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Subgroup temperaments: Difference between revisions

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[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
=== Oceanfront ===
Related temperaments: [[archytas clan #Superpyth|superpyth]], [[archytas clan #Ultrapyth|ultrapyth]]
[[Subgroup]]: 2.3.7.13/5
[[Comma list]]: 64/63 ({{monzo| 6 -2 -1 0 }}), 91/90 ({{monzo| -1 -2 1 1 }})
{{Mapping|legend=3| 1 0 6 -5 | 0 1 -2 4 }}
: mapping generators: ~2, ~3
[[Optimal tuning]]s:
* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1197.2656{{c}}, ~3/2 = 710.1993{{c}}
* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 711.7413{{c}}
{{Optimal ET sequence|legend=1| 5, 17, 22, 27, 32, 59 }}
[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents
Scales: [[Oceanfront scales]]


=== Darian calendar ===
=== Darian calendar ===
Line 222: Line 202:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[Tp tuning|subgroup]] [[WE]]: ~2 = 1199.4965{{c}}, ~3/2 = 703.1192{{c}}
* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1199.4965{{c}}, ~3/2 = 703.1192{{c}}
* [[Tp tuning|subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.4225{{c}}
* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.4225{{c}}


{{Optimal ET sequence|legend=1| 12, 17, 29 }}
{{Optimal ET sequence|legend=1| 12, 17, 29 }}
Line 244: Line 224:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[Tp tuning|subgroup]] [[WE]]: ~2 = 1199.7072{{c}}, ~26/15 = 951.2727{{c}}
* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1199.7072{{c}}, ~26/15 = 951.2727{{c}}
* [[Tp tuning|subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~26/15 = 951.5016{{c}}
* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~26/15 = 951.5016{{c}}


{{Optimal ET sequence|legend=1| 24, 29, 111, 140, 169, 198 }}
{{Optimal ET sequence|legend=1| 24, 29, 111, 140, 169, 198 }}
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[Tp tuning|subgroup]] [[WE]]: ~2 = 1200.0242{{c}}, ~21/20 = 83.0177{{c}}
* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1200.0242{{c}}, ~21/20 = 83.0177{{c}}
* [[Tp tuning|subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 83.0144{{c}}
* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 83.0144{{c}}


{{Optimal ET sequence|legend=1| 14, 29, 101, 130, 159 }}
{{Optimal ET sequence|legend=1| 14, 29, 101, 130, 159 }}
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[[Optimal tuning]]:
[[Optimal tuning]]:
* [[Tp tuning|subgroup]] [[WE]]: ~2 = 1200.0206{{c}}, ~49/40 = 350.9724{{c}}
* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1200.0206{{c}}, ~49/40 = 350.9724{{c}}
* [[Tp tuning|subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 350.9743{{c}}
* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 350.9743{{c}}


{{Optimal ET sequence|legend=1| 7, 17, 24, 41, 65, 106, 253, 359, 465, 1036, 1501, 1966*, 5433* }}
{{Optimal ET sequence|legend=1| 7, 17, 24, 41, 65, 106, 253, 359, 465, 1036, 1501, 1966*, 5433* }}
Line 293: Line 273:
{{See also| Chromatic pairs #Tobago }}
{{See also| Chromatic pairs #Tobago }}


Tobago, the 10 & 14 temperament in the 2.3.11.13/5 subgroup, extends [[neutral]] and [[barbados]].  
Tobago, the 10 & 14 temperament in the 2.3.11.13/5 subgroup, extends [[rastmic clan #Neutral|neutral]] and [[#Barbados|barbados]].  


[[Subgroup]]: 2.3.11.13/5
[[Subgroup]]: 2.3.11.13/5
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[Tp tuning|subgroup]] [[WE]]: ~55/39 = 599.9845{{c}}, ~26/15 = 950.6637{{c}}
* [[Tp tuning|Subgroup]] [[WE]]: ~55/39 = 599.9845{{c}}, ~26/15 = 950.6637{{c}}
* [[Tp tuning|subgroup]] [[CWE]]: ~55/39 = 600.0000{{c}}, ~26/15 = 950.6776{{c}}
* [[Tp tuning|Subgroup]] [[CWE]]: ~55/39 = 600.0000{{c}}, ~26/15 = 950.6776{{c}}


