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Subgroup temperaments: Difference between revisions

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== 2.5/3… subgroups ==
== 2.5/3… subgroups ==


=== Greeley ===
=== Magicaltet ===
{{See also| Chromatic pairs #Magicaltet }}
 
Magicaltet is related to [[supermagic]], [[superkleismic]], and [[magic]].
 
[[Subgroup]]: 2.5/3.7.11
 
[[Comma list]]: 100/99 = {{monzo| 2 2 0 -1 }}, 385/384 = {{monzo| -7 1 1 1 }}
 
{{Mapping|legend=2| 1 0 5 2 | 0 1 -3 2 }}
 
: mapping generators: ~2, ~5/3
 
{{Mapping|legend=3| 1 -1/2 1/2 2 4 | 0 1/2 -1/2 3 -2 }}
 
: [[gencom]]: [2 6/5; 100/99 385/384]
 
[[Optimal tuning]]s:
* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1\1, ~5/3 = 877.3426
* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1\1, ~5/3 = 877.351
 
{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 67, 93* }}
 
<nowiki>*</nowiki> wart for 5/3
 
[[Tp tuning #T2 tuning|RMS error]]: 1.206 cents
 
=== Starlingtet ===
{{See also | Chromatic pairs #Starlingtet }}
 
Starlingtet, the 4 &amp; 15 temperament in the 2.5/3.7/3 subgroup, is related to [[starling]] as well as to [[myna]].
 
[[Subgroup]]: 2.5/3.7/3
 
[[Comma list]]: [[126/125]]
 
{{Mapping|legend=2| 1 0 -1 | 0 1 3 }}
 
{{Mapping|legend=3| 1 -1 0 1 | 0 4/3 1/3 -5/3 }}
 
: [[gencom]]: [2 6/5; 126/125]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 311.154
 
{{Optimal ET sequence|legend=1| 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.8398 cents
 
==== Greeley ====
{{See also| Chromatic pairs #Greeley }}
 
Related temperaments: [[Porcupine family #Opossum|Opossum]], [[Starling temperaments #Nusecond|Nusecond]]
Related temperaments: [[Porcupine family #Opossum|Opossum]], [[Starling temperaments #Nusecond|Nusecond]]


Line 838: Line 888:


