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{{Technical data page}}
{{Technical data page}}
The '''compton family''', otherwise known as the '''aristoxenean family''', of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[Pythagorean comma]] ([[ratio]]: 531441/524288, {{monzo|legend=1| -19 12 }}, and hence the fifths form a closed 12-note [[circle of fifths]], identical to [[12edo]]. While the tuning of the fifth will be that of 12edo, two [[cent]]s flat, the tuning of the larger primes is not so constrained, and the point of these temperaments is to improve on it.
The '''compton family''', otherwise known as the '''aristoxenean family''', of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[Pythagorean comma]] ([[ratio]]: 531441/524288, {{monzo|legend=1| -19 12 }}, and hence the fifths form a closed 12-note [[circle of fifths]], identical to [[12edo]]. While the tuning of the fifth is fixed to 7 steps of 12edo, about 2{{cent}} flat of [[just]], these temperaments aim to add tunings for higher primes which are more in tune than in 12edo.


== Compton ==
== Compton ==
{{Main| Compton }}
{{Main| Compton }}


5-limit compton is also known as ''aristoxenean''. It tempers out the Pythagorean comma and has a period of 1\12, so it is the 12edo circle of fifths with an independent dimension for the harmonic 5. Equivalent generators are [[5/4]], [[6/5]], [[10/9]], [[16/15]] (the [[secor]]), [[45/32]], [[135/128]] and most importantly, [[81/80]]. In terms of [[equal temperament]]s, it is the {{nowrap| 12 & 72 }} temperament, and [[72edo]], [[84edo]] or [[240edo]] make for good tunings.  
5-limit compton tempers out the Pythagorean comma and has a period of 1\12, so it is the 12edo circle of fifths with an independent dimension for the harmonic 5. Equivalent generators are [[5/4]], [[6/5]], [[10/9]], [[16/15]] (the [[secor]]), [[45/32]], [[135/128]] and most importantly, [[81/80]]. In terms of [[equal temperament]]s, compton is the {{nowrap| 12 & 72 }} temperament; its [[ploidacot]] is dodecaploid acot. [[72edo]], [[84edo]] or [[240edo]] make for good tunings.
 
This temperament is documented as ''aristoxenean'' in [[Tonalsoft Encyclopedia]].  


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 20: Line 22:
* [[CWE]]: ~256/243 = 100.0000{{c}}, ~5/4 = 385.3590{{c}} (~81/80 = 14.6410{{c}})
* [[CWE]]: ~256/243 = 100.0000{{c}}, ~5/4 = 385.3590{{c}} (~81/80 = 14.6410{{c}})
: error map: {{val| 0.000 -1.955 -0.955 }}
: error map: {{val| 0.000 -1.955 -0.955 }}
<!-- * [[CTE]]: ~256/243 = 100.000{{c}}, ~5/4 = 386.314{{c}} (~81/80 = 13.686{{c}})
: [[error map]]: {{val| 0.000 -1.955 0.000 }}
* [[POTE]]: ~256/243 = 100.000{{c}}, ~5/4 = 384.884{{c}} (~81/80 = 15.116{{c}})
: error map: {{val| 0.000 -1.955 -1.431 }} -->


{{Optimal ET sequence|legend=1| 12, 48, 60, 72, 84, 156, 240, 396b, 636bbc }}
{{Optimal ET sequence|legend=1| 12, 48, 60, 72, 84, 156, 240, 396b, 636bbc }}
Line 32: Line 30:
{{Main| Compton }}
{{Main| Compton }}


Septimal compton is also known as ''waage''. In terms of the normal list, compton adds 413343/409600 ({{monzo| -14 10 -2 1 }}) to the Pythagorean comma; however, it can also be characterized by saying it adds [[225/224]].  
In terms of the [[normal forms #Normal forms for commas|normal comma list]], septimal compton adds 413343/409600 ({{monzo| -14 10 -2 1 }}) to the Pythagorean comma; however, it can also be characterized by saying it adds [[225/224]]. Other important commas of this temperament are 250047/250000, the [[landscape comma]], which sets [[63/50]] to 1/3 of an octave, and 390625/388962, the [[dimcomp comma]], which sets [[25/21]] to 1/4 of an octave.
 
