Diatonic semitone: Difference between revisions
Add Wikipedia box, improve lead section (formulation now makes it clear that there are multiple intervals that can be called chromatic semitone), misc. edits |
No edit summary |
||
| (9 intermediate revisions by 5 users not shown) | |||
| Line 1: | Line 1: | ||
{{Wikipedia|Semitone#Minor second}} | {{Infobox|Title=Diatonic minor second|Header 1=MOS|Data 1=[[5L 2s]]|Header 2=Other names|Data 2=Minor 1-diastep, diatonic semitone, diatone|Header 3=Generator span|Data 3=-5 generators|Header 4=Tuning range|Data 4=0-171{{c}}|Header 5=Basic tuning|Data 5=100{{c}}|Header 6=Function on root|Data 6=Leading tone, supertonic|Header 7=Interval regions|Data 7=[[Comma and diesis]], [[Semitone (interval region)|Semitone]], [[Neutral second]]|Header 8=Associated just intervals|Data 8=[[16/15]], [[256/243]]|Header 9=Octave complement|Data 9=[[Major seventh (interval region)|Major seventh]]}}{{Wikipedia|Semitone #Minor second}} | ||
A '''diatonic semitone''', '''minor second''' or '''limma''' is the small step of a [[diatonic]] scale. | A '''diatonic semitone''', '''minor second''', or '''limma''' is the small step of a [[diatonic]] scale. | ||
In [[just intonation]], an interval may be classified as a diatonic semitone if it is reasonably mapped to [[7edo|1\7]] and [[24edo|2\24]] (precisely one step of the diatonic scale and one step of the chromatic scale). | In [[just intonation]], an interval may be classified as a diatonic semitone if it is reasonably mapped to [[7edo|1\7]] and [[24edo|2\24]] (precisely one step of the diatonic scale and one step of the chromatic scale). The use of 24edo's 2\24 as the mapping criteria here rather than [[12edo]]'s 1\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]]. | ||
== Examples == | == Examples == | ||
| Line 8: | Line 8: | ||
* [[16/15]], the classic diatonic semitone (5-limit) | * [[16/15]], the classic diatonic semitone (5-limit) | ||
* [[128/121]], the Axirabian diatonic semitone (11-limit; specifically belonging to the 2.3.11 subgroup) | * [[128/121]], the Axirabian diatonic semitone (11-limit; specifically belonging to the 2.3.11 subgroup) | ||
== Notation == | |||
The number of steps a limma is mapped to in an EDO is referred to as its [[limmanosity]], or penta-sharpness. | |||
== Etymology == | |||
According to the OED, the earliest English use of limma and [[apotome]] (alt. spelling "apotomy") with its musical as opposed to mathematical<ref>https://www.scientificlib.com/en/Mathematics/LX/Apotome.html</ref> meaning, is in 1694 in ''A Treatise of the Natural Grounds and Principles of Harmony''<ref>https://ota.bodleian.ox.ac.uk/repository/xmlui/bitstream/handle/20.500.12024/A44132/A44132.html</ref> by Church of England clergyman and natural philosopher William Holder. A relevant quote is "Difference between ... Tone Maj. and Limma. Apotome 2187 to 2048". The words are formed from the Greek, with "apo" meaning "away", "tome" meaning "cut" and limma meaning "remnant". So we begin with a major whole tone; the part cut away is the apotome (chromatic semitone) and the remnant is the limma (diatonic semitone). | |||
== See also == | == See also == | ||
* [[Chromatic semitone]] | * [[Chromatic semitone]] | ||
== References == | |||
<references /> | |||
[[Category:Diatonic]] | [[Category:Diatonic]] | ||
[[Category:Semitone]] | [[Category:Semitone]] | ||
Latest revision as of 00:44, 30 August 2025
| MOS | 5L 2s |
| Other names | Minor 1-diastep, diatonic semitone, diatone |
| Generator span | -5 generators |
| Tuning range | 0-171 ¢ |
| Basic tuning | 100 ¢ |
| Function on root | Leading tone, supertonic |
| Interval regions | Comma and diesis, Semitone, Neutral second |
| Associated just intervals | 16/15, 256/243 |
| Octave complement | Major seventh |
A diatonic semitone, minor second, or limma is the small step of a diatonic scale.
In just intonation, an interval may be classified as a diatonic semitone if it is reasonably mapped to 1\7 and 2\24 (precisely one step of the diatonic scale and one step of the chromatic scale). The use of 24edo's 2\24 as the mapping criteria here rather than 12edo's 1\12 better captures the characteristics of many intervals in the 11- and 13-limit.
Examples
- 256/243, the Pythagorean diatonic semitone (3-limit)
- 16/15, the classic diatonic semitone (5-limit)
- 128/121, the Axirabian diatonic semitone (11-limit; specifically belonging to the 2.3.11 subgroup)
Notation
The number of steps a limma is mapped to in an EDO is referred to as its limmanosity, or penta-sharpness.
Etymology
According to the OED, the earliest English use of limma and apotome (alt. spelling "apotomy") with its musical as opposed to mathematical[1] meaning, is in 1694 in A Treatise of the Natural Grounds and Principles of Harmony[2] by Church of England clergyman and natural philosopher William Holder. A relevant quote is "Difference between ... Tone Maj. and Limma. Apotome 2187 to 2048". The words are formed from the Greek, with "apo" meaning "away", "tome" meaning "cut" and limma meaning "remnant". So we begin with a major whole tone; the part cut away is the apotome (chromatic semitone) and the remnant is the limma (diatonic semitone).