User:Dummy index/Semitritave: Difference between revisions

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.

|-

| 23

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http://x31eq.com/cgi-bin/rt.cgi?limit=3_5%2F2_16%2F7_11%2F8_13%2F2&ets=b24_b66p&tuning=po

===b24 & b32 as microdiminished===

Subgroup: 3.5.11

http://x31eq.com/cgi-bin/rt.cgi?limit=3_5_11&ets=b32_b24&tuning=po

===b38 & b54 as microsensi===

Line 223:

Line 228:

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]]:

<math>\sqrt{3}^{\sqrt{2} - 1}</math> ≈ 394¢

951¢ => 2 * 394¢ + 1 * 163¢ => 5 * 163¢ + 2 * 68¢

1 * 951¢ + 1 * 394¢ => 3 * 394¢ + 1 * 163¢ => 3 * 231¢ + 4 * 163¢ (3L 4s (1345¢ equivalent))

2 * 951¢ + 1 * 394¢ => 5 * 394¢ + 2 * 163¢ (5L 2s (2296¢ equivalent))

231¢ is near 8/7, 163¢ is near 11/10.

http://x31eq.com/cgi-bin/rt.cgi?limit=3_8_10_7_11_19&ets=b10_b34&tuning=po

==Memo==

Line 235:

Line 249:

[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) ~~

~~Hints for silver [[Metallic MOS]] ~~

~~<math>\sqrt{3}^{\sqrt{2} - 1}</math> ≈ 394¢ ~~

~~1 * 951¢ + 1 * 394¢ => 3 * 394¢ + 1 * 163¢ => 3 * 231¢ + 4 * 163¢ (3L 4s) ~~

~~2 * 951¢ + 1 * 394¢ => 5 * 394¢ + 2 * 163¢ (5L 2s) ~~

@@ 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.
 |-
 | 23
@@ 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
+===b24 & b32 as microdiminished===
+Subgroup: 3.5.11
+http://x31eq.com/cgi-bin/rt.cgi?limit=3_5_11&ets=b32_b24&tuning=po
 ===b38 & b54 as microsensi===
@@ Line 223: / Line 228: @@
 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
 ==Memo==
@@ Line 235: / Line 249: @@
 [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 />
-* 951¢ + 1 * 394¢ => 3 * 394¢ + 1 * 163¢ => 3 * 231¢ + 4 * 163¢ (3L 4s)<br />
-* 951¢ + 1 * 394¢ => 5 * 394¢ + 2 * 163¢ (5L 2s)<br />