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Vishnu family: Difference between revisions

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m →Vishy: readd CE as it's lower damage on 7. also this is a rly inaccurate temp so having 4 digits after the decimal point of the cents value is definitely objectively overkill
m Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "
 
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Comma list: 3025/3024, 4375/4374, 5632/5625
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:  
Optimal tunings:  
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Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625
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:  
Optimal tunings:  
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Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374
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:  
Optimal tuning:  
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Comma list: 441/440, 8019/8000, 65625/65536
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:  
Optimal tunings:  
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Comma list: 126/125, 385/384, 1350/1331
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:  
Optimal tunings:  
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Comma list: 105/104, 126/125, 144/143, 847/845
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:  
Optimal tunings:  
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== Vishy ==
== 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. 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.
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.  


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.
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
[[Subgroup]]: 2.3.5.7
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~7/5 = 598.870{{c}}, ~25/24 = 70.644{{c}}
* [[WE]]: ~7/5 = 598.8702{{c}}, ~25/24 = 70.6439{{c}}
: [[error map]]: {{val| -2.260 -0.982 -3.895 +12.463 }}
: [[error map]]: {{val| -2.260 -0.982 -3.895 +12.463 }}
* [[CWE]]: ~7/5 = 600.000{{c}}, ~25/24 = 71.911{{c}}
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~25/24 = 71.9109{{c}}
: error map: {{val| 0.000 +0.969 +0.654 +18.141 }}
: error map: {{val| 0.000 +0.969 +0.654 +18.141 }}
* [[CEE]]: ~7/5 = 600.000{{c}}, ~25/24 = 71.954{{c}}
: error map: {{val| 0.000 -5.631 -2.175 +15.313 }}


{{Optimal ET sequence|legend=0| 16, 18, 34d }}
{{Optimal ET sequence|legend=0| 16, 18, 34d }}
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Comma list: 50/49, 176/175, 864/847
Comma list: 50/49, 176/175, 864/847


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


Optimal tunings:  
Optimal tunings:  
* WE: ~7/5 = 598.823{{c}}, ~25/24 = 70.710{{c}}
* WE: ~7/5 = 598.8234{{c}}, ~25/24 = 70.7100{{c}}
* CWE: ~7/5 = 600.000{{c}}, ~25/24 = 71.104{{c}}
: error map: {{val| -2.353 -1.631 -4.327 +11.984 +2.879 }}
* CEE: ~7/5 = 600.000{{c}}, ~25/24 = 72.021{{c}}
* 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 }}
{{Optimal ET sequence|legend=0| 16, 18e, 34d }}
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Comma list: 9801/9800, 131072/130977, 151263/151250
Comma list: 9801/9800, 131072/130977, 151263/151250


Mapping: {{mapping| 6 5 12 22 33 | 0 7 3 -8 -19 }}
{{Mapping|legend=0| 6 5 12 22 33 | 0 7 3 -8 -19 }}


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


Mapping: {{mapping| 6 5 12 22 33 28 | 0 7 3 -8 -19 -9 }}
{{Mapping|legend=0| 6 5 12 22 33 28 | 0 7 3 -8 -19 -9 }}


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


Mapping: {{mapping| 6 5 12 22 33 28 30 | 0 7 3 -8 -19 -9 -7 }}
{{Mapping|legend=0| 6 5 12 22 33 28 30 | 0 7 3 -8 -19 -9 -7 }}


Optimal tunings:  
Optimal tunings:  
Line 305: Line 306:
Comma list: 2401/2400, 9801/9800, 172032/171875
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:  
Optimal tunings:  
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Comma list: 9801/9800, 41503/41472, 172032/171875
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:  
Optimal tunings:  
Line 355: Line 356:
Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655
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:  
Optimal tunings:  
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