{{Optimal ET sequence|legend=1| 10, 14, 24, 82, 106, 130, 154 }}
{{Optimal ET sequence|legend=1| 10, 14, 24, 82, 106, 130, 154 }}
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[Tp tuning|subgroup]] [[WE]]: ~2 = 1199.6281{{c}}, ~26/15 = 951.3060{{c}}
* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1199.6281{{c}}, ~26/15 = 951.3060{{c}}
* [[Tp tuning|subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~26/15 = 951.5580{{c}}
* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~26/15 = 951.5580{{c}}


{{Optimal ET sequence|legend=1| 5, 19*, 24, 29, 169, 198, 227, 256, 285, 314, 343 }}
{{Optimal ET sequence|legend=1| 5, 19*, 24, 29, 169, 198, 227, 256, 285, 314, 343 }}
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[[Tp tuning #T2 tuning|RMS error]]: 0.2513 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.2513 cents
=== Seventeen-cot ===
Seventeen-cot may be described as the 29 & 465 temperament in the 2.3.11/5.13/5 subgroup. It tempers out the [[tendoartisma]] in the 2.3.13/5 subgroup. It can be generated with a ~2/1 octave and a ~169/165 generator which is 1/17 of a ~3/2 perfect fifth. It was named by {{u|FilterNashi}} in 2026.
[[Subgroup]]: 2.3.11/5.13/5
[[Comma basis]]: 43940/43923 ({{monzo| 2 -1 -4 3 }}), 225000/224939 ({{monzo| 3 2 -3 -2 }})
{{Mapping|legend=3| 1 1 1 1 | 0 17 4 11 }}
: mapping generators: ~2, ~169/165
[[Optimal tuning]]s:
* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1199.993492{{c}}, ~169/165 = 41.291827{{c}}
: [[error map]]: {{val| -0.0065 -0.0004 +0.1566 -0.0104 }}
* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.000000, ~169/165 = 41.291746{{c}}
: error map: {{val| 0.0000 +0.0047 +0.1628 -0.0047 }}
{{Optimal ET sequence|legend=1| 29, 262, 291, 320, 349, 378, 407, 436, 465, 959, 1424, 6161* }}
[[Badness]] (Sintel): 0.080


=== Blackweed ===
=== Blackweed ===
Line 362: Line 362:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[Tp tuning|subgroup]] [[WE]]: ~8/7 = 238.851{{c}}, ~11/7 = 782.457{{c}}
* [[Tp tuning|Subgroup]] [[WE]]: ~8/7 = 238.851{{c}}, ~11/7 = 782.457{{c}}
: [[error map]]: {{val| -5.746 +8.852 -0.035 }}
: [[error map]]: {{val| -5.746 +8.852 -0.035 }}
* [[Tp tuning|subgroup]] [[CWE]]: ~8/7 = 240.000{{c}}, ~11/7 = 784.967{{c}}
* [[Tp tuning|Subgroup]] [[CWE]]: ~8/7 = 240.000{{c}}, ~11/7 = 784.967{{c}}
: error map: {{val| 0.000 +18.045 +2.475 }}
: error map: {{val| 0.000 +18.045 +2.475 }}


Line 385: Line 385:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[Tp tuning|subgroup]] [[WE]]: ~2 = 1199.3706{{c}}, ~11/7 = 703.4872{{c}}
* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1199.3706{{c}}, ~11/7 = 703.4872{{c}}
* [[Tp tuning|subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~11/7 = 703.8328{{c}}
* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~11/7 = 703.8328{{c}}


{{Optimal ET sequence|legend=1| 12, 17, 29, 75, 104 }}
{{Optimal ET sequence|legend=1| 12, 17, 29, 75, 104 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
=== Fendo ===
Fendo tempers out [[40/39]] in the 2.3.13/5 subgroup. This equates [[4/3]] with the tendo third [[13/10]]. Fendo can be viewed as an alternative interpretation of scales, chords, etc. commonly associated with [[father family #Father|father]], as it is sometimes perceived that father's characteristics tend to suggest harmonic function more than to actually serve as a temperament. It was named by [[User: VectorGraphics|Vector]] in 2025 as a contraction of ''fourth'' and ''tendo third''.
In fendo, the fourth / tendo third serves the role of both, making the main chords of triadic harmony in fendo essentially suspended chords.
[[5edo]] and [[13edo]] make good fendo tunings.
[[Subgroup]]: 2.3.13/5
[[Comma list]]: 40/39 ({{monzo| 3 -1 -1 }})
{{Mapping|legend=3| 1 0 3 | 0 1 -1 }}
: mapping generators: ~2, ~3
[[Optimal tuning]]s:
* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1195.6502{{c}}, ~3/2 = 709.8204{{c}}
* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 710.1529{{c}}
{{Optimal ET sequence|legend=1| 1, 2, 3, 5, 17*, 22*, 27*, 32* }}
<nowiki/>* Wart for 13/5


