Talk:Essential tempering comma - Revision history

Fredg999: Fredg999 moved page Talk:Essential tempering commas to Talk:Essential tempering comma: WP:PLURAL

2023-03-05T06:01:07Z

Fredg999 moved page Talk:Essential tempering commas to Talk:Essential tempering comma: WP:PLURAL

← Older revision	Revision as of 06:01, 5 March 2023
(No difference)

FloraC at 13:21, 11 March 2022

2022-03-11T13:21:15Z

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	Can anyone check it out? [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 14:44, 7 January 2022 (UTC) -- Updated [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 12:28, 11 March 2022 (UTC)		Can anyone check it out? [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 14:44, 7 January 2022 (UTC) -- Updated [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 12:28, 11 March 2022 (UTC)

			== Not a definition, but a derivation? ==
			It seems it's more appropriate to label Gene's formula a method, or a derivation to approach what it intends to find. Editing the page accordingly. [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 13:21, 11 March 2022 (UTC)

FloraC at 12:28, 11 March 2022

2022-03-11T12:28:39Z

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	== Definition still wrong ==		== Definition still wrong ==
			Despite my earlier attempt to frame Gene's definition for identifying essentially tempered triads (and excluding tetrads), now I find it also fails this task.

	~~Despite my earlier attempt to frame it for identifying essentially tempered triads (and excluding tetrads), now I find it also fails this task.~~ For example, 121/120 induces essentially tempered triads. One of them is 1-11/8-5/3 with steps 11/8-11/9-6/5. Although 11/10 and 12/11 are interchangeable in the chord construction, ~~the pair of~~ 11/8 and 15/11 ~~isn~~'t since 11/8 is 11-odd-limit and 15/11 isn't, which constitutes the source of the tempering essence.		For example, 121/120 induces essentially tempered triads. One of them is 1-11/8-5/3 with steps 11/8-11/9-6/5. Although 11/10 and 12/11 are interchangeable in the chord construction, 11/8 and 15/11 aren't since 11/8 is 11-odd-limit and 15/11 isn't, which constitutes the source of the tempering essence.

	~~How about this~~ definition:		Further investigation suggests that the definition is probably a sufficient (and not necessary) condition for identifying essentially tempered chords.
	~~# There are three intervals ''i'', ''j'', and ''k'' in S such that ''c'' = ''ij''/''k'', and~~
	~~# None of ''c<sup>n</sup>i'', ''c<sup>n</sup>j'', and ''c<sup>n</sup>k''~~ is a ~~member of S, where ''n'' is a nonzero integer~~.

	Can anyone check it out? [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 14:44, 7 January 2022 (UTC)		My revised definition:
			# There are three ratios ''r''<sub>1</sub>, ''r''<sub>2</sub>, and ''r''<sub>3</sub> in S such that ''c'' = ''r''<sub>1</sub>''r''<sub>2</sub>/''r''<sub>3</sub>, and
			# ''c<sup>n</sup>r<sub>i</sub>'' is not a member of S for ''i'' = 1, 2, 3, where ''n'' is a nonzero integer.

			Can anyone check it out? [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 14:44, 7 January 2022 (UTC) -- Updated [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 12:28, 11 March 2022 (UTC)

FloraC: /* Definition still wrong */ new section

2022-01-07T14:44:34Z

Definition still wrong: new section

← Older revision		Revision as of 14:44, 7 January 2022
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	{{WSArchiveLink}}		{{WSArchiveLink}}

			== Definition still wrong ==

			Despite my earlier attempt to frame it for identifying essentially tempered triads (and excluding tetrads), now I find it also fails this task. For example, 121/120 induces essentially tempered triads. One of them is 1-11/8-5/3 with steps 11/8-11/9-6/5. Although 11/10 and 12/11 are interchangeable in the chord construction, the pair of 11/8 and 15/11 isn't since 11/8 is 11-odd-limit and 15/11 isn't, which constitutes the source of the tempering essence.

			How about this definition:
			# There are three intervals ''i'', ''j'', and ''k'' in S such that ''c'' = ''ij''/''k'', and
			# None of ''c<sup>n</sup>i'', ''c<sup>n</sup>j'', and ''c<sup>n</sup>k'' is a member of S, where ''n'' is a nonzero integer.

			Can anyone check it out? [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 14:44, 7 January 2022 (UTC)

Mike Battaglia: 1 revision imported: Moving archived Wikispaces discussion to subpage

2018-10-01T18:02:35Z

1 revision imported: Moving archived Wikispaces discussion to subpage

← Older revision	Revision as of 18:02, 1 October 2018
(No difference)

WikispacesArchive>Mike Battaglia: Text replacement - "'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''" to "'''All discussion below is archived from the Wikispaces export in its original unaltered form.''' ''...

2018-10-01T18:01:16Z

Text replacement - "'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''" to "'''All discussion below is archived from the Wikispaces export in its original unaltered form.''' <span style="color:#800000">''...

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	~~= ARCHIVED WIKISPACES DISCUSSION BELOW =~~		{{WSArchiveLink}}
	~~'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''~~

	~~<span style="color:#800000">'''PLEASE MAKE ANY NEW COMMENTS <u>ABOVE</u> THIS SECTION.'''</span> Anything below here is for archival purposes only.~~

	~~----~~

	~~== could someone provide an example application? ==~~
	~~I am just left wondering why this is important. There seems to be a lot left implicit here that isn't apparent to me why I would care.~~

	~~- '''cmloegcmluin''' March 19, 2016, 04:44:04 PM UTC-0700~~
	~~----~~

Mike Battaglia: Text replacement - "'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''" to "'''All discussion below is archived from the Wikispaces export in its original unaltered form.''' ''...

2018-09-20T07:00:33Z

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	= ARCHIVED WIKISPACES DISCUSSION BELOW =		= ARCHIVED WIKISPACES DISCUSSION BELOW =
	'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''		'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''

			<span style="color:#800000">'''PLEASE MAKE ANY NEW COMMENTS <u>ABOVE</u> THIS SECTION.'''</span> Anything below here is for archival purposes only.

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Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

New page

= ARCHIVED WIKISPACES DISCUSSION BELOW =
'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''
----

== could someone provide an example application? ==
I am just left wondering why this is important. There seems to be a lot left implicit here that isn't apparent to me why I would care.

- '''cmloegcmluin''' March 19, 2016, 04:44:04 PM UTC-0700
----