User talk:Xenwolf: Difference between revisions

Line 300:

:::: In the case of [[9/7]], we have two prime factors to consider- the 3-limit, and the 7-limit. Now, I can already assure you that you can only use one tempered 7-limit interval max before the absolute error exceeds 3.5 cents, as after [[7/4]], the next interval in the 7-limit chain is [[49/32]], and the difference between the JI version and the 159edo-tempered version exceeds 3.5 cents, and this is also true for the 205edo-tempered version of 49/32. However, when two different EDOs have the same number of intervals of a given p-limit that can be stacked before the absolute error exceeds 3.5 cents, it is the absolute error in cents of the tempered stack relative to the JI equvalent that determines which EDO is superior for representing that p-limit, with the better EDO for representation having the smaller absolute error in cents. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:05, 8 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]]. 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" ratings 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- 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]]. 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" ratings 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)

Revision as of 02:15, 9 October 2020 view source Aura (talk \| contribs) autopatrolled, emailconfirmed 5,920 edits No edit summary ← Older edit		Revision as of 02:17, 9 October 2020 view source Aura (talk \| contribs) autopatrolled, emailconfirmed 5,920 edits No edit summary Newer edit →
Line 300:		Line 300:
	:::: In the case of [[9/7]], we have two prime factors to consider- the 3-limit, and the 7-limit. Now, I can already assure you that you can only use one tempered 7-limit interval max before the absolute error exceeds 3.5 cents, as after [[7/4]], the next interval in the 7-limit chain is [[49/32]], and the difference between the JI version and the 159edo-tempered version exceeds 3.5 cents, and this is also true for the 205edo-tempered version of 49/32. However, when two different EDOs have the same number of intervals of a given p-limit that can be stacked before the absolute error exceeds 3.5 cents, it is the absolute error in cents of the tempered stack relative to the JI equvalent that determines which EDO is superior for representing that p-limit, with the better EDO for representation having the smaller absolute error in cents. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 20:05, 8 October 2020 (UTC)		:::: In the case of [[9/7]], we have two prime factors to consider- the 3-limit, and the 7-limit. Now, I can already assure you that you can only use one tempered 7-limit interval max before the absolute error exceeds 3.5 cents, as after [[7/4]], the next interval in the 7-limit chain is [[49/32]], and the difference between the JI version and the 159edo-tempered version exceeds 3.5 cents, and this is also true for the 205edo-tempered version of 49/32. However, when two different EDOs have the same number of intervals of a given p-limit that can be stacked before the absolute error exceeds 3.5 cents, it is the absolute error in cents of the tempered stack relative to the JI equvalent that determines which EDO is superior for representing that p-limit, with the better EDO for representation having the smaller absolute error in cents. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 20:05, 8 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]]. 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" ratings 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- 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]]. 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" ratings 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)