18/17: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

~~| Ratio = 18/17~~

~~| Monzo = 1 2 0 0 0 0 -1~~

~~| Cents = 98.95459~~

| Name = small septendecimal semitone

| Color name = 17u1, su ~~semitone~~

| Color name = 17u1, su unison

~~| FJS name = A1<sub>17</sub>~~

| Sound = jid_18_17_pluck_adu_dr220.mp3

| Comma = yes

}}

In [[17-limit]] [[just intonation]], '''18/17''' is the '''small septendecimal semitone''' of about ~~99¢~~. It is very close to [[12edo~~|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¢).

~~There exists a disagreement in different~~ notation systems on whether 18/17 should be ~~notated as~~ a diatonic semitone or a chromatic semitone. In [[Functional Just System]], it is a chromatic semitone, ~~whereas in~~ [[Helmholtz-Ellis notation]], it is a diatonic semitone.

== Terminology and notation ==

Conceptualization systems disagree on whether [[17/16]] should be a [[diatonic semitone]] or a [[chromatic semitone]], and as a result the disagreement propagates to all intervals of [[harmonic class|HC17]]. See [[17-limit]] for a detailed discussion.

For 18/17 specifically:

* In the [[Functional Just System]], it is a chromatic semitone, separated by [[4131/4096]] from the [[2187/2048|Pythagorean augmented unison (2187/2048)]].

* In [[Helmholtz-Ellis notation]], it is a diatonic semitone, separated by [[2187/2176]] from the [[256/243|Pythagorean minor second (256/243)]].

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]]

* [[18/17s equal temperament|AS18/17]] - its ambitonal sequence

~~[[Category:17-limit]]~~

== References ==

~~[[Category:Interval]]~~

~~[[Category:Ratio]]~~

[[Category:Second]]

[[Category:Chroma]]

[[Category:Semitone]]

[[Category:~~Superparticular~~]]

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

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
-| Ratio = 18/17
-| Monzo = 1 2 0 0 0 0 -1
-| Cents = 98.95459
 | Name = small septendecimal semitone
-| Color name = 17u1, su semitone
+| Color name = 17u1, su unison
-| FJS name = A1<sub>17</sub>
 | Sound = jid_18_17_pluck_adu_dr220.mp3
+| Comma = yes
 }}
-In [[17-limit]] [[just intonation]], '''18/17''' is the '''small septendecimal semitone''' of about 99¢. It is very close to [[12edo|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¢).
-There exists a disagreement in different notation systems on whether 18/17 should be notated as a diatonic semitone or a chromatic semitone. In [[Functional Just System]], it is a chromatic semitone, whereas in [[Helmholtz-Ellis notation]], it is a diatonic semitone.
+== Terminology and notation ==
+Conceptualization systems disagree on whether [[17/16]] should be a [[diatonic semitone]] or a [[chromatic semitone]], and as a result the disagreement propagates to all intervals of [[harmonic class|HC17]]. See [[17-limit]] for a detailed discussion.
+For 18/17 specifically:
+* In the [[Functional Just System]], it is a chromatic semitone, separated by [[4131/4096]] from the [[2187/2048|Pythagorean augmented unison (2187/2048)]].
+* In [[Helmholtz-Ellis notation]], it is a diatonic semitone, separated by [[2187/2176]] from the [[256/243|Pythagorean minor second (256/243)]].
+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 19: / Line 34: @@
 * [[Gallery of just intervals]]
 * [[List of superparticular intervals]]
-* [[18/17s equal temperament|AS18/17]] - its ambitonal sequence
-[[Category:17-limit]]
+== References ==
-[[Category:Interval]]
+<references/>
-[[Category:Ratio]]
 [[Category:Second]]
 [[Category:Chroma]]
 [[Category:Semitone]]
-[[Category:Superparticular]]
+[[Category:Commas named after their interval size]]