Xenharmonic Wiki

Catalog of rank-4 temperaments: Difference between revisions

← Older editNewer edit →
VisualWikitext
Move nexus here
(2 intermediate revisions by the same user not shown)
Line 407: Line 407:
Comma list: 273/272, 441/440, 561/560
Comma list: 273/272, 441/440, 561/560


Mapping: {{mapping| 1 0 0 0 -3 11 7 | 0 1 0 0 2 -4 -3 | 0 0 1 0 -1 2 2 | 0 0 0 1 2 -2 -1 }}
{{Mapping|legend=0| 1 0 0 0 -3 11 7 | 0 1 0 0 2 -4 -3 | 0 0 1 0 -1 2 2 | 0 0 0 1 2 -2 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 633: Line 633:


== Vishdelismic (5632/5625) ==
== Vishdelismic (5632/5625) ==
Vishdelismic tempers out 5632/5625, the [[vishdelisma]], and adds to [[vishdelic]] an independent generator for prime 7. From 5632/5625 = ([[176/175]])/([[225/224]]), vishdelismic has the feature of making [[14/9]], [[25/16]], and [[11/7]] equidistant.
[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


Line 911: Line 913:
Comma list: 1216/1215, 1540/1539, 2080/2079
Comma list: 1216/1215, 1540/1539, 2080/2079


Mapping: {{mapping| 1 0 0 0 -8 -13 -6 | 0 1 0 0 9 12 5 | 0 0 1 0 0 -1 1 | 0 0 0 1 -1 0 0 }}
{{Mapping|legend=0| 1 0 0 0 -8 -13 -6 | 0 1 0 0 9 12 5 | 0 0 1 0 0 -1 1 | 0 0 0 1 -1 0 0 }}


Optimal tunings:  
Optimal tunings:  
Line 1,022: Line 1,024:
Comma list: 2080/2079, 3510/3509, 4096/4095
Comma list: 2080/2079, 3510/3509, 4096/4095


Mapping: {{mapping| 1 0 0 0 17 12 -21 | 0 1 0 0 -5 -2 11 | 0 0 1 0 0 -1 0 | 0 0 0 1 -2 -1 3 }}
{{Mapping|legend=0| 1 0 0 0 17 12 -21 | 0 1 0 0 -5 -2 11 | 0 0 1 0 0 -1 0 | 0 0 0 1 -2 -1 3 }}


Optimal tunings:  
Optimal tunings:  
Line 1,041: Line 1,043:
Comma list: 2080/2079, 3250/3249, 4096/4095
Comma list: 2080/2079, 3250/3249, 4096/4095


Mapping: {{mapping| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }}
{{Mapping|legend=0| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }}


Optimal tunings:
Optimal tunings:
Line 1,058: Line 1,060:
Comma list: 2080/2079, 3250/3249, 3510/3509, 4096/4095
Comma list: 2080/2079, 3250/3249, 3510/3509, 4096/4095


Mapping: {{mapping| 1 0 0 1 15 11 -13 6 -18 | 0 1 0 0 -5 -2 5 -2 -11 | 0 0 1 0 0 -1 2 1 0 | 0 0 0 2 -4 -2 5 -1 6 }}
{{Mapping|legend=0| 1 0 0 1 15 11 -13 6 -18 | 0 1 0 0 -5 -2 5 -2 -11 | 0 0 1 0 0 -1 2 1 0 | 0 0 0 2 -4 -2 5 -1 6 }}


Optimal tunings:
Optimal tunings:
Line 1,077: Line 1,079:
Comma list: 2080/2079, 4096/4095, 35000/34969
Comma list: 2080/2079, 4096/4095, 35000/34969


Mapping: {{mapping| 1 0 0 1 15 11 -13 | 0 1 0 0 -5 -2 5 | 0 0 1 0 0 -1 2 | 0 0 0 2 -4 -2 5 }}
{{Mapping|legend=0| 1 0 0 1 15 11 -13 | 0 1 0 0 -5 -2 5 | 0 0 1 0 0 -1 2 | 0 0 0 2 -4 -2 5 }}
: mapping generators: ~2, ~3, ~5, ~187/100
: mapping generators: ~2, ~3, ~5, ~187/100


Line 1,095: Line 1,097:
Comma list: 2080/2079, 3250/3249, 4096/4095, 4200/4199
Comma list: 2080/2079, 3250/3249, 4096/4095, 4200/4199


Mapping: {{mapping| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }}
{{Mapping|legend=0| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 1,112: Line 1,114:
Comma list: 2080/2079, 3250/3249, 3510/3509, 4096/4095, 4200/4199
Comma list: 2080/2079, 3250/3249, 3510/3509, 4096/4095, 4200/4199


