No-fives subgroup temperaments: Difference between revisions

Hemif is the no-5 [[restriction]] of [[hemififths]], and the add-7 [[extension]] of [[namo]].

: [[error map]]: {{val| -0.270 +0.586 -0.284 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~2187/1792 = 351.4569{{c}}

{{Optimal ET sequence|legend=1| 17, 41, 58, 99, 239, 338, 437, 775b, 1212bb }}

[[Badness]] (Sintel): 0.901

Subgroup-val mapping: {{mapping| 1 1 -1 2 | 0 2 13 5 }}

Optimal tunings:  

* WE: ~2 = 1199.2633{{c}}, ~11/9 = 351.3189{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.4593{{c}}

{{Optimal ET sequence|legend=0| 17, 41, 58, 99e }}

Badness (Sintel): 0.409

Optimal tunings:  

* WE: ~2 = 1198.7603{{c}}, ~11/9 = 351.3275{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.6042{{c}}

{{Optimal ET sequence|legend=0| 17, 41, 58, 331deeeffff }}

Badness (Sintel): 0.358

Related temperaments: [[bunya]].

Subgroup-val mapping: {{mapping| 1 1 -1 2 0 | 0 4 26 10 29 }}

: mapping generators: ~2, ~21/19

Optimal tunings:

* WE: ~2 = 1199.2636{{c}}, ~21/19 = 175.6963{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~21/19 = 175.7665{{c}}

{{Optimal ET sequence|legend=0| 34dh, 41, 116e, 157e }}

Badness (Sintel): 0.984

{{See also| Heartland }}

This temperament is the common [[restriction]] of [[monkey]] and [[sesquiquartififths]].  

[[Subgroup]]: 2.3.7

[[Comma list]]: 34451725707/34359738368

{{Mapping|legend=2| 1 1 5 | 0 4 -15 }}

: mapping generators: ~2, ~567/512

* [[WE]]: ~2 = 1200.0845{{c}}, ~567/512 = 175.4449{{c}}

: [[error map]]: {{val| +0.085 -0.091 -0.076 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~567/512 = 175.4307{{c}}

: error map: {{val| 0.000 -0.232 -0.286 }}

{{Optimal ET sequence|legend=1| 7, 27d, 34, 41, 89, 130, 171, 643, 814, 985, 1156 }}

[[Badness]] (Sintel): 0.959

Comma list: 243/242, 65536/65219

Subgroup-val mapping: {{mapping| 1 1 5 2 | 0 4 -15 10 }}

* WE: ~2 = 1199.8467{{c}}, ~256/231 = 175.3468{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~256/231 = 175.3691{{c}}

{{Optimal ET sequence|legend=0| 7, 34, 41, 89, 130, 349e, 479e }}

Badness (Sintel): 0.801

Comma list: 243/242, 513/512, 1083/1078

Subgroup-val mapping: {{mapping| 1 1 5 2 6 | 0 4 -15 10 -12 }}

Optimal tunings:  

* WE: ~2 = 1199.9531{{c}}, ~21/19 = 175.3344{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~21/19 = 175.3417{{c}}

{{Optimal ET sequence|legend=0| 7, 34, 41, 89, 130, 219 }}

This temperament is the common [[restriction]] of [[tsaharuk]] and [[quanic]].  

{{Mapping|legend=2| 1 1 0| 0 5 24 }}

: mapping generators: ~2, ~243/224

* [[WE]]: ~2 = 1200.0302{{c}}, ~243/224 = 140.3698{{c}}

: [[error map]]: {{val| +0.030 -0.076 +0.050 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~243/224 = 140.3681{{c}}

: error map: {{val| 0.000 -0.115 +0.008 }}

{{Optimal ET sequence|legend=1| 17, 60, 77, 94, 171, 265, 436, 2351, 2787, 3223, 3659, 4095, 7754b }}

[[Badness]] (Sintel): 0.670

Comma list: 1331/1323, 19712/19683

Subgroup-val mapping: {{mapping| 1 1 0 1 | 0 5 24 21 }}

Optimal tunings:  

* CWE: ~2 = 1200.0000{{c}}, ~88/81 = 140.4133{{c}}

{{Optimal ET sequence|legend=0| 17, 60e, 77, 94 }}

Badness (Sintel): 0.887

Comma list: 352/351, 729/728, 1331/1323

 

 

 

 

 

[[Subgroup]]: 2.3.7

[[Comma list]]: {{monzo| 83 -1 -29 }}

{{Mapping|legend=2| 1 -4 3 | 0 29 -1 }}

[[Optimal tuning]]s:

* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 231.1024{{c}}

{{Optimal ET sequence|legend=0| 26, 83, 109, 135, 566, 701, 836, 971, 1106, 2077, 5260, 7337, 9414d }}

[[Badness]] (Sintel): 3.06

Subgroup: 2.3.7.11

Comma list: 43923/43904, 5767168/5764801

Subgroup-val mapping: {{mapping| 1 -4 3 5 | 0 29 -1 -8 }}

Optimal tunings:

* WE: ~2 = 1200.0050{{c}}, ~8/7 = 231.1024{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 231.1015{{c}}

{{Optimal ET sequence|legend=0| 26, 83, 109, 135, 566, 701, 836, 971, 1807, 2778, 4585 }}

See [[5th-octave temperaments #Slendroschismic]].

See [[15th-octave temperaments #Pentadecoid]].

Defined as the {{nowrap| 320 & 1803 }} temperament, in the 2.3.7.13.17.19 on the basis of the fact that 1803 tropical years make up almost exactly 100 saros cycles.