Mint temperaments: Difference between revisions
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* [[Dominant (temperament)|Dominant]] (+64/63) → [[Meantone family #Dominant|Meantone family]] | * [[Dominant (temperament)|Dominant]] (+64/63) → [[Meantone family #Dominant|Meantone family]] | ||
* ''[[Armodue (temperament)|Armodue]]'' (+135/128) → [[Mavila family #Armodue|Mavila family]] | * ''[[Armodue (temperament)|Armodue]]'' (+135/128) → [[Mavila family #Armodue|Mavila family]] | ||
* ''[[ | * ''[[Mujannabic]]'' (+25/24) → [[Dicot family #Mujannabic|Dicot family]] | ||
* [[Beep]] (+21/20) → [[Bug family #Beep|Bug family]] | * [[Beep]] (+21/20) → [[Bug family #Beep|Bug family]] | ||
* ''[[August]]'' (+128/125) → [[Augmented family #August|Augmented family]] | * ''[[August]]'' (+128/125) → [[Augmented family #August|Augmented family]] | ||
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* ''[[Smate]]'' (+2048/1875) → [[Smate family #Septimal smate|Smate family]] | * ''[[Smate]]'' (+2048/1875) → [[Smate family #Septimal smate|Smate family]] | ||
* ''[[Darkstone]]'' (+1875/1792) → [[Magic family #Darkstone|Magic family]] | * ''[[Darkstone]]'' (+1875/1792) → [[Magic family #Darkstone|Magic family]] | ||
* ''[[ | * ''[[Rip]]'' (+2560/2401) → [[Ripple family #Rip|Ripple family]] | ||
* ''[[Whitewood]]'' (+2187/2048) → [[Whitewood family #Septimal whitewood|Whitewood family]] | * ''[[Whitewood]]'' (+2187/2048) → [[Whitewood family #Septimal whitewood|Whitewood family]] | ||
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* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/6 = 231.845{{c}} | * [[CWE]]: ~2 = 1200.0000{{c}}, ~7/6 = 231.845{{c}} | ||
: error map: {{val| 0.000 +6.291 +85.850 -24.498 }} | : error map: {{val| 0.000 +6.291 +85.850 -24.498 }} | ||
{{Optimal ET sequence|legend=1| 1bd, …, 4bcd, 5 }} | {{Optimal ET sequence|legend=1| 1bd, …, 4bcd, 5 }} | ||
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: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Lafayette]].'' | : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Lafayette]].'' | ||
Named by [[Gene Ward Smith]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_18891.html Yahoo! Tuning Group | ''Progression temperament'']</ref>, progression tempers out [[392/375]] and may be described as the {{nowrap| 8d & 9 }} temperament. It has a generator that is a somewhat flat neutral second, three make [[5/4]], five make [[3/2]], and seven make [[7/4]], with a [[ploidacot]] signature of pentacot. Related temperaments include [[secund]] and [[jerome]], which only differ by the mapping of 5. [[17edo]] is an obvious tuning for progression. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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* [[CWE]]: ~2 = 1200.000{{c}}, ~15/14 = 139.8991{{c}} | * [[CWE]]: ~2 = 1200.000{{c}}, ~15/14 = 139.8991{{c}} | ||
: error map: {{val| 0.000 -2.460 +33.384 +10.468 }} | : error map: {{val| 0.000 -2.460 +33.384 +10.468 }} | ||
{{Optimal ET sequence|legend=1| 8d, 9, 17c }} | {{Optimal ET sequence|legend=1| 8d, 9, 17c }} | ||
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Comma list: 36/35, 56/55, 77/75 | Comma list: 36/35, 56/55, 77/75 | ||
{{Mapping|legend=0| 1 1 2 2 3 | 0 5 3 7 4 }} | |||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1194.7089{{c}}, ~12/11 = 140.1262{{c}} | * WE: ~2 = 1194.7089{{c}}, ~12/11 = 140.1262{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 139.8776{{c}} | * CWE: ~2 = 1200.0000{{c}}, ~12/11 = 139.8776{{c}} | ||
{{Optimal ET sequence|legend=0| 8d, 9, 17c }} | {{Optimal ET sequence|legend=0| 8d, 9, 17c }} | ||
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Comma list: 26/25, 36/35, 56/55, 66/65 | Comma list: 26/25, 36/35, 56/55, 66/65 | ||