Mapping: {{mapping| 1 0 0 1 15 11 -13 6 -18 | 0 1 0 0 -5 -2 5 -2 -11 | 0 0 1 0 0 -1 2 1 0 | 0 0 0 2 -4 -2 5 -1 6 }}
{{Mapping|legend=0| 1 0 0 1 15 11 -13 6 -18 | 0 1 0 0 -5 -2 5 -2 -11 | 0 0 1 0 0 -1 2 1 0 | 0 0 0 2 -4 -2 5 -1 6 }}


Optimal tunings:
Optimal tunings:
Line 1,202: Line 1,204:
Comma list: 352/351, 715/714, 155771/155520
Comma list: 352/351, 715/714, 155771/155520


Mapping: {{mapping| 1 0 -6 0 1 6 0 | 0 1 3 0 2 -1 3 | 0 0 5 0 -1 -1 3 | 0 0 0 1 0 0 -1 }}
{{Mapping|legend=0| 1 0 -6 0 1 6 0 | 0 1 3 0 2 -1 3 | 0 0 5 0 -1 -1 3 | 0 0 0 1 0 0 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 1,217: Line 1,219:
Comma list: 352/351, 715/714, 1463/1458, 2057/2052
Comma list: 352/351, 715/714, 1463/1458, 2057/2052


Mapping: {{mapping| 1 0 -6 0 1 6 0 0 | 0 1 3 0 2 -1 3 4 | 0 0 5 0 -1 -1 3 1 | 0 0 0 1 0 0 -1 -1 }}
{{Mapping|legend=0| 1 0 -6 0 1 6 0 0 | 0 1 3 0 2 -1 3 4 | 0 0 5 0 -1 -1 3 1 | 0 0 0 1 0 0 -1 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 1,236: Line 1,238:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~121/96 = 400.0154{{c}}, ~3/2 = 950.9883{{c}}, ~5/4 = 386.2216{{c}}, ~7/4 = 968.7338{{c}}
* [[WE]]: ~121/96 = 400.0154{{c}}, ~1331/768 = 950.9883{{c}}, ~5/4 = 386.2216{{c}}, ~7/4 = 968.7338{{c}}
: [[error map]]: {{val| +0.046 +0.022 -0.000 -0.000 -0.207 }}
: [[error map]]: {{val| +0.046 +0.022 -0.000 -0.000 -0.207 }}
* [[CWE]]: ~121/96 = 400.0000{{c}}, ~3/2 = 950.9685{{c}}, ~5/4 = 386.2485{{c}}, ~7/4 = 968.7470{{c}}
* [[CWE]]: ~121/96 = 400.0000{{c}}, ~1331/768 = 950.9685{{c}}, ~5/4 = 386.2485{{c}}, ~7/4 = 968.7470{{c}}
: error map: {{val| 0.000 -0.018 -0.065 -0.079 -0.349 }}
: error map: {{val| 0.000 -0.018 -0.065 -0.079 -0.349 }}


Line 1,250: Line 1,252:
Comma list: 676/675, 6656/6655
Comma list: 676/675, 6656/6655


Mapping: {{mapping| 3 0 0 0 8 -3 | 0 2 0 0 1 3 | 0 0 1 0 0 1 | 0 0 0 1 0 0 }}
{{Mapping|legend=0| 3 0 0 0 8 -3 | 0 2 0 0 1 3 | 0 0 1 0 0 1 | 0 0 0 1 0 0 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~121/96 = 400.0003{{c}}, ~3/2 = 951.0845{{c}}, ~5/4 = 386.5832{{c}}, ~7/4 = 968.8238{{c}}
* WE: ~121/96 = 400.0003{{c}}, ~1331/768 = 951.0845{{c}}, ~5/4 = 386.5832{{c}}, ~7/4 = 968.8238{{c}}
* CWE: ~121/96 = 400.0000{{c}}, ~3/2 = 951.0840{{c}}, ~5/4 = 386.5837{{c}}, ~7/4 = 968.8241{{c}}
* CWE: ~121/96 = 400.0000{{c}}, ~1331/768 = 951.0840{{c}}, ~5/4 = 386.5837{{c}}, ~7/4 = 968.8241{{c}}


{{Optimal ET sequence|legend=0| 9, 15, 24, 39c/df, 48c, 57f, 63, 72, 87, 111, 159, 183, 198, 270 }}
{{Optimal ET sequence|legend=0| 9, 15, 24, 39c/df, 48c, 57f, 63, 72, 87, 111, 159, 183, 198, 270 }}
Retrieved from "https://en.xen.wiki/w/Catalog_of_rank-4_temperaments"