Talk:Meantone: Difference between revisions

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As you can see, only the first Harrison's comma entry has a bad Eigenmonzo (that also does not currently have a Xenharmonic Wiki page); all the rest have Xenharmonic Wiki pages, and they keep getting simpler until 1/10 Harrison's comma, after which they get more complex again, with a pass through [[64/63]] as an Eigenmonzo rather than a tempering comma fraction (but not the same as the line with the 64/63 Eigenmonzo at a fifth of 702.272¢ that was removed on 2024-07-30T10:10:27 -- still haven't figured out where that one came from). Indeed, the actual table appears to contain a subset of the above entries, but with no explanation in the comments column.

While checking the above, I noticed that flattening the fifth by 1/7 of the Archytas septimal comma does have the additional use of generating as its Eigenmonzo the flattone comma [-17 9 0 1⟩ (does this comma have an official name? -- it doesn't seem to have its own page). Inspired by this, I also looked to see if other listed Archytas septimal comma fractions produced as their Eigenmonzos the Harrison's comma [-13 10 0 -1⟩ or the flattertone comma [-24 17 0 -1⟩, but I did not see either of these, so those must require Archytas comma fractions that are not listed (I have not yet tried to the math to figure out what they are).

While checking the above, I noticed that flattening the fifth by 1/7 of the Archytas septimal comma does have the additional use of generating as its Eigenmonzo the flattone comma [-17 9 0 1⟩ (does this comma have an official name? -- it doesn't seem to have its own page). Inspired by this, I also looked to see if other listed Archytas septimal comma fractions produced as their Eigenmonzos the Harrison's comma [-13 10 0 -1⟩ or the flattertone comma [-24 17 0 -1⟩ (does this have an official name? -- it doesn't seem to have its own page either), but I did not see either of these, so those must require Archytas comma fractions that are not listed (I have not yet tried to the math to figure out what they are).

So I would recommend integrating the above table into the septimal meantone tuning table, since Harrison's comma is the comma other than the syntonic comma that really fits in with the septimal meantone tuning spectrum, but maybe leaving in Archytas septimal comma fractional flattenings that produce as their Eigenmonzos commas that are used in 7-limit meantone extensions.

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 As you can see, only the first Harrison's comma entry has a bad Eigenmonzo (that also does not currently have a Xenharmonic Wiki page); all the rest have Xenharmonic Wiki pages, and they keep getting simpler until 1/10 Harrison's comma, after which they get more complex again, with a pass through [[64/63]] as an Eigenmonzo rather than a tempering comma fraction (but not the same as the line with the 64/63 Eigenmonzo at a fifth of 702.272¢ that was removed on 2024-07-30T10:10:27 -- still haven't figured out where that one came from).  Indeed, the actual table appears to contain a subset of the above entries, but with no  explanation in the comments column.
-While checking the above, I noticed that flattening the fifth by 1/7 of the Archytas septimal comma does have the additional use of generating as its Eigenmonzo the flattone comma [-17 9 0 1⟩ (does this comma have an official name? -- it doesn't seem to have its own page).  Inspired by this, I also looked to see if other listed Archytas septimal comma fractions produced as their Eigenmonzos the Harrison's comma [-13 10 0 -1⟩ or the flattertone comma [-24 17 0 -1⟩, but I did not see either of these, so those must require Archytas comma fractions that are not listed (I have not yet tried to the math to figure out what they are).
+While checking the above, I noticed that flattening the fifth by 1/7 of the Archytas septimal comma does have the additional use of generating as its Eigenmonzo the flattone comma [-17 9 0 1⟩ (does this comma have an official name? -- it doesn't seem to have its own page).  Inspired by this, I also looked to see if other listed Archytas septimal comma fractions produced as their Eigenmonzos the Harrison's comma [-13 10 0 -1⟩ or the flattertone comma [-24 17 0 -1⟩ (does this have an official name? -- it doesn't seem to have its own page either), but I did not see either of these, so those must require Archytas comma fractions that are not listed (I have not yet tried to the math to figure out what they are).
 So I would recommend integrating the above table into the septimal meantone tuning table, since Harrison's comma is the comma other than the syntonic comma that really fits in with the septimal meantone tuning spectrum, but maybe leaving in Archytas septimal comma fractional flattenings that produce as their Eigenmonzos commas that are used in 7-limit meantone extensions.