40/39: Difference between revisions

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'''40/39''' is the difference between the third octave of the third [[5/4]] (40 = 5 ⋅ 2<sup>3</sup>) and the fifth of the thirteenth partial of the same root (39 = 13 ⋅ 3). If tempered out, it ~~tempers together~~ [[5~~-limit~~]] and [[13~~-limit~~]]~~] intervals. However~~, 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~~. In particular [[5/4]]~[[39/32]] and [[6/5]]~[[16/13]] are temperings~~.

'''40/39''' is the difference between the third octave of the third [[5/4]] (40 = 5 ⋅ 2<sup>3</sup>) and the fifth of the thirteenth partial of the same root (39 = 13 ⋅ 3). If tempered out, it equates [[39/32]] with [[5/4]] and thus [[6/5]] with [[16/13]], so that 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.

== 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| //| }}.

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-'''40/39''' is the difference between the third octave of the third [[5/4]] (40 = 5 ⋅ 2<sup>3</sup>) and the fifth of the thirteenth partial of the same root (39 = 13 ⋅ 3). If tempered out, it tempers together [[5-limit]] and [[13-limit]]] intervals. However, 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. In particular [[5/4]]~[[39/32]] and [[6/5]]~[[16/13]] are temperings.
+'''40/39''' is the difference between the third octave of the third [[5/4]] (40 = 5 ⋅ 2<sup>3</sup>) and the fifth of the thirteenth partial of the same root (39 = 13 ⋅ 3). If tempered out, it equates [[39/32]] with [[5/4]] and thus [[6/5]] with [[16/13]], so that 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.
 == 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| //| }}.