Vishnu family: Difference between revisions

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=== Overview to extensions ===

The second comma in the comma list defines which 7-limit family member we are looking at. Septimal vishnu (118 & 152) adds [[4375/4374]]. Narayana (84 & 118) adds [[65625/65536]]. Vishnean (16 & 50) adds [[126/125]]. There is also an unnamed 50 & 84 temperament, which tempers out [[225/224]]. These all use the same generators as classical vishnu.

The second comma in the comma list defines which 7-limit family member we are looking at. Septimal vishnu (118 & 152) adds [[4375/4374]]. Narayana (84 & 118) adds [[65625/65536]]. Vishnean (16 & 50) adds [[126/125]]. Vishy (16 & 18) adds [[50/49]]. There is also an unnamed 50 & 84 temperament, which tempers out [[225/224]]. These all use the same generators as classical vishnu.

Quarvish (68 & 270) adds [[2401/2400]], splitting the generator in four. Decavish adds [[420175/419904]], ~~with a 1/10~~-octave period.

Trivish (84 & 186) adds [[250047/250000]], splitting the semi-octave period in three. Quarvish (68 & 270) adds [[2401/2400]], splitting the generator in four. Decavish (50 & 220) adds [[420175/419904]], splitting the semi-octave period in five.

== Septimal vishnu ==

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Comma list: 3025/3024, 4375/4374, 5632/5625

~~Mapping:~~ {{~~mapping~~| 2 4 5 10 10 | 0 -7 -3 -37 -26 }}

Optimal tunings:

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Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625

~~Mapping:~~ {{~~mapping~~| 2 4 5 10 10 17 | 0 -7 -3 -37 -26 -81 }}

Optimal tunings:

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Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374

~~Mapping:~~ {{~~mapping~~| 2 4 5 10 10 1 | 0 -7 -3 -37 -26 54 }}

Optimal tuning:

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Comma list: 441/440, 8019/8000, 65625/65536

~~Mapping:~~ {{~~mapping~~| 2 4 5 3 3 | 0 -7 -3 22 33 }}

Optimal tunings:

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== Vishnean ==

Named by [[Petr Pařízek]] in 2011<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, vishnean is a low-complexity low-accuracy extension of vishnu that tempers out 126/125, the [[starling comma]].

Named by [[Petr Pařízek]] in 2011<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, vishnean is a low-complexity low-accuracy extension of vishnu that tempers out 126/125, the [[starling comma]]. It is also supported unideally by the [[84edo|84d]] ({{nowrap| {{=}} 34 + 50 }}) val, as the 7 is flat but the 11 is sharp such that they have opposing tendencies.

[[Subgroup]]: 2.3.5.7

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Comma list: 126/125, 385/384, 1350/1331

~~Mapping:~~ {{~~mapping~~| 2 4 5 5 8 | 0 -7 -3 5 -9 }}

Optimal tunings:

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Comma list: 105/104, 126/125, 144/143, 847/845

~~Mapping:~~ {{~~mapping~~| 2 4 5 5 8 8 | 0 -7 -3 5 -9 -5 }}

Optimal tunings:

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Badness (Sintel): 1.68

== Vishy ==

Named by [[Godtone]] in 2026 after its inaccurate but simple interpretation of its half-octave period as [[7/5]][[~]][[10/7]], vishy tempers out [[50/49]] and represents the absolute simplest way to reach prime 7 by interpreting three ~25/24 generators as a significantly flat [[~]][[8/7]]. Its mapping might be deemed favorable because of all primes being reached in a negative number of generators, with the most complex, 11, being reached in -9 (as in vishnean). In fact, this temperament's mapping is identical to that of [[vishnean]] up to a simpler, higher-damage mapping of 7 in the same direction as all the other primes.

The extreme tuning 50edo tunes 11 approximately pure and 7 a little better via the 50d val (= 16 + 34d), but damages 3, 7/3 and 11/7 significantly more than CWE, and has a dubiously flat-tending 5-limit. However, in light of this, one might consider [[84edo]] via the 84dd val (= 34d + 50d), where 7 is ~1.7{{c}} sharper but everything else is significantly more accurate, with the exception of a sharper 11; especially, the 5-limit is approximately in-tune, so that with its more accurate 11 (and marginally more accurate 7) it is a good alternative to 34edo.

