Diaschismic family: Difference between revisions

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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 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.

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.

[[Subgroup]]: 2.3.5.7

@@ Line 706: / Line 706: @@
 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 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.
+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.
 [[Subgroup]]: 2.3.5.7