In either the 5- or 7-limit, 240edo is an excellent tuning, with [[81/80]] coming in at 15 cents exactly. In the 12edo, the major third is sharp by 13.686 cents, and the minor third flat by 15.641 cents; adjusting these down and up by 15 cents puts them in excellent tune.  


In either the 5- or 7-limit, 240edo is an excellent tuning, with 81/80 coming in at 15 cents exactly. In the 12edo, the major third is sharp by 13.686 cents, and the minor third flat by 15.641 cents; adjusting these down and up by 15 cents puts them in excellent tune.
Septimal compton is catalogued as ''waage'' in [[Graham Breed]]'s [https://x31eq.com/temper/ temperament finder].  


In terms of the normal comma list, we may add 8019/8000 to get to the 11-limit version of compton, which also adds [[441/440]]. For this 72edo can be recommended as a tuning. In 11-limit compton, intervals of 5 are off by one generator, intervals of 7 are off by two generators, and intervals of 11 are off by 3 generators.  
In terms of the normal comma list, we may add [[8019/8000]] to get to the 11-limit version of compton, which also adds [[441/440]] and has a natural extension to the 13-limit. In 13-limit compton, intervals of 5, 7, 11, and 13 are off by one, two, three, and four generators, respectively. For these, 72edo can be recommended as a tuning.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 49: Line 49:
* [[CWE]]: ~256/243 = 100.0000{{c}}, ~5/4 = 384.1429{{c}} (~126/125 = 15.8571{{c}})
* [[CWE]]: ~256/243 = 100.0000{{c}}, ~5/4 = 384.1429{{c}} (~126/125 = 15.8571{{c}})
: error map: {{val| 0.000 -1.955 -2.171 -0.540 }}
: error map: {{val| 0.000 -1.955 -2.171 -0.540 }}
<!-- * [[CTE]]: ~200/189 = 100.000{{c}}, ~5/4 = 384.922{{c}} (~126/125 = 15.078{{c}})
: [[error map]]: {{val| 0.000 -1.955 -1.392 -1.017 }}
* [[POTE]]: ~200/189 = 100.000{{c}}, ~5/4 = 383.775{{c}} (~126/125 = 16.225{{c}})
: error map: {{val| 0.000 -1.955 -2.538 -1.275 }} -->


{{Optimal ET sequence|legend=1| 12, …, 60, 72, 228, 300c, 372bc, 444bc }}
{{Optimal ET sequence|legend=1| 12, …, 60, 72, 228, 300c, 372bc, 444bc }}
Line 68: Line 64:
* WE: ~35/33 = 100.0633{{c}}, ~5/4 = 383.5087{{c}} (~100/99 = 16.7446{{c}})
* WE: ~35/33 = 100.0633{{c}}, ~5/4 = 383.5087{{c}} (~100/99 = 16.7446{{c}})
* CWE: ~35/33 = 100.0000{{c}}, ~5/4 = 383.5958{{c}} (~100/99 = 16.4042{{c}})
* CWE: ~35/33 = 100.0000{{c}}, ~5/4 = 383.5958{{c}} (~100/99 = 16.4042{{c}})
<!-- * CTE: ~35/33 = 100.000{{c}}, ~5/4 = 384.324{{c}} (~100/99 = 15.676{{c}})
* POTE: ~35/33 = 100.000{{c}}, ~5/4 = 383.266{{c}} (~100/99 = 16.734{{c}}) -->


{{Optimal ET sequence|legend=0| 12, …, 60e, 72 }}
{{Optimal ET sequence|legend=0| 12, …, 60e, 72 }}
Line 85: Line 79:
* WE: ~35/33 = 100.0508{{c}}, ~5/4 = 384.1577{{c}} (~100/99 = 16.0454{{c}})
* WE: ~35/33 = 100.0508{{c}}, ~5/4 = 384.1577{{c}} (~100/99 = 16.0454{{c}})
* CWE: ~35/33 = 100.0000{{c}}, ~5/4 = 384.1782{{c}} (~100/99 = 15.8218{{c}})
* CWE: ~35/33 = 100.0000{{c}}, ~5/4 = 384.1782{{c}} (~100/99 = 15.8218{{c}})
<!-- * CTE: ~35/33 = 100.000{{c}}, ~5/4 = 384.685{{c}} (~105/104 = 15.315{{c}})
* POTE: ~35/33 = 100.000{{c}}, ~5/4 = 383.963{{c}} (~105/104 = 16.037{{c}}) -->