[[Tp tuning#T2 tuning|RMS error]]: 1.034 cents
[[Tp tuning#T2 tuning|RMS error]]: 1.034 cents
==== Skateboard ====
{{See also| Chromatic pairs #Skateboard }}
Skateboard is related to [[thrasher]].
[[Subgroup]]: 2.5/3.7/3.11.13/9
[[Comma list]]: 56/55, 91/90, 100/99
{{Mapping|legend=2| 1 0 -1 2 2 | 0 1 3 2 -2 }}
{{Mapping|legend=3| 1 -3/7 4/7 11/7 4 -6/7 | 0 0 -1 -3 -2 2 }}
: [[gencom]]: [2 6/5; 56/55 91/90 100/99]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 313.842
{{Optimal ET sequence|legend=1| 11, 15, 19, 23, 42d, 65d }}
[[Tp tuning #T2 tuning|RMS error]]: 2.396 cents
=== Indium ===
{{See also | Chromatic pairs #Indium }}
Indium can be described as the 8 &amp; 33 temperament in the 2.5/3.7/3.11/3 subgroup.
[[Subgroup]]: 2.5/3.7/3.11/3
[[Comma list]]: [[3025/3024]], [[3125/3087]]
{{Mapping|legend=2| 1 0 0 2 | 0 6 10 -1 }}
{{Mapping|legend=3| 1 -1/2 -1/2 -1/2 3/2 | 0 -15/4 9/4 25/4 -19/4 }}
: [[gencom]]: [2 12/11; 3025/3024 3125/3087]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~12/11 = 147.010
{{Optimal ET sequence|legend=1| 33, 41, 49, 57, 106, 204, 253 }}
[[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents
=== Semidim ===
{{See also| Chromatic pairs #Semidim }}
Semidim can be described as the 8 &amp; 29 temperament in the 2.5/3.7/3.11/3.13/3 subgroup.
[[Subgroup]]: 2.5/3.7/3.11/3.13/3
[[Comma list]]: [[121/120]], [[169/168]], [[275/273]]
{{Mapping|legend=2| 1 3 5 3 4 | 0 -6 -10 -3 -5 }}
{{Mapping|legend=3| 1 -3 0 2 0 1 | 0 24/5 -6/5 -26/5 9/5 -1/5 }}
: [[gencom]]: [2 13/10; 121/120 169/168 275/273]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 453.242
{{Optimal ET sequence|legend=1| 5, 8, 13, 21, 29, 37, 44, 45, 188bde }}
[[Tp tuning #T2 tuning|RMS error]]: 1.052 cents
=== Gariberttet ===
{{See also | Chromatic pairs #Gariberttet }}
Gariberttet can be described as the 4 &amp; 29 temperament in the 2.5/3.7/3.13/11 subgroup.
[[Subgroup]]: 2.5/3.7/3.13/11
[[Comma list]]: [[275/273]], [[847/845]]
{{Mapping|legend=2| 1 0 0 0 | 0 3 5 1 }}
{{Mapping|legend=3| 1 0 0 0 0 0 | 0 -8/3 1/3 7/3 -1/2 1/2 }}
: [[gencom]]: [2 13/11; 275/273 847/845]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/11 = 293.679
{{Optimal ET sequence|legend=1| 29, 33, 37, 41, 45, 49, 78, 94, 143d, 237bd, 380bd }}
[[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents
=== Sentry ===
{{See also | Chromatic pairs #Sentry }}
Sentry, the 3 &amp; 5 temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].
[[Subgroup]]: 2.5/3.9/7
[[Comma list]]: [[245/243]]
{{Mapping|legend=2| 1 0 0 | 0 2 1 }}
{{Mapping|legend=3| 1 0 0 0 | 0 0 2 -1 }}
: [[gencom]]: [2 9/7; 245/243]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~9/7 = 440.902
{{Optimal ET sequence|legend=1| 8, 11, 19, 30, 41, 49, 52, 145b, 166c, 197bc, 215c, 264bc }}
[[Tp tuning #T2 tuning|RMS error]]: 0.7105 cents
=== Marveltwintri ===
{{See also| Chromatic pairs #Marveltwintri }}
Marveltwintri can be described as the 3 &amp; 4 temperament in the 2.5/3.13/9 subgroup.
[[Subgroup]]: 2.5/3.13/9
[[Comma list]]: [[325/324]]
{{Mapping|legend=2| 1 0 2 | 0 1 -2 }}
{{Mapping|legend=3| 1 -1/6 5/6 0 0 -1/3 | 0 -1/2 -3/2 0 0 1 }}
: [[gencom]]: [2 6/5; 325/324]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 317.139
{{Optimal ET sequence|legend=1| 11, 15, 19, 34, 53, 87, 140, 185, 219, 253, 287b, 321b }}
[[Tp tuning #T2 tuning|RMS error]]: 0.2444 cents
== 2.….7/3… subgroups ==
=== Guanyintet ===
{{See also | Chromatic pairs #Guanyintet }}
Guanyintet, the 4 &amp; 9 temperament in the 2.5.7/3.11/3 subgroup, is related to [[guanyin]] as well as to [[orwell]].
[[Subgroup]]: 2.5.7/3.11/3
[[Comma list]]: [[176/175]], [[540/539]]
{{Mapping|legend=2| 1 0 2 -2 | 0 3 -1 5 }}
{{Mapping|legend=3| 1 -4/3 3 -1/3 5/3 | 0 4/3 -3 7/3 -11/3 }}
: [[gencom]]: [2 7/6; 176/175 540/539]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 270.093
{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 89, 191bc, 227bc, 231bc, 271bc, 311bc, 316bcd }}
[[Tp tuning #T2 tuning|RMS error]]: 0.6028 cents
==== Laz ====
{{See also | Chromatic pairs #Laz }}
Laz is related to [[georgian]] as well as to [[winston]].
[[Subgroup]]: 2.5.7/3.11/3.13/3
[[Comma list]]: [[144/143]], [[176/175]], [[196/195]]
{{Mapping|legend=2| 1 0 2 -2 6 | 0 3 -1 5 -5 }}
{{Mapping|legend=3| 1 -5/4 3 -1/4 7/4 -1/4 | 0 -1/4 -3 3/4 -21/4 19/4 }}
: [[gencom]]: [2 7/6; 144/143 176/175 196/195]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 269.300
{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 58, 156bde, 205bde }}
[[Tp tuning #T2 tuning|RMS error]]: 0.8790 cents
=== Kryptonite ===
{{See also| Chromatic pairs #Kryptonite }}
Kryptonite is related to [[krypton]].
[[Subgroup]]: 2.5.7/3.11/3.13/3
[[Comma list]]: 56/55, 78/77, 91/90
{{Mapping|legend=2| 1 2 1 2 2 | 0 -3 -2 1 -1 }}
{{Mapping|legend=3| 1 -5/4 2 -1/4 3/4 3/4 | 0 -1/2 3 3/2 -3/2 1/2 }}
: [[gencom]]: [2 13/12; 56/55 78/77 91/90]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/12 = 132.428
{{Optimal ET sequence|legend=1| 9, 63, 82bd, 91bde }}
[[Tp tuning #T2 tuning|RMS error]]: 2.545 cents
=== Kiribati ===
{{See also| Chromatic pairs #Kiribati }}
Kiribati is related to [[nakika]] as well as to [[octacot]].
[[Subgroup]]: 2.9/5.7/3.11/9
[[Comma list]]: 100/99, 245/242
{{Mapping|legend=2| 1 1 1 0 | 0 -2 3 4 }}
{{Mapping|legend=3| 1 1/10 -4/5 11/10 1/5 | 0 -3/2 -1 3/2 1 }}
: [[gencom]]: [2 21/20; 100/99 245/242]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~21/20 = 87.892
{{Optimal ET sequence|legend=1| 13, 14, 27, 41, 55, 191bd, 232bcd, 273bcd }}
[[Tp tuning #T2 tuning|RMS error]]: 1.245 cents
=== Mothwelltri ===
{{See also| Chromatic pairs #Mothwelltri }}
Mothwelltri, the 1 &amp; 4 temperament in the 2.7/3.11 subgroup, is related to [[orwell]].
[[Subgroup]]: 2.7/3.11
[[Comma list]]: [[99/98]]
{{Mapping|legend=2| 1 0 1 | 0 1 2 }}
{{Mapping|legend=3| 1 -1/2 0 1/2 3 | 0 -1/2 0 1/2 2 }}
: [[gencom]]: [2 7/6; 99/98]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 273.174
{{Optimal ET sequence|legend=1| 9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc }}
[[Tp tuning #T2 tuning|RMS error]]: 1.064 cents