=== Barbados ===
=== Barbados ===
Barbados is the restriction of [[#Bridgetown|bridgetown]] to the 2.3.13/5 subgroup. The [[minimax tuning]] for this makes the generator the cube root of 20/13, or 248.5953 cents. Edos which may be used for it are [[24edo]], [[29edo]], [[53edo]] and [[111edo]], with [[mos scale]]s of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales.
Barbados is the restriction of [[#Bridgetown|bridgetown]] to the 2.3.13/5 subgroup, and tempers out [[676/675]] alone. The [[minimax tuning]] for this makes the generator the cube root of 20/13, or 248.5953 cents. Edos which may be used for it are [[24edo]], [[29edo]], [[53edo]] and [[111edo]], with [[mos scale]]s of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales.


[[Subgroup]]: 2.3.13/5
[[Subgroup]]: 2.3.13/5
Line 403: Line 425:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[Tp tuning|subgroup]] [[WE]]: ~2 = 1199.9502{{c}}, ~26/15 = 951.0713{{c}}
* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1199.9502{{c}}, ~26/15 = 951.0713{{c}}
* [[Tp tuning|subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~26/15 = 951.0933{{c}}
* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~26/15 = 951.0933{{c}}


{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 29, 53, 82, 135 }}
{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 29, 53, 82, 135 }}
Line 412: Line 434:
; Music
; Music
* ''[[Desert Island Rain]]'' by [[Sevish]] – [https://web.archive.org/web/20201127013711/http://micro.soonlabel.com/gene_ward_smith/Others/Sevish/Sevish%20-%20Desert%20Island%20Rain.mp3 play] | [https://sevish.bandcamp.com/track/desert-island-rain Bandcamp] | [https://soundcloud.com/sevish/desert-island-rain SoundCloud] | [https://www.youtube.com/watch?v=Gcgawrr2xao YouTube] – in 313edo tuned Barbados[9]
* ''[[Desert Island Rain]]'' by [[Sevish]] – [https://web.archive.org/web/20201127013711/http://micro.soonlabel.com/gene_ward_smith/Others/Sevish/Sevish%20-%20Desert%20Island%20Rain.mp3 play] | [https://sevish.bandcamp.com/track/desert-island-rain Bandcamp] | [https://soundcloud.com/sevish/desert-island-rain SoundCloud] | [https://www.youtube.com/watch?v=Gcgawrr2xao YouTube] – in 313edo tuned Barbados[9]
=== Seventeen-cot ===
Seventeen-cot is a rank-2 temperament in the 2.3.13/5 and 2.3.11/5.13/5 subgroups. It tempers out the [[Tendoartisma]] in the 2.3.13/5 subgroup. It can be generated with a ~2/1 octave and a ~2250/2197 or ~169/165 generator which is a 17th of a ~3/2 perfect fifth. It can be described as the 29 & 146 temperament in these subgroups.
====2.3.13/5 subgroup====
Comma basis: {{monzo| -6 -11 17 }} (2.3.13/5)
edo join: 29 & 146
{{Mapping|legend=3| 1 1 1 | 0 17 11 }}
: mapping generators: ~2, ~2250/2197
Optimal tunings:
* WE: ~2 = 1200.0001354{{c}}, ~2250/2197 = 41.2914993{{c}}
: error map: {{val| +0.0001354 +0.0006234 -0.0073197}}
* CWE: ~2 = 2/1, ~2250/2197 = 41.2915011{{c}}
: error map: {{val| 0.0000000 +0.0005177 -0.0074359}}
edos: 29, 465, 494, 436, 523, 407, 378, 349, 30[-3], 28[+3], 320, 291, 59[-3], 262
Badness (Sintel): 0.064
====2.3.11/5.13/5 subgroup====
Comma basis: 225000/224939, 43940/43923
edo join: 29 & 146
{{Mapping|legend=3| 1 1 1 1 | 0 17 4 11 }}
: mapping generators: ~2, ~169/165
Optimal tunings:
* WE: ~2 = 1199.9934923{{c}}, ~169/165 = 41.2918271{{c}}
: error map: {{val| -0.0065077 -0.0004485 +0.1565720 -0.0103579}}
* CWE: ~2 = 2/1, ~169/165 = 41.2917463{{c}}
: error map: {{val| 0.0000000 +0.0046870 +0.1627569 -0.0043781}}
edos: 29, 465, 494, 436, 523, 407, 378, 349, 320, 291, 30[-3], 262, 28[+3], 233
Badness (Sintel): 0.080


