Xenharmonic Wiki

No-fives subgroup temperaments: Difference between revisions

← Older editNewer edit →
VisualWikitext
Sort by badness
Switch to Sintel's badness, WE & CWE tunings (7/)
Line 487: Line 487:


=== Bleu ===
=== Bleu ===
Bleu can be described as the {{nowrap| 8d & 9 }} temperament in the no-5 13-limit.  
Bleu can be described as the {{nowrap| 8d & 9 }} temperament in the no-5 13-limit, and is the common [[restriction]] of [[progression]] and [[jerome]].  


[[Subgroup]]: 2.3.7
[[Subgroup]]: 2.3.7
Line 864: Line 864:


== Temperaments with a 2.3.11 gene ==
== Temperaments with a 2.3.11 gene ==
=== Neutral ===
See [[Rastmic clan #Neutral]].
==== Namo ====
See [[Rastmic clan #Namo]].
=== Io ===
=== Io ===
Io is a very low-complexity temperament which tempers out the undecimal quartertone [[33/32]]. This equates very different intervals (for example, the generator itself represents both [[3/2]] and [[16/11]]), and as such some consider it to be an [[exotemperament]]. It has an extremely wide generator range, but the most accurate tunings are generally inside the range of [[flattone]] temperament.
Io is a very low-complexity temperament which tempers out the undecimal quartertone [[33/32]]. This equates very different intervals (for example, the generator itself represents both [[3/2]] and [[16/11]]), and as such some consider it to be an [[exotemperament]]. It has an extremely wide generator range, but the most accurate tunings are generally inside the range of [[flattone]] temperament.


The name Io was coined by [[User:CompactStar|CompactStar]] in 2024 based on the [[color notation|color name]] ilo, prior to which it could only be termed as "undecimal temperament" with 33/32 being known as the undecimal comma.
The name ''io'' was coined by [[User:CompactStar|CompactStar]] in 2024 based on the [[Kite's color notation|color name]] ''ilo'', prior to which it could only be termed as "undecimal temperament" with 33/32 being known as the undecimal comma.


[[Subgroup]]: 2.3.11
[[Subgroup]]: 2.3.11
Line 874: Line 880:


{{Mapping|legend=2| 1 0 5 | 0 1 -1 }}
{{Mapping|legend=2| 1 0 5 | 0 1 -1 }}
: mapping generators: ~2, ~3
: mapping generators: ~2, ~3


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 692.713
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1206.6866{{c}}, ~3/2 = 691.7837{{c}}
: [[error map]]: {{val| +6.687 -3.485 -16.355 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 689.2066{{c}}
: error map: {{val| 0.000 -12.748 -40.525 }}


{{Optimal ET sequence|legend=1| 2, 5, 7, 12e }}
{{Optimal ET sequence|legend=1| 2, 5, 7, 12e, 40ee, 47eee, 54beee, 61beeee }}


[[Badness]]: 0.185
[[Badness]] (Sintel): 0.185


=== Paralimmal ===
=== Paralimmal ===
Line 889: Line 898:


{{Mapping|legend=2| 1 0 4 | 0 3 -1 }}
{{Mapping|legend=2| 1 0 4 | 0 3 -1 }}
: mapping generators: ~2, ~16/11


[[Optimal tuning]] ([[CTE]]): ~2 = 1/1, ~[[16/11]] = 634.320
[[Optimal tuning]]s:
 
* [[WE]]: ~2 = 1197.9124{{c}}, ~16/11 = 634.1269{{c}}
{{Optimal ET sequence|legend=1| 11b, 13, 15, 17 }}
: [[error map]]: {{val| -2.088 +0.426 +6.205 }}
 
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/11 = 634.9546{{c}}
[[Tp tuning #T2 tuning|RMS error]]: 1.237 cents
: error map: {{val| 0.000 +2.909 +13.727 }}


