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User:Dummy index/Semitritave: Difference between revisions

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==False octave==
==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==
==2*N-edt==
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| 24edo
| 24edo
| hypopent
| hypopent
| "Fifth" is 11\19edst ≈ 11/8. Can convert easily from 19edo. "minor tenth" (e.g. (19+3+2)\19edst) ~ 2/1.
| "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
| 23
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==Rank-2 temperaments==
==Rank-2 temperaments==


===Tribilo as micromeantone===
===Tribilo as a micromeantone===
{{See also|Tribilo family}}
{{See also|Tribilo family}}


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[[POTE generator]]: ~121/96 = 400.0108 (or ~11/8 = 550.9667)
[[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>
[[Badness]]: 2.44 × 10<sup>-3</sup>
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http://x31eq.com/cgi-bin/rt.cgi?limit=3_2_11_13%2F5_17&ets=b38_b62&tuning=po
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
Subgroup: 3.5/2.11/8
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[[Tp tuning|POL2 generator]]: ~288/275 = 82.9018 (or ~11/8 = 551.083)
[[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]]:  
[[Tp tuning #T2 tuning|RMS error]]:  
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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
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===
===b32 & b56 as a microdiminished===


Subgroup: 3.5.11
Subgroup: 3.16.5.11


http://x31eq.com/cgi-bin/rt.cgi?limit=3_5_11&ets=b32_b24&tuning=po
http://x31eq.com/cgi-bin/rt.cgi?limit=3_16_5_11&ets=b32_b56&tuning=po
===b38 & b54 as microsensi===
===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
Subgroup: 3.2.7.11/5
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[[Tp tuning|POL2 generator]]: ~896/729 = 351.4241 (or ~99/70 = 599.5534)
[[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]]:  
[[Tp tuning #T2 tuning|RMS error]]:  
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http://x31eq.com/cgi-bin/rt.cgi?limit=3_2_7_11%2F5_13%2F5&ets=b38_b54&tuning=po
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
Subgroup: 3.5.7.26
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[[POTE generator]]: ~26/21 = 367.0018 (or ~7/5 = 583.9757)
[[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>
[[Badness]]: 1.43 × 10<sup>-3</sup>
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|(2/1)
|(2/1)
|-
|-
|8ve
|octave
|1344.885
|1344.885
|3L + 4s
|3L + 4s
|C
|C
|24/11
|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/>
<references/>
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