Therefore, it should be noted that as only the mapping of 7 differs from vishnean, using both mappings in any of [[34edo]], [[50edo]] and [[84edo]] (with [[2.3.5.11 subgroup]] fixed) could be seen as the primary and opportunistic utility of this temperament, by using whichever mapping of 7 happens to be more convenient or convincing in a given harmonic situation (if indeed the 7 is felt to be accurate enough).

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 50/49, 110592/109375

[[Optimal tuning]]s:

* [[WE]]: ~7/5 = 598.8702{{c}}, ~25/24 = 70.6439{{c}}

: [[error map]]: {{val| -2.260 -0.982 -3.895 +12.463 }}

* [[CWE]]: ~7/5 = 600.0000{{c}}, ~25/24 = 71.9109{{c}}

: error map: {{val| 0.000 +0.969 +0.654 +18.141 }}

Badness (Sintel): 3.96

=== 11-limit ===

Other than [[176/175]], 11-limit vishy also tempers out [[625/616]] and [[1331/1323]].

Subgroup: 2.3.5.7.11

Comma list: 50/49, 176/175, 864/847

Optimal tunings:

* WE: ~7/5 = 598.8234{{c}}, ~25/24 = 70.7100{{c}}

: error map: {{val| -2.353 -1.631 -4.327 +11.984 +2.879 }}

* CWE: ~7/5 = 600.0000{{c}}, ~25/24 = 71.1044{{c}}

: error map: {{val| 0.000 -6.099 -2.375 +15.113 +0.498 }}

Badness (Sintel): 2.03

== Trivish ==

Trivish tempers out 250047/250000, the [[landscape comma]], with a 1/6-octave period. It may be described as the {{nowrap| 84 & 186 }} temperament. It is more significant in the [[11-limit]], where it tempers out the [[kalisma]] and the [[olympia]]. In the [[13-limit]], the generator can be taken as a [[~]][[14/13]]. [[270edo]] is an obvious tuning for it, but it can be tuned to [[354edo]], [[624edo]] or [[894edo]]. It was named by [[Flora Canou]] in 2026 for the fact that it splits the period of vishnu in three.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 250047/250000, 134217728/133984375

: mapping generators: ~18375/16384, ~2205/2048

[[Optimal tuning]]s:

* [[WE]]: ~18375/16384 = 199.9885{{c}}, ~2205/2048 = 128.8583{{c}}

: [[error map]]: {{val| -0.069 -0.005 +0.123 +0.054 }}

* [[CWE]]: ~18375/16384 = 200.0000{{c}}, ~2205/2048 = 128.8643{{c}}

: error map: {{val| 0.000 +0.095 +0.279 +0.256 }}

[[Badness]] (Sintel): 1.51

=== 11-limit ===

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 131072/130977, 151263/151250

Optimal tunings:

* WE: ~55/49 = 199.9885{{c}}, ~320/297 = 128.8582{{c}}

* CWE: ~55/49 = 200.0000{{c}}, ~320/297 = 128.8661{{c}}

Badness (Sintel): 0.807

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: 1716/1715, 2080/2079, 4096/4095, 34398/34375

Optimal tunings:

* WE: ~55/49 = 199.9922{{c}}, ~14/13 = 128.8565{{c}}

* CWE: ~55/49 = 200.0000{{c}}, ~14/13 = 128.8621{{c}}

Badness (Sintel): 0.791

=== 2.3.5.7.11.13.19 subgroup ===

Subgroup: 2.3.5.7.11.13.19

Comma list: 1521/1520, 1716/1715, 2080/2079, 2376/2375, 3250/3249

Optimal tunings:

* WE: ~55/49 = 199.9909{{c}}, ~14/13 = 128.8564{{c}}

* CWE: ~55/49 = 200.0000{{c}}, ~14/13 = 128.8630{{c}}

Badness (Sintel): 0.591

== Quarvish ==

Quarvish tempers out 2401/2400, the [[breedsma]], and may be described as the {{nowrap| 68 & ~~202~~ }} temperament.

Quarvish tempers out 2401/2400, the [[breedsma]], and may be described as the {{nowrap| 68 & 270 }} temperament.

[[Subgroup]]: 2.3.5.7

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Comma list: 2401/2400, 9801/9800, 172032/171875

~~Mapping:~~ {{~~mapping~~| 2 4 5 6 6 | 0 -28 -12 -13 31 }}

Optimal tunings:

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== Decavish ==

Decavish tempers out the [[wizma]] as well as the [[linus comma]], and may be described as the {{nowrap| 50 & ~~270~~ }} temperament. It was named by [[Xenllium]] in 2021 for the fact that its period is 1/10 octave.

