21/20: Difference between revisions
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{{Wikipedia|Septimal chromatic semitone}} | {{Wikipedia|Septimal chromatic semitone}} | ||
'''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 [[4/3]] and [[7/5]], [[8/7]] and [[6/5]], or [[5/3]] and [[7/4]]. | '''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 [[4/3]] and [[7/5]], [[8/7]] and [[6/5]], or [[5/3]] and [[7/4]]. | ||
== Terminology == | == 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>Marc Sabat. [https://masa.plainsound.org/pdfs/crystal-growth.pdf ''Three Crystal Growth Algorithms in 23-limit constrained Harmonic Space'']. Plainsound Music Edition, 2008.</ref>. | 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>Marc Sabat. [https://masa.plainsound.org/pdfs/crystal-growth.pdf ''Three Crystal Growth Algorithms in 23-limit constrained Harmonic Space'']. Plainsound Music Edition, 2008.</ref>. | ||
== In music == | |||
In what is known as an authentic cadence, there is a resolution from the V chord to the I chord. If the V is a [[4:5:6:7|harmonic seventh chord]], its harmonic seventh ([[21/16]] above the tonic) resolves down to the major third of the I chord ([[5/4]]) by a step of 21/20. | |||
== Approximation == | == Approximation == | ||
{{Interval edo approximation|21/20}} | {{Interval edo approximation|21/20}} | ||