User talk:Aura: Difference between revisions

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:::::::::::: Good catch of typo -- fixed this. Also rechecked the rest, but didn't find any more. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:30, 10 April 2025 (UTC)

:::::::::::: Scrolling through these table groups, I started noticing interesting things, like how even though the 11th harmonic is the only one with stable mapping all the way through 11L 2s, some of the others have stable mapping in sections, like the 3rd harmonic has stable mapping in the middle section but is all over the place in both the hard and soft ends, but the 9th harmonic actually does okay in the hard end, as does the 17th harmonic (both of these get to be all over the place in the soft end), and the 5th and 13th harmonics have stable mapping in the soft end as long as the EDO values are not too large.

:::::::::::: In partial contrast, with 17L 2s, the harmonic/subharmonics of the generator have unstable mapping (because no simple ratio with a reasonable sized numerator and denominator fits into this zone), but the 3rd harmonic is nearly rock-solid (and 112b is a respectable if overly-complex quarter-comma meantone approximation), although presumably its mapping would break if I put in the rest of the right-most column of the MOS spectrum table. And there the 5th harmonic seems very much usable in the soft end of the scale tuning spectrum as long as the EDO sizes don't get too large (and even then, sometimes it is still okay), which looks to me like enabling a 2.3.5.23 meantone extension; it goes all over the place in the hard end, but there the 25th harmonic shines and is rock-solid as long as you don't go harder than 36edo (basic), and the 13th harmonic just barely misses being rock-solid in this zone (just barely breaks on 125edo, for which 125f would be not bad). Although those harmonics would also appear less solid if I included the rest of the MOS tuning spectrum.

:::::::::::: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:28, 10 April 2025 (UTC)

@@ Line 384: / Line 384: @@
 :::::::::::: Good catch of typo -- fixed this.  Also rechecked the rest, but didn't find any more.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:30, 10 April 2025 (UTC)
+:::::::::::: Scrolling through these table groups, I started noticing interesting things, like how even though the 11th harmonic is the only one with stable mapping all the way through 11L&nbsp;2s, some of the others have stable mapping in sections, like the 3rd harmonic has stable mapping in the middle section but is all over the place in both the hard and soft ends, but the 9th harmonic actually does okay in the hard end, as does the 17th harmonic (both of these get to be all over the place in the soft end), and the 5th and 13th harmonics have stable mapping in the soft end as long as the EDO values are not too large.
+:::::::::::: In partial contrast, with 17L&nbsp;2s, the harmonic/subharmonics of the generator have unstable mapping (because no simple ratio with a reasonable sized numerator and denominator fits into this zone), but the 3rd harmonic is nearly rock-solid (and 112b is a respectable if overly-complex quarter-comma meantone approximation), although presumably its mapping would break if I put in the rest of the right-most column of the MOS spectrum table.  And there the 5th harmonic seems very much usable in the soft end of the scale tuning spectrum as long as the EDO sizes don't get too large (and even then, sometimes it is still okay), which looks to me like enabling a 2.3.5.23 meantone extension; it goes all over the place in the hard end, but there the 25th harmonic shines and is rock-solid as long as you don't go harder than 36edo (basic), and the 13th harmonic just barely misses being rock-solid in this zone (just barely breaks on 125edo, for which 125f would be not bad).  Although those harmonics would also appear less solid if I included the rest of the MOS tuning spectrum.
+:::::::::::: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:28, 10 April 2025 (UTC)