{{Mapping|legend=0| 1 1 2 2 3 3 | 0 5 3 7 4 6 }} | |||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1195.3694{{c}}, ~13/12 = 140.2080{{c}} | * WE: ~2 = 1195.3694{{c}}, ~13/12 = 140.2080{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.9749{{c}} | * CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.9749{{c}} | ||
{{Optimal ET sequence|legend=0| 8d, 9, 17c }} | {{Optimal ET sequence|legend=0| 8d, 9, 17c }} | ||
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Comma list: 26/25, 36/35, 51/50, 56/55, 66/65 | Comma list: 26/25, 36/35, 51/50, 56/55, 66/65 | ||
{{Mapping|legend=0| 1 1 2 2 3 3 4 | 0 5 3 7 4 6 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1193.8350{{c}}, ~13/12 = 140.6779{{c}} | * WE: ~2 = 1193.8350{{c}}, ~13/12 = 140.6779{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 140.5885{{c}} | * CWE: ~2 = 1200.0000{{c}}, ~13/12 = 140.5885{{c}} | ||
{{Optimal ET sequence|legend=0| 8d, 9, 17cg }} | {{Optimal ET sequence|legend=0| 8d, 9, 17cg }} | ||
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Comma list: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65 | Comma list: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65 | ||
{{Mapping|legend=0| 1 1 2 2 3 3 4 4 | 0 5 3 7 4 6 1 2 }} | |||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1196.1446{{c}}, ~13/12 = 140.0276{{c}} | * WE: ~2 = 1196.1446{{c}}, ~13/12 = 140.0276{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 140.0301{{c}} | * CWE: ~2 = 1200.0000{{c}}, ~13/12 = 140.0301{{c}} | ||
{{Optimal ET sequence|legend=0| 8d, 9, 17cg }} | {{Optimal ET sequence|legend=0| 8d, 9, 17cg }} | ||
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== Subklei == | == Subklei == | ||
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Delorean]].'' | : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Delorean]].'' | ||
Subklei is likely named for its flatter minor third generator than [[kleismic]]. It tempers out [[1029/1000]] as well as [[2401/2400]] and can be described as {{nowrap| 17c & 21 }}. Its [[ploidacot]] is delta-hexacot. Note that in the data below, the generator is the [[5/3]][[~]][[12/7]] major sixth, so that six generators minus four octaves give the [[3/2|perfect fifth]]. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/3 = 915.4228{{c}} | * [[CWE]]: ~2 = 1200.0000{{c}}, ~5/3 = 915.4228{{c}} | ||
: error map: {{val| 0.000 -9.418 +21.646 +8.288 }} | : error map: {{val| 0.000 -9.418 +21.646 +8.288 }} | ||
{{Optimal ET sequence|legend=1| 4, 13cd, 17c, 21, 38c }} | {{Optimal ET sequence|legend=1| 4, 13cd, 17c, 21, 38c }} | ||
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Comma list: 36/35, 77/75, 352/343 | Comma list: 36/35, 77/75, 352/343 | ||
{{Mapping|legend=0| 1 -3 -3 -1 -8 | 0 6 7 5 15 }} | |||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1196.3345{{c}}, ~5/3 = 913.9469{{c}} | * WE: ~2 = 1196.3345{{c}}, ~5/3 = 913.9469{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 916.2970{{c}} | * CWE: ~2 = 1200.0000{{c}}, ~5/3 = 916.2970{{c}} | ||
{{Optimal ET sequence|legend=0| 4e, …, 13cdee, 17c }} | {{Optimal ET sequence|legend=0| 4e, …, 13cdee, 17c }} | ||
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Comma list: 26/25, 36/35, 66/65, 352/343 | Comma list: 26/25, 36/35, 66/65, 352/343 | ||
{{Mapping|legend=0| 1 3 4 4 7 7 | 0 6 7 5 15 14 }} | |||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1196.0784{{c}}, ~5/3 = 914.1466{{c}} | * WE: ~2 = 1196.0784{{c}}, ~5/3 = 914.1466{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 916.6712{{c}} | * CWE: ~2 = 1200.0000{{c}}, ~5/3 = 916.6712{{c}} | ||
{{Optimal ET sequence|legend=0| 4ef, …, 13cdeef, 17c }} | {{Optimal ET sequence|legend=0| 4ef, …, 13cdeef, 17c }} | ||
