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| === Slendroschismic === | | === Slendroschismic === |
| {{see also| 5th-octave temperaments #Slendroschismic }}
| | See [[5th-octave temperaments #Slendroschismic]]. |
| In slendroschismic, the period (1＼5) is given a very accurate interpretation of [[147/128]] = ([[3/2]])/([[8/7]])<sup>2</sup> = [[8/7]] * [[1029/1024|1029/1024 = S7/S8]], which is a significant interval as it is the "harmonic 5edostep" in that it's a [[rooted]] (/2^n) interval that approximates 1＼5 very well. The generator is [[1029/1024]], the difference between [[8/7]] and [[147/128]] and therefore between 3/2 and (8/7)<sup>3</sup>. The temperament is named for the very "slender" generator as well as as a pun on "[[slendric]]" (which it shouldn't be confused with). One can consider this as a microtemperament counterpart to [[cloudy]], which equates them.
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| [[Subgroup]]: 2.3.7
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| [[Comma list]]: 68719476736/68641485507
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| {{Mapping|legend=1|5 8 14|0 -2 1}}
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| [[Tp tuning|POL2 generator]]: ~1029/1024 = 8.9906
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| {{Optimal ET sequence|legend=1| 130, 135, 265, 400, 935, 1335, 1735 }}
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| [[Tp tuning #T2 tuning|RMS error]]: 0.0212 cents
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| Related temperaments: [[Pental family|hemipental]]
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| ==== Pentadecoid ==== | | ==== Pentadecoid ==== |
| {{see also| 15th-octave temperaments #Pentadecoid }}
| | See [[15th-octave temperaments #Pentadecoid]]. |
| In pentadecoid, the period (1＼15) is given an interpretation of [[22/21]], and four of them represent keenanismic minor third, [[77/64]] = ([[147/128]]) * ([[22/21]]). The temperament is named for an analog of its relating temperaments, [[decoid]] (130 & 140) and [[decoid|triacontoid]] (120 & 150). Triacontoid is a weak extension of pentadecoid, as well as [[Landscape microtemperaments|slendscape]] (255 & 270).
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| [[Subgroup]]: 2.3.7.11
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| [[Comma list]]: 1362944/1361367, 1771561/1769472
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| [[Mapping]]: {{mapping| 15 108 0 94 | 0 -2 1 -1 }}
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| : mapping generators: ~22/21, ~7
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| [[Optimal tuning]] ([[CTE]]): ~22/21 = 1＼15, ~8/7 = 231.0071 (~1029/1024 = 8.9929)
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| {{Optimal ET sequence|legend=1| 120, 135, 660, 795, 930, 1065, 1200 }}
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| [[Tp tuning #T2 tuning|RMS error]]: 0.0570 cents
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| === Hectosaros leap week === | | === Hectosaros leap week === |