Talk:Essential tempering comma: Difference between revisions
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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. | |||
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. | |||
Further investigation suggests that the definition is probably a sufficient (and not necessary) condition for identifying essentially tempered chords. | |||
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) | |||
== 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) | |||
Latest revision as of 06:01, 5 March 2023
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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.
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.
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 r1, r2, and r3 in S such that c = r1r2/r3, and
- cnri is not a member of S for i = 1, 2, 3, where n is a nonzero integer.
Can anyone check it out? FloraC (talk) 14:44, 7 January 2022 (UTC) -- Updated 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. FloraC (talk) 13:21, 11 March 2022 (UTC)