Escapade family: Difference between revisions

[[Comma list]]: 4294967296/4271484375

* [[WE]]: ~2 = 1199.8082{{c}}, ~16875/16384 = 55.2840{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~16875/16384 = 55.2961{{c}}

[[Badness]] (Sintel): 1.965

Since (an ideally slightly flat) 4/3 is split into 9 generators, it makes sense to equate the 3-generator interval to [[11/10]] by tempering out 4000/3993, and therefore the generator to {{nowrap| (11/10)/(16/15) {{=}} [[33/32]] }}; this does minimal damage to the temperament. This structure in 2.3.5.11 occurs in all extensions of escapade to include prime 7, and therefore will be considered the fount of all further extensions.

Comma list: 4000/3993, 5632/5625

{{Mapping|legend=2| 1 2 2 3 | 0 -9 7 10 }}

Optimal tunings:

* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 55.2770{{c}}

{{Optimal ET sequence|legend=0| 21, 22, 43, 65, 87, 152, 369, 521e }}

Badness (Sintel): 0.335

=== 2.3.5.11.31 subgroup ===

One may note that the generator represents the square root of [[16/15]] and therefore it would be logical to also temper out [[961/960]] ({{S|31}}) so that the generator is equated to {{nowrap| [[32/31]][[~]][[31/30]] }} in addition to 33/32.

For intervals along the chain of generators in the 2.3.5.11.31 subgroup temperament, out to 22 generators up, see the third column of [[16ed5/3 #Intervals]].

Comma list: 496/495, 961/960, 4000/3993

{{Mapping|legend=2| 1 2 2 3 5 | 0 -9 7 10 -1 }}

Optimal tunings:

* CWE: ~2 = 1200.0000{{c}}, ~32/31 = 55.2759{{c}}

{{Optimal ET sequence|legend=0| 21, 22, 43, 65, 87, 152, 369, 521e, 673e }}

Badness (Sintel): 0.251

= Strong extensions =

== Escaped ==

This temperament was also known as ''sensa'' in earlier materials because it tempers out 245/243, 352/351, and 385/384 as a sensamagic temperament. ''Not to be confused with the {{nowrap| 19e & 27 }} temperament (sensi extension).''

* [[WE]]: ~2 = 1199.9190{{c}}, ~28/27 = 55.1186{{c}}

: [[error map]]: {{val| -0.081 +1.816 -0.646 -2.232 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~28/27 = 55.1242{{c}}

[[Badness]] (Sintel): 2.25

=== 11-limit ===

{{Mapping|legend=0| 1 2 2 4 3 | 0 -9 7 -26 10 }}

Optimal tunings:

* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 55.1271{{c}}

Badness (Sintel): 1.18

=== 13-limit ===

{{Mapping|legend=0| 1 2 2 4 3 2 | 0 -9 7 -26 10 37 }}

Optimal tunings:

* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 55.1382{{c}}

Badness (Sintel): 1.30

== Alphaquarter ==

Given the slightly sharp ~[[3/2]] in ideal tunings of escapade (between [[65edo]] and [[87edo]]), it does very little damage to temper out [[5120/5103]] to extend it to prime 7; the cost is that the harmonic 7 is exceedingly complex, located all the way at 61 generators up.

* [[WE]]: ~2 = 1199.7349{{c}}, ~16128/15625 = 55.2306{{c}}

: [[error map]]: {{val| -0.265 +0.439 -0.230 +0.242 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~16128/15625 = 55.2405{{c}}

[[Badness]] (Sintel): 2.95

=== 11-limit ===

{{Mapping|legend=0| 1 2 2 0 3 | 0 -9 7 61 10 }}

Optimal tunings:

* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 55.2407{{c}}

Badness (Sintel): 0.980

=== 13-limit ===

{{Mapping|legend=0| 1 2 2 0 3 2 | 0 -9 7 61 10 37 }}

Optimal tunings:

* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 55.2328{{c}}

Badness (Sintel): 1.047

* [[WE]]: ~2 = 1198.9926{{c}}, ~49/48 = 55.2809{{c}}

: [[error map]]: {{val| -1.007 -1.498 -1.363 +7.028 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/48 = 55.3479{{c}}

[[Badness]] (Sintel): 1.97

=== 11-limit ===

{{Mapping|legend=0| 1 2 2 3 3 | 0 -9 7 -4 10 }}

Optimal tunings:

* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 55.3574{{c}}

Badness (Sintel): 1.21

=== 13-limit ===

{{Mapping|legend=0| 1 2 2 3 3 3 | 0 -9 7 -4 10 15 }}

Optimal tunings:

* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 55.5480{{c}}

Badness (Sintel): 1.457

= Weak extensions =

== Septisuperfourth ==

[[Optimal tuning]]s:

* [[WE]]: ~343/243 = 599.8762{{c}}, ~405/392 = 55.3089{{c}}

: [[error map]]: {{val| -0.248 -0.230 +0.353 +0.674 }}

* [[CWE]]: ~343/243 = 600.0000{{c}}, ~405/392 = 55.3273{{c}}

[[Badness]] (Sintel): 1.50

=== 11-limit ===

{{Mapping|legend=0| 2 4 4 7 6 | 0 -9 7 -15 10 }}

Optimal tunings:

* CWE: ~99/70 = 600.0000{{c}}, ~33/32 = 55.3081{{c}}

{{Optimal ET sequence|legend=0| 22, 86, 108, 130, 152, 282, 434de, 716dee, 1150cdddeee }}

Badness (Sintel): 0.814

{{Mapping|legend=0| 2 4 4 7 6 11 | 0 -9 7 -15 10 -39 }}

Optimal tunings:

* CWE: ~99/70 = 600.0000{{c}}, ~33/32 = 55.3295{{c}}

{{Optimal ET sequence|legend=0| 22f, 108f, 130, 282, 976cddeeeff }}

Badness (Sintel): 0.946

This temperament is also known as ''biscapade''.

{{Mapping|legend=0| 2 4 4 7 6 5 | 0 -9 7 -15 10 26 }}

Optimal tunings:

* CWE: ~55/39 = 600.0000{{c}}, ~33/32 = 55.3584{{c}}

Badness (Sintel): 1.37

== Arch ==

* [[WE]]: ~2 = 1199.9246{{c}}, ~64/63 = 27.6662{{c}}

: [[error map]]: {{val| -0.075 -0.097 +0.862 -0.661 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~64/63 = 27.6676{{c}}

: error map: {{val| 0.000 +0.029 +1.032 -0.461 }}

{{Optimal ET sequence|legend=1| 43, 87, 130, 217, 347 }}

=== 11-limit ===

{{Mapping|legend=0| 1 2 2 2 3 | 0 -18 14 35 20 }}

Optimal tunings:

* CWE: ~2 = 1200.0000{{c}}, ~64/63 = 27.6617{{c}}

{{Optimal ET sequence|legend=0| 43, 87, 130, 217, 347e }}

Badness (Sintel): 1.21

=== 13-limit ===

{{Mapping|legend=0| 1 2 2 2 3 4 | 0 -18 14 35 20 -13 }}

Optimal tunings:

* CWE: ~2 = 1200.0000{{c}}, ~64/63 = 27.6594{{c}}

Badness (Sintel): 0.806

[[Category:Catalogs of rank-2 temperaments]]