Mint temperaments: Difference between revisions

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Line 6:

* [[Dominant (temperament)|Dominant]] (+64/63) → [[Meantone family #Dominant|Meantone family]]

* ''[[Armodue (temperament)|Armodue]]'' (+135/128) → [[Mavila family #Armodue|Mavila family]]

* ''[[~~Dicot~~]]'' (+25/24) → [[Dicot family|Dicot family]]

* ''[[Mujannabic]]'' (+25/24) → [[Dicot family #Mujannabic|Dicot family]]

* [[Beep]] (+21/20) → [[Bug family #Beep|Bug family]]

* ''[[August]]'' (+128/125) → [[Augmented family #August|Augmented family]]

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* ''[[Smate]]'' (+2048/1875) → [[Smate family #Septimal smate|Smate family]]

* ''[[Darkstone]]'' (+1875/1792) → [[Magic family #Darkstone|Magic family]]

* ''[[~~Ripple~~]]'' (+2560/2401) → [[Ripple family #~~Septimal ripple~~|Ripple family]]

* ''[[Rip]]'' (+2560/2401) → [[Ripple family #Rip|Ripple family]]

* ''[[Whitewood]]'' (+2187/2048) → [[Whitewood family #Septimal whitewood|Whitewood family]]

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: ''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 ~~can~~ 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. [[17edo]] is an obvious tuning for it.

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

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Comma list: 36/35, 56/55, 77/75

~~Mapping:~~ {{~~mapping~~| 1 1 2 2 3 | 0 5 3 7 4 }}

Optimal tunings:

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Comma list: 26/25, 36/35, 56/55, 66/65

~~Mapping:~~ {{~~mapping~~| 1 1 2 2 3 3 | 0 5 3 7 4 6 }}

Optimal tunings:

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Comma list: 26/25, 36/35, 51/50, 56/55, 66/65

~~Mapping:~~ {{~~mapping~~| 1 1 2 2 3 3 4 | 0 5 3 7 4 6 1 }}

Optimal tunings:

Line 110:

Comma list: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65

~~Mapping:~~ {{~~mapping~~| 1 1 2 2 3 3 4 4 | 0 5 3 7 4 6 1 2 }}

Optimal tunings:

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Comma list: 36/35, 77/75, 352/343

~~Mapping:~~ {{~~mapping~~| 1 -3 -3 -1 -8 | 0 6 7 5 15 }}

Optimal tunings:

Line 162:

Comma list: 26/25, 36/35, 66/65, 352/343

~~Mapping:~~ {{~~mapping~~| 1 3 4 4 7 7 | 0 6 7 5 15 14 }}

Optimal tunings:

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Comma list: 36/35, 56/55, 1029/1000

~~Mapping:~~ {{~~mapping~~| 1 -3 -3 -1 5 | 0 6 7 5 -2 }}

Optimal tunings:

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Comma list: 36/35, 56/55, 66/65, 640/637

~~Mapping:~~ {{~~mapping~~| 1 -3 -3 -1 5 6 | 0 6 7 5 -2 -3 }}

Optimal tunings:

Line 229:

Comma list: 36/35, 56/55, 2541/2500

~~Mapping:~~ {{~~mapping~~| 1 -4 -2 -4 1 | 0 9 7 11 4 }}

Optimal tunings:

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Comma list: 36/35, 56/55, 66/65, 507/500

~~Mapping:~~ {{~~mapping~~| 1 -4 -2 -4 1 0 | 0 9 7 11 4 6 }}

Optimal tunings:

Line 259:

Comma list: 36/35, 51/50, 56/55, 66/65, 170/169

~~Mapping:~~ {{~~mapping~~| 1 -4 -2 -4 1 0 1 | 0 9 7 11 4 6 5 }}

Optimal tunings:

Line 296:

Comma list: 36/35, 121/120, 352/343

~~Mapping:~~ {{~~mapping~~| 1 2 3 3 4 | 0 -7 -11 -3 -9 }}

Optimal tunings:

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Comma list: 36/35, 66/65, 143/140, 352/343

~~Mapping:~~ {{~~mapping~~| 1 2 3 3 4 4 | 0 -7 -11 -3 -9 -5 }}

Optimal tunings:

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== References ==

[[Category:Mint temperaments| ]]

[[Category:Temperament collections]]

[[Category:~~Mint temperaments| ]] <!~~-~~- main article -->~~

[[Category:Catalogs of rank-2 temperaments]]

~~[[Category:Rank~~ 2]]

