18/17: Difference between revisions

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In [[17-limit]] [[just intonation]], '''18/17''' is the '''small septendecimal semitone''' of about ~~99¢~~. It is very close to [[12edo]]'s "half step" of 100¢, and fairly close to the "large septendecimal semitone" of [[17/16]] (~105¢).

In [[17-limit]] [[just intonation]], '''18/17''' is the '''small septendecimal semitone''' of about 99{{cent}}. It is very close to [[12edo]]'s "half step" of 100¢, and fairly close to the "large septendecimal semitone" of [[17/16]] (~105¢).

== Terminology and notation ==

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The term ''small septendecimal semitone'' omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal semitone of 17/16.

== Temperaments ==

{{w|Vincenzo Galilei}} (1520-1591) proposed a tuning based on eleven 18/17 semitones and one larger semitone of about 111.5{{cent}} (the [[octave complement]])<ref>Barbour, J. Murray. ''[https://archive.org/details/tuningtemperamen00barb/page/n7/mode/2up Tuning and temperament: a historical survey]'', p. 57.</ref>. This [[well temperament]] provides seven wide perfect fifths of about 705.2{{cent}} and five narrow perfect fifths of about 692.7{{cent}}, whose distribution is [[maximally even]] instead of grouping together the wide and the narrow fifths along the [[circle of fifths]], as is often the case in other well temperaments.

The following [[linear temperament]]s are [[generate]]d by a [[~]]18/17 in the 2.3.5.17 and 2.3.5.17.19 [[subgroup]]s:

* [[Quintaleap]]

* [[Quindromeda]]

* [[Schismatic_family#Quintilischis_(2.3.5.17)|Quintilischis]].

Note that all of these reach [[4/3]] as a stack of five 18/17 intervals (tempering out the [[quinticular comma]]).

Some [[12th-octave temperaments]] treat ~18/17 as the period, including [[compton]]'s 17-limit extension.

== See also ==

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* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

* [[1ed18/~~17]] – equal multiplication of this interval~~

== References ==

[[Category:Second]]

[[Category:Chroma]]

[[Category:Semitone]]

[[Category:Commas named after their interval size]]

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 }}
-In [[17-limit]] [[just intonation]], '''18/17''' is the '''small septendecimal semitone''' of about 99¢. It is very close to [[12edo]]'s "half step" of 100¢, and fairly close to the "large septendecimal semitone" of [[17/16]] (~105¢).
+In [[17-limit]] [[just intonation]], '''18/17''' is the '''small septendecimal semitone''' of about 99{{cent}}. It is very close to [[12edo]]'s "half step" of 100¢, and fairly close to the "large septendecimal semitone" of [[17/16]] (~105¢).
 == Terminology and notation ==
@@ Line 16: / Line 16: @@
 The term ''small septendecimal semitone'' omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal semitone of 17/16.
+== Temperaments ==
+{{w|Vincenzo Galilei}} (1520-1591) proposed a tuning based on eleven 18/17 semitones and one larger semitone of about 111.5{{cent}} (the [[octave complement]])<ref>Barbour, J. Murray. ''[https://archive.org/details/tuningtemperamen00barb/page/n7/mode/2up Tuning and temperament: a historical survey]'', p.&nbsp;57.</ref>. This [[well temperament]] provides seven wide perfect fifths of about 705.2{{cent}} and five narrow perfect fifths of about 692.7{{cent}}, whose distribution is [[maximally even]] instead of grouping together the wide and the narrow fifths along the [[circle of fifths]], as is often the case in other well temperaments.
+The following [[linear temperament]]s are [[generate]]d by a [[~]]18/17 in the 2.3.5.17 and 2.3.5.17.19 [[subgroup]]s:
+* [[Quintaleap]]
+* [[Quindromeda]]
+* [[Schismatic_family#Quintilischis_(2.3.5.17)|Quintilischis]].
+{{todo|complete list}}
+Note that all of these reach [[4/3]] as a stack of five 18/17 intervals (tempering out the [[quinticular comma]]).
+Some [[12th-octave temperaments]] treat ~18/17 as the period, including [[compton]]'s 17-limit extension.
 == See also ==
@@ Line 22: / Line 34: @@
 * [[Gallery of just intervals]]
 * [[List of superparticular intervals]]
-* [[1ed18/17]] – equal multiplication of this interval
+== References ==
+<references/>
 [[Category:Second]]
 [[Category:Chroma]]
 [[Category:Semitone]]
+[[Category:Commas named after their interval size]]