== 2.….9/7… subgroups ==
== 2.….9/7… subgroups ==


=== Marveltri ===
=== Marveltri ===
Marveltri, the 3 &amp; 13 temperament in the 2.5.9/7 subgroup, is related to marvel, magic, and the unnamed 22 &amp; 47 temperament.  
{{See also| Chromatic pairs #Marveltri }}
 
Marveltri, the 3 &amp; 13 temperament in the 2.5.9/7 subgroup, is related to [[marvel]], [[magic]], and the unnamed 22 &amp; 47 temperament.  


[[Subgroup]]: 2.5.9/7
[[Subgroup]]: 2.5.9/7
Line 893: Line 1,179:


== 2.….7/5… subgroups ==
== 2.….7/5… subgroups ==
=== Hydrothermal ===
=== Hydrothermal ===
A tuning whose distinctively sharp (but still consonant) fifth, and flat (but still consonant) octave, lend it a mysterious, heavy atmosphere. The 6-tone (hexatonic) MOS is melodically interesting and flavorful. The 18-tone MOS is a useful 'chromatic' scale for taking subsets of.
A tuning whose distinctively sharp (but still consonant) fifth, and flat (but still consonant) octave, lend it a mysterious, heavy atmosphere. The 6-tone (hexatonic) MOS is melodically interesting and flavorful. The 18-tone MOS is a useful 'chromatic' scale for taking subsets of.
Line 905: Line 1,192:


