Talk:Meantone: Difference between revisions

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== Unlisted(?) strong 7-limit Meantone extension (maybe related to Catasyc or Laruquadbiyoti?) ==

The Septimal Meantone tempering out Harrison's comma ([-13 10 0 -1⟩ = 59049/57344) thus equating [[7/4]] to C-A♯ (fifthspan +10) actually does not give the proper closest approximation to the 7th harmonic for some of the higher-numered equal divisions of the octave having fifths more flat than 50EDO. For a few of these, the next closer approximation equates [[7/4]] to C-G𝄪𝄪(*) (fifthspan +29), tempering out the comma |-43 29 0 -1⟩ = 68630377364883/61572651155456. This starts with [[69edo]], for which a [[Lumatone mapping for 69edo|Lumatone mapping]] has recently been demonstrated [https://www.youtube.com/watch?v=ZAqPonAHuUM&lc=Ugy-2hiGCW-YSngIvmZ4AaABAg.AIVXd3HGZlYAIZiyHbHV7H for playing music that sounds pretty good]. While I am not a keyboard player myself, the reach does look like it might be a bit awkward in combination with [[Devichromic chords]] on the layout for that, but very easily reached on the sharp Diatonic layout as long as it doesn't fall into the crack of missed notes, and somewhat awkward on the flat Diatonic layout if the crack of missed notes can be avoided for both it and its root note. I have tried searching for this comma on Xenharmonic Wiki by monzo and ratio, but it does not turn up, and nothing hinting at such an extension is currently in Meantone or Meantone family. Unfortunately I haven't thought of a good placeholder name for this yet (unlike Mildtone in the section above), so temporarily I'll have to make do without.

The Septimal Meantone tempering out Harrison's comma ([-13 10 0 -1⟩ = 59049/57344) thus equating [[7/4]] to C-A♯ (fifthspan +10) actually does not give the proper closest approximation to the 7th harmonic for some of the higher-numered equal divisions of the octave having fifths more flat than 50EDO. For a few of these, the next closer approximation equates [[7/4]] to C-G𝄪𝄪(*) (fifthspan +29), tempering out the comma |-43 29 0 -1⟩ = 68630377364883/61572651155456. This starts with [[69edo]], for which a [[Lumatone mapping for 69edo|Lumatone mapping]] has recently been demonstrated [https://www.youtube.com/watch?v=ZAqPonAHuUM&lc=Ugy-2hiGCW-YSngIvmZ4AaABAg.AIVXd3HGZlYAIZiyHbHV7H for playing music that sounds pretty good] (edit: [[https://www.youtube.com/shorts/4XBELeySMPk another example]). While I am not a keyboard player myself, the reach does look like it might be a bit awkward in combination with [[Devichromic chords]] on the layout for that, but very easily reached on the sharp Diatonic layout as long as it doesn't fall into the crack of missed notes, and somewhat awkward on the flat Diatonic layout if the crack of missed notes can be avoided for both it and its root note. I have tried searching for this comma on Xenharmonic Wiki by monzo and ratio, but it does not turn up, and nothing hinting at such an extension is currently in Meantone or Meantone family. Unfortunately I haven't thought of a good placeholder name for this yet (unlike Mildtone in the section above), so temporarily I'll have to make do without.

(*)For readability, it would be best to find a better way of notating this in an actual score, since otherwise a simple 4:5:6:7 chord will produce overlapping notes with C-G𝄪♯.

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I have not yet done any work to see what higher-limit extensions would go with Mildtone beyond clicking on the "11-limit" and "13-limit" buttons in x31eq to see what output it would yield; with "13-limit", it starts to come up with rather odd output, so I stopped there.

Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:41, 27 May 2025 (UTC)

Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:41, 27 May 2025 (UTC)<br>

Last modifed: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:30, 11 June 2025 (UTC) (added another supporting sound sample)

@@ Line 310: / Line 310: @@
 == Unlisted(?) strong 7-limit Meantone extension (maybe related to Catasyc or Laruquadbiyoti?) ==
-The Septimal Meantone tempering out Harrison's comma ([-13 10 0 -1⟩ = 59049/57344) thus equating [[7/4]] to C-A♯ (fifthspan +10) actually does not give the proper closest approximation to the 7th harmonic for some of the higher-numered equal divisions of the octave having fifths more flat than 50EDO.  For a few of these, the next closer approximation equates [[7/4]] to C-G𝄪𝄪(*) (fifthspan +29), tempering out the comma |-43 29 0 -1⟩ = 68630377364883/61572651155456.  This starts with [[69edo]], for which a [[Lumatone mapping for 69edo|Lumatone mapping]] has recently been demonstrated [https://www.youtube.com/watch?v=ZAqPonAHuUM&lc=Ugy-2hiGCW-YSngIvmZ4AaABAg.AIVXd3HGZlYAIZiyHbHV7H for playing music that sounds pretty good].  While I am not a keyboard player myself, the reach does look like it might be a bit awkward in combination with [[Devichromic chords]] on the layout for that, but very easily reached on the sharp Diatonic layout as long as it doesn't fall into the crack of missed notes, and somewhat awkward on the flat Diatonic layout if the crack of missed notes can be avoided for both it and its root note.  I have tried searching for this comma on Xenharmonic Wiki by monzo and ratio, but it does not turn up, and nothing hinting at such an extension is currently in Meantone or Meantone family.  Unfortunately I haven't thought of a good placeholder name for this yet (unlike Mildtone in the section above), so temporarily I'll have to make do without.
+The Septimal Meantone tempering out Harrison's comma ([-13 10 0 -1⟩ = 59049/57344) thus equating [[7/4]] to C-A♯ (fifthspan +10) actually does not give the proper closest approximation to the 7th harmonic for some of the higher-numered equal divisions of the octave having fifths more flat than 50EDO.  For a few of these, the next closer approximation equates [[7/4]] to C-G𝄪𝄪(*) (fifthspan +29), tempering out the comma |-43 29 0 -1⟩ = 68630377364883/61572651155456.  This starts with [[69edo]], for which a [[Lumatone mapping for 69edo|Lumatone mapping]] has recently been demonstrated [https://www.youtube.com/watch?v=ZAqPonAHuUM&lc=Ugy-2hiGCW-YSngIvmZ4AaABAg.AIVXd3HGZlYAIZiyHbHV7H for playing music that sounds pretty good] (edit:  [[https://www.youtube.com/shorts/4XBELeySMPk another example]).  While I am not a keyboard player myself, the reach does look like it might be a bit awkward in combination with [[Devichromic chords]] on the layout for that, but very easily reached on the sharp Diatonic layout as long as it doesn't fall into the crack of missed notes, and somewhat awkward on the flat Diatonic layout if the crack of missed notes can be avoided for both it and its root note.  I have tried searching for this comma on Xenharmonic Wiki by monzo and ratio, but it does not turn up, and nothing hinting at such an extension is currently in Meantone or Meantone family.  Unfortunately I haven't thought of a good placeholder name for this yet (unlike Mildtone in the section above), so temporarily I'll have to make do without.
 (*)For readability, it would be best to find a better way of notating this in an actual score, since otherwise a simple 4:5:6:7 chord will produce overlapping notes with C-G𝄪♯.
@@ Line 381: / Line 381: @@
 I have not yet done any work to see what higher-limit extensions would go with Mildtone beyond clicking on the "11-limit" and "13-limit" buttons in x31eq to see what output it would yield; with "13-limit", it starts to come up with rather odd output, so I stopped there.
-Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:41, 27 May 2025 (UTC)
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:41, 27 May 2025 (UTC)<br>
+Last modifed:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:30, 11 June 2025 (UTC) (added another supporting sound sample)