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.

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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== 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]]. (It is also supported unideally by the {{nowrap| ~~val 34 + 50~~ {{=}} ~~[[84edo|84d]]~~ }}, ~~unideal~~ as the 7 is flat but the 11 is sharp ~~s.t~~ they have opposing tendencies.)

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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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

Mapping: {{mapping| 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 }}

Badness (Sintel): 2.03

== Trivish ==

@@ 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.
 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 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]]. (It is also supported unideally by the {{nowrap| val 34 + 50 {{=}} [[84edo|84d]] }}, unideal as the 7 is flat but the 11 is sharp s.t they have opposing tendencies.)
+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 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: {{mapping| 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 ==