197edo: Difference between revisions

Line 1:

'''197edo''' is the [[EDO|equal division of the octave]] into 197 parts of 6.0914 cents each. It gives excellent results for tuning both marvel, the planar temperament tempering out 225/224, and [[Kleismic_family|catakleismic]], the temperament [[tempering_out|tempering out]] both 225/224 and 4375/4374, which has wedgie <<6 5 22 -6 18 37||. Among [[Patent_val|patent vals]], in fact, it gives the best results for both. In fact, the [[11-limit]] patent val <197 312 457 553 682| has a [[comma-basis]] [225/224, 4375/4374, 441/440, 65536/65219], so taking 225/224 and 441/440 together ([[Marvel family|prodigy temperament]]) also works well with 197edo, and taking 225/224, 441/440, and 4375/4374 (an alternative 11-limit catakleismic) is once again excellently tuned by 197edo.

'''197edo''' is the [[EDO|equal division of the octave]] into 197 parts of 6.0914 cents each. It gives excellent results for tuning both marvel, the planar temperament tempering out 225/224, and [[Kleismic_family|catakleismic]], the temperament [[tempering_out|tempering out]] both 225/224 and 4375/4374, which has wedgie <<6 5 22 -6 18 37||. Among [[Patent_val|patent vals]], in fact, it gives the best results for both. In fact, the [[11-limit]] patent val <197 312 457 553 682| has a [[comma basis]] [225/224, 4375/4374, 441/440, 65536/65219], so taking 225/224 and 441/440 together ([[Marvel family|prodigy temperament]]) also works well with 197edo, and taking 225/224, 441/440, and 4375/4374 (an alternative 11-limit catakleismic) is once again excellently tuned by 197edo.

If we use 197e, the <197 312 457 553 681| val, we can also use 197edo as an excellent tuning for the 11-limit version of marvel temperament, tempering out 385/384 as well as 225/224. If we add 4375/4374 to the comma list for 11-limit [[Marvel family|marvel]], we get 11-limit catakleismic, and 197edo with the above val is also an excellent tuning for that.

Revision as of 22:53, 8 November 2021 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,170 edits hyphenate and link comma-basis ← Older edit		Revision as of 20:19, 12 November 2021 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,170 edits unhyphenate "comma basis" Newer edit →
Line 1:		Line 1:
	'''197edo''' is the [[EDO\|equal division of the octave]] into 197 parts of 6.0914 cents each. It gives excellent results for tuning both marvel, the planar temperament tempering out 225/224, and [[Kleismic_family\|catakleismic]], the temperament [[tempering_out\|tempering out]] both 225/224 and 4375/4374, which has wedgie <<6 5 22 -6 18 37\|\|. Among [[Patent_val\|patent vals]], in fact, it gives the best results for both. In fact, the [[11-limit]] patent val <197 312 457 553 682\| has a [[comma-basis]] [225/224, 4375/4374, 441/440, 65536/65219], so taking 225/224 and 441/440 together ([[Marvel family\|prodigy temperament]]) also works well with 197edo, and taking 225/224, 441/440, and 4375/4374 (an alternative 11-limit catakleismic) is once again excellently tuned by 197edo.		'''197edo''' is the [[EDO\|equal division of the octave]] into 197 parts of 6.0914 cents each. It gives excellent results for tuning both marvel, the planar temperament tempering out 225/224, and [[Kleismic_family\|catakleismic]], the temperament [[tempering_out\|tempering out]] both 225/224 and 4375/4374, which has wedgie <<6 5 22 -6 18 37\|\|. Among [[Patent_val\|patent vals]], in fact, it gives the best results for both. In fact, the [[11-limit]] patent val <197 312 457 553 682\| has a [[comma basis]] [225/224, 4375/4374, 441/440, 65536/65219], so taking 225/224 and 441/440 together ([[Marvel family\|prodigy temperament]]) also works well with 197edo, and taking 225/224, 441/440, and 4375/4374 (an alternative 11-limit catakleismic) is once again excellently tuned by 197edo.

	If we use 197e, the <197 312 457 553 681\| val, we can also use 197edo as an excellent tuning for the 11-limit version of marvel temperament, tempering out 385/384 as well as 225/224. If we add 4375/4374 to the comma list for 11-limit [[Marvel family\|marvel]], we get 11-limit catakleismic, and 197edo with the above val is also an excellent tuning for that.		If we use 197e, the <197 312 457 553 681\| val, we can also use 197edo as an excellent tuning for the 11-limit version of marvel temperament, tempering out 385/384 as well as 225/224. If we add 4375/4374 to the comma list for 11-limit [[Marvel family\|marvel]], we get 11-limit catakleismic, and 197edo with the above val is also an excellent tuning for that.