2L 8s: Difference between revisions
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{{User:IlL/Template:RTT restriction}} | {{User:IlL/Template:RTT restriction}} | ||
{{Infobox MOS | {{Infobox MOS | ||
| Name = | | Name = pajaroid | ||
| Periods = 2 | | Periods = 2 | ||
| nLargeSteps = 2 | | nLargeSteps = 2 | ||
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}} | }} | ||
'''2L 8s''' or ''' | '''2L 8s''' or '''pajaroid''' is the MOS pattern of the [[decatonic|decatonic]] scale of [[Paul_Erlich|Paul Erlich]] and others.<!-- | ||
The only significant harmonic entropy minimum that is [[Rothenberg_propriety|proper]] is the decatonic scale itself ([[Diaschismic_family|pajara]][10]), in which the period is 7/5~10/7 (tempered to be the same interval), one generator down from that makes [[4/3|4/3]], and another generator down makes [[5/4|5/4]]. More than a few people think this is a beautiful scale that deserves a lot of investigation and use, with some going so far as to say it's the next step up from the diatonic scale that preserves the most desirable features of diatonic melody and harmony. Paul Erlich's original paper on this scale can be found at either of these links: | The only significant harmonic entropy minimum that is [[Rothenberg_propriety|proper]] is the decatonic scale itself ([[Diaschismic_family|pajara]][10]), in which the period is 7/5~10/7 (tempered to be the same interval), one generator down from that makes [[4/3|4/3]], and another generator down makes [[5/4|5/4]]. More than a few people think this is a beautiful scale that deserves a lot of investigation and use, with some going so far as to say it's the next step up from the diatonic scale that preserves the most desirable features of diatonic melody and harmony. Paul Erlich's original paper on this scale can be found at either of these links: | ||
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Improper harmonic entropy minima include [[Meantone_family#Injera|injera]] (which is similar to pajara except that 5/4 is now four generators '''up''' and no periods) and [[Diaschismic_family#Shrutar|shrutar]] (which is basically pajara with the generator divided in two). | Improper harmonic entropy minima include [[Meantone_family#Injera|injera]] (which is similar to pajara except that 5/4 is now four generators '''up''' and no periods) and [[Diaschismic_family#Shrutar|shrutar]] (which is basically pajara with the generator divided in two). | ||
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In addition to the true MOS form, LssssLssss, these scales also exist in a near-MOS form, LsssssLsss, in which the period is the only interval class with more than two flavors. In the case of the decatonic scale, LssssLssss is called the "symmetric" scale and LsssssLsss is called the "pentachordal" scale (because it has two identical "pentachords" in the same way that the diatonic scale has two identical tetrachords). | In addition to the true MOS form, LssssLssss, these scales also exist in a near-MOS form, LsssssLsss, in which the period is the only interval class with more than two flavors. In the case of the decatonic scale, LssssLssss is called the "symmetric" scale and LsssssLsss is called the "pentachordal" scale (because it has two identical "pentachords" in the same way that the diatonic scale has two identical tetrachords). | ||
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| | 2\46 | | | 2\46 | ||
| | 52.17 | | | 52.17 | ||
| style="text-align:center;" | Shrutar is around here | | style="text-align:center;" | <!--Shrutar is around here--> | ||
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| | 21\268 | | | 21\268 | ||
| | 94.03 | | | 94.03 | ||
| style="text-align:center;" | <span style="display: block; text-align: center;">Golden | | style="text-align:center;" | <span style="display: block; text-align: center;">Golden pajaroid <!--(Injera [bad tuning])--></span> | ||
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| | 96 | | | 96 | ||
| style="text-align:center;" | Injera is around here | | style="text-align:center;" | <!--Injera is around here--> | ||
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| | 34\382 | | | 34\382 | ||
| | 106.81 | | | 106.81 | ||
| style="text-align:center;" | Golden | | style="text-align:center;" | Golden pajaroid <!--(Srutal/pajara)--> | ||
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| | 107.14 | | | 107.14 | ||
| style="text-align:center;" | Srutal/pajara | | style="text-align:center;" | <!--Srutal/pajara is around here--> | ||
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| | 109.09 | | | 109.09 | ||
| style="text-align:center;" | Optimum rank range (L/s=3/2) | | style="text-align:center;" | Optimum rank range (L/s=3/2) pajaroid | ||
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