{{Optimal ET sequence|legend=0| 12f, …, 60eff, 72, 228f }}
{{Optimal ET sequence|legend=0| 12f, …, 60eff, 72, 228f }}
Line 102: Line 94:
* WE: ~18/17 = 100.0658{{c}}, ~5/4 = 384.0024{{c}} (~100/99 = 16.2607{{c}})
* WE: ~18/17 = 100.0658{{c}}, ~5/4 = 384.0024{{c}} (~100/99 = 16.2607{{c}})
* CWE: ~18/17 = 100.0000{{c}}, ~5/4 = 383.9647{{c}} (~100/99 = 16.0353{{c}})
* CWE: ~18/17 = 100.0000{{c}}, ~5/4 = 383.9647{{c}} (~100/99 = 16.0353{{c}})
<!-- * CTE: ~18/17 = 100.000{{c}}, ~5/4 = 384.685{{c}} (~105/104 = 15.315{{c}})
* POTE: ~18/17 = 100.000{{c}}, ~5/4 = 383.750{{c}} (~105/104 = 16.250{{c}}) -->


{{Optimal ET sequence|legend=0| 12f, 60eff, 72 }}
{{Optimal ET sequence|legend=0| 12f, 60eff, 72 }}
Line 119: Line 109:
* WE: ~35/33 = 100.0926{{c}}, ~5/4 = 382.9660{{c}} (~100/99 = 17.4045{{c}})
* WE: ~35/33 = 100.0926{{c}}, ~5/4 = 382.9660{{c}} (~100/99 = 17.4045{{c}})
* CWE: ~35/33 = 100.0000{{c}}, ~5/4 = 382.7748{{c}} (~100/99 = 17.2252{{c}})
* CWE: ~35/33 = 100.0000{{c}}, ~5/4 = 382.7748{{c}} (~100/99 = 17.2252{{c}})
<!-- * CTE: ~35/33 = 100.000{{c}}, ~5/4 = 383.552{{c}} (~100/99 = 16.448{{c}})
* POTE: ~35/33 = 100.000{{c}}, ~5/4 = 382.612{{c}} (~100/99 = 17.388{{c}}) -->


{{Optimal ET sequence|legend=0| 12, 60e, 72, 204cdef, 276cdeff }}
{{Optimal ET sequence|legend=0| 12, 60e, 72, 204cdef, 276cdeff }}
Line 136: Line 124:
* WE: ~18/17 = 100.0941{{c}}, ~5/4 = 382.9567{{c}} (~100/99 = 17.4796{{c}})
* WE: ~18/17 = 100.0941{{c}}, ~5/4 = 382.9567{{c}} (~100/99 = 17.4796{{c}})
* CWE: ~18/17 = 100.0000{{c}}, ~5/4 = 382.7381{{c}} (~100/99 = 17.2619{{c}})
* CWE: ~18/17 = 100.0000{{c}}, ~5/4 = 382.7381{{c}} (~100/99 = 17.2619{{c}})
<!-- * CTE: ~18/17 = 100.000{{c}}, ~5/4 = 383.552{{c}} (~100/99 = 16.448{{c}})
* POTE: ~18/17 = 100.000{{c}}, ~5/4 = 382.597{{c}} (~100/99 = 17.403{{c}}) -->


{{Optimal ET sequence|legend=0| 12, 60e, 72, 204cdefg, 276cdeffgg }}
{{Optimal ET sequence|legend=0| 12, 60e, 72, 204cdefg, 276cdeffgg }}
Line 144: Line 130:


== Catler ==
== Catler ==
In terms of the normal comma list, catler is characterized by the addition of the [[schisma]], 32805/32768, to the Pythagorean comma, though it can also be characterized as adding 81/80, [[128/125]] or [[648/625]]. In any event, the 5-limit is exactly the same as the 5-limit of 12edo. Catler can also be characterized as the {{nowrap| 12 & 24 }} temperament. [[36edo]] or [[48edo]] are possible tunings. Possible generators are [[36/35]], [[21/20]], [[15/14]], [[8/7]], [[7/6]], [[9/7]], [[7/5]], and most importantly, [[64/63]].   
In terms of the normal comma list, catler is characterized by the addition of the schisma, [[32805/32768]], to the Pythagorean comma, though it can also be characterized as adding [[81/80]], [[128/125]] or [[648/625]]. In any event, the 5-limit is exactly the same as the 5-limit of 12edo. Catler can also be characterized as the {{nowrap| 12 & 24 }} temperament. [[36edo]] or [[48edo]] are possible tunings. Possible generators are [[36/35]], [[21/20]], [[15/14]], [[8/7]], [[7/6]], [[9/7]], [[7/5]], and most importantly, [[64/63]].   


