21/20: Difference between revisions

Line 4:

| Monzo = -2 1 -1 1

| Cents = 84.4672

| Name = minor semitone, large septimal chroma

| Name = septimal minor semitone, large septimal chroma

| Color name = zg2, zogu 2nd

| FJS name = m275

Line 12:

'''21/20''' is a small semitone of about 85 cents. It may be found in [[7-limit]] [[just intonation]] as, for example, the difference between [[8/7]] and [[6/5]], or between [[5/3]] and [[7/4]].

~~Although~~ called a ''chroma'' for its proximity (and conflation in systems like septimal [[meantone]]) with the major chroma [[135/128]], ~~21/20~~ is a ''diatonic semitone'' in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] ~~because it is~~ [[5120/5103]] ~~smaller than~~ the ~~Pythagorean~~ minor ~~second~~ [[~~256~~/~~243~~]].

== Terminology ==

21/20 is traditionally called a ''chroma'', perhaps for its proximity (and conflation in systems like septimal [[meantone]]) with the major chroma [[135/128]]. However, it is a ''diatonic semitone'' in both [[Helmholtz-Ellis notation]] and [[Functional Just System]], viewed as the Pythagorean minor second [[256/243]] altered by [[5120/5103]]. [[Marc Sabat]] has taken to call it the ''minor diatonic semitone'' in the same material where [[15/14]] is also named as the major chromatic semitone<ref>[https://marsbat.space/pdfs/crystal-growth.pdf Marc Sabat (2008) Three Crystal Growth Algorithms in 23-limit constrained Harmonic Space]</ref>.

== See also ==

@@ Line 4: / Line 4: @@
 | Monzo = -2 1 -1 1
 | Cents = 84.4672
-| Name = minor semitone, <br>large septimal chroma
+| Name = septimal minor semitone, <br>large septimal chroma
 | Color name = zg2, zogu 2nd
 | FJS name = m2<sup>7</sup><sub>5</sub>
@@ Line 12: / Line 12: @@
 '''21/20''' is a small semitone of about 85 cents. It may be found in [[7-limit]] [[just intonation]] as, for example, the difference between [[8/7]] and [[6/5]], or between [[5/3]] and [[7/4]].
-Although called a ''chroma'' for its proximity (and conflation in systems like septimal [[meantone]]) with the major chroma [[135/128]], 21/20 is a ''diatonic semitone'' in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is [[5120/5103]] smaller than the Pythagorean minor second [[256/243]].
+== Terminology ==
+/20 is traditionally called a ''chroma'', perhaps for its proximity (and conflation in systems like septimal [[meantone]]) with the major chroma [[135/128]]. However, it is a ''diatonic semitone'' in both [[Helmholtz-Ellis notation]] and [[Functional Just System]], viewed as the Pythagorean minor second [[256/243]] altered by [[5120/5103]]. [[Marc Sabat]] has taken to call it the ''minor diatonic semitone'' in the same material where [[15/14]] is also named as the major chromatic semitone<ref>[https://marsbat.space/pdfs/crystal-growth.pdf Marc Sabat (2008) Three Crystal Growth Algorithms in 23-limit constrained Harmonic Space]</ref>.
+<references/>
 == See also ==