4L 3s: Difference between revisions

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Parasoft smitonic can be considered "meantone smitonic". This is because these tunings share the following features with [[meantone]] diatonic tunings:

* The large step is a "meantone", somewhere between near-10/9 (as in [[32edo]]) and near-9/8 (as in [[18edo]]).

* The ~~major mosthird~~ (made of two large steps) is a roughly [[meantone]]-sized major third, thus is a stand-in for the classical diatonic major third.

* The augmented smithird (made of two large steps) is a roughly [[meantone]]-sized major third, thus is a stand-in for the classical diatonic major third.

Parasoft smitonic tunings have both minor fifths and major fifths about equally off a just ~~perfect~~ fifth, and they have otherwise fairly convincing versions of both diatonic structure and tertian harmony, provided you frequently modify using the comma-like smichromas. For this reason, parasoft might be the most accessible smitonic tuning range.

Parasoft smitonic tunings have both minor fifths and major fifths about equally off a just fifth, and they have otherwise fairly convincing versions of both diatonic structure and tertian harmony, provided you frequently modify using the comma-like smichromas. For this reason, parasoft might be the most accessible smitonic tuning range.

Parasoft smitonic EDOs include [[18edo]], [[25edo]], and [[43edo]].

* 18edo can be used to make large and small steps more distinct (the step ratio is 3/2, thus 18edo smitonic is distorted [[19edo]] diatonic), or for its nearly pure 9/8. It also makes rising fifths (733.3c, a perfect ~~mossixth~~) and falling fifths (666.7c, a major ~~mosfifth~~) almost equally off from a just ~~perfect~~ fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.

* 18edo can be used to make large and small steps more distinct (the step ratio is 3/2, thus 18edo smitonic is distorted [[19edo]] diatonic), or for its nearly pure 9/8. It also makes rising fifths (733.3c, a perfect smisixth) and falling fifths (666.7c, a major smififth) almost equally off from a just fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.

* [[25edo]] can be used to make the ~~major mosthird~~ a good [[5/4]] (384¢).

* [[25edo]] can be used to make the augmented smithird a good [[5/4]] (384¢).

The sizes of the generator, large step and small step of smitonic are as follows in various parasoft smitonic tunings.

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 Parasoft smitonic can be considered "meantone smitonic". This is because these tunings share the following features with [[meantone]] diatonic tunings:
 * The large step is a "meantone", somewhere between near-10/9 (as in [[32edo]]) and near-9/8 (as in [[18edo]]).
-* The major mosthird (made of two large steps) is a roughly [[meantone]]-sized major third, thus is a stand-in for the classical diatonic major third.
+* The augmented smithird (made of two large steps) is a roughly [[meantone]]-sized major third, thus is a stand-in for the classical diatonic major third.
-Parasoft smitonic tunings have both minor fifths and major fifths about equally off a just perfect fifth, and they have otherwise fairly convincing versions of both diatonic structure and tertian harmony, provided you frequently modify using the comma-like smichromas. For this reason, parasoft might be the most accessible smitonic tuning range.
+Parasoft smitonic tunings have both minor fifths and major fifths about equally off a just fifth, and they have otherwise fairly convincing versions of both diatonic structure and tertian harmony, provided you frequently modify using the comma-like smichromas. For this reason, parasoft might be the most accessible smitonic tuning range.
 Parasoft smitonic EDOs include [[18edo]], [[25edo]], and [[43edo]].
-* 18edo can be used to make large and small steps more distinct (the step ratio is 3/2, thus 18edo smitonic is distorted [[19edo]] diatonic), or for its nearly pure 9/8. It also makes rising fifths (733.3c, a perfect mossixth) and falling fifths (666.7c, a major mosfifth) almost equally off from a just perfect fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.
+* 18edo can be used to make large and small steps more distinct (the step ratio is 3/2, thus 18edo smitonic is distorted [[19edo]] diatonic), or for its nearly pure 9/8. It also makes rising fifths (733.3c, a perfect smisixth) and falling fifths (666.7c, a major smififth) almost equally off from a just fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.
-* [[25edo]] can be used to make the major mosthird a good [[5/4]] (384¢).
+* [[25edo]] can be used to make the augmented smithird a good [[5/4]] (384¢).
 The sizes of the generator, large step and small step of smitonic are as follows in various parasoft smitonic tunings.