User:Dummy index/Semitritave: Difference between revisions

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@@ Line 58: / Line 58: @@
 ==False octave==
-Semitritave is available for [[Ed5/3 through ed7/3|false octave]]. Differ from [[acoustic phi]] or [[ed7/4]], two equave makes 3:1, well-known equave.
+Assuming the semitritave is available for [[Ed5/3 through ed7/3|false octave]]. Differ from [[acoustic phi]] or [[ed7/4]], two equave makes 3:1, well-known equave.
 ==2*N-edt==
@@ Line 94: / Line 94: @@
 | 24edo
 | hypopent
-| "Fifth" is 11\19edst ≈ 11/8. Can convert easily from 19edo.
+| "Fifth" is 11\19edst ≈ 11/8. Can convert easily from 19edo. "minor tenth" (e.g. (19+3+2)\19edst) ~ 2/1. "Major triad" ≈ 16:19:22.
 |-
 | 23
@@ Line 135: / Line 135: @@
 ==Rank-2 temperaments==
-===Tribilo as micromeantone===
+===Tribilo as a micromeantone===
 {{See also|Tribilo family}}
@@ Line 148: / Line 148: @@
 [[POTE generator]]: ~121/96 = 400.0108 (or ~11/8 = 550.9667)
-Optimal GPV sequence: b14, b24, b38, b138, b176, b214, b242
+[[Optimal ET sequence]]: b14, b24, b38, b138, b176, b214, b252
 [[Badness]]: 2.44 × 10<sup>-3</sup>
@@ Line 156: / Line 156: @@
 http://x31eq.com/cgi-bin/rt.cgi?limit=3_2_11_13%2F5_17&ets=b38_b62&tuning=po
-===b24 & b66 as microaugust===
+===b24 & b66 as a microaugust===
 Subgroup: 3.5/2.11/8
@@ Line 168: / Line 168: @@
 [[Tp tuning|POL2 generator]]: ~288/275 = 82.9018 (or ~11/8 = 551.083)
-Optimal GPV sequence: b24, b66, b90, b114, b138, b252
+[[Optimal ET sequence]]: b24, b66, b90, b114, b138, b252
 [[Tp tuning #T2 tuning|RMS error]]:
@@ Line 176: / Line 176: @@
 http://x31eq.com/cgi-bin/rt.cgi?limit=3_5%2F2_16%2F7_11%2F8_13%2F2&ets=b24_b66p&tuning=po
-===b38 & b54 as microsensi===
+===b32 & b56 as a microdiminished===
+Subgroup: 3.16.5.11
+http://x31eq.com/cgi-bin/rt.cgi?limit=3_16_5_11&ets=b32_b56&tuning=po
+===subgroup 3.7.11 seems to be a lot===
+===Vulture (no-fives Buzzard)===
+Subgroup: 3.2.7
+http://x31eq.com/cgi-bin/rt.cgi?limit=3_2_7&ets=b8_b84&tuning=po
+===b38 & b54 as a microsensi===
 Subgroup: 3.2.7.11/5
@@ Line 188: / Line 199: @@
 [[Tp tuning|POL2 generator]]: ~896/729 = 351.4241 (or ~99/70 = 599.5534)
-Optimal GPV sequence: b38, b54, b92
+[[Optimal ET sequence]]: b38, b54, b92
 [[Tp tuning #T2 tuning|RMS error]]:
@@ Line 196: / Line 207: @@
 http://x31eq.com/cgi-bin/rt.cgi?limit=3_2_7_11%2F5_13%2F5&ets=b38_b54&tuning=po
-===b26 & b88 as microoneirotonic===
+===b26 & b88 as a microoneirotonic===
 Subgroup: 3.5.7.26
@@ Line 208: / Line 219: @@
 [[POTE generator]]: ~26/21 = 367.0018 (or ~7/5 = 583.9757)
-Optimal GPV sequence: b10, b16, b26, b62, b88, b114
+[[Optimal ET sequence]]: b10, b16, b26, b62, b88, b114
 [[Badness]]: 1.43 × 10<sup>-3</sup>
@@ Line 223: / Line 234: @@
 Related temperament: [[mirkat]]
-==Relationship==
+==Another periods==
-On this micromeantone, "minor tenth" (e.g. "(19+3+2)\19") ~ 2/1. Re-breaking by real octave, results in [[6L 3s]] i. e. LsLLLsLLs, tribilo or triforce.