[[Support]]ing [[ET]]s: {{EDOs|4, 6, 8, 10, 18, 28, 46, 64, 110}}
[[Support]]ing [[ET]]s: {{EDOs|4, 6, 8, 10, 18, 28, 46, 64, 110}}
=== Edson ===
{{See also| Chromatic pairs #Edson }}
Edson is related to [[pele]] and [[andromeda]].
[[Subgroup]]: 2.3.7/5.11/5.13/5
[[Comma list]]: [[196/195]] = {{monzo| 2 -1 2 0 -1 }}, [[352/351]] = {{monzo| 5 -3 0 1 -1 }}, [[364/363]] = {{monzo| 2 -1 1 -2 1 }}
{{Mapping|legend=2| 1 0 10 17 22 | 0 1 -6 -10 -13 }}
: mapping generators: ~2, ~3
{{Mapping|legend=3| 1 1 -5 -1 2 4 | 0 1 29/4 5/4 -11/4 -23/4 }}
: [[gencom]]: [2 3/2; 196/195, 352/351, 364/363]
[[Optimal tuning]]s:
* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1\1, ~3/2 = 703.4398
* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1\1, ~3/2 = 703.414
{{Optimal ET sequence|legend=1| 12, 17, 29 }}
[[Tp tuning #T2 tuning|RMS error]]: 0.5102 cents
=== Haumea ===
{{See also| Chromatic pairs #Haumea }}
Related temperaments include [[bridgetown]], [[namaka]], [[hemigari]], [[barbados]], and [[parizekmic]].
[[Subgroup]]: 2.3.7/5.11/5.13/5
[[Comma list]]: [[352/351]], [[676/675]], [[847/845]]
{{Mapping|legend=2| 1 0 10 -6 -1 | 0 2 -12 9 3 }}
{{Mapping|legend=3| 1 2 -3/4 -11/4 9/4 5/4 | 0 -2 0 12 -9 -3 }}
: [[gencom]]: [2 15/13; 352/351 676/675 847/845]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.491
{{Optimal ET sequence|legend=1| 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd }}
[[Tp tuning #T2 tuning|RMS error]]: 0.2668 cents


=== Historical ===
=== Historical ===
Line 919: Line 1,252:


[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents
=== Terrain ===
{{See also| Chromatic pairs #Terrain }}
Terrain, the 6 &amp; 21 temperament in the 2.7/5.9/5 subgroup, is related to [[domain (temperament)|domain]]. It is a remarkable temperament, in that while its complexity is low, it has no discernible error. The 1–7/5–9/5 and 1–9/7–9/5 chords are characteristic.
[[Subgroup]]: 2.7/5.9/5
[[Comma list]]: [[250047/250000]]
{{Mapping|legend=2| 3 4 0 | 0 -1 1 }}
{{Mapping|legend=3| 3 10/9 -7/9 2/9 | 0 -2/3 -1/3 2/3 }}
: [[gencom]]: [63/50 10/9; 250047/250000]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~63/50 = 1\3, ~10/9 = 182.461
{{Optimal ET sequence|legend=1| 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558 }}
[[Tp tuning #T2 tuning|RMS error]]: 0.00844 cents
=== Tridec ===
{{See also| Chromatic pairs #Tridec }}
Tridec, the 5 &amp; 8 temperament in the 2.7/5.11/5.13/5 subgroup, extends [[#Petrtri]].
[[Subgroup]]: 2.7/5.11/5.13/5
[[Comma list]]: [[847/845]], [[1001/1000]]
{{Mapping|legend=2| 1 2 0 1 | 0 -4 3 1 }}
{{Mapping|legend=3| 1 0 -3/4 5/4 -3/4 1/4 | 0 0 0 -4 3 1 }}
: [[gencom]]: [2 13/10; 847/845 1001/1000]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 454.556
{{Optimal ET sequence|legend=1| 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc }}
[[Tp tuning #T2 tuning|RMS error]]: 0.1613 cents