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Comma list: 36/35, 56/55, 1029/1000 | Comma list: 36/35, 56/55, 1029/1000 | ||
{{Mapping|legend=0| 1 -3 -3 -1 5 | 0 6 7 5 -2 }} | |||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1196.3809{{c}}, ~5/3 = 913.4153{{c}} | * WE: ~2 = 1196.3809{{c}}, ~5/3 = 913.4153{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 915.8804{{c}} | * CWE: ~2 = 1200.0000{{c}}, ~5/3 = 915.8804{{c}} | ||
{{Optimal ET sequence|legend=0| 4, 13cd, 17c, 38ce }} | {{Optimal ET sequence|legend=0| 4, 13cd, 17c, 38ce }} | ||
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Comma list: 36/35, 56/55, 66/65, 640/637 | Comma list: 36/35, 56/55, 66/65, 640/637 | ||
{{Mapping|legend=0| 1 -3 -3 -1 5 6 | 0 6 7 5 -2 -3 }} | |||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1196.5477{{c}}, ~5/3 = 913.4822{{c}} | * WE: ~2 = 1196.5477{{c}}, ~5/3 = 913.4822{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 915.9416{{c}} | * CWE: ~2 = 1200.0000{{c}}, ~5/3 = 915.9416{{c}} | ||
{{Optimal ET sequence|legend=0| 4, 17c, 38ce }} | {{Optimal ET sequence|legend=0| 4, 17c, 38ce }} | ||
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== Naian == | == Naian == | ||
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Naian]].'' | : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Naian]].'' | ||
Named by [[Xenllium]] in 2026, naian may be described as {{nowrap| 8d & 21 }} with a [[ploidacot]] signature of epsilon-enneacot. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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* [[CWE]]: ~2 = 1200.0000{{c}}, ~75/49 = 743.9885{{c}} | * [[CWE]]: ~2 = 1200.0000{{c}}, ~75/49 = 743.9885{{c}} | ||
: error map: {{val| 0.000 -6.059 +21.606 +15.047 }} | : error map: {{val| 0.000 -6.059 +21.606 +15.047 }} | ||
{{Optimal ET sequence|legend=1| 8d, 21, 29cd }} | {{Optimal ET sequence|legend=1| 8d, 21, 29cd }} | ||
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Comma list: 36/35, 56/55, 2541/2500 | Comma list: 36/35, 56/55, 2541/2500 | ||
{{Mapping|legend=0| 1 -4 -2 -4 1 | 0 9 7 11 4 }} | |||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1194.3937{{c}}, ~75/49 = 741.2117{{c}} | * WE: ~2 = 1194.3937{{c}}, ~75/49 = 741.2117{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~75/49 = 744.2018{{c}} | * CWE: ~2 = 1200.0000{{c}}, ~75/49 = 744.2018{{c}} | ||
{{Optimal ET sequence|legend=0| 8d, 21, 29cde }} | {{Optimal ET sequence|legend=0| 8d, 21, 29cde }} | ||
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Comma list: 36/35, 56/55, 66/65, 507/500 | Comma list: 36/35, 56/55, 66/65, 507/500 | ||
{{Mapping|legend=0| 1 -4 -2 -4 1 0 | 0 9 7 11 4 6 }} | |||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1193.8564{{c}}, ~20/13 = 740.9635{{c}} | * WE: ~2 = 1193.8564{{c}}, ~20/13 = 740.9635{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.2703{{c}} | * CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.2703{{c}} | ||
{{Optimal ET sequence|legend=0| 8d, 21, 29cdef }} | {{Optimal ET sequence|legend=0| 8d, 21, 29cdef }} | ||
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Comma list: 36/35, 51/50, 56/55, 66/65, 170/169 | Comma list: 36/35, 51/50, 56/55, 66/65, 170/169 | ||
{{Mapping|legend=0| 1 -4 -2 -4 1 0 1 | 0 9 7 11 4 6 5 }} | |||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1194.2330{{c}}, ~20/13 = 741.1242{{c}} | * WE: ~2 = 1194.2330{{c}}, ~20/13 = 741.1242{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.2679{{c}} | * CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.2679{{c}} | ||
{{Optimal ET sequence|legend=0| 8d, 21, 29cdef }} | {{Optimal ET sequence|legend=0| 8d, 21, 29cdef }} | ||
