Xenharmonic Wiki

Catalog of rank-4 temperaments: Difference between revisions

← Older editNewer edit →
VisualWikitext
+topsy ({847/845, 1001/1000}) by community request
+intro, +ptolemismic, +rastmic
Line 1: Line 1:
A '''rank-4 temperament''' has a period and three additional independent generators. Typical examples include [[7-limit]] [[JI]], full 11-limit temperament with a one-dimensional comma basis, and full 13-limit temperament with a two-dimensional comma basis.
== Ptolemismic (100/99) ==
Subgroup: 2.3.5.7.11
[[Comma list]]: [[100/99]]
[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 0 -2 }}, {{val| 0 0 1 0 2 }}, {{val| 0 0 0 1 0 }}]
[[POTE generator]]s: ~3/2 = 704.9532, ~5/4 = 384.0675, ~7/4 = 970.8803
{{Val list|legend=1| 7d, 8d, 10e, 12, 15, 19, 22, 27e, 34d, 41, 90e, 131e }} <nowiki>*</nowiki>
<nowiki>*</nowiki> [[optimal patent val]]: [[104edo|104]]
[[Badness]]: 0.0225 × 10<sup>-6</sup>
== Rastmic (243/242) ==
Subgroup: 2.3.5.7.11
[[Comma list]]: [[243/242]]
[[Mapping]]: [{{val| 1 1 0 0 2 }}, {{val| 0 2 0 0 5 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 0}}]
[[POTE generator]]s: ~11/9 = 350.5254, ~5/4 = 386.1653, ~7/4 = 968.6464
{{Val list|legend=1| 7d, 10, 14c, 17c, 24, 27e, 31, 41, 58, 72, 130, 202 }}
[[Badness]]: 0.05088 × 10<sup>-6</sup>
== Werckismic (441/440) ==
== Werckismic (441/440) ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 441/440
[[Comma list]]: [[441/440]]


[[Mapping]]: [{{val| 1 0 0 0 -3 }}, {{val| 0 1 0 0 2 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 1 2 }}]
[[Mapping]]: [{{val| 1 0 0 0 -3 }}, {{val| 0 1 0 0 2 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 1 2 }}]
Line 72: Line 102:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 385/384
[[Comma list]]: [[385/384]]


[[Mapping]]: [{{val| 1 0 0 0 7 }}, {{val| 0 1 0 0 1 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 1 -1 }}]
[[Mapping]]: [{{val| 1 0 0 0 7 }}, {{val| 0 1 0 0 1 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 1 -1 }}]
Line 172: Line 202:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 540/539
[[Comma list]]: [[540/539]]


[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 0 3 }}, {{val| 0 0 1 0 1 }}, {{val| 0 0 0 1 -2 }}]
[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 0 3 }}, {{val| 0 0 1 0 1 }}, {{val| 0 0 0 1 -2 }}]
Line 227: Line 257:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 3025/3024
[[Comma list]]: [[3025/3024]]


[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 1 2 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 2 1 }}]
[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 1 2 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 2 1 }}]
Line 238: Line 268:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 9801/9800
[[Comma list]]: [[9801/9800]]


[[Mapping]]: [{{val| 2 0 0 0 3 }}, {{val| 0 1 0 0 -2 }}, {{val| 0 0 1 0 1 }}, {{val| 0 0 0 1 1 }}]
[[Mapping]]: [{{val| 2 0 0 0 3 }}, {{val| 0 1 0 0 -2 }}, {{val| 0 0 1 0 1 }}, {{val| 0 0 0 1 1 }}]
Line 268: Line 298:
[[Category:Rank 4| ]] <!-- main article -->
[[Category:Rank 4| ]] <!-- main article -->
{{IoT}}
{{IoT}}
{{Todo| add introduction | expand }}
{{Todo| expand }}
Retrieved from "https://en.xen.wiki/w/Catalog_of_rank-4_temperaments"