Semitone (interval region): Difference between revisions
m Fix links |
Use todo template, improve linking, remove bold on terms which aren't lemmas |
||
| Line 1: | Line 1: | ||
{{Wikipedia}} | {{Wikipedia}} | ||
{{About|the [[interval region]]|the interval size unit of exactly 100 cents|Interval size measure#Gross}} | {{About|the [[interval region]]|the interval size unit of exactly 100 cents|Interval size measure#Gross}} | ||
A '''semitone''' is an interval that is near 100 [[cent]]s in size, distinct from [[ | A '''semitone''' is an interval that is near 100 [[cent]]s in size, distinct from [[commas and dieses]] (less than 60 cents), and from [[major second]]s (about 200 cents). A rough tuning range for the semitone is about 50 cents to 140 cents, though this is extremely wide; some might prefer to restrict it to around 70 cents to 130 cents. | ||
Semitones tend to fall into one of two functional categories, based on the system being used: | Semitones tend to fall into one of two functional categories, based on the system being used: | ||
| Line 10: | Line 10: | ||
== In just intonation == | == In just intonation == | ||
=== By prime limit === | === By prime limit === | ||
In the low prime limits, up to the 5-limit, in which the West has developed a formal system of diatonic harmony, the distinction between diatonic and chromatic semitones is the clearest, so a pair of 2 semitones will be provided for each. However, higher than the 5-limit, function as diatonic vs. chromatic tends to become less clear, and larger intervals can be seen as belonging to neither category. | In the low prime limits, up to the 5-limit, in which the West has developed a formal system of diatonic harmony, the distinction between diatonic and chromatic semitones is the clearest, so a pair of 2 semitones will be provided for each. However, higher than the 5-limit, function as diatonic vs. chromatic tends to become less clear, and larger intervals can be seen as belonging to neither category. | ||
* In the 3-limit: | * In the 3-limit: | ||
** The ''' | ** The ''limma'', or ''Pythagorean diatonic semitone'', is a ratio of [[256/243]], and is about 90 cents. | ||
** The ''' | ** The ''apotome'', or ''Pythagorean chromatic semitone'', is a ratio of [[2187/2048]], and is about 114 cents. | ||
* In the 5-limit: | * In the 5-limit: | ||
** The | ** The ''classical diatonic semitone'' is a ratio of [[16/15]], and is about 112 cents. | ||
** The | ** The ''classical chromatic semitone'' is a ratio of [[25/24]], and is about 71 cents. | ||
*** There is also a | *** There is also a ''ptolemaic chromatic semitone'', which is a ratio of [[135/128]], and is about 92 cents. | ||
* In higher limits: | * In higher limits: | ||
** The 7-limit | ** The 7-limit ''third-tone'' is a ratio of [[28/27]], and is about 63 cents. | ||
** The 7-limit | ** The 7-limit ''minor semitone'' is a ratio of [[21/20]], and is about 84 cents. | ||
** The 7-limit | ** The 7-limit ''major semitone'' is a ratio of [[15/14]], and is about 119 cents. | ||
** The 11-limit | ** The 11-limit ''minor semitone'' is a ratio of [[22/21]], and is about 81 cents. | ||
** The 13-limit | ** The 13-limit ''sinaic'' is a ratio of [[14/13]], and is about 128 cents. | ||
** The 13-limit | ** The 13-limit ''greater 2/3-tone'' is a ratio of [[13/12]], and is about 139 cents. | ||
** The 17-limit | ** The 17-limit ''large semitone'' is a ratio of [[17/16]], and is about 104 cents. | ||
** The 17-limit | ** The 17-limit ''small semitone'' is a ratio of [[18/17]], and is about 99 cents. | ||
=== By delta === | === By delta === | ||
| Line 109: | Line 108: | ||
== In EDOs == | == In EDOs == | ||
The following table lists the best tuning of 16/15, 25/24, and other semitones if present, in various significant [[ | The following table lists the best tuning of 16/15, 25/24, and other semitones if present, in various significant [[EDO]]s. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
| Line 190: | Line 189: | ||
== In regular temperaments == | == In regular temperaments == | ||
Two important, simple semitone ratios are 16/15 and 25/24. The following notable temperaments are generated by them: | Two important, simple semitone ratios are 16/15 and 25/24. The following notable temperaments are generated by them: | ||
=== Temperaments that use 25/24 as a generator === | === Temperaments that use 25/24 as a generator === | ||
* [[Vishnu]], which stacks seven 25/24s to make a just [[perfect fourth]] of [[4/3]] | |||
* Vishnu, which stacks seven 25/24s to make a just [[perfect fourth]] of [[4/3]] | * [[Chlorine]], equivalent to [[17edo]], stacking seventeen 25/24s to make an octave | ||
* Chlorine, equivalent to [[17edo]], stacking seventeen 25/24s to make an octave | |||
=== Temperaments that use 16/15 as a generator === | === Temperaments that use 16/15 as a generator === | ||
{{todo|inline=1|complete list}} | |||
When 25/24 is tempered out, it leads to [[dicot]] temperament. | When 25/24 is tempered out, it leads to [[dicot]] temperament. | ||
When 16/15 is tempered out, it leads to [[father]] temperament. | When 16/15 is tempered out, it leads to [[father]] temperament. | ||
{{Navbox intervals}} | {{Navbox intervals}} | ||
[[Category:12edo]] | [[Category:12edo]] | ||