Decavish tempers out the [[wizma]] as well as the [[linus comma]], and may be described as the {{nowrap| 50 & 220 }} temperament. It was named by [[Xenllium]] in 2021 for the fact that its period is 1/10 octave.

[[Subgroup]]: 2.3.5.7

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Comma list: 9801/9800, 41503/41472, 172032/171875

~~Mapping:~~ {{~~mapping~~| 10 6 19 14 36 | 0 7 3 10 -1 }}

Optimal tunings:

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Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655

~~Mapping:~~ {{~~mapping~~| 10 6 19 14 36 37 | 0 7 3 10 -1 0 }}

Optimal tunings:

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[[Category:Vishnu family| ]]

[[Category:Temperament families]]

[[Category:~~Vishnu family| ]] <!~~-~~- main article -->~~

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

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

@@ Line 23: / Line 23: @@
 === Overview to extensions ===
-The second comma in the comma list defines which 7-limit family member we are looking at. Septimal vishnu (118 & 152) adds [[4375/4374]]. Narayana (84 & 118) adds [[65625/65536]]. Vishnean (16 & 50) adds [[126/125]]. There is also an unnamed 50 & 84 temperament, which tempers out [[225/224]]. These all use the same generators as classical vishnu.
+The second comma in the comma list defines which 7-limit family member we are looking at. Septimal vishnu (118 & 152) adds [[4375/4374]]. Narayana (84 & 118) adds [[65625/65536]]. Vishnean (16 & 50) adds [[126/125]]. Vishy (16 & 18) adds [[50/49]]. There is also an unnamed 50 & 84 temperament, which tempers out [[225/224]]. These all use the same generators as classical vishnu.
-Quarvish (68 & 270) adds [[2401/2400]], splitting the generator in four. Decavish adds [[420175/419904]], with a 1/10-octave period.
+Trivish (84 & 186) adds [[250047/250000]], splitting the semi-octave period in three. Quarvish (68 & 270) adds [[2401/2400]], splitting the generator in four. Decavish (50 & 220) adds [[420175/419904]], splitting the semi-octave period in five.
 == Septimal vishnu ==
@@ Line 51: / Line 51: @@
 Comma list: 3025/3024, 4375/4374, 5632/5625
-Mapping: {{mapping| 2 4 5 10 10 | 0 -7 -3 -37 -26 }}
+{{Mapping|legend=0| 2 4 5 10 10 | 0 -7 -3 -37 -26 }}
 Optimal tunings:
@@ Line 66: / Line 66: @@
 Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625
-Mapping: {{mapping| 2 4 5 10 10 17 | 0 -7 -3 -37 -26 -81 }}
+{{Mapping|legend=0| 2 4 5 10 10 17 | 0 -7 -3 -37 -26 -81 }}
 Optimal tunings:
@@ Line 81: / Line 81: @@
 Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374
-Mapping: {{mapping| 2 4 5 10 10 1 | 0 -7 -3 -37 -26 54 }}
+{{Mapping|legend=0| 2 4 5 10 10 1 | 0 -7 -3 -37 -26 54 }}
 Optimal tuning:
@@ Line 115: / Line 115: @@
 Comma list: 441/440, 8019/8000, 65625/65536
-Mapping: {{mapping| 2 4 5 3 3 | 0 -7 -3 22 33 }}
+{{Mapping|legend=0| 2 4 5 3 3 | 0 -7 -3 22 33 }}
 Optimal tunings:
@@ Line 126: / Line 126: @@
 == Vishnean ==
-Named by [[Petr Pařízek]] in 2011<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, vishnean is a low-complexity low-accuracy extension of vishnu that tempers out 126/125, the [[starling comma]].
+Named by [[Petr Pařízek]] in 2011<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, vishnean is a low-complexity low-accuracy extension of vishnu that tempers out 126/125, the [[starling comma]]. It is also supported unideally by the [[84edo|84d]] ({{nowrap| {{=}} 34 + 50 }}) val, as the 7 is flat but the 11 is sharp such that they have opposing tendencies.
