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How can commas of size near the step size of 17edo be tempered out? I sorted the suspicious three to the end of the table and set it into italic. I think they should be deleted better from this table.
- xenwolf June 05, 2011, 11:27:00 AM UTC-0700
Using the stated val, which is the 13-limit 17edo patent val, it is indeed the case that the commas in question are tempered out. I'll add a comment.
- genewardsmith June 05, 2011, 11:33:36 AM UTC-0700
If I could only understand it! Would it be possible to make an example for 25/24 in the 17edo here? I thought "tempering out a comma" means only "to make it disappear" - am I really so wrong? ...please be some more patient with me!
- xenwolf June 05, 2011, 11:47:32 AM UTC-0700
17-EDO's patent val maps 5/4 to 353 cents, and two of those make up a 3/2. Using the patent val, that equates 25/16 ((5/4)*(5/4)) with 24/16 ((3/2)*(8/8)), meaning 25/24 is tempered out. But if we don't assume the patent val, we will end up with a different comma list. I, for instance, think of 17 as approximating 25 but not 5, and map it to the ~777-cent interval. On that mapping, 25/24 is definitely NOT tempered out.
- igliashon September 21, 2011, 01:38:27 PM UTC-0700
So in other words, in that mapping 25 could be considered a "pseudo-prime", since it's not actually a prime number, but its root (5) is not represented.
The 23rd harmonic is also represented too, by the way (23:16 is a little sharp). So we could consider 17edo a 22.214.171.124.13.23.25 temperament. In other words, it's 27-odd limit with no 5, 17, or 19, and with 25 treated as though it were prime.
- MasonGreen1 March 01, 2016, 07:25:23 PM UTC-0800
Has anyone examined the no-fives "zeta function" tunings? I've seen no-twos tunings evaluated, but not no-fives.
Among no-fives tunings, 17 is pretty good, isn't it? I suspect 12 would still be a zeta edo even if the fifth harmonic were ignored. 17 would probably be the next one after 12. Not sure about 19edo; it doesn't have a good 7 and doesn't match 11 at all, so as a no-fives tuning, it's not so great and 17 is probably better than 19.
- MasonGreen1 March 01, 2016, 07:30:59 PM UTC-0800
17-comma example: The 17-comma is a difference between 17 fifths (octave reduced) and octave. The fifth of 17-edo is ~4 cents sharp, and stacking 17 of these adds up to ~68 cents, equating it with octave.
- PiotrGrochowski October 11, 2016, 06:39:27 AM UTC-0700
Note that you don't need to use the patent val. In patent val, 25/24 is tempered out and 81/80 maps to 1 step. However, there is alternative 5 that maps 25/24 to 2 steps (allowing a neutral third between major and minor third) and tempers out 81/80.
- PiotrGrochowski October 14, 2016, 12:14:18 AM UTC-0700
There are some unusually large ratios being included in the list of 17edo's approximated ratios. I question their relevance for inclusion, as several are too large to be of salience in any otonal or utonal harmonic context. While it's hard to know where exactly to draw the line, I generally place it at the 31st harmonic at the outermost, while preferring to avoid anything beyond the 21st harmonic unless absolutely necessary.
- What? I don't see any primes beyond 17 in that column. PiotrGrochowski (talk) 07:17, 23 September 2018 (UTC)