Sensamagic clan: Difference between revisions

Line 162:

: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Stump]].''

Pycnic is related to [[triton]], but its mapping differs for the [[5/1|~~5th~~ harmonic]]. It is also related to [[liese]], from which its mapping differs for the [[7/1|~~7th~~ harmonic]].

Pycnic is related to [[triton]], but its mapping differs for the [[7/1|7th harmonic]]. It is also related to [[liese]], from which its mapping differs for the [[5/1|5th harmonic]].

The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being two cents sharp of it in the CWE tuning for instance. Pycnic has [[mos]] of size 9, 11, 13, 15, 17… which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune.

Line 182:

[[Badness]] (Sintel): 1.87

== Xenia ==

: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Xenial]].''

Xenia is related to [[Starling temperaments #Xenial|xenial]], but its mapping differs for the [[7/1|7th harmonic]]. It may be described as {{nowrap| 19 & 51c }} or {{nowrap| 19 & 70d }}, which tempers out the sensamagic and keega, [[1029/1000]].

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 245/243, 1029/1000

: mapping generators: ~2, ~9/5

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1201.0862{{c}}, ~9/5 = 1012.0503{{c}}

: [[error map]]: {{val| +1.0862, -0.0196, +5.5068, -9.8977 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/5 = 1011.2199{{c}}

: error map: {{val| 0.0000 -0.9760, +4.4243, -11.7475 }}

[[Badness]] (Sintel): 2.25

== Magus ==

@@ Line 162: / Line 162: @@
 : ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Stump]].''
-Pycnic is related to [[triton]], but its mapping differs for the [[5/1|5th harmonic]]. It is also related to [[liese]], from which its mapping differs for the [[7/1|7th harmonic]].
+Pycnic is related to [[triton]], but its mapping differs for the [[7/1|7th harmonic]]. It is also related to [[liese]], from which its mapping differs for the [[5/1|5th harmonic]].
 The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being two cents sharp of it in the CWE tuning for instance. Pycnic has [[mos]] of size 9, 11, 13, 15, 17… which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune.
@@ Line 182: / Line 182: @@
 [[Badness]] (Sintel): 1.87
+== Xenia ==
+: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Xenial]].''
+Xenia is related to [[Starling temperaments #Xenial|xenial]], but its mapping differs for the [[7/1|7th harmonic]]. It may be described as {{nowrap| 19 & 51c }} or {{nowrap| 19 & 70d }}, which tempers out the sensamagic and keega, [[1029/1000]].
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 245/243, 1029/1000
+{{Mapping|legend=1| 1 -6 -12 -9 | 0 9 17 14 }}
+: mapping generators: ~2, ~9/5
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1201.0862{{c}}, ~9/5 = 1012.0503{{c}}
+: [[error map]]: {{val| +1.0862, -0.0196, +5.5068, -9.8977 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/5 = 1011.2199{{c}}
+: error map: {{val| 0.0000 -0.9760, +4.4243, -11.7475 }}
+{{Optimal ET sequence|legend=1| 19, 70d, 89d }}
+[[Badness]] (Sintel): 2.25
 == Magus ==