== 2.….11/5… subgroups ==
== 2.….11/5… subgroups ==
=== Bridgetown ===
{{See also| Chromatic pairs #Bridgetown }}
Bridgetown, the 5 &amp; 24 temperament in the 2.3.11/5.13/5 subgroup, is related to [[haumea]] and [[barbados]].
[[Subgroup]]: 2.3.11/5.13/5
[[Comma list]]: [[352/351]], [[676/675]]
{{Mapping|legend=2| 1 0 -6 -1 | 0 2 9 3 }}
{{Mapping|legend=3| 1 2 -5/3 0 4/3 1/3 | 0 -2 4 0 -5 1 }}
: [[gencom]]: [2 15/13; 352/351 676/675]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.399
{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314 }}
[[Tp tuning #T2 tuning|RMS error]]: 0.2513 cents
=== Petrtri ===
{{See also| Chromatic pairs #Petrtri }}
Petrtri can be described as 3 &amp; 5 temperament in the 2.11/5.13/5 subgroup.
[[Subgroup]]: 2.11/5.13/5
[[Comma list]]: [[2200/2197]]
{{Mapping|legend=2| 1 0 1| 0 3 1 }}
{{Mapping|legend=3| 1 0 -1/3 0 -1/3 2/3 | 0 0 -4/3 0 5/3 -1/3 }}
: [[gencom]]: [2 13/10; 2200/2197]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 455.012
{{Optimal ET sequence|legend=1| 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c }}
[[Tp tuning #T2 tuning|RMS error]]: 0.0749 cents
=== Hypnosis ===
=== Hypnosis ===
Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]]
Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]]
Line 939: Line 1,357:
=== Pepperoni ===
=== Pepperoni ===
{{Main| Parapyth }}
{{Main| Parapyth }}
{{See also| Chromatic pairs #Pepperoni }}


Pepperoni is the 5 &amp; 12 temperament in the 2.3.11/7.13/7 subgroup. The [[Peppermint-24|Pepper fifth]], which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.
Pepperoni is generated by a fifth and can be described as the 5 &amp; 12 temperament in the 2.3.11/7.13/7 subgroup. It is the single-chain retraction of [[parapyth]]. The [[Peppermint-24|Pepper fifth]], which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.


[[Subgroup]]: 2.3.11/7.13/7
[[Subgroup]]: 2.3.11/7.13/7
Line 978: Line 1,397:
<nowiki>*</nowiki> wart for 3/2
<nowiki>*</nowiki> wart for 3/2


=== Oceanfront ===
==== Tobago ====
Related temperaments: [[Archytas clan #Superpyth|superpyth]], [[Archytas clan #Ultrapyth|ultrapyth]]
{{See also| Chromatic pairs #Tobago }}
 
Tobago, the 10 &amp; 14 temperament in the 2.3.11.13/5 subgroup, extends [[neutral]] and [[barbados]].
 
[[Subgroup]]: 2.3.11.13/5


[[Subgroup]]: 2.3.7.13/5
[[Comma list]]: [[243/242]], [[676/675]]


[[Comma list]]: 64/63, 91/90
{{Mapping|legend=2| 2 0 -1 -2 | 0 2 5 3 }}


{{Mapping|legend=2| 1 0 6 -5 | 0 1 -2 4 }}
{{Mapping|legend=3| 2 4 -2 0 9 2 | 0 -2 3/2 0 -5 -3/2 }}


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 713.910
: [[gencom]]: [55/39 15/13; 243/242 676/675]


{{Optimal ET sequence|legend=1| 5, 22, 27, 32, 37 }}
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~55/39 = 1\2, ~15/13 = 249.312


[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents
{{Optimal ET sequence|legend=1| 10, 14, 24, 58, 82, 130 }}


Scales: [[Oceanfront scales]]
[[Tp tuning #T2 tuning|RMS error]]: 0.3533 cents


=== Pakkanian hemipyth ===
==== Pakkanian hemipyth ====


[[Subgroup]]: 2.3.11.13/5.17  
[[Subgroup]]: 2.3.11.13/5.17  
Line 1,010: Line 1,433:


<nowiki>*</nowiki> wart for 13/5
<nowiki>*</nowiki> wart for 13/5
=== Oceanfront ===
Related temperaments: [[Archytas clan #Superpyth|superpyth]], [[Archytas clan #Ultrapyth|ultrapyth]]
[[Subgroup]]: 2.3.7.13/5
[[Comma list]]: 64/63, 91/90
{{Mapping|legend=2| 1 0 6 -5 | 0 1 -2 4 }}
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 713.910
{{Optimal ET sequence|legend=1| 5, 22, 27, 32, 37 }}
[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents
Scales: [[Oceanfront scales]]


== 2.….49/5… subgroups ==
== 2.….49/5… subgroups ==
Retrieved from "https://en.xen.wiki/w/Subgroup_temperaments"