17/16: Difference between revisions

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* In [[Functional Just System]], it is a diatonic semitone, separated by [[4131/4096]] from the [[256/243|Pythagorean minor second (256/243)]]. It is also called the '''minor diatonic semitone''', which contrasts the [[5-limit]] major diatonic semitone of [[16/15]] by [[256/255]], about 6.8{{c}}.

* In [[Helmholtz–Ellis notation]], it is a chromatic semitone, separated by [[2187/2176]] from the [[2187/2048|Pythagorean augmented unison (2187/2048)]].

It could also be reasonable to treat 17/16 as the formal comma for prime 17 in its own right, as it is roughly the same size as the 3-limit accidental 2187/2048.

The term ''large septendecimal semitone'' omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the small septendecimal semitone of 18/17.

== Approximation ==

== Temperaments ==

The 17/16 interval generates [[srutal archagall]] with a half-octave period, where it also represents [[16/15]] and [[18/17]]. With a full-octave period it generates [[septendesemi]], the 80 & 103 temperament. It is also a good generator for [[lithium]] with a 1/3-octave period, as well as the less accurate [[august]].

It is very close to 7 steps of [[80edo]], and is tempered as such in many [[80th-octave temperaments]].

== See also ==

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 * In [[Functional Just System]], it is a diatonic semitone, separated by [[4131/4096]] from the [[256/243|Pythagorean minor second (256/243)]]. It is also called the '''minor diatonic semitone''', which contrasts the [[5-limit]] major diatonic semitone of [[16/15]] by [[256/255]], about 6.8{{c}}.
 * In [[Helmholtz–Ellis notation]], it is a chromatic semitone, separated by [[2187/2176]] from the [[2187/2048|Pythagorean augmented unison (2187/2048)]].
+It could also be reasonable to treat 17/16 as the formal comma for prime 17 in its own right, as it is roughly the same size as the 3-limit accidental 2187/2048.
 The term ''large septendecimal semitone'' omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the small septendecimal semitone of 18/17.
+== Approximation ==
+{{Interval edo approximation|17/16}}
+== Temperaments ==
+The 17/16 interval generates [[srutal archagall]] with a half-octave period, where it also represents [[16/15]] and [[18/17]]. With a full-octave period it generates [[septendesemi]], the 80 & 103 temperament. It is also a good generator for [[lithium]] with a 1/3-octave period, as well  as the less accurate [[august]].
+It is very close to 7 steps of [[80edo]], and is tempered as such in many [[80th-octave temperaments]].
 == See also ==