+<math>\sqrt{3}^{\sqrt{2}} \approx \varphi^{\varphi}</math> (off by 3 cents). However, this does not mean that acoustic phi and semitritave should be used together.
+Divide or reverse divide by silver [[Metallic MOS]]:<br />
+<math>\sqrt{3}^{\sqrt{2} - 1}</math> ≈ 394¢<br />
+¢ => 2 * 394¢ + 1 * 163¢ => 5 * 163¢ + 2 * 68¢<br />
+* 951¢ + 1 * 394¢ => 3 * 394¢ + 1 * 163¢ => 3 * 231¢ + 4 * 163¢ (3L 4s (1345¢ equivalent))<br />
+* 951¢ + 1 * 394¢ => 5 * 394¢ + 2 * 163¢ (5L 2s (2296¢ equivalent))<br />
+¢ is near 8/7, 163¢ is near 11/10.<br />
+http://x31eq.com/cgi-bin/rt.cgi?limit=3_8_10_7_11_19&ets=b10_b34&tuning=po
+===== 3L 4s (1345¢ equivalent) =====
+{| class="wikitable"
+!
+!Cents
+!In L's and s's
+!Notation
+!Approximate ratios<ref>based on treating as a 3.8.10.7.11.19 subgroup; other approaches are possible.</ref>
+|-
+|unison
+|0
+|0L + 0s
+|C
+|1/1
+|-
+|neutral 2nd
+|163.162
+|0L + 1s
+|vD
+|11/10, 10/9, 21/19
+|-
+|major 2nd
+|230.746
+|1L + 0s
+|D
+|8/7, 9/8
+|-
+|neutral 3rd
+|393.908
+|1L + 1s
+|vE
+|5/4, 24/19
+|-
+|perfect 4th
+|557.070
+|1L + 2s
+|F
+|11/8
+|-
+|perfect 5th
+|787.816
+|2L + 2s
+|G
+|30/19, 11/7
+|-
+|neutral 6th
+|950.978
+|2L + 3s
+|vA
+|19/11, 33/19
+|-
+|neutral 7th
+|1181.723
+|3L + 3s
+|vB
+|(2/1)
+|-
+|octave
+|1344.885
+|3L + 4s
+|C
+|24/11
+|-
+|neutral 9th
+|1508.047
+|3L + 5s
+|vD
+|12/5,19/8
+|-
+|major 9th
+|1575.631
+|4L + 4s
+|D
+|(5/2)
+|-
+|neutral 10th
+|1738.793
+|4L + 5s
+|vE
+|30/11,19/7
+|-
+|perfect 11th
+|1901.955
+|4L + 6s
+|F
+|3/1
+|}
+<references/>
+s ≈ 326.324¢ ≈ (6/5),11/9
 ==Memo==
@@ Line 235: / Line 345: @@
 [http://x31eq.com/cgi-bin/pregular.cgi?limit=3.2.5.13.17&error=5.0 3.2.5.13.17 => 54edt],
 [http://x31eq.com/cgi-bin/pregular.cgi?limit=3.10.14.17.11%2F8&error=5.0 3.10.14.17.11/8 => 62edt]
-<math>\sqrt{3}^{\sqrt{2}} \approx \varphi^{\varphi}</math> (off by 3 cents)<br />
-Hints for silver [[Metallic MOS]]<br />
-<math>\sqrt{3}^{\sqrt{2} - 1}</math> ≈ 394¢<br />
-* 851¢ + 1 * 394¢ => 3 * 394¢ + 1 * 163¢ => 3 * 231¢ + 4 * 163¢ (3L 4s)<br />
-* 851¢ + 1 * 394¢ => 5 * 394¢ + 2 * 163¢ (5L 2s)<br />