40/39: Difference between revisions

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=== Unintendo ===

This temperament was accidentally ~~named~~ when [[User:VectorGraphics|Vector]] described [[fendo]] as tempering out 40/39 in the 2.3.5.13 subgroup. The mistake has since been corrected. Its generators are a sharp perfect fifth and a flat major third. It can be described as {{nowrap| 7 & 15 & 10 }}. It equates 39/32 with 5/4 and equates 13/8 with 5/3, so it does not assosciate major with greater neutral and minor with lesser neutral as one would expect (see [[65/64]]), but the other way around.

This temperament was accidentally discovered when [[User:VectorGraphics|Vector]] described [[fendo]] as tempering out 40/39 in the 2.3.5.13 subgroup. The mistake has since been corrected, and the 2.3.5.13 temperament was renamed to "unintendo" to reflect its unintended discovery. Its generators are a sharp perfect fifth and a flat major third. It can be described as {{nowrap| 7 & 15 & 10 }}. It equates 39/32 with 5/4 and equates 13/8 with 5/3, so it does not assosciate major with greater neutral and minor with lesser neutral as one would expect (see [[65/64]]), but the other way around.

[[Subgroup]]: 2.3.5.13

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* [[CWE]]: ~2 = 1200{{c}}, ~3/2 = 710.153{{c}}, ~5/4 = 383.023{{c}}

[[Badness]] (~~Dirichlet~~): 0.227

[[Badness]] (Sintel): 0.227

== Notation ==

=== Sagittal notation ===

In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal | \\! }} and is called the '''13/5 small diesis''', or '''13/5S''' for short, because the simplest interval it notates is 13/5 (equiv. 13/10), as for example in C-F{{nbhsp}}{{sagittal | \\! }}. The primary role of {{ sagittal | \\! }} is [[6561/6400 #Sagittal notation|6400/6561]] (25S). The upward version is called '''5/13S''' or '''13/5S up''' and is represented (in a secondary role) by {{sagittal| //| }}.

@@ Line 10: / Line 10: @@
 === Unintendo ===
-This temperament was accidentally named when [[User:VectorGraphics|Vector]] described [[fendo]] as tempering out 40/39 in the 2.3.5.13 subgroup. The mistake has since been corrected. Its generators are a sharp perfect fifth and a flat major third. It can be described as {{nowrap| 7 & 15 & 10 }}. It equates 39/32 with 5/4 and equates 13/8 with 5/3, so it does not assosciate major with greater neutral and minor with lesser neutral as one would expect (see [[65/64]]), but the other way around.
+This temperament was accidentally discovered when [[User:VectorGraphics|Vector]] described [[fendo]] as tempering out 40/39 in the 2.3.5.13 subgroup. The mistake has since been corrected, and the 2.3.5.13 temperament was renamed to "unintendo" to reflect its unintended discovery. Its generators are a sharp perfect fifth and a flat major third. It can be described as {{nowrap| 7 & 15 & 10 }}. It equates 39/32 with 5/4 and equates 13/8 with 5/3, so it does not assosciate major with greater neutral and minor with lesser neutral as one would expect (see [[65/64]]), but the other way around.
 [[Subgroup]]: 2.3.5.13
@@ Line 23: / Line 23: @@
 * [[CWE]]: ~2 = 1200{{c}}, ~3/2 = 710.153{{c}}, ~5/4 = 383.023{{c}}
-[[Badness]] (Dirichlet): 0.227
+[[Badness]] (Sintel): 0.227
 == Notation ==
 === Sagittal notation ===
 In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal | \\! }} and is called the '''13/5 small diesis''', or '''13/5S''' for short, because the simplest interval it notates is 13/5 (equiv. 13/10), as for example in C-F{{nbhsp}}{{sagittal | \\! }}. The primary role of {{ sagittal | \\! }} is [[6561/6400 #Sagittal notation|6400/6561]] (25S). The upward version is called '''5/13S''' or '''13/5S up''' and is represented (in a secondary role) by {{sagittal| //| }}.