Lesser tendoneutralisma: Difference between revisions

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The '''lesser tendoneutralisma''' is a [[small comma]] of the 2.3.13 subgroup which is the amount by which a stack of twelve [[16/13]]'s minus three [[octave]]s exceeds [[3/2]]; that is, it is equal to ([[16/13]])12 / ([[3/2]]) / ([[2/1]])3 and so equivalently also to ([[16/13]])11 / ([[39/4]]). Because the ~11{{cent}} of error is distributed over twelve [[16/13]]'s in the pure-3's tuning, it is a very accurate way of connecting a chain of 13's to prime 3. A slightly less accurate but still good way of doing this is using the [[greater tendoneutralisma]]. Very importantly, both are distinct ways of mapping 2.3.13, so that you can't combine them unless you want to use the trivial tuning of [[10edo]], so that edos > 10 which have a good 3 and 13 will usually pick between one of these two mappings.

The '''lesser tendoneutralisma''' is a [[small comma]] of the 2.3.13 subgroup which is the amount by which a stack of twelve [[16/13]]'s minus three [[octave]]s exceeds [[3/2]]; that is, it is equal to ([[16/13]])12 / ([[3/2]]) / ([[2/1]])3 and so equivalently also to ([[16/13]])11 / ([[39/4]]). Because the ~11{{cent}} of error is distributed over twelve [[16/13]]'s in the pure-3's tuning, it is a very accurate way of connecting a chain of 13's to prime 3. A slightly less accurate but still good way of doing this is using the [[greater tendoneutralisma]]. Very importantly, both are distinct ways of mapping 2.3.13, so that you can't combine them unless you want to use the trivial tuning of [[10edo]], so that edos > 10 which have a good 3 and 13 will usually pick between one of these two mappings. (A much simpler but (relatively) much higher error way of mapping 3 for those that prefer sharp fifths is by tempering ([[16/13]])2/([[3/2]]) = [[512/507]].)

== Temperaments ==

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== See also ==

* [[Greater tendoneutralisma]]

* [[512/507]]

* [[Tridecapyth comma]]

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-The '''lesser tendoneutralisma''' is a [[small comma]] of the 2.3.13 subgroup which is the amount by which a stack of twelve [[16/13]]'s minus three [[octave]]s exceeds [[3/2]]; that is, it is equal to ([[16/13]])<sup>12</sup> / ([[3/2]]) / ([[2/1]])<sup>3</sup> and so equivalently also to ([[16/13]])<sup>11</sup> / ([[39/4]]). Because the ~11{{cent}} of error is distributed over twelve [[16/13]]'s in the pure-3's tuning, it is a very accurate way of connecting a chain of 13's to prime 3. A slightly less accurate but still good way of doing this is using the [[greater tendoneutralisma]]. Very importantly, both are distinct ways of mapping 2.3.13, so that you can't combine them unless you want to use the trivial tuning of [[10edo]], so that edos > 10 which have a good 3 and 13 will usually pick between one of these two mappings.
+The '''lesser tendoneutralisma''' is a [[small comma]] of the 2.3.13 subgroup which is the amount by which a stack of twelve [[16/13]]'s minus three [[octave]]s exceeds [[3/2]]; that is, it is equal to ([[16/13]])<sup>12</sup> / ([[3/2]]) / ([[2/1]])<sup>3</sup> and so equivalently also to ([[16/13]])<sup>11</sup> / ([[39/4]]). Because the ~11{{cent}} of error is distributed over twelve [[16/13]]'s in the pure-3's tuning, it is a very accurate way of connecting a chain of 13's to prime 3. A slightly less accurate but still good way of doing this is using the [[greater tendoneutralisma]]. Very importantly, both are distinct ways of mapping 2.3.13, so that you can't combine them unless you want to use the trivial tuning of [[10edo]], so that edos > 10 which have a good 3 and 13 will usually pick between one of these two mappings. (A much simpler but (relatively) much higher error way of mapping 3 for those that prefer sharp fifths is by tempering ([[16/13]])<sup>2</sup>/([[3/2]]) = [[512/507]].)
 == Temperaments ==
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 == See also ==
 * [[Greater tendoneutralisma]]
+* [[512/507]]
 * [[Tridecapyth comma]]