5L 3s: Difference between revisions
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== Name == | == Name == | ||
{{TAMNAMS name}} | {{TAMNAMS name}} 'Oneiro' is sometimes used as a shortened form. | ||
'Father' is sometimes also used to denote 5L 3s, but it's a misnomer, as [[father]] is technically an abstract [[regular temperament]] (although a very inaccurate one), not a generator range. There are father tunings which generate 3L 5s. A more correct but still not quite correct name would be 'father[8]' or 'father octatonic'. "Father" is also vague regarding the number of notes, because optimal generators for it also generate [[3L 2s]]. | 'Father' is sometimes also used to denote 5L 3s, but it's a misnomer, as [[father]] is technically an abstract [[regular temperament]] (although a very inaccurate one), not a generator range. There are father tunings which generate 3L 5s. A more correct but still not quite correct name would be 'father[8]' or 'father octatonic'. "Father" is also vague regarding the number of notes, because optimal generators for it also generate [[3L 2s]]. | ||
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=== Hypohard tunings === | === Hypohard tunings === | ||
[[Hypohard]] oneirotonic tunings have step ratios between 2:1 and 3:1 and can be considered "meantone oneirotonic" | [[Hypohard]] oneirotonic tunings have step ratios between 2:1 and 3:1 and can be considered "meantone oneirotonic", sharing the following features with [[meantone]] diatonic tunings: | ||
* The large step is a "meantone", around the range of [[10/9]] to [[9/8]]. | * The large step is a "meantone", around the range of [[10/9]] to [[9/8]]. | ||
* The major 2-mosstep is a [[meantone]]- to [[flattone]]-sized major third, thus is a stand-in for the classical diatonic major third. | * The major 2-mosstep is a [[meantone]]- to [[flattone]]-sized major third, thus is a stand-in for the classical diatonic major third. | ||
* With step ratios between 5:2 and 2:1, the minor 2-mosstep is close to [[7/6]]. | * With step ratios between 5:2 and 2:1, the minor 2-mosstep is close to [[7/6]]. | ||
The set of identifications above is associated with [[5L 3s/Temperaments#A-Team|A-Team]] temperament. | The set of identifications above is associated with [[5L 3s/Temperaments#A-Team|A-Team]] temperament. EDOs that are in the hypohard range include [[13edo]], [[18edo]], and [[31edo]]. | ||
EDOs that are in the hypohard range include [[13edo]], [[18edo]], and [[31edo]]. | |||
* 13edo has characteristically small 1-mossteps of about 185¢. It is uniformly compressed 12edo, so it has distorted versions of non-diatonic 12edo scales. It essentially has the best [[11/8]] out of all hypohard tunings. | * 13edo has characteristically small 1-mossteps of about 185¢. It is uniformly compressed 12edo, so it has distorted versions of non-diatonic 12edo scales. It essentially has the best [[11/8]] out of all hypohard tunings. | ||
* 18edo can be used for a large step ratio of 3, (thus 18edo oneirotonic is distorted 17edo diatonic, or for its nearly pure 9/8 and 7/6. It also makes rising fifths (733.3¢, a perfect 5-mosstep) and falling fifths (666.7¢, a major 4-mosstep) 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 for a large step ratio of 3, (thus 18edo oneirotonic is distorted 17edo diatonic, or for its nearly pure 9/8 and 7/6. It also makes rising fifths (733.3¢, a perfect 5-mosstep) and falling fifths (666.7¢, a major 4-mosstep) almost equally off from a just perfect fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry. | ||