Semitone (interval region): Difference between revisions

A '''semitone''' is an interval that makes up part of a [[tone]], often as one step of a 12-tone chromatic scale. In [[just intonation]], an interval may be classified as a semitone if it is reasonably mapped to [[24edo|2\24]]. 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]]. Semitones come in two functional categories based on their number of steps in the [[5L 2s|diatonic]] scale:  

* [[Diatonic semitone]]s, minor seconds (m2), or limmas,

* [[Chromatic semitone]]s, augmented unisons (A1), or chromas.

As a concrete [[interval region]], it is typically near 100{{cent}} in size, distinct from [[commas and dieses]] (less than 60{{c}}), and from [[neutral second]]s (about 150{{c}}). A rough tuning range for the semitone is about 60{{c}} to 125{{c}} according to [[Margo Schulter]]'s theory of interval regions.  

The intervals covered in this article range from 50{{c}} to 140{{c}}.  

** The ''limma'', or ''Pythagorean diatonic semitone'', is a ratio of [[256/243]], and is about 90{{c}}.

** The ''apotome'', or ''Pythagorean chromatic semitone'', is a ratio of [[2187/2048]], and is about 114{{c}}.

** The ''classical diatonic semitone'' is a ratio of [[16/15]], and is about 112{{c}}.

** The ''classical chromatic semitone'' is a ratio of [[25/24]], and is about 71{{c}}.

*** There is also a ''ptolemaic chromatic semitone'', which is a ratio of [[135/128]], and is about 92{{c}}.

** The 7-limit ''third-tone'' is a ratio of [[28/27]], and is about 63{{c}}.

** The 7-limit ''minor semitone'' is a ratio of [[21/20]], and is about 84{{c}}.

** The 7-limit ''major semitone'' is a ratio of [[15/14]], and is about 119{{c}}.

** The 11-limit ''minor semitone'' is a ratio of [[22/21]], and is about 81{{c}}.

** The 13-limit ''sinaic'' is a ratio of [[14/13]], and is about 128{{c}}.

** The 13-limit ''greater 2/3-tone'' is a ratio of [[13/12]], and is about 139{{c}}.

** The 17-limit ''large semitone'' is a ratio of [[17/16]], and is about 104{{c}}.

** The 17-limit ''small semitone'' is a ratio of [[18/17]], and is about 99{{c}}.

| [[13/12]]

| 139{{c}}

| [[14/13]]

| 128{{c}}

| [[15/14]]

| 119{{c}}

| [[16/15]]

| 112{{c}}

| [[17/16]]

| 104{{c}}

| [[18/17]]

| 99{{c}}

| [[19/18]]

| 94{{c}}

| [[20/19]]

| 89{{c}}

| [[21/20]]

| 85{{c}}

| [[22/21]]

| 81{{c}}

| [[23/22]]

| 77{{c}}

| [[24/23]]

| 74{{c}}

| [[25/24]]

| 71{{c}}

| [[26/25]]

| 68{{c}}

| [[27/26]]

| 65{{c}}

| [[28/27]]

| 63{{c}}

| [[29/28]]

| 61{{c}}

| [[30/29]]

| 59{{c}}

| [[31/30]]

| 57{{c}}

| [[32/31]]

| 55{{c}}

| [[33/32]]

| 53{{c}}

| [[35/34]]

| 50{{c}}

| 12

| colspan="2" | 100{{c}}

|  

| 15

| colspan="2" | 80{{c}}

|  

| 16

| colspan="2" | 75{{c}}

|  

| 17

| 141{{c}}

| 71{{c}}

|  

| 19

| 126{{c}}

| 63{{c}}

|  

| 22

| 109{{c}}

| 55{{c}}

|  

| 24

| 100{{c}}

| 50{{c}}

|  

| 25

| 96{{c}}

| *

|  

| 26

| colspan="2" | 92{{c}}

|  

| 27

| 133{{c}}

| 89{{c}}

|  

| 29

| 124{{c}}

| 83{{c}}

|  

| 31

| 116{{c}}

| 77{{c}}

|  

| 34

| 106{{c}}

| 71{{c}}

|  

| 53

| 113{{c}}

| 68{{c}}

| 91{{c}} ≈ 256/243