Xenharmonic Wiki

Harmonisma: Difference between revisions

← Older edit

FloraC (talk | contribs)

4 user groups
27,393 edits
VisualWikitext
Eufalesio (talk | contribs)
autopatrolled
939 edits
Added alfheim
 
(One intermediate revision by the same user not shown)
Line 23: Line 23:


Here, for example 33/32 is 4/3 vs. 11/8; 91/88 is 22/13 vs. 7/4; 121/117 is 13/11 vs. 11/9; and 28/27 is 9/8 vs. 7/6.
Here, for example 33/32 is 4/3 vs. 11/8; 91/88 is 22/13 vs. 7/4; 121/117 is 13/11 vs. 11/9; and 28/27 is 9/8 vs. 7/6.
=== Harmonismatic ===
=== Harmonismatic ===
Harmonismatic is a natural detemperament of [[parapyth]] where the last generator can be taken to be 352/351~364/363. [[Kalimera]] and [[Catalog of rank-4 temperaments#Alfheim (10648/10647, 1664000/1663893)|alfheim]] are [[weak extension]]<nowiki/>s to the whole 13-limit.
Harmonismatic is a natural detemperament of parapyth where the last generator can be taken to be 352/351~364/363. Extensions of this temperament to the whole 13-limit include [[kalimera]] and [[alfheim]].  


[[Subgroup]]: 2.3.7.11.13
[[Subgroup]]: 2.3.7.11.13
Line 30: Line 31:
[[Comma list]]: 10648/10647
[[Comma list]]: 10648/10647


[[Mapping]]:
{{Mapping|legend=3| 1 0 0 1 3 | 0 1 0 0 −1 | 0 0 1 1 1 | 0 0 0 -2 -3 }}
{| class="right-all"
|[⟨
|1
|0
|0
|1
|3
|],
|-
|⟨
|0
|1
|0
|0
| -1
|],
|-
|⟨
|0
|0
|1
|1
|1
|],
|-
|⟨
|0
|0
|0
| -2
| -3
|]]
|}
 
: mapping generators: ~2, ~3, ~7, ~44/39
: mapping generators: ~2, ~3, ~7, ~44/39


[[Optimal tuning]]:
[[Optimal tuning]]:  
 
* [[WE]]: ~2 = 1199.9974{{c}}, ~3/2 = 701.9619{{c}}, ~7/4 = 968.8378{{c}}, ~44/39 = 208.7715{{c}}
* [[WE]]: ~2 = 1199.9974{{c}}, ~3/2 = 701.9619{{c}}, ~7/4 = 968.8378{{c}}, ~44/39 = 208.7715{{c}}
: [[error map]]: {{val| -0.003 +0.004 +0.007 -0.031 +0.024 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9615{{c}}, ~7/4 = 968.8365{{c}}, ~44/39 = 208.7728{{c}}
: error map: {{val| 0.000 +0.007 +0.011 -0.027 +0.029 }}


: [[error map]]: {{val|-0.003 +0.004 +0.007 -0.031 +0.024}}
{{Optimal ET sequence|legend=1| 12f, 16, 17, 41, 46, 58, 87, 103, 104, 149, 166, 207, 270, 431, 477, 701, 971, 1012, 1178, 1282, 1489, 1506, 1983, 7455, 7662, 9645, 11628, 13134, 15117, 17100 }}
 
* [[CWE]]: ~99/70 = 1200.0000{{c}}, ~3/2 = 701.9615{{c}}, ~7/4 = 968.8365{{c}}, ~44/39 = 208.7728{{c}}
 
: error map: {{val|0.000 +0.007 +0.011 -0.027 +0.029}}
 
{{Optimal ET sequence|12f, 16, 17, 41, 46, 58, 87, 103, 104, 149, 166, 207, 270, 431, 477, 701, 971, 1012, 1178, 1282, 1489, 1506, 1983, 7455, 7662, 9645, 11628, 13134, 15117|legend=1}}


[[Badness]] (Sintel): 0.0382
[[Badness]] (Sintel): 0.0382
Retrieved from "https://en.xen.wiki/w/Harmonisma"