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 159: Line 145:
* [[CWE]]: ~16/15 = 100.0000{{c}}, ~7/4 = 972.0971{{c}} (~64/63 = 27.9029{{c}})
* [[CWE]]: ~16/15 = 100.0000{{c}}, ~7/4 = 972.0971{{c}} (~64/63 = 27.9029{{c}})
: error map: {{val| 0.000 -1.955 +13.686 +3.271 }}
: error map: {{val| 0.000 -1.955 +13.686 +3.271 }}
<!-- * [[CTE]]: ~16/15 = 100.000{{c}}, ~7/4 = 968.826{{c}} (~64/63 = 31.174{{c}})
: [[error map]]: {{val| 0.000 -1.955 +13.686 0.000 }}
* [[POTE]]: ~16/15 = 100.000{{c}}, ~7/4 = 973.210{{c}} (~64/63 = 26.790{{c}})
: error map: {{val| 0.000 -1.955 +13.686 +4.384 }} -->


{{Optimal ET sequence|legend=1| 12, 24, 36, 48c, 84c }}
{{Optimal ET sequence|legend=1| 12, 24, 36, 48c, 84c }}
Line 176: Line 158:


Optimal tunings:  
Optimal tunings:  
* CTE: ~16/15 = 99.8542{{c}}, ~7/4 = 975.8519{{c}} (~64/63 = 22.6896{{c}})
* WE: ~16/15 = 99.8542{{c}}, ~7/4 = 975.8519{{c}} (~64/63 = 22.6896{{c}})
* POTE: ~16/15 = 100.0000{{c}}, ~7/4 = 976.4125{{c}} (~64/63 = 23.5875{{c}})
* CWE: ~16/15 = 100.0000{{c}}, ~7/4 = 976.4125{{c}} (~64/63 = 23.5875{{c}})
<!-- * CTE: ~16/15 = 100.000{{c}}, ~7/4 = 973.779{{c}} (~64/63 = 26.221{{c}})
* POTE: ~16/15 = 100.000{{c}}, ~7/4 = 977.277{{c}} (~64/63 = 22.723{{c}}) -->


{{Optimal ET sequence|legend=0| 12, 36e, 48c }}
{{Optimal ET sequence|legend=0| 12, 36e, 48c }}
Line 193: Line 173:


Optimal tunings:  
Optimal tunings:  
* CTE: ~16/15 = 99.8791{{c}}, ~7/4 = 970.9614{{c}} (~64/63 = 27.8300{{c}})
* WE: ~16/15 = 99.8791{{c}}, ~7/4 = 970.9614{{c}} (~64/63 = 27.8300{{c}})
* POTE: ~16/15 = 100.0000{{c}}, ~7/4 = 972.2549{{c}} (~64/63 = 27.7451{{c}})
* CWE: ~16/15 = 100.0000{{c}}, ~7/4 = 972.2549{{c}} (~64/63 = 27.7451{{c}})
<!-- * CTE: ~16/15 = 100.000{{c}}, ~7/4 = 972.823{{c}} (~64/63 = 27.177{{c}})
* POTE: ~16/15 = 100.000{{c}}, ~7/4 = 972.136{{c}} (~64/63 = 27.864{{c}}) -->


{{Optimal ET sequence|legend=0| 12e, 36, 48c, 84c }}
{{Optimal ET sequence|legend=0| 12e, 36, 48c, 84c }}
Line 210: Line 188:


Optimal tunings:  
Optimal tunings:  
* CTE: ~16/15 = 99.8519{{c}}, ~7/4 = 965.7912{{c}} (~64/63 = 32.7275{{c}})
* WE: ~16/15 = 99.8519{{c}}, ~7/4 = 965.7912{{c}} (~64/63 = 32.7275{{c}})
* POTE: ~16/15 = 100.0000{{c}}, ~7/4 = 965.8666{{c}} (~64/63 = 34.1334{{c}})
* CWE: ~16/15 = 100.0000{{c}}, ~7/4 = 965.8666{{c}} (~64/63 = 34.1334{{c}})
<!-- * CTE: ~16/15 = 100.000{{c}}, ~7/4 = 961.874{{c}} (~64/63 = 38.126{{c}})
* POTE: ~16/15 = 100.000{{c}}, ~7/4 = 967.224{{c}} (~64/63 = 32.776{{c}}) -->


{{Optimal ET sequence|legend=0| 12, 24, 36, 72ce }}
{{Optimal ET sequence|legend=0| 12, 24, 36 }}


Badness (Sintel): 1.14
Badness (Sintel): 1.14
Line 227: Line 203:


Optimal tunings:  
Optimal tunings:  
* CTE: ~16/15 = 99.8308{{c}}, ~7/4 = 961.1391{{c}} (~40/39 = 37.1694{{c}})
* WE: ~16/15 = 99.8308{{c}}, ~7/4 = 961.1391{{c}} (~40/39 = 37.1694{{c}})
* POTE: ~16/15 = 100.0000{{c}}, ~7/4 = 961.1435{{c}} (~40/39 = 38.8565{{c}})
* CWE: ~16/15 = 100.0000{{c}}, ~7/4 = 961.1435{{c}} (~40/39 = 38.8565{{c}})
<!-- * CTE: ~16/15 = 100.000{{c}}, ~7/4 = 956.375{{c}} (~40/39 = 43.625{{c}})
* POTE: ~16/15 = 100.000{{c}}, ~7/4 = 962.778{{c}} (~40/39 = 37.232{{c}}) -->


{{Optimal ET sequence|legend=0| 12f, 24, 36f }}
{{Optimal ET sequence|legend=0| 12f, 24, 36f }}
Line 246: Line 220:
* WE: ~18/17 = 99.8958{{c}}, ~7/4 = 959.2226{{c}} (~40/39 = 39.7354{{c}})
* WE: ~18/17 = 99.8958{{c}}, ~7/4 = 959.2226{{c}} (~40/39 = 39.7354{{c}})
* CWE: ~18/17 = 100.0000{{c}}, ~7/4 = 959.4216{{c}} (~40/39 = 40.5784{{c}})
* CWE: ~18/17 = 100.0000{{c}}, ~7/4 = 959.4216{{c}} (~40/39 = 40.5784{{c}})
<!-- * CTE: ~18/17 = 100.000{{c}}, ~7/4 = 956.375{{c}} (~40/39 = 43.625{{c}})
* POTE: ~18/17 = 100.000{{c}}, ~7/4 = 960.223{{c}} (~40/39 = 39.777{{c}}) -->


{{Optimal ET sequence|legend=0| 12f, 24, 36f }}
{{Optimal ET sequence|legend=0| 12f, 24, 36f }}
Line 263: Line 235:
* WE: ~18/17 = 99.9058{{c}}, ~7/4 = 958.9307{{c}} (~40/39 = 40.1270{{c}})
* WE: ~18/17 = 99.9058{{c}}, ~7/4 = 958.9307{{c}} (~40/39 = 40.1270{{c}})
* CWE: ~18/17 = 100.0000{{c}}, ~7/4 = 959.2303{{c}} (~40/39 = 40.7697{{c}})
* CWE: ~18/17 = 100.0000{{c}}, ~7/4 = 959.2303{{c}} (~40/39 = 40.7697{{c}})
<!-- * CTE: ~18/17 = 100.000{{c}}, ~7/4 = 956.375{{c}} (~40/39 = 43.625{{c}})
* POTE: ~18/17 = 100.000{{c}}, ~7/4 = 959.835{{c}} (~40/39 = 40.165{{c}}) -->


