Talk:7/4
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7/4 in 94edo
I don't know if you know this, Xenwolf, but 94edo is pretty good for 7/4 as well. --Aura (talk) 18:28, 25 October 2020 (UTC)
- Yeah, 76\94 ( == 38\47, 9702.213 cents), is only 1.39 cents above 7/4. In 47edo it's within the relative tolerance limit (7%), in 94edo it's not. It's definitely not a bad approximation (only off by 10.9% of a 1\94). At first, I hand-calculated this table. Now I have a little python program (which is unfortunately incorruptible!) that has 2 parameters: the interval itself and the threshold of error magnitude (both, rel and abs). The upper EDO bound is currently fixed to 200, but could be a parameter, the separation of the rel and abs thresholds would possible as well. I know this is not really an answer to your non-question, but maybe helps to better understand why 94edo is not in the list: this decision has nothing to do with musical critera but only with with he difficulty to formalize harmonic quality (or my lack of imagination). --Xenwolf (talk) 20:40, 25 October 2020 (UTC)
- Even if the calculations of this program are right, as I'm sure they are, no program is incorruptible- because somewhere in the production chain, it's sourced from something made by fallible humans. Nevertheless, as I'm sure the calculations are right, I'll accept the remainder of your explanation. As to whether or not these tables are useful, I'd say they are ultimately only useful for the articles dealing with the prime harmonics and their octave compliments. That said, there needs to be an additional column added to the charts. Specifically we need to add the number of times the tempered interval in question can be stacked without the absolute error between the tempered stack and its just counterpart exceeding 3.5 cents, or half a step- whichever is smaller. --Aura (talk) 21:25, 25 October 2020 (UTC)
- I read half a step as 50% of 1\edo? Concerning the prime harmonics (their octave complements share the exact same table), is it actually that indisputable? I know the concept of consistency but I find it questionable already in cases like 7/5: this interval can probably be used independently of the fact that it can be derived from 7/4 and 5/4; another example is the great approximation of 11/7 in 23edo. Whatever, would you say that tables would useful to you if there was this column with the amount of repetitions within the limit you described? --Xenwolf (talk) 21:53, 25 October 2020 (UTC)
- You are correct in your reading of half a step as 1\edo. While it is true that 7/5 can be used independently can be used independently of the fact that it can be derived from 7/4 and 5/4, consistency is my main concern with these intervals, as wherever the p-limits from which intervals like 7/5 are derived are poorly represented and or subject to contortion in any given EDO, it seems to either call the consistency of the derived intervals into question and or open up multiple possible representations in a given EDO. --Aura (talk) 22:14, 25 October 2020 (UTC)