=== Neutral ===
{{Optimal ET sequence|legend=1| 2, 11b, 13, 15, 17 }}
See [[Rastmic clan #Neutral]]


==== Namo ====
[[Badness]] (Sintel): 0.984
See [[Rastmic clan #Namo]]


=== Huxley ===
==== Huxley ====
{{Main| Huxley }}
{{Main| Huxley }}


Huxley, the 4 & 13 temperament in the 2.3.11.13 subgroup, extends [[lovecraft]]. Specifically it tunes the ~13/8 to exactly half of ~8/3.  
Huxley, the {{nowrap| 4 & 13 }} temperament in the 2.3.11.13 subgroup, extends [[lovecraft]]. Specifically it tunes the ~13/8 to exactly half of ~8/3.  


[[Subgroup]]: 2.3.11.13
Subgroup: 2.3.11.13


[[Comma list]]: 512/507, 1352/1331
Comma list: 512/507, 1352/1331


{{Mapping|legend=2| 1 3 3 3 | 0 -6 2 3 }}
Subgroup-val mapping: {{mapping| 1 -3 5 6 | 0 6 -2 -3 }}
: mapping generators: ~2, ~22/13


: mapping generators: ~2, ~13/11
Optimal tunings:  
 
* WE: ~2 = 1198.0036{{c}}, ~22/13 = 916.0595{{c}}
[[Optimal tuning]]s:  
* CWE: ~2 = 1200.0000{{c}}, ~22/13 = 917.5184{{c}}
* [[CTE]]: ~2 = 1\1, ~13/11 = 282.726
* [[CWE]]: ~2 = 1\1, ~13/11 = 282.482


{{Optimal ET sequence|legend=1| 4, 13, 17 }}
{{Optimal ET sequence|legend=0| 4, 13, 17 }}


[[Badness]]: 0.0263
Badness (Sintel): 1.31


=== Aerophore ===
=== Aerophore ===
Line 929: Line 936:


{{Mapping|legend=2| 1 0 -6 -6 | 0 2 12 13 }}
{{Mapping|legend=2| 1 0 -6 -6 | 0 2 12 13 }}
: mapping generators: ~2, ~19/11
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1202.6380{{c}}, ~19/11 = 947.4782{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~19/11 = 945.7779{{c}}
{{Optimal ET sequence|legend=1| 14, 19, 33 }}
[[Badness]] (Sintel): 1.59
=== Semaerophore ===
[[Subgroup]]: 2.3.7.11
[[Comma list]]: 49/48, 729/704
{{Mapping|legend=2| 1 0 2 -6 | 0 2 1 12 }}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1204.9027{{c}}, ~7/4 = 948.7772{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 945.4959{{c}}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~19/11 = 945.4
{{Optimal ET sequence|legend=1| 14, 33d, 47de }}


{{Optimal ET sequence|legend=1| 9eehh, 14, 19, 33 }}
[[Badness]] (Sintel): 1.27


==== Semaerophore ====
==== 2.3.7.11.19 ====
[[Subgroup]]: 2.3.7.11.19
Subgroup: 2.3.7.11.19
 
Comma list: 49/48, 77/76, 729/704


[[Comma list]]: 49/48, 77/76, 729/704
Subgroup-val mapping: {{mapping| 1 0 2 -6 -6 | 0 2 1 12 13 }}


{{Mapping|legend=2| 1 0 2 -6 -6 | 0 2 1 12 13 }}
Optimal tunings:
* WE: ~2 = 1204.9645{{c}}, ~7/4 = 948.5749{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 945.2236{{c}}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/4 = 944.667
{{Optimal ET sequence|legend=0| 14, 33d, 47deh }}


{{Optimal ET sequence|legend=1| 9eehh, 14, 33d, 47deh }}
Badness (Sintel): 1.08


== Temperaments with a 2.3.13 gene ==
== Temperaments with a 2.3.13 gene ==
Retrieved from "https://en.xen.wiki/w/No-fives_subgroup_temperaments"