{{Optimal ET sequence|legend=0| 12f, 24, 36f }}
{{Optimal ET sequence|legend=0| 12f, 24, 36f }}
Line 280: Line 250:
* WE: ~18/17 = 99.9301{{c}}, ~7/4 = 961.6396{{c}} (~64/63 = 37.6617{{c}})
* WE: ~18/17 = 99.9301{{c}}, ~7/4 = 961.6396{{c}} (~64/63 = 37.6617{{c}})
* CWE: ~18/17 = 100.0000{{c}}, ~7/4 = 962.1413{{c}} (~64/63 = 37.8587{{c}})
* CWE: ~18/17 = 100.0000{{c}}, ~7/4 = 962.1413{{c}} (~64/63 = 37.8587{{c}})
<!-- * CTE: ~16/15 = 100.000{{c}}, ~7/4 = 961.255{{c}} (~64/63 = 38.745{{c}})
* POTE: ~16/15 = 100.000{{c}}, ~7/4 = 962.312{{c}} (~64/63 = 37.688{{c}}) -->


{{Optimal ET sequence|legend=0| 12, 24, 36 }}
{{Optimal ET sequence|legend=0| 12, 24, 36 }}
Line 297: Line 265:
* WE: ~18/17 = 99.9556{{c}}, ~7/4 = 961.4763{{c}} (~64/63 = 38.0796{{c}})
* WE: ~18/17 = 99.9556{{c}}, ~7/4 = 961.4763{{c}} (~64/63 = 38.0796{{c}})
* CWE: ~18/17 = 100.0000{{c}}, ~7/4 = 961.8075{{c}} (~64/63 = 38.1925{{c}})
* CWE: ~18/17 = 100.0000{{c}}, ~7/4 = 961.8075{{c}} (~64/63 = 38.1925{{c}})
<!-- * CTE: ~18/17 = 100.000{{c}}, ~7/4 = 961.255{{c}} (~64/63 = 38.745{{c}})
* POTE: ~18/17 = 100.000{{c}}, ~7/4 = 961.903{{c}} (~64/63 = 38.097{{c}}) -->


{{Optimal ET sequence|legend=0| 12, 24, 36, 60c }}
{{Optimal ET sequence|legend=0| 12, 24, 36, 60c }}
Line 314: Line 280:
* WE: ~18/17 = 99.9545{{c}}, ~7/4 = 961.4829{{c}} (~64/63 = 38.0624{{c}})
* WE: ~18/17 = 99.9545{{c}}, ~7/4 = 961.4829{{c}} (~64/63 = 38.0624{{c}})
* CWE: ~18/17 = 100.0000{{c}}, ~7/4 = 961.8354{{c}} (~64/63 = 38.1646{{c}})
* CWE: ~18/17 = 100.0000{{c}}, ~7/4 = 961.8354{{c}} (~64/63 = 38.1646{{c}})
<!-- * CTE: ~18/17 = 100.000{{c}}, ~7/4 = 961.255{{c}} (~64/63 = 38.745{{c}})
* POTE: ~18/17 = 100.000{{c}}, ~7/4 = 961.920{{c}} (~64/63 = 38.080{{c}}) -->


{{Optimal ET sequence|legend=0| 12, 24, 36, 60c }}
{{Optimal ET sequence|legend=0| 12, 24, 36, 60c }}
Line 322: Line 286:


== Duodecim ==
== Duodecim ==
Duodecim uses exactly the same mapping as the 7-limit of 12edo, only correcting its poor approximation of prime 11.
[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


Line 335: Line 301:
* [[CWE]]: ~16/15 = 100.0000{{c}}, ~11/8 = 562.2258{{c}} (~55/54 = 37.7742{{c}})
* [[CWE]]: ~16/15 = 100.0000{{c}}, ~11/8 = 562.2258{{c}} (~55/54 = 37.7742{{c}})
: error map: {{val| 0.000 -1.955 +13.686 +31.174 +10.908 }}
: error map: {{val| 0.000 -1.955 +13.686 +31.174 +10.908 }}
<!-- * [[CTE]]: ~16/15 = 100.000{{c}}, ~11/8 = 551.318{{c}} (~33/32 = 48.682{{c}})
: [[error map]]: {{val| 0.000 -1.955 +13.686 +31.174 0.000 }}
* [[POTE]]: ~16/15 = 100.000{{c}}, ~11/8 = 565.023{{c}} (~55/54 = 34.977{{c}})
: error map: {{val| 0.000 -1.955 +13.686 +31.174 +13.705 }} -->


