User talk:Xenwolf: Difference between revisions

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:::: Using [http://musictheory.zentral.zone/huntsystemcalc.html the same calculator] that you linked, I tested how 159edo and 205edo each represent this set of intervals- [[3/2]], [[9/8]], [[27/16]], [[81/64]], [[243/128]], [[729/512]], [[5/4]], [[25/16]], [[125/64]], [[625/512]], [[7/4]], [[49/32]], [[343/256]], [[11/8]], [[121/64]], [[13/8]], [[169/128]], [[17/16]] and [[289/256]]- the stipulation being that the odd-limit of any interval in the set has to be less than 1024. I looked for the number of "P" ratings given by both 205edo and 159edo, as "P" ratings are the only ratings I'm really interested in at this point, and I also looked at their distribution. Both 205edo and 159edo give 7 "P" ratings total out of this set, and are surpassed in this respect by [[147edo]], which has 8. However, one of the P-rated intervals for 147edo is for 343/326, the best approximation of which cannot be reached by stacking three of 147edo's best tempered version of 7/4 and octave reducing, thus resulting in this interval's disqualification. Furthermore, the 147edo-tempered versions of six of the other 7 intervals in the starting interval set given a "P" rating in Hunt's system have absolute errors in cents that are ''greater'' than those of their 159edo-tempered counterparts which are also P-rated- a decisive loss for 147edo on that front. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:13, 9 October 2020 (UTC)

:::: As for the remaining head to head comparison of 159edo and 205edo in terms of how good their representation is, one of the P-rated intervals for 205edo is 49/32, the best approximation of which cannot be reached by stacking two of 205edo's best tempered version of 7/4 and octave reducing, resulting in this interval's disqualification. Four of 205edo's remaining P-rated intervals are all solidly in the in the 5-limit chain, and another P-rated interval is 17/16- the 205edo-tempered version of which is better than the 159edo-tempered version- the final P-rated interval for 205edo is 3/2, and 159edo-tempered version of this interval has less absolute error in cents than the 205edo-tempered version, leaving 205edo with only 5 P-rated intervals that are not outperformed by their 159edo counterparts. This means a decisive loss for 205edo ~~in the areas where it counts the most~~. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:40, 9 October 2020 (UTC)

:::: As for the remaining head to head comparison of 159edo and 205edo in terms of how good their representation is, one of the P-rated intervals for 205edo is 49/32, the best approximation of which cannot be reached by stacking two of 205edo's best tempered version of 7/4 and octave reducing, resulting in this interval's disqualification. Four of 205edo's remaining P-rated intervals are all solidly in the in the 5-limit chain, and another P-rated interval is 17/16- the 205edo-tempered version of which is better than the 159edo-tempered version- the final P-rated interval for 205edo is 3/2, and 159edo-tempered version of this interval has less absolute error in cents than the 205edo-tempered version, leaving 205edo with only 5 P-rated intervals that are not outperformed by their 159edo counterparts. This means a decisive loss for 205edo. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:40, 9 October 2020 (UTC)

Revision as of 02:40, 9 October 2020 view source Aura (talk \| contribs) autopatrolled, emailconfirmed 5,920 edits No edit summary ← Older edit		Revision as of 02:41, 9 October 2020 view source Aura (talk \| contribs) autopatrolled, emailconfirmed 5,920 edits No edit summary Newer edit →
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	:::: Using [http://musictheory.zentral.zone/huntsystemcalc.html the same calculator] that you linked, I tested how 159edo and 205edo each represent this set of intervals- [[3/2]], [[9/8]], [[27/16]], [[81/64]], [[243/128]], [[729/512]], [[5/4]], [[25/16]], [[125/64]], [[625/512]], [[7/4]], [[49/32]], [[343/256]], [[11/8]], [[121/64]], [[13/8]], [[169/128]], [[17/16]] and [[289/256]]- the stipulation being that the odd-limit of any interval in the set has to be less than 1024. I looked for the number of "P" ratings given by both 205edo and 159edo, as "P" ratings are the only ratings I'm really interested in at this point, and I also looked at their distribution. Both 205edo and 159edo give 7 "P" ratings total out of this set, and are surpassed in this respect by [[147edo]], which has 8. However, one of the P-rated intervals for 147edo is for 343/326, the best approximation of which cannot be reached by stacking three of 147edo's best tempered version of 7/4 and octave reducing, thus resulting in this interval's disqualification. Furthermore, the 147edo-tempered versions of six of the other 7 intervals in the starting interval set given a "P" rating in Hunt's system have absolute errors in cents that are ''greater'' than those of their 159edo-tempered counterparts which are also P-rated- a decisive loss for 147edo on that front. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 02:13, 9 October 2020 (UTC)		:::: Using [http://musictheory.zentral.zone/huntsystemcalc.html the same calculator] that you linked, I tested how 159edo and 205edo each represent this set of intervals- [[3/2]], [[9/8]], [[27/16]], [[81/64]], [[243/128]], [[729/512]], [[5/4]], [[25/16]], [[125/64]], [[625/512]], [[7/4]], [[49/32]], [[343/256]], [[11/8]], [[121/64]], [[13/8]], [[169/128]], [[17/16]] and [[289/256]]- the stipulation being that the odd-limit of any interval in the set has to be less than 1024. I looked for the number of "P" ratings given by both 205edo and 159edo, as "P" ratings are the only ratings I'm really interested in at this point, and I also looked at their distribution. Both 205edo and 159edo give 7 "P" ratings total out of this set, and are surpassed in this respect by [[147edo]], which has 8. However, one of the P-rated intervals for 147edo is for 343/326, the best approximation of which cannot be reached by stacking three of 147edo's best tempered version of 7/4 and octave reducing, thus resulting in this interval's disqualification. Furthermore, the 147edo-tempered versions of six of the other 7 intervals in the starting interval set given a "P" rating in Hunt's system have absolute errors in cents that are ''greater'' than those of their 159edo-tempered counterparts which are also P-rated- a decisive loss for 147edo on that front. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 02:13, 9 October 2020 (UTC)

	:::: As for the remaining head to head comparison of 159edo and 205edo in terms of how good their representation is, one of the P-rated intervals for 205edo is 49/32, the best approximation of which cannot be reached by stacking two of 205edo's best tempered version of 7/4 and octave reducing, resulting in this interval's disqualification. Four of 205edo's remaining P-rated intervals are all solidly in the in the 5-limit chain, and another P-rated interval is 17/16- the 205edo-tempered version of which is better than the 159edo-tempered version- the final P-rated interval for 205edo is 3/2, and 159edo-tempered version of this interval has less absolute error in cents than the 205edo-tempered version, leaving 205edo with only 5 P-rated intervals that are not outperformed by their 159edo counterparts. This means a decisive loss for 205edo ~~in the areas where it counts the most~~. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 02:40, 9 October 2020 (UTC)		:::: As for the remaining head to head comparison of 159edo and 205edo in terms of how good their representation is, one of the P-rated intervals for 205edo is 49/32, the best approximation of which cannot be reached by stacking two of 205edo's best tempered version of 7/4 and octave reducing, resulting in this interval's disqualification. Four of 205edo's remaining P-rated intervals are all solidly in the in the 5-limit chain, and another P-rated interval is 17/16- the 205edo-tempered version of which is better than the 159edo-tempered version- the final P-rated interval for 205edo is 3/2, and 159edo-tempered version of this interval has less absolute error in cents than the 205edo-tempered version, leaving 205edo with only 5 P-rated intervals that are not outperformed by their 159edo counterparts. This means a decisive loss for 205edo. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 02:40, 9 October 2020 (UTC)