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 | '''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 == | == 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| //| }}. | 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| //| }}. | ||
Revision as of 20:33, 12 November 2024
| Interval information |
tridecimal minor diesis
reduced
40/39 is the difference between the third octave of the third 5/4 (40 = 5 ⋅ 23) 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 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 . The primary role of is 6400/6561 (25S). The upward version is called 5/13S or 13/5S up and is represented (in a secondary role) by .