{{Optimal ET sequence|legend=1| 12, 24d, 36d }}
{{Optimal ET sequence|legend=1| 12, 24d, 36d }}
Line 345: Line 307:


== Hours ==
== Hours ==
The hours temperament has a period of 1/24 octave and tempers out the [[cataharry comma]] (19683/19600) and the mirwomo comma (33075/32768). The name ''hours'' was named for the reason that the period is 1/24 octave and there are 24 hours per day.
The hours temperament has a period of 1/24 octave and tempers out the [[cataharry comma]] (19683/19600) and the mirwomo comma (33075/32768). Its ploidacot is 24-ploid acot. The name ''hours'' was given for the reason that the period is 1/24 octave and there are 24 hours per day.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 360: Line 322:
* [[CWE]]: ~36/35 = 50.0000{{c}}, ~5/4 = 384.0719{{c}} (~81/80 = 15.9281{{c}})
* [[CWE]]: ~36/35 = 50.0000{{c}}, ~5/4 = 384.0719{{c}} (~81/80 = 15.9281{{c}})
: error map: {{val| 0.000 -1.955 -2.242 -2.898 }}
: error map: {{val| 0.000 -1.955 -2.242 -2.898 }}
<!-- * [[CTE]]: ~36/35 = 50.000{{c}}, ~5/4 = 384.226{{c}} (~81/80 = 15.774{{c}})
: [[error map]]: {{val| 0.000 -1.955 -2.088 -3.052 }}
* [[POTE]]: ~36/35 = 50.000{{c}}, ~5/4 = 384.033{{c}} (~81/80 = 15.967{{c}})
: error map: {{val| 0.000 -1.955 -2.280 -2.859 }} -->


{{Optimal ET sequence|legend=1| 24, 48, 72, 312bd, 384bcdd, 456bcdd, 528bcdd, 600bccdd }}
{{Optimal ET sequence|legend=1| 24, 48, 72, 312bd, 384bcdd, 456bcdd, 528bcdd, 600bccdd }}
Line 379: Line 337:
* WE: ~36/35 = 50.0301{{c}}, ~5/4 = 384.2848{{c}} (~121/120 = 15.9559{{c}})
* WE: ~36/35 = 50.0301{{c}}, ~5/4 = 384.2848{{c}} (~121/120 = 15.9559{{c}})
* CWE: ~36/35 = 50.0000{{c}}, ~5/4 = 384.0825{{c}} (~121/120 = 15.9175{{c}})
* CWE: ~36/35 = 50.0000{{c}}, ~5/4 = 384.0825{{c}} (~121/120 = 15.9175{{c}})
<!-- * CTE: ~36/35 = 50.000{{c}}, ~5/4 = 384.226{{c}} (~121/120 = 15.774{{c}})
* POTE: ~36/35 = 50.000{{c}}, ~5/4 = 384.054{{c}} (~121/120 = 15.946{{c}}) -->


{{Optimal ET sequence|legend=0| 24, 48, 72, 312bd, 384bcdd, 456bcdde, 528bcdde }}
{{Optimal ET sequence|legend=0| 24, 48, 72, 312bd, 384bcdd, 456bcdde, 528bcdde }}
Line 396: Line 352:
* WE: ~36/35 = 50.0358{{c}}, ~5/4 = 384.9267{{c}} (~121/120 = 15.3594{{c}})
* WE: ~36/35 = 50.0358{{c}}, ~5/4 = 384.9267{{c}} (~121/120 = 15.3594{{c}})
* CWE: ~36/35 = 50.0000{{c}}, ~5/4 = 384.7662{{c}} (~121/120 = 15.2338{{c}})
* CWE: ~36/35 = 50.0000{{c}}, ~5/4 = 384.7662{{c}} (~121/120 = 15.2338{{c}})
<!-- * CTE: ~36/35 = 50.000{{c}}, ~5/4 = 385.420{{c}} (~121/120 = 14.580{{c}})
* POTE: ~36/35 = 50.000{{c}}, ~5/4 = 384.652{{c}} (~121/120 = 15.348{{c}}) -->


{{Optimal ET sequence|legend=0| 24, 48f, 72, 168df, 240dff }}
{{Optimal ET sequence|legend=0| 24, 48f, 72, 168df, 240dff }}
Line 404: Line 358:


== Gamelstearn ==
== Gamelstearn ==
The gamelstearn temperament has a period of 1/36 octave and tempers out the [[gamelisma]] (1029/1024) and the [[stearnsma]] (118098/117649).  
The gamelstearn temperament has a period of 1/36 octave and tempers out the [[gamelisma]] (1029/1024) and the [[stearnsma]] (118098/117649). Its ploidacot is 36-ploid acot.  


