28/27: Difference between revisions

Line 4:

| Monzo = 2 -3 0 1

| Cents = 62.9609

| Name = septimal chroma, septimal third-tone, <br>subminor second, septimal minor second

| Name = small septimal chroma, septimal third-tone, <br>subminor second, septimal minor second

| Color name = z2, zo 2nd

| FJS name = m2<sup>7</sup>

Line 10:

}}

The [[superparticular]] interval '''28/27''' (also '''septimal chroma''' or '''septimal third-tone''') 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]].

The [[superparticular]] interval '''28/27''' (also '''small septimal chroma''' or '''septimal third-tone''') 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]].

~~If treated as an interval~~ in ~~its own right, it may be described as the~~ septimal ~~subminor second, since it differs from~~ the ~~Pythagorean minor second~~ [[~~256~~/~~243~~]] by [[~~64/63~~]], and ~~from~~ [[16/15]] by [[36/35]]. This is analogous to the septimal major second [[8/7]], which has the same relationship with [[9/8]] and ~~[[10/9]], respectively. 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.

== See also ==

* [[27/14]] – its [[octave complement]]

* [[~~Trienstonic clan~~]]

* [[List of superparticular intervals]]

* [[Gallery of Just Intervals]]

* [[Trienstonic clan]], where it is tempered out

* [[Wikipedia:Septimal third tone|Septimal third tone - Wikipedia]]

[[Category:7-limit]]

[[Category:Interval]]

[[Category:Ratio]]

[[Category:Superparticular]]

[[Category:Second]]

[[Category:Semitone]]

[[Category:Third tone]]

~~[[Category:Chroma]]~~

@@ Line 4: / Line 4: @@
 | Monzo = 2 -3 0 1
 | Cents = 62.9609
-| Name = septimal chroma, septimal third-tone, <br>subminor second, septimal minor second
+| Name = small septimal chroma, septimal third-tone, <br>subminor second, septimal minor second
 | Color name = z2, zo 2nd
 | FJS name = m2<sup>7</sup>
@@ Line 10: / Line 10: @@
 }}
-The [[superparticular]] interval '''28/27''' (also '''septimal chroma''' or '''septimal third-tone''') 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]].
+The [[superparticular]] interval '''28/27''' (also '''small septimal chroma''' or '''septimal third-tone''') 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]].
-If treated as an interval in its own right, it may be described as the septimal subminor second, since it differs from the Pythagorean minor second [[256/243]] by [[64/63]], and from [[16/15]] by [[36/35]]. This is analogous to the septimal major second [[8/7]], which has the same relationship with [[9/8]] and [[10/9]], respectively. 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.
 == See also ==
 * [[27/14]] – its [[octave complement]]
-* [[Trienstonic clan]]
+* [[List of superparticular intervals]]
 * [[Gallery of Just Intervals]]
+* [[Trienstonic clan]], where it is tempered out
 * [[Wikipedia:Septimal third tone|Septimal third tone - Wikipedia]]
 [[Category:7-limit]]
 [[Category:Interval]]
+[[Category:Ratio]]
 [[Category:Superparticular]]
 [[Category:Second]]
 [[Category:Semitone]]
 [[Category:Third tone]]
-[[Category:Chroma]]