Kirnberger's atom: Difference between revisions

Line 12:

Kirnberger's atom is tempered out in such notable EDOs as {{EDOs| 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 3684, 4296, 4308, 4908, 7980, 12276, 16572, 20868, 25164, 29460, 33756, and 46032 }}, leading to the [[Very high accuracy temperaments #Atomic|atomic temperament]], in which eleven schismas make up a syntonic comma and twelve schismas make up a [[Pythagorean comma]]; any tuning system ([[41edo]], for example) which the number of divisions of the octave is not multiple of 12 cannot be tempering out the Kirnberger's atom.

However, if one wants to accurately represent the interval without tempering it out, there are very large EDOs that do this. [[78005edo]] not only has a step size that's very close to Kirnberger's atom and consistently represents it, but it's also one of, if not the most accurate 5-limit EDO for its size. [[78123edo]]'s step size is even closer, but Kirnberger's atom is not consistently represented (1 step via [[Direct approximation|direct mapping]] and 3 steps by [[patent val]])

However, if one wants to accurately represent the interval without tempering it out, there are very large EDOs that do this. [[78005edo]] not only has a step size that's very close to Kirnberger's atom and consistently represents it, but it's also one of, if not the most accurate 5-limit EDO for its size. [[78123edo]]'s step size is even closer, but Kirnberger's atom is not consistently represented (1 step via [[Direct approximation|direct mapping]] and 3 steps by [[patent val]]).

Revision as of 10:34, 17 March 2024 view source Tristanbay (talk \| contribs) 457 edits Added a section about the comma's relationship with larger EDOs like 78005 Tags: Visual edit Mobile edit Mobile web edit ← Older edit		Revision as of 10:35, 17 March 2024 view source Tristanbay (talk \| contribs) 457 edits m Added a period (also, I meant paragraph for the previous edit, not section) Tags: Visual edit Mobile edit Mobile web edit Newer edit →
Line 12:		Line 12:
	Kirnberger's atom is tempered out in such notable EDOs as {{EDOs\| 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 3684, 4296, 4308, 4908, 7980, 12276, 16572, 20868, 25164, 29460, 33756, and 46032 }}, leading to the [[Very high accuracy temperaments #Atomic\|atomic temperament]], in which eleven schismas make up a syntonic comma and twelve schismas make up a [[Pythagorean comma]]; any tuning system ([[41edo]], for example) which the number of divisions of the octave is not multiple of 12 cannot be tempering out the Kirnberger's atom.		Kirnberger's atom is tempered out in such notable EDOs as {{EDOs\| 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 3684, 4296, 4308, 4908, 7980, 12276, 16572, 20868, 25164, 29460, 33756, and 46032 }}, leading to the [[Very high accuracy temperaments #Atomic\|atomic temperament]], in which eleven schismas make up a syntonic comma and twelve schismas make up a [[Pythagorean comma]]; any tuning system ([[41edo]], for example) which the number of divisions of the octave is not multiple of 12 cannot be tempering out the Kirnberger's atom.

	However, if one wants to accurately represent the interval without tempering it out, there are very large EDOs that do this. [[78005edo]] not only has a step size that's very close to Kirnberger's atom and consistently represents it, but it's also one of, if not the most accurate 5-limit EDO for its size. [[78123edo]]'s step size is even closer, but Kirnberger's atom is not consistently represented (1 step via [[Direct approximation\|direct mapping]] and 3 steps by [[patent val]])		However, if one wants to accurately represent the interval without tempering it out, there are very large EDOs that do this. [[78005edo]] not only has a step size that's very close to Kirnberger's atom and consistently represents it, but it's also one of, if not the most accurate 5-limit EDO for its size. [[78123edo]]'s step size is even closer, but Kirnberger's atom is not consistently represented (1 step via [[Direct approximation\|direct mapping]] and 3 steps by [[patent val]]).