 [[Subgroup]]: 2.3.5.7
@@ Line 149: / Line 149: @@
 Comma list: 126/125, 385/384, 1350/1331
-Mapping: {{mapping| 2 4 5 5 8 | 0 -7 -3 5 -9 }}
+{{Mapping|legend=0| 2 4 5 5 8 | 0 -7 -3 5 -9 }}
 Optimal tunings:
@@ Line 164: / Line 164: @@
 Comma list: 105/104, 126/125, 144/143, 847/845
-Mapping: {{mapping| 2 4 5 5 8 8 | 0 -7 -3 5 -9 -5 }}
+{{Mapping|legend=0| 2 4 5 5 8 8 | 0 -7 -3 5 -9 -5 }}
 Optimal tunings:
@@ Line 173: / Line 173: @@
 Badness (Sintel): 1.68
+== Vishy ==
+Named by [[Godtone]] in 2026 after its inaccurate but simple interpretation of its half-octave period as [[7/5]][[~]][[10/7]], vishy tempers out [[50/49]] and represents the absolute simplest way to reach prime 7 by interpreting three ~25/24 generators as a significantly flat [[~]][[8/7]]. Its mapping might be deemed favorable because of all primes being reached in a negative number of generators, with the most complex, 11, being reached in -9 (as in vishnean). In fact, this temperament's mapping is identical to that of [[vishnean]] up to a simpler, higher-damage mapping of 7 in the same direction as all the other primes.
+The extreme tuning 50edo tunes 11 approximately pure and 7 a little better via the 50d val (= 16 + 34d), but damages 3, 7/3 and 11/7 significantly more than CWE, and has a dubiously flat-tending 5-limit. However, in light of this, one might consider [[84edo]] via the 84dd val (= 34d + 50d), where 7 is ~1.7{{c}} sharper but everything else is significantly more accurate, with the exception of a sharper 11; especially, the 5-limit is approximately in-tune, so that with its more accurate 11 (and marginally more accurate 7) it is a good alternative to 34edo.
+Therefore, it should be noted that as only the mapping of 7 differs from vishnean, using both mappings in any of [[34edo]], [[50edo]] and [[84edo]] (with [[2.3.5.11 subgroup]] fixed) could be seen as the primary and opportunistic utility of this temperament, by using whichever mapping of 7 happens to be more convenient or convincing in a given harmonic situation (if indeed the 7 is felt to be accurate enough).
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 50/49, 110592/109375
+{{Mapping|legend=1| 2 4 5 6 | 0 -7 -3 -3 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~7/5 = 598.8702{{c}}, ~25/24 = 70.6439{{c}}
+: [[error map]]: {{val| -2.260 -0.982 -3.895 +12.463 }}
+* [[CWE]]: ~7/5 = 600.0000{{c}}, ~25/24 = 71.9109{{c}}
+: error map: {{val| 0.000 +0.969 +0.654 +18.141 }}
+{{Optimal ET sequence|legend=0| 16, 18, 34d }}
+Badness (Sintel): 3.96
+=== 11-limit ===
+Other than [[176/175]], 11-limit vishy also tempers out [[625/616]] and [[1331/1323]].
+Subgroup: 2.3.5.7.11
+Comma list: 50/49, 176/175, 864/847
+{{Mapping|legend=0| 2 4 5 6 8 | 0 -7 -3 -3 -9 }}
+Optimal tunings:
+* WE: ~7/5 = 598.8234{{c}}, ~25/24 = 70.7100{{c}}
+: error map: {{val| -2.353 -1.631 -4.327 +11.984 +2.879 }}
+* CWE: ~7/5 = 600.0000{{c}}, ~25/24 = 71.1044{{c}}
+: error map: {{val| 0.000 -6.099 -2.375 +15.113 +0.498 }}
+{{Optimal ET sequence|legend=0| 16, 18e, 34d }}
+Badness (Sintel): 2.03
+== Trivish ==
+Trivish tempers out 250047/250000, the [[landscape comma]], with a 1/6-octave period. It may be described as the {{nowrap| 84 & 186 }} temperament. It is more significant in the [[11-limit]], where it tempers out the [[kalisma]] and the [[olympia]]. In the [[13-limit]], the generator can be taken as a [[~]][[14/13]]. [[270edo]] is an obvious tuning for it, but it can be tuned to [[354edo]], [[624edo]] or [[894edo]]. It was named by [[Flora Canou]] in 2026 for the fact that it splits the period of vishnu in three.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 250047/250000, 134217728/133984375
