Talk:Essential tempering comma: Difference between revisions

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~~= ARCHIVED WIKISPACES DISCUSSION BELOW =~~

~~'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''~~

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== ~~could someone provide an example application?~~ ==

== Definition still wrong ==

~~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~~.

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.

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

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.

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Further investigation suggests that the definition is probably a sufficient (and not necessary) condition for identifying essentially tempered chords.

My revised definition:

# There are three ratios ''r''1, ''r''2, and ''r''3 in S such that ''c'' = ''r''1''r''2/''r''3, and

# ''cnri'' 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)

== 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)

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-= ARCHIVED WIKISPACES DISCUSSION BELOW =
+{{WSArchiveLink}}
-'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''
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-== could someone provide an example application? ==
+== Definition still wrong ==
-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.
+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.
-- '''cmloegcmluin''' March 19, 2016, 04:44:04 PM UTC-0700
+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.
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+Further investigation suggests that the definition is probably a sufficient (and not necessary) condition for identifying essentially tempered chords.
+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)
+== 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)