: +2.134

I'm hoping that someone can make tables for Just Approximation like the ones found on the page for 94edo... --Aura (talk) 07:18, 7 September 2020 (UTC)

Done. FloraC (talk) 09:02, 7 September 2020 (UTC)

Thanks! Once we do a lot more exploring of 159edo, I hope to put our findings here. After all, there's no way I'm just letting an EDO as useful as this just languish anymore. --Aura (talk) 13:08, 7 September 2020 (UTC)

I have 159edo's patent val for primes up to the 19 limit- ⟨159 252 369 446 550 588 650 675]. How consistent is this EDO when it comes to this group of primes? (preceding unsigned comment by Aura (talk))

According to Scala it's only consistent up to 17-odd limit. It might still be consistent when we add some higher odd numbers, though. IlL (talk) 15:36, 7 September 2020 (UTC)

Let's check it out then... let's try 19, 21, 23, 25, 27, 29 and 31... --Aura (talk) 15:39, 7 September 2020 (UTC)

Easy to speculate with an understanding of relative error. It's consistent in 17-limit or no-17 29-limit. FloraC (talk) 15:41, 7 September 2020 (UTC)

Wait... why specifically a no-17 29-limit? Is it consistent in 19-limit or 23-limit? Perhaps I ought to reveal one final patent val for 159edo- that of the 23-prime limit... --Aura (talk) 15:54, 7 September 2020 (UTC)

Okay, so, if 159edo is extended to the 23-prime, 159edo has the patent val of ⟨159 252 369 446 550 588 650 675 719]... --Aura (talk) 16:01, 7 September 2020 (UTC)

I must admit that the main reason I'm interested in whether or not 159edo is consistent up to the 23-limit is because I'm currently compiling a list of Just Intervals corresponding to the various steps in 159edo, and 23 is the highest prime I've had to use so far... --Aura (talk) 16:08, 7 September 2020 (UTC)

Okay, I've managed to confirm that 159edo is not consistent in the 19-odd limit as the difference between the best 17/16 and the best 19/16 is 25 steps, while the best 19/17 is 26 steps... Not good at all... Looks like I need to search for several new values for step sizes --Aura (talk) 16:32, 7 September 2020 (UTC)

159edo has two intervals in 29-limit with >50% relative error —- 19/17 and 29/17. That's why you have to decide, full 17-limit or no-17 29-limit. FloraC (talk) 03:03, 8 September 2020 (UTC)

Afaik no edo between 94 and 282 is fully consistent in 23-limit. There's 111, 149 and 217 fully consistent in 19-limit. 94 is special consistency-wise but it's not superior in accuracy, so not all edos above 94 need to directly compare with it, especially when there's nothing to relate them. FloraC (talk) 02:59, 8 September 2020 (UTC)

I have used 94edo in the past, and the article on 94edo states that it is "a remarkable all-around utility temperament", while 159edo has other strengths, so I figured a comparison was at least somewhat warranted in this case. However, if such a comparison is not really warranted here, I'll remove the comparison altogether. --Aura (talk) 03:35, 8 September 2020 (UTC)