No-fives subgroup temperaments: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 688: / Line 688: @@
 === Slendrismic ===
 {{see also| 5th-octave temperaments #Slendrismic }}
-In slendrismic, 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.
+In slendrismic, 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.
 [[Subgroup]]: 2.3.7
@@ Line 703: / Line 703: @@
 Related temperaments: [[Pental family|hemipental]]
+==== Pentadecoid ====
+{{see also| 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 &amp; 140) and [[decoid|triacontoid]]  (120 &amp; 150). Triacontoid is a weak extension of pentadecoid, as well as [[Landscape microtemperaments|slendscape]] (255 &amp; 270).
+[[Subgroup]]: 2.3.7.11
+[[Comma list]]: 1362944/1361367, 1771561/1769472
+[[Mapping]]: {{mapping| 15 108 0 94 | 0 -2 1 -1 }}
+: mapping generators: ~22/21, ~7
+[[Optimal tuning]] ([[CTE]]): ~22/21 = 1＼15, ~8/7 = 231.0071 (~1029/1024 = 8.9929)
+{{Optimal ET sequence|legend=1| 120, 135, 660, 795, 930, 1065, 1200 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.0570 cents
 === Hectosaros leap week ===