+{{Mapping|legend=1| 6 5 12 22 | 0 7 3 -8 }}
+: mapping generators: ~18375/16384, ~2205/2048
+[[Optimal tuning]]s:
+* [[WE]]: ~18375/16384 = 199.9885{{c}}, ~2205/2048 = 128.8583{{c}}
+: [[error map]]: {{val| -0.069 -0.005 +0.123 +0.054 }}
+* [[CWE]]: ~18375/16384 = 200.0000{{c}}, ~2205/2048 = 128.8643{{c}}
+: error map: {{val| 0.000 +0.095 +0.279 +0.256 }}
+{{Optimal ET sequence|legend=1| 84, 186, 270, 624, 894, 1164 }}
+[[Badness]] (Sintel): 1.51
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 9801/9800, 131072/130977, 151263/151250
+{{Mapping|legend=0| 6 5 12 22 33 | 0 7 3 -8 -19 }}
+Optimal tunings:
+* WE: ~55/49 = 199.9885{{c}}, ~320/297 = 128.8582{{c}}
+* CWE: ~55/49 = 200.0000{{c}}, ~320/297 = 128.8661{{c}}
+{{Optimal ET sequence|legend=0| 84, 186, 270, 624, 894, 1164 }}
+Badness (Sintel): 0.807
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 1716/1715, 2080/2079, 4096/4095, 34398/34375
+{{Mapping|legend=0| 6 5 12 22 33 28 | 0 7 3 -8 -19 -9 }}
+Optimal tunings:
+* WE: ~55/49 = 199.9922{{c}}, ~14/13 = 128.8565{{c}}
+* CWE: ~55/49 = 200.0000{{c}}, ~14/13 = 128.8621{{c}}
+{{Optimal ET sequence|legend=0| 84, 186, 270, 624, 894, 2058f }}
+Badness (Sintel): 0.791
+=== 2.3.5.7.11.13.19 subgroup ===
+Subgroup: 2.3.5.7.11.13.19
+Comma list: 1521/1520, 1716/1715, 2080/2079, 2376/2375, 3250/3249
+{{Mapping|legend=0| 6 5 12 22 33 28 30 | 0 7 3 -8 -19 -9 -7 }}
+Optimal tunings:
+* WE: ~55/49 = 199.9909{{c}}, ~14/13 = 128.8564{{c}}
+* CWE: ~55/49 = 200.0000{{c}}, ~14/13 = 128.8630{{c}}
+{{Optimal ET sequence|legend=0| 84, 186, 270, 624, 894 }}
+Badness (Sintel): 0.591
 == Quarvish ==
-Quarvish tempers out 2401/2400, the [[breedsma]], and may be described as the {{nowrap| 68 & 202 }} temperament.
+Quarvish tempers out 2401/2400, the [[breedsma]], and may be described as the {{nowrap| 68 & 270 }} temperament.
 [[Subgroup]]: 2.3.5.7
@@ Line 199: / Line 306: @@
 Comma list: 2401/2400, 9801/9800, 172032/171875
-Mapping: {{mapping| 2 4 5 6 6 | 0 -28 -12 -13 31 }}
+{{Mapping|legend=0| 2 4 5 6 6 | 0 -28 -12 -13 31 }}
 Optimal tunings:
@@ Line 210: / Line 317: @@
 == Decavish ==
-Decavish tempers out the [[wizma]] as well as the [[linus comma]], and may be described as the {{nowrap| 50 & 270 }} temperament. It was named by [[Xenllium]] in 2021 for the fact that its period is 1/10 octave.
+Decavish tempers out the [[wizma]] as well as the [[linus comma]], and may be described as the {{nowrap| 50 & 220 }} temperament. It was named by [[Xenllium]] in 2021 for the fact that its period is 1/10 octave.
 [[Subgroup]]: 2.3.5.7
@@ Line 234: / Line 341: @@
 Comma list: 9801/9800, 41503/41472, 172032/171875
-Mapping: {{mapping| 10 6 19 14 36 | 0 7 3 10 -1 }}
+{{Mapping|legend=0| 10 6 19 14 36 | 0 7 3 10 -1 }}
 Optimal tunings:
@@ Line 249: / Line 356: @@
 Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655
-Mapping: {{mapping| 10 6 19 14 36 37 | 0 7 3 10 -1 0 }}
+{{Mapping|legend=0| 10 6 19 14 36 37 | 0 7 3 10 -1 0 }}
 Optimal tunings:
@@ Line 262: / Line 369: @@
 <references/>
+[[Category:Vishnu family| ]] <!-- main article -->
 [[Category:Temperament families]]
-[[Category:Vishnu family| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]