Sensamagic clan: Difference between revisions

{{Mapping|legend=2| 1 1 2 | 0 2 -1 }}

These temperaments are distributed into different family pages.

* ''[[Hedgehog]]'' (+50/49) → [[Porcupine family #Hedgehog|Porcupine family]]

The others are weak extensions. Father tempers out [[16/15]], splitting the generator in two. Godzilla tempers out [[49/48]] with a hemitwelfth period. Sidi tempers out [[25/24]], splitting the generator in two with a hemitwelfth period. Clyde tempers out [[3136/3125]] with a 1/6-twelfth period. Superpyth tempers out [[64/63]], splitting the generator in six. Magic tempers out [[225/224]] with a 1/5-twelfth period. Octacot tempers out [[2401/2400]], splitting the generator in five. Hemiaug tempers out [[128/125]]. Pentacloud tempers out [[16807/16384]]. These split the generator in seven. Bamity tempers out [[64827/64000]], splitting the generator in nine. Rodan tempers out [[1029/1024]], splitting the generator in ten. Shrutar tempers out [[2048/2025]], splitting the generator in eleven. Finally, escaped tempers out [[65625/65536]], splitting the generator in sixteen.  

Considered below are bohpier, pycnic, salsa, superenneadecal, superthird, magus and leapweek.

Mapping: {{mapping| 1 0 0 0 2 | 0 13 19 23 12 }}

Mapping: {{mapping| 1 0 0 0 2 2 | 0 13 19 23 12 14 }}

Mapping: {{mapping| 1 0 0 0 0 | 0 39 57 69 85 }}

Mapping: {{mapping| 1 0 0 0 0 0 | 0 39 57 69 85 91 }}

: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #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]].

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 a cent sharp of it in the POTE 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.

== Salsa ==

{{See also| Schismatic family }}

[[Comma list]]: 245/243, 32805/32768

{{Mapping|legend=1| 1 1 7 -1 | 0 2 -16 13 }}

: mapping generators: ~2, ~128/105

* [[WE]]: ~2 = 1200.7707{{c}}, ~128/105 = 351.2748{{c}}

: [[error map]]: {{val| +0.771 +1.365 -1.315 -3.024 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~128/105 = 351.0471{{c}}

: error map: {{val| 0.000 +0.139 -3.068 -5.213 }}

 

{{Optimal ET sequence|legend=1| 17, 24, 41, 106d, 147d, 188cd }}

 

=== 11-limit ===

 

 

 

 

Badness (Sintel): 1.30

 

 

 

 

* WE: ~2 = 1199.9362{c}}, ~11/9 = 351.0061{{c}}

 

 

Badness (Sintel): 1.27

Mapping: {{mapping| 1 -2 2 -6 -6 | 0 11 1 27 29 }}

Mapping: {{mapping| 1 -2 2 -6 -6 5 | 0 11 1 27 29 -4 }}

Superenneadecal is a cousin of [[enneadecal]] but sharper fifth is used to temper 245/243.

Mapping: {{mapping| 19 0 14 -7 96 | 0 1 1 2 -1 }}

Mapping: {{mapping| 19 0 14 -7 96 10 | 0 1 1 2 -1 2 }}

Mapping: {{mapping| 1 -5 -5 -10 2 | 0 18 20 35 4 }}

Mapping: {{mapping| 1 -5 -5 -10 2 -8 | 0 18 20 35 4 32 }}

Mapping: {{mapping| 1 0 42 -21 -14 | 0 1 -25 15 11 }}

Mapping: {{mapping| 1 0 42 -21 -14 -9 | 0 1 -25 15 11 8 }}

Mapping: {{mapping| 1 0 42 -21 -14 -9 -34 | 0 1 -25 15 11 8 24 }}

Mapping: {{mapping| 1 0 42 -21 -14 -9 39 | 0 1 -25 15 11 8 -22 }}

[[Category:Pages with mostly numerical content]]

[[Category:Sensamagic clan| ]] <!-- main article -->

[[Category:Rank 2]]

[[Category:Listen]]