Vishnu family: Difference between revisions

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== Vishy ==

Named by [[~~User:Godtone|~~Godtone]] after its inaccurate but simple interpretation of its half-octave period as ~~[[~]]~~[[7/5]][[~]][[10/7]], vishy represents the absolute simplest way to reach prime 7 by interpreting three ~~chromas (~~~25/24 ~~gens)~~ 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. It is also supported by [[50edo]] via the 50d [[val]], recommendable for its lower damage on prime 7, being close to an optimal tuning of it ~~(when disregarding note count of the edo)~~. It's also recommendable in [[84edo]] via the 84dd val, where 7 is ~1.7{{c}} sharper but everything else is significantly more accurate.

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. It is also supported by [[50edo]] via the 50d [[val]], recommendable for its lower damage on prime 7, being close to an optimal tuning of it. It is also recommendable in [[84edo]] via the 84dd val, where 7 is ~1.7{{c}} sharper but everything else is significantly more accurate.

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.

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[[Subgroup]]: 2.3.5.7

[[Comma list]]: ~~6115295232~~/~~6103515625~~, ~~[[50~~/~~49]]~~

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

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

Optimal tuning:

[[Optimal tuning]]s:

* CE: ~7/5 = 600.~~000~~{{c}}, ~25/24 = 71.~~954~~{{c}}

* [[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.~~964~~

Badness (Sintel): 3.96

=== 11-limit ===

Subgroup: 2.3.5.7.11

Comma list: [[176/175~~]], [[625/616]]~~, ~~[[1331~~/~~1323]]~~

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

Mapping: {{mapping| 2 4 5 6 8 | 0 -7 -3 -3 -9 }}

Optimal ~~tuning~~:

Optimal tunings:

* CE: ~7/5 = 600.~~000~~{{c}}, ~25/24 = 72.~~021~~{{c}}

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

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

Badness (Sintel): 2.~~028~~

Badness (Sintel): 2.03

== Trivish ==

@@ Line 175: / Line 175: @@
 == Vishy ==
-Named by [[User:Godtone|Godtone]] after its inaccurate but simple interpretation of its half-octave period as [[~]][[7/5]][[~]][[10/7]], vishy represents the absolute simplest way to reach prime 7 by interpreting three chromas (~25/24 gens) 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. It is also supported by [[50edo]] via the 50d [[val]], recommendable for its lower damage on prime 7, being close to an optimal tuning of it (when disregarding note count of the edo). It's also recommendable in [[84edo]] via the 84dd val, where 7 is ~1.7{{c}} sharper but everything else is significantly more accurate.
+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. It is also supported by [[50edo]] via the 50d [[val]], recommendable for its lower damage on prime 7, being close to an optimal tuning of it. It is also recommendable in [[84edo]] via the 84dd val, where 7 is ~1.7{{c}} sharper but everything else is significantly more accurate.
 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.
@@ Line 181: / Line 181: @@
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 6115295232/6103515625, [[50/49]]
+[[Comma list]]: 50/49, 110592/109375
-Mapping: {{mapping| 2 4 5 6 | 0 -7 -3 -3 }}
+{{Mapping|legend=1| 2 4 5 6 | 0 -7 -3 -3 }}
-Optimal tuning:
+[[Optimal tuning]]s:
-* CE: ~7/5 = 600.000{{c}}, ~25/24 = 71.954{{c}}
+* [[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): 3.964
+Badness (Sintel): 3.96
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: [[176/175]], [[625/616]], [[1331/1323]]
+Comma list: 50/49, 176/175, 864/847
 Mapping: {{mapping| 2 4 5 6 8 | 0 -7 -3 -3 -9 }}
-Optimal tuning:
+Optimal tunings:
-* CE: ~7/5 = 600.000{{c}}, ~25/24 = 72.021{{c}}
+* WE: ~7/5 = 598.8234{{c}}, ~25/24 = 70.7100{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~25/24 = 71.1044{{c}}
 {{Optimal ET sequence|legend=0| 16, 18e, 34d }}
-Badness (Sintel): 2.028
+Badness (Sintel): 2.03
 == Trivish ==