@@ Line 6: / Line 6: @@
 * [[Dominant (temperament)|Dominant]] (+64/63) → [[Meantone family #Dominant|Meantone family]]
 * ''[[Armodue (temperament)|Armodue]]'' (+135/128) → [[Mavila family #Armodue|Mavila family]]
-* ''[[Dicot]]'' (+25/24) → [[Dicot family|Dicot family]]
+* ''[[Mujannabic]]'' (+25/24) → [[Dicot family #Mujannabic|Dicot family]]
 * [[Beep]] (+21/20) → [[Bug family #Beep|Bug family]]
 * ''[[August]]'' (+128/125) → [[Augmented family #August|Augmented family]]
@@ Line 14: / Line 14: @@
 * ''[[Smate]]'' (+2048/1875) → [[Smate family #Septimal smate|Smate family]]
 * ''[[Darkstone]]'' (+1875/1792) → [[Magic family #Darkstone|Magic family]]
-* ''[[Ripple]]'' (+2560/2401) → [[Ripple family #Septimal ripple|Ripple family]]
+* ''[[Rip]]'' (+2560/2401) → [[Ripple family #Rip|Ripple family]]
 * ''[[Whitewood]]'' (+2187/2048) → [[Whitewood family #Septimal whitewood|Whitewood family]]
@@ Line 41: / Line 41: @@
 : ''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 can 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. [[17edo]] is an obvious tuning for it.
+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
@@ Line 65: / Line 65: @@
 Comma list: 36/35, 56/55, 77/75
-Mapping: {{mapping| 1 1 2 2 3 | 0 5 3 7 4 }}
+{{Mapping|legend=0| 1 1 2 2 3 | 0 5 3 7 4 }}
 Optimal tunings:
@@ Line 80: / Line 80: @@
 Comma list: 26/25, 36/35, 56/55, 66/65
-Mapping: {{mapping| 1 1 2 2 3 3 | 0 5 3 7 4 6 }}
+{{Mapping|legend=0| 1 1 2 2 3 3 | 0 5 3 7 4 6 }}
 Optimal tunings:
@@ Line 95: / Line 95: @@
 Comma list: 26/25, 36/35, 51/50, 56/55, 66/65
-Mapping: {{mapping| 1 1 2 2 3 3 4 | 0 5 3 7 4 6 1 }}
+{{Mapping|legend=0| 1 1 2 2 3 3 4 | 0 5 3 7 4 6 1 }}
 Optimal tunings:
@@ Line 110: / Line 110: @@
 Comma list: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65
-Mapping: {{mapping| 1 1 2 2 3 3 4 4 | 0 5 3 7 4 6 1 2 }}
+{{Mapping|legend=0| 1 1 2 2 3 3 4 4 | 0 5 3 7 4 6 1 2 }}
 Optimal tunings:
@@ Line 147: / Line 147: @@
 Comma list: 36/35, 77/75, 352/343
-Mapping: {{mapping| 1 -3 -3 -1 -8 | 0 6 7 5 15 }}
+{{Mapping|legend=0| 1 -3 -3 -1 -8 | 0 6 7 5 15 }}
 Optimal tunings:
@@ Line 162: / Line 162: @@
 Comma list: 26/25, 36/35, 66/65, 352/343
-Mapping: {{mapping| 1 3 4 4 7 7 | 0 6 7 5 15 14 }}
+{{Mapping|legend=0| 1 3 4 4 7 7 | 0 6 7 5 15 14 }}
 Optimal tunings:
@@ Line 177: / Line 177: @@
 Comma list: 36/35, 56/55, 1029/1000
-Mapping: {{mapping| 1 -3 -3 -1 5 | 0 6 7 5 -2 }}
+{{Mapping|legend=0| 1 -3 -3 -1 5 | 0 6 7 5 -2 }}
 Optimal tunings:
@@ Line 192: / Line 192: @@
 Comma list: 36/35, 56/55, 66/65, 640/637
-Mapping: {{mapping| 1 -3 -3 -1 5 6 | 0 6 7 5 -2 -3 }}
+{{Mapping|legend=0| 1 -3 -3 -1 5 6 | 0 6 7 5 -2 -3 }}
 Optimal tunings:
@@ Line 229: / Line 229: @@
 Comma list: 36/35, 56/55, 2541/2500
-Mapping: {{mapping| 1 -4 -2 -4 1 | 0 9 7 11 4 }}
+{{Mapping|legend=0| 1 -4 -2 -4 1 | 0 9 7 11 4 }}
 Optimal tunings:
@@ Line 244: / Line 244: @@
 Comma list: 36/35, 56/55, 66/65, 507/500
-Mapping: {{mapping| 1 -4 -2 -4 1 0 | 0 9 7 11 4 6 }}
+{{Mapping|legend=0| 1 -4 -2 -4 1 0 | 0 9 7 11 4 6 }}
 Optimal tunings:
@@ Line 259: / Line 259: @@
 Comma list: 36/35, 51/50, 56/55, 66/65, 170/169
-Mapping: {{mapping| 1 -4 -2 -4 1 0 1 | 0 9 7 11 4 6 5 }}
+{{Mapping|legend=0| 1 -4 -2 -4 1 0 1 | 0 9 7 11 4 6 5 }}
 Optimal tunings:
@@ Line 296: / Line 296: @@
 Comma list: 36/35, 121/120, 352/343
-Mapping: {{mapping| 1 2 3 3 4 | 0 -7 -11 -3 -9 }}
+{{Mapping|legend=0| 1 2 3 3 4 | 0 -7 -11 -3 -9 }}
 Optimal tunings:
@@ Line 311: / Line 311: @@
 Comma list: 36/35, 66/65, 143/140, 352/343
-Mapping: {{mapping| 1 2 3 3 4 4 | 0 -7 -11 -3 -9 -5 }}
+{{Mapping|legend=0| 1 2 3 3 4 4 | 0 -7 -11 -3 -9 -5 }}
 Optimal tunings:
@@ Line 374: / Line 374: @@
 == References ==
+[[Category:Mint temperaments| ]] <!-- main article -->
 [[Category:Temperament collections]]
-[[Category:Mint temperaments| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]

Mint temperaments: Difference between revisions

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