=== Fiventeen ===
=== Fiventeen ===
Line 475: Line 456:
[[Subgroup]]: 2.3.19/7
[[Subgroup]]: 2.3.19/7


[[Comma list]]: [[57/56]] ({{Monzo| -3 1 1 }})
[[Comma list]]: [[57/56]] ({{monzo| -3 1 1 }})


{{Mapping|legend=3| 1 0 3 | 0 1 -1 }}
{{Mapping|legend=3| 1 0 3 | 0 1 -1 }}
Line 494: Line 475:


=== Commatose ===
=== Commatose ===
Commatose is a [[Dual-fifth temperaments|dual-fifth temperament]] which uses the Pythagorean comma as a generator. It was developed by [[Eliora]] to highlight the near-perfect expression of 9/8 by [[1789edo]], while at the same time the fact that it completely misses 3/2. It is described as the 460 & 1329 temperament. In the 13-limit extension 24 generators are equal to [[~]][[13/9]].
Commatose is a uses the Pythagorean comma as a generator. It was developed by [[Eliora]] to highlight the near-perfect expression of 9/8 by [[1789edo]], while at the same time the fact that it completely misses 3/2. It is described as the 460 & 1329 temperament. In the 13-limit extension 24 generators are equal to [[~]][[13/9]].


[[Subgroup]]: 2.9.5.7
[[Subgroup]]: 2.9.5.7
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[[Comma list]]: {{monzo| 28 -2 -19 8 }}, {{monzo| 9 -25 23 6 }}
[[Comma list]]: {{monzo| 28 -2 -19 8 }}, {{monzo| 9 -25 23 6 }}


{{Mapping|legend=3| 1 9 6 13 | 0 -298 -188 -521 }}
{{Mapping|legend=3| 1 -289 -182 -508 | 0 298 188 521 }}
: mapping generators: ~2, ~1048576/531441


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~531441/524288 = 23.4765
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9727{{c}}, ~1048576/531441 = 1176.4969{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~1048576/531441 = 1176.5236{{c}}


{{Optimal ET sequence|legend=1| 460, 869, 1329 }}
{{Optimal ET sequence|legend=1| 460, 869, 1329 }}


[[Badness]]: 0.611
[[Badness]] (Sintel): 30.9


==== 2.9.5.7.11 ====
==== 2.9.5.7.11 ====
Line 513: Line 497:
Comma list: {{monzo| -7 7 -3 2 -4 }}, {{monzo| 17 0 -13 1 3 }}, {{monzo| 11 -2 -6 7 -3 }}
Comma list: {{monzo| -7 7 -3 2 -4 }}, {{monzo| 17 0 -13 1 3 }}, {{monzo| 11 -2 -6 7 -3 }}


Sval mapping: {{mapping| 1 9 6 13 16 | 0 -298 -188 -521 -641 }}
{{Mapping|legend=2| 1 -289 -182 -508 -625 | 0 298 188 521 641 }}


Optimal tuning (CTE): ~2 = 1\1, ~531441/524288 = 23.4767
Optimal tunings:
* WE: ~2 = 1199.9833{{c}}, ~531441/524288 = 1176.5070{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~531441/524288 = 1176.5234{{c}}


{{Optimal ET sequence|legend=1| 460, 869e, 1329, 1789, 3118 }}
{{Optimal ET sequence|legend=0| 460, 869e, 1329, 1789, 3118 }}


