Diaschismic family: Difference between revisions

Line 704:

== Echidna ==

Echidna adds 1728/1715 to the commas and takes 9/7 as a generator. It may be called the 22 & 58 temperament. [[58edo]] or [[80edo]] make for good tunings, or their vals can be added to {{val| 138 219 321 388 }}.

Echidna adds 1728/1715 to the commas and takes 9/7 as a generator. It may be called the 22 & 58 temperament. [[58edo]] or [[80edo]] make for good tunings, or their vals can be added to {{val| 138 219 321 388 }} (138cde).

Echidna becomes more interesting when extended to be an 11-limit temperament by adding 176/175, 896/891 or 540/539 to the commas, where the same tunings can be used as before. It then is able to represent the entire 11-limit diamond to within about six cents of error, within a compass of 24 notes. The 22 note ~~2MOS~~ gives scope for this, and the 36 note ~~MOS~~ much more. Better yet, it is related to three important 11-limit ~~(and higher) EDOs~~: 22edo, ~~the~~ trivial tuning, is the smallest consistent in the 11-odd-limit, corresponding to the merge of this temperament with [[hedgehog]]; [[58edo]] is the smallest tuning that is ''distinctly'' consistent in the 11-odd-limit ~~(and the smallest consistent in the [[17-odd-limit]])~~ and [[80edo]] is the third smallest distinctly consistent in the 11-odd-limit ~~(and is the smallest consistent in the [[19-odd-limit]] and the no-21's [[23-odd-limit]])~~ and arguably about as accurate as echidna can be, although it has a significantly sharp 7/4 (which some prefer)~~. The second smallest equal temperament distinctly consistent in the 11-odd-limit is [[72edo]], a very strong [[11-limit]] (and higher) system~~.

Echidna becomes more interesting when extended to be an 11-limit temperament by adding 176/175, 896/891 or 540/539 to the commas, where the same tunings can be used as before. It then is able to represent the entire 11-limit diamond to within about six cents of error, within a compass of 24 notes. The 22-note 2mos gives scope for this, and the 36-note mos much more. Better yet, it is related to three important 11-limit edos: 22edo, a trivial tuning, is the smallest consistent in the 11-odd-limit, corresponding to the merge of this temperament with [[hedgehog]]; [[58edo]] is the smallest tuning that is distinctly consistent in the 11-odd-limit and [[80edo]] is the third smallest distinctly consistent in the 11-odd-limit and arguably about as accurate as echidna can be, although it has a significantly sharp 7/4 (which some prefer).

[[Subgroup]]: 2.3.5.7

@@ Line 704: / Line 704: @@
 == Echidna ==
-Echidna adds 1728/1715 to the commas and takes 9/7 as a generator. It may be called the 22 &amp; 58 temperament. [[58edo]] or [[80edo]] make for good tunings, or their vals can be added to {{val| 138 219 321 388 }}.
+Echidna adds 1728/1715 to the commas and takes 9/7 as a generator. It may be called the 22 &amp; 58 temperament. [[58edo]] or [[80edo]] make for good tunings, or their vals can be added to {{val| 138 219 321 388 }} (138cde).
-Echidna becomes more interesting when extended to be an 11-limit temperament by adding 176/175, 896/891 or 540/539 to the commas, where the same tunings can be used as before. It then is able to represent the entire 11-limit diamond to within about six cents of error, within a compass of 24 notes. The 22 note 2MOS gives scope for this, and the 36 note MOS much more. Better yet, it is related to three important 11-limit (and higher) EDOs: 22edo, the trivial tuning, is the smallest consistent in the 11-odd-limit, corresponding to the merge of this temperament with [[hedgehog]]; [[58edo]] is the smallest tuning that is ''distinctly'' consistent in the 11-odd-limit (and the smallest consistent in the [[17-odd-limit]]) and [[80edo]] is the third smallest distinctly consistent in the 11-odd-limit (and is the smallest consistent in the [[19-odd-limit]] and the no-21's [[23-odd-limit]]) and arguably about as accurate as echidna can be, although it has a significantly sharp 7/4 (which some prefer). The second smallest equal temperament distinctly consistent in the 11-odd-limit is [[72edo]], a very strong [[11-limit]] (and higher) system.
+Echidna becomes more interesting when extended to be an 11-limit temperament by adding 176/175, 896/891 or 540/539 to the commas, where the same tunings can be used as before. It then is able to represent the entire 11-limit diamond to within about six cents of error, within a compass of 24 notes. The 22-note 2mos gives scope for this, and the 36-note mos much more. Better yet, it is related to three important 11-limit edos: 22edo, a trivial tuning, is the smallest consistent in the 11-odd-limit, corresponding to the merge of this temperament with [[hedgehog]]; [[58edo]] is the smallest tuning that is distinctly consistent in the 11-odd-limit and [[80edo]] is the third smallest distinctly consistent in the 11-odd-limit and arguably about as accurate as echidna can be, although it has a significantly sharp 7/4 (which some prefer).
 [[Subgroup]]: 2.3.5.7