28/27: Difference between revisions
m Mention of enneadecal |
It need to be pointed out the names differ by contexts (and "septimal third-tone" sounds most neutral so I place it first) |
||
| Line 4: | Line 4: | ||
| Monzo = 2 -3 0 1 | | Monzo = 2 -3 0 1 | ||
| Cents = 62.9609 | | Cents = 62.9609 | ||
| Name = | | Name = septimal third-tone, <br>small septimal chroma, <br>subminor second, <br>septimal minor second, <br>trienstonic comma | ||
| Color name = z2, zo 2nd | | Color name = z2, zo 2nd | ||
| FJS name = m2<sup>7</sup> | | FJS name = m2<sup>7</sup> | ||
| Line 10: | Line 10: | ||
}} | }} | ||
The [[superparticular]] interval '''28/27''' | The [[superparticular]] interval '''28/27''', '''septimal third-tone''' or '''small septimal chroma''' has the seventh triangular number as a numerator and is the difference between [[15/14]] and [[10/9]], [[9/8]] and [[7/6]], [[9/7]] and [[4/3]], [[3/2]] and [[14/9]], [[12/7]] and [[16/9]], and [[9/5]] and [[28/15]]. | ||
Although called a ''chroma'' for its proximity (and conflation in systems like [[septimal meantone]]) with the classic chroma [[25/24]], 28/27 is a ''diatonic semitone'' in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is [[64/63]] smaller than the Pythagorean minor second [[256/243]]. Hence, it may be described as the '''septimal minor second''' or '''subminor second''' if treated as an interval in its own right. This is analogous to the septimal major second [[8/7]], which has the same relationship with [[9/8]], and such classification suggests the function of a strong leading tone added to the traditional harmony. | Although called a ''chroma'' for its proximity (and conflation in systems like [[septimal meantone]]) with the classic chroma [[25/24]], 28/27 is a ''diatonic semitone'' in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is [[64/63]] smaller than the Pythagorean minor second [[256/243]]. Hence, it may be described as the '''septimal minor second''' or '''subminor second''' if treated as an interval in its own right. This is analogous to the septimal major second [[8/7]], which has the same relationship with [[9/8]], and such classification suggests the function of a strong leading tone added to the traditional harmony. | ||
It is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament. | It is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament. | ||
On the other side of things, it may be called the '''trienstonic comma''' if treated as a [[comma]] to be tempered out, and in fact the [[trienstonic clan]] does exactly that. | |||
== See also == | == See also == | ||
| Line 31: | Line 33: | ||
[[Category:Third tone]] | [[Category:Third tone]] | ||
[[Category:Chroma]] | [[Category:Chroma]] | ||
[[Category:Medium comma]] | |||
[[Category:Trienstonic]] | |||