Badness: 0.165
Badness (Sintel): 8.67


==== 2.9.5.7.11.13 ====
==== 2.9.5.7.11.13 ====
Line 526: Line 512:
Comma list: 123201/123200, 1016064/1015625, 2250423/2249390, 2599051/2598156
Comma list: 123201/123200, 1016064/1015625, 2250423/2249390, 2599051/2598156


Sval mapping: {{mapping| 0 9 6 13 16 10 | -298 -188 -521 -641 -322 }}
{{Mapping|legend=2| 0 -289 -182 -508 -625 -312 | 0 298 188 521 641 322 }}


Optimal tuning (CTE): ~2 = 1\1, ~3575/3528 = 23.4767
Optimal tunings:
* WE: ~2 = 1200.0000{{c}}, ~7056/3575 = 23.4767{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7056/3575 = 23.4767{{c}}


{{Optimal ET sequence|legend=1| 460, 869e, 1329, 1789, 3118 }}
{{Optimal ET sequence|legend=0| 460, 869e, 1329, 1789, 3118 }}


Badness: 0.0564
Badness (Sintel): 3.30


=== Daemotertiaschis ===
=== Daemotertiaschis ===
{{See also|Schismatic family#Tertiaschis}}
{{See also|Schismatic family #Tertiaschis}}
Daemotertiaschis is produced by taking every other generator of tertiaschis, and the subgroup is chosen so it tempers out exactly the same commas. It is notable due to offering a [[7L 4s|daemotonic 7L 4s]] scale of reasonable hardness (hence the name ― daemo- + tertiaschis), which is notoriously difficult to approximate with simple JI or RTT methods.
 
Daemotertiaschis is produced by taking every other generator of tertiaschis, and the subgroup is chosen so it tempers out exactly the same commas. It is notable due to offering a [[7L 4s|daemotonic 7L 4s]] scale of reasonable hardness (hence the name – daemo- + tertiaschis), which is notoriously difficult to approximate with simple JI or RTT methods.


Subgroup: 2.9.5.7.33.13.17
Subgroup: 2.9.5.7.33.13.17
Line 542: Line 531:
Comma list: 325/324, 375/374, 385/384, 595/594, 10985/10976
Comma list: 325/324, 375/374, 385/384, 595/594, 10985/10976


{{Mapping|legend=2|1 1 11 -16 13 -18 20|0 3 -12 26 -11 30 -22}}
{{Mapping|legend=2| 1 1 11 -16 13 -18 20 | 0 3 -12 26 -11 30 -22 }}
: mapping generators: ~2, ~33/20
 
Optimal tunings:
* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1200.3019{{c}}, 33/20 = 868.1949{{c}}
* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, 33/20 = 867.9773{{c}}


Optimal tuning (CTE): ~2 = 1\1, 33/20 = 867.982
{{Optimal ET sequence|legend=1| 47, 159, 206, 253, 459* }}


[[Support]]ing [[ET]]s: {{Optimal ET sequence|47, 65f, 112, 159, 206, 253}}
Badness (Sintel): 0.439


=== Baldy ===
=== Baldy ===
{{See also|Schismatic family #Garibaldi}}
{{See also| Chromatic pairs #Baldy }}
{{See also|No-threes subgroup temperaments #Frostburn}}


Baldy results from taking every other generator of the [[garibaldi]] temperament. One of the best extension is 2.9.5.7.13 subgroup with mapping 13/8 to +10 whole tones, as well as the cassandra temperament.
Baldy is every other step of [[schismatic family #Garibaldi|garibaldi]]. It is also the add-9 extension of [[no-threes subgroup temperaments #Frostburn|frostburn]]. One of the best extension is to the 2.9.5.7.13 subgroup, mapping 13/8 to +10 whole tones, the same as the cassandra temperament.


[[Subgroup]]: 2.9.5.7
[[Subgroup]]: 2.9.5.7
Line 558: Line 551:
[[Comma list]]: 225/224, 3125/3087
[[Comma list]]: 225/224, 3125/3087


{{Mapping|legend=3| 1 3 3 4 | 0 1 -4 -7 }}
{{Mapping|legend=3| 1 0 15 25 | 0 1 -4 -7 }}
: mapping generators: ~2, ~9


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 204.170
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.1233{{c}}, ~9/8 = 204.1913{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/8 = 204.1549{{c}}


{{Optimal ET sequence|legend=1| 6, 29, 35, 41, 47 }}
{{Optimal ET sequence|legend=1| 6, 29, 35, 41, 47, 194 }}