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== Slurpee == | == Slurpee == | ||
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Slurpee]].'' | : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Slurpee]].'' | ||
Slurpee may be described as the {{nowrap| 16 & 17c }} temperament. It has a generator that is a somewhat flat semitone of [[~]][[21/20]], three make [[8/7]], seven make [[4/3]], and eleven make [[8/5]], with a [[ploidacot]] signature of omega-heptacot. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 72.4941{{c}} | * [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 72.4941{{c}} | ||
: error map: {{val| 0.000 -9.414 +16.251 +13.692 }} | : error map: {{val| 0.000 -9.414 +16.251 +13.692 }} | ||
{{Optimal ET sequence|legend=1| 16, 17c, 33 }} | {{Optimal ET sequence|legend=1| 16, 17c, 33 }} | ||
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Comma list: 36/35, 121/120, 352/343 | Comma list: 36/35, 121/120, 352/343 | ||
{{Mapping|legend=0| 1 2 3 3 4 | 0 -7 -11 -3 -9 }} | |||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1198.4220{{c}}, ~21/20 = 72.2015{{c}} | * WE: ~2 = 1198.4220{{c}}, ~21/20 = 72.2015{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 72.4470{{c}} | * CWE: ~2 = 1200.0000{{c}}, ~21/20 = 72.4470{{c}} | ||
{{Optimal ET sequence|legend=0| 16, 17c, 33 }} | {{Optimal ET sequence|legend=0| 16, 17c, 33 }} | ||
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Comma list: 36/35, 66/65, 143/140, 352/343 | Comma list: 36/35, 66/65, 143/140, 352/343 | ||
{{Mapping|legend=0| 1 2 3 3 4 4 | 0 -7 -11 -3 -9 -5 }} | |||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1199.0238{{c}}, ~21/20 = 72.3506{{c}} | * WE: ~2 = 1199.0238{{c}}, ~21/20 = 72.3506{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 72.4956{{c}} | * CWE: ~2 = 1200.0000{{c}}, ~21/20 = 72.4956{{c}} | ||
{{Optimal ET sequence|legend=0| 16, 17c, 33 }} | {{Optimal ET sequence|legend=0| 16, 17c, 33 }} | ||
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== Shallowtone == | == Shallowtone == | ||
{{Main| Shallowtone }} | |||
: ''For the 5-limit version, see [[Syntonic–chromatic equivalence continuum #Shallowtone (5-limit)]].'' | : ''For the 5-limit version, see [[Syntonic–chromatic equivalence continuum #Shallowtone (5-limit)]].'' | ||
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* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 681.2447{{c}} | * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 681.2447{{c}} | ||
: error map: {{val| 0.000 -20.710 +1.239 +6.110 }} | : error map: {{val| 0.000 -20.710 +1.239 +6.110 }} | ||
{{Optimal ET sequence|legend=1| 7, 30b, 37b }} | {{Optimal ET sequence|legend=1| 7, 30b, 37b }} | ||
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* WE: ~2 = 1202.0285{{c}}, ~3/2 = 682.4922{{c}} | * WE: ~2 = 1202.0285{{c}}, ~3/2 = 682.4922{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 681.3267{{c}} | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 681.3267{{c}} | ||
{{Optimal ET sequence|legend=0| 7, 30b, 37b }} | {{Optimal ET sequence|legend=0| 7, 30b, 37b }} | ||
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* WE: ~2 = 1201.4928{{c}}, ~3/2 = 682.1188{{c}} | * WE: ~2 = 1201.4928{{c}}, ~3/2 = 682.1188{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 681.2669{{c}} | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 681.2669{{c}} | ||
{{Optimal ET sequence|legend=0| 7, 30b, 37b }} | {{Optimal ET sequence|legend=0| 7, 30b, 37b }} | ||
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== References == | == References == | ||
[[Category:Mint temperaments| ]] <!-- main article --> | |||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category: | [[Category:Catalogs of rank-2 temperaments]] | ||