It used to be named "decades".
It used to be called ''decades'', but was renamed in 2025 after the above two commas because the old name was deemed too confusing.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 421: Line 375:
* [[CWE]]: ~49/48 = 33.3333{{c}}, ~5/4 = 385.1512{{c}} (~81/80 = 14.8488{{c}})
* [[CWE]]: ~49/48 = 33.3333{{c}}, ~5/4 = 385.1512{{c}} (~81/80 = 14.8488{{c}})
: error map: {{val| 0.000 -1.955 -1.162 -2.159 }}
: error map: {{val| 0.000 -1.955 -1.162 -2.159 }}
<!-- * [[CTE]]: ~49/48 = 33.333{{c}}, ~5/4 = 386.314{{c}} (~81/80 = 13.686{{c}})
: [[error map]]: {{val| 0.000 -1.955 0.000 -2.159 }}
* [[POTE]]: ~49/48 = 33.333{{c}}, ~5/4 = 384.764{{c}} (~81/80 = 15.236{{c}})
: error map: {{val| 0.000 -1.955 -1.549 -2.159 }} -->


{{Optimal ET sequence|legend=1| 36, 72, 252, 324bd, 396bd }}
{{Optimal ET sequence|legend=1| 36, 72, 252, 324bd, 396bd }}
Line 440: Line 390:
* WE: ~49/48 = 33.3504{{c}}, ~5/4 = 384.3474{{c}} (~81/80 = 15.8576{{c}})
* WE: ~49/48 = 33.3504{{c}}, ~5/4 = 384.3474{{c}} (~81/80 = 15.8576{{c}})
* CWE: ~49/48 = 33.333{{c}}, ~5/4 = 384.5541{{c}} (~81/80 = 15.4459{{c}})
* CWE: ~49/48 = 33.333{{c}}, ~5/4 = 384.5541{{c}} (~81/80 = 15.4459{{c}})
<!-- * CTE: ~49/48 = 33.333{{c}}, ~5/4 = 385.797{{c}} (~81/80 = 14.203{{c}})
* POTE: ~49/48 = 33.333{{c}}, ~5/4 = 384.150{{c}} (~81/80 = 15.850{{c}}) -->


{{Optimal ET sequence|legend=0| 36, 72, 396bd }}
{{Optimal ET sequence|legend=0| 36, 72, 396bd }}
Line 461: Line 409:
* [[CWE]]: ~100/99 = 16.6667{{c}}, ~13/8 = 838.2660{{c}} (~364/363 = 4.9326{{c}})
* [[CWE]]: ~100/99 = 16.6667{{c}}, ~13/8 = 838.2660{{c}} (~364/363 = 4.9326{{c}})
: error map: {{val| 0.000 -1.955 -2.980 -2.159 -1.318 -2.262 }}
: error map: {{val| 0.000 -1.955 -2.980 -2.159 -1.318 -2.262 }}
<!-- * [[CTE]]: ~100/99 = 16.667{{c}}, ~13/8 = 840.528{{c}} (~325/324 = 7.194{{c}})
: [[error map]]: {{val| 0.000 -1.955 -2.980 -2.159 -1.318 0.000 }}
* [[POTE]]: ~100/99 = 16.667{{c}}, ~13/8 = 837.814{{c}} (~364/363 = 4.481{{c}})
: error map: {{val| 0.000 -1.955 -2.980 -2.159 -1.318 -2.713 }} -->


{{Optimal ET sequence|legend=1| 72, 144, 216c, 288cdf }}
{{Optimal ET sequence|legend=1| 72, 144, 216c, 288cdf }}
Line 471: Line 415:


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Compton family| ]] <!-- main article -->
[[Category:Compton family| ]] <!-- main article -->
[[Category:Compton| ]] <!-- key article -->
[[Category:Compton| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Compton_family"