Related temperament: [[Schismatic family #Garibaldi|Garibaldi]]
[[Badness]] (Sintel): 0.274


==== 2.9.5.7.13 ====
==== 2.9.5.7.13 subgroup ====
{{See also|Chromatic pairs #Baldy}}
Subgroup: 2.9.5.7.13


Baldy is every other step of [[garibaldi]], without the mapping of prime 11. It can be described as the 6 &amp; 35 temperament.
Comma list: 225/224, 325/324, 640/637


[[Subgroup]]: 2.9.5.7.13
{{Mapping|legend=2| 1 0 15 25 -28 | 0 1 -4 -7 10 }}


[[Comma list]]: [[225/224]], [[325/324]], [[640/637]]
{{Mapping|legend=4| 1 0 15 25 0 28 | 0 1/2 -4 -7 0 10 }}


{{Mapping|legend=3| 1 0 15 25 -28 | 0 1 -4 -7 10 }}
Optimal tunings:
 
* WE: ~2 = 1200.0155{{c}}, ~9/8 = 204.0931{{c}}
{{Mapping|legend=5| 1 3/2 3 4 0 2 | 0 1/2 -4 -7 0 10 }}
* CWE: ~2 = 1200.0000{{c}}, ~9/8 = 204.0902{{c}}
 
: [[gencom]]: [2 9/8; 225/224 325/324 640/637]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 204.090


{{Optimal ET sequence|legend=1| 6, 11, 17, 23, 29, 35, 41, 47, 100, 147, 488cd, 635cd }}
{{Optimal ET sequence|legend=0| 6, 35, 41, 47, 100, 147 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.5999 cents
Badness (Sintel): 0.386


Related temperament: [[Schismatic family #Garibaldi|Cassandra]]
RMS error: 0.5999 cents


==== Baldanders ====
==== Baldanders ====
Baldanders results from taking every other generator of the andromeda, with mapping 11/8 to -9 whole tones.
Baldanders results from taking every other generator of the [[schismatic family #Andromeda|andromeda]], mapping 11/8 to -9 whole tones.


Subgroup: 2.9.5.7.11
Subgroup: 2.9.5.7.11
Line 596: Line 588:
Comma list: 100/99, 225/224, 245/242
Comma list: 100/99, 225/224, 245/242


{{Mapping|legend=3| 1 3 3 4 5 | 0 1 -4 -7 -9 }}
{{Mapping|legend=2| 1 0 15 25 32 | 0 1 -4 -7 -9 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/8 = 204.743
Optimal tunings:
* WE: ~2 = 1200.1917{{c}}, ~9/8 = 204.7755{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~9/8 = 204.7197{{c}}


{{Optimal ET sequence|legend=1| 6, 23de, 29, 35, 41 }}
{{Optimal ET sequence|legend=0| 6, 23de, 29, 35, 41 }}


Related temperament: [[Schismatic family #Garibaldi|Andromeda]]
Badness (Sintel): 0.389


===== 2.9.5.7.11.13 =====
===== 2.9.5.7.11.13 =====
Line 609: Line 603:
Comma list: 100/99, 144/143, 225/224, 245/242
Comma list: 100/99, 144/143, 225/224, 245/242


{{Mapping|legend=3| 1 3 3 4 5 2 | 0 1 -4 -7 -9 10 }}
{{Mapping|legend=2| 1 0 15 25 32 -28 | 0 1 -4 -7 -9 10 }}
 
Optimal tunings:
* WE: ~2 = 1199.6385{{c}}, ~9/8 = 204.3526{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~9/8 = 204.4234{{c}}


Optimal tuning (POTE): ~2 = 1\1, ~9/8 = 204.414
{{Optimal ET sequence|legend=0| 6, 35, 41, 47, 88e }}


{{Optimal ET sequence|legend=1| 6, 23def, 29f, 35, 41, 47 }}
Badness (Sintel): 0.653


=== Glacial ===
=== Glacial ===
Line 635: Line 633:


Music:
Music:
* ''[[Thundersnow]]'' - [[Sevish]] (2021)
* ''[[Thundersnow]]'' by [[Sevish]] (2021)


=== Mabon ===
=== Mabon ===
Retrieved from "https://en.xen.wiki/w/Subgroup_temperaments"