152edo: Difference between revisions
→Theory: discuss the extensions beyond the 13-limit |
→Regular temperament properties: +no-17 19-limit and no-17 23-limit |
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| Line 48: | Line 48: | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| 241 -152 }} | ||
| {{ | | {{Mapping| 152 241 }} | ||
| −0.213 | | −0.213 | ||
| 0.213 | | 0.213 | ||
| Line 56: | Line 56: | ||
| 2.3.5 | | 2.3.5 | ||
| 1600000/1594323, {{monzo| 32 -7 -9 }} | | 1600000/1594323, {{monzo| 32 -7 -9 }} | ||
| {{ | | {{Mapping| 152 241 353 }} | ||
| −0.218 | | −0.218 | ||
| 0.174 | | 0.174 | ||
| Line 63: | Line 63: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 4375/4374, 5120/5103, 16875/16807 | | 4375/4374, 5120/5103, 16875/16807 | ||
| {{ | | {{Mapping| 152 241 353 427 }} | ||
| −0.362 | | −0.362 | ||
| 0.291 | | 0.291 | ||
| Line 70: | Line 70: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 540/539, 1375/1372, 4000/3993, 5120/5103 | | 540/539, 1375/1372, 4000/3993, 5120/5103 | ||
| {{ | | {{Mapping| 152 241 353 427 526 }} | ||
| −0.365 | | −0.365 | ||
| 0.260 | | 0.260 | ||
| Line 77: | Line 77: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 352/351, 540/539, 625/624, 729/728, 1575/1573 | | 352/351, 540/539, 625/624, 729/728, 1575/1573 | ||
| {{ | | {{Mapping| 152 241 353 427 526 563 }} (152f) | ||
| −0.494 | | −0.494 | ||
| 0.373 | | 0.373 | ||
| 4.73 | | 4.73 | ||
|- | |||
| 2.3.5.7.11.13.19 | |||
| 352/351, 400/399, 495/494, 540/539, 625/624, 1331/1330 | |||
| {{Mapping| 152 241 353 427 526 563 646 }} (152f) | |||
| −0.507 | |||
| 0.347 | |||
| 4.40 | |||
|- | |||
| 2.3.5.7.11.13.19.23 | |||
| 300/299, 352/351, 400/399, 484/483, 495/494, 540/539, 576/575 | |||
| {{Mapping| 152 241 353 427 526 563 646 688 }} (152f) | |||
| −0.535 | |||
| 0.333 | |||
| 4.22 | |||
|} | |} | ||
* 152et (152fg val) has lower absolute errors in the 11-, 19-, and 23-limit than any previous equal temperaments. In the 11-limit it is the first to beat [[130edo|130]] and is superseded by [[224edo|224]]. In the 19- and 23-limit it is the first to beat [[140edo|140]] and is superseded by [[159edo|159]]. | * 152et (152fg val) has lower absolute errors in the 11-, 19-, and 23-limit than any previous equal temperaments. In the 11-limit it is the first to beat [[130edo|130]] and is superseded by [[224edo|224]]. In the 19- and 23-limit it is the first to beat [[140edo|140]] and is superseded by [[159edo|159]]. | ||
| Line 191: | Line 205: | ||
| [[Hemienneadecal]] | | [[Hemienneadecal]] | ||
|} | |} | ||
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[ | <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[normal lists|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||