User talk:Xenwolf: Difference between revisions

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:::: For prime limits that form the backbone of key signature navigation such as the 3-limit and the 11-limit, having a high number of tempered intervals that can be stacked without exceeding an unnoticeable comma's distance of 3.5 cents is actually pretty important. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:52, 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 p-limit intervals 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 a given 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 p-limit intervals 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 a given 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)

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	:::: For prime limits that form the backbone of key signature navigation such as the 3-limit and the 11-limit, having a high number of tempered intervals that can be stacked without exceeding an unnoticeable comma's distance of 3.5 cents is actually pretty important. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 19:52, 8 October 2020 (UTC)		:::: For prime limits that form the backbone of key signature navigation such as the 3-limit and the 11-limit, having a high number of tempered intervals that can be stacked without exceeding an unnoticeable comma's distance of 3.5 cents is actually pretty important. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 19:52, 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 p-limit intervals 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 a given 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 p-limit intervals 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 a given 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)