4L 3s: Difference between revisions
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== Tuning ranges == | == Tuning ranges == | ||
=== | === Parasoft === | ||
[[Parasoft]] smitonic tunings have step ratios between 5/4 and 3/2, which implies a generator sharper than 5\18 = 333.33¢ and flatter than 9\32 = 337.5¢. | |||
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 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 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. | ||
EDOs | Parasoft smitonic EDOs include [[18edo]], [[25edo]], [[32edo]], 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 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. | ||
* [[25edo]] can be used to make the major mosthird a good [[5/4]] (384¢). | * [[25edo]] can be used to make the major mosthird a good [[5/4]] (384¢). | ||
The sizes of the generator, large step and small step of smitonic are as follows in various | The sizes of the generator, large step and small step of smitonic are as follows in various parasoft smitonic tunings. | ||
{| class="wikitable right-2 right-3 right-4 right-5" | {| class="wikitable right-2 right-3 right-4 right-5" | ||
|- | |- | ||
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|} | |} | ||
=== Hyposoft smitonic === | === Hyposoft smitonic === | ||
[[Hyposoft]] tunings of smitonic have [[step ratio]]s between 3/2 and 2/1 which implies that the generator is a supraminor third sharper than 3\11 = 327.27¢ and flatter than 5\18 = 333.33¢. | |||
The large step is a sharper major second in these tunings than in | The large step is a sharper major second in these tunings than in parasoft tunings. These tunings could be considered "[[parapyth]] smitonic" or "[[archy]] smitonic", in analogy to parasoft smitonic being meantone smitonic. | ||
{| class="wikitable right-2 right-3 right-4 right-5" | {| class="wikitable right-2 right-3 right-4 right-5" | ||
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| 3\29, 124.14 | | 3\29, 124.14 | ||
|} | |} | ||
=== | === Hypohard === | ||
[[ | [[Hypohard]] tunings have [[step ratio]]s between 2 and 3, implying a generator sharper than 4\15 = 320¢ and flatter than 3\11 = 327.27¢. The large step tends to approximate [[8/7]], and the major smifourth (2 large steps + 1 small step) tends to approximate [[11/8]]; [[26edo]] is stellar in both of these approximations. | ||
Hypohard smitonic edos include [[11edo]], [[15edo]], [[26edo]], and [[37edo]]. | |||
The sizes of the generator, large step and small step of smitonic are as follows in various | The sizes of the generator, large step and small step of smitonic are as follows in various hypohard smitonic tunings. | ||
{| class="wikitable right-2 right-3 right-4 right-5" | {| class="wikitable right-2 right-3 right-4 right-5" | ||
|- | |- | ||
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|} | |} | ||
=== | === Parahard === | ||
In parahard smitonic (step ratio between 3 and 4, thus with generator between 5\19, 315.79¢ and 4\15, 320¢), the generator is close to a pure [[6/5]] minor third, and 6 minor thirds are used to reach a perfect fifth. The 7-note MOS only has one perfect fifth, so extending the chain to bigger MOSes, such as the [[4L 7s]] 11-note MOS, is suggested for getting 5-limit harmony. | |||
EDOs that | EDOs that have parahard smitonic include [[15edo]], [[19edo]], [[34edo]], and [[53edo]]. | ||
The sizes of the generator, large step and small step of smitonic are as follows in various | The sizes of the generator, large step and small step of smitonic are as follows in various parahard smitonic tunings. | ||
{| class="wikitable right-2 right-3 right-4 right-5" | {| class="wikitable right-2 right-3 right-4 right-5" | ||
|- | |- | ||
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! [[19edo]] | ! [[19edo]] | ||
! [[34edo]] | ! [[34edo]] | ||
! | ! [[53edo]] | ||
! JI intervals represented | ! JI intervals represented | ||
|- | |- | ||
| Line 594: | Line 593: | ||
| 5\19, 315.79 | | 5\19, 315.79 | ||
| 9\34, 317.65 | | 9\34, 317.65 | ||
| | | 316.98 | ||
| 6/5 | | 6/5 | ||
|- | |- | ||
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| 4\19, 252.63 | | 4\19, 252.63 | ||
| 7\34, 247.06 | | 7\34, 247.06 | ||
| | | 249.06 | ||
| 15/13, 23/20 | | 15/13, 23/20 | ||
|- | |- | ||
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| 1\19, 63.16 | | 1\19, 63.16 | ||
| 2\34, 70.59 | | 2\34, 70.59 | ||
| | | 67.92 | ||
| 25/24 | | 25/24 | ||
|} | |} | ||
== Intervals == | == Intervals == | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||