21/20: Difference between revisions
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== 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>. | ||
== Interval chain == | |||
An [[interval chain]] of 21/20s stacked on top of one another comes close to approximating some important [[JI]] intervals. The error between the approximation and the target JI interval may be tempered out in some [[regular temperaments]]. | |||
Some examples include: | |||
* A stack of two 21/20 upwards is ~4¢ from [[11/10]] | |||
* A stack of seven 21/20 upwards is ~9¢ from [[7/5]] | |||
* A stack of ten 21/20 upwards is ~4¢ from [[13/8]] | |||
* A stack of twelve 21/20 upwards is ~4¢ from [[9/5]] | |||
and | |||
* A stack of six 21/20 downwards is ~10¢ from [[3/2]] | |||
* A stack of nine 21/20 downwards is ~5¢ from [[9/7]] | |||
* A stack of eleven 21/20 downwards is ~4¢ from [[7/6]] | |||
When treated as a scale, this interval chain can be called the '''[[ambitonal sequence]] of 21/20''' ('''AS21/20''' or '''1ed21/20'''). | |||
1ed21/20 is equal to approximately 14.2067 EDO, and as a result of tethering between compressed 14 and heavily stretched 15 it is quite xenharmonic in its sound. It is related to the [[nautilus]], [[sextilifourths]] and [[floral]] temperaments. | |||
1ed21/20 offers a possible approximation of the no-3s [[11-limit]]. It might alternatively be used as a [[dual-fifth tuning]]. | |||
{{Harmonics in equal|1|21|20|intervals=prime}} | |||
== See also == | == See also == | ||
* [[40/21]] – its [[octave complement]] | * [[40/21]] – its [[octave complement]] | ||
* [[10/7]] – its [[fifth complement]] | * [[10/7]] – its [[fifth complement]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||