Interval region: Difference between revisions

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It is well-known that there are infinite possible intervals, even if one confines one's view to a single octave. This includes the rational intervals of [[just intonation]] and the irrational intervals of [[EDO]]s, [[edonoi]]s, and other systems. However, it is helpful to consider '''interval categories''', which there may be a finite number to consider.

It is well-known that there are infinite possible intervals, even if one confines one's view to a single octave. This includes the rational intervals of [[just intonation]] and the irrational intervals of [[EDO]]s, [[edonoi]]s, and other systems. However, it is helpful to consider '''interval regions''' (or '''interval categories'''), which there may be a finite number to consider.

==~~The Schulter System~~==

== Extended-diatonic interval names ==

Many interval naming systems extend the diatonic interval names by adding new [[interval qualities]] to the usual set. While some systems preserve the fifth-based structure entirely, other systems define regions based on the proximity to the intervals associated with the diatonic intervals, which are then divided into finer subregions.

[[~~Margo_Schulter|~~Margo Schulter]] describes her system for categorizing intervals in [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum], which begins:

== Schulter system ==

[[Margo Schulter]] describes her system for categorizing intervals in ''[http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum]'', which begins:

~~''"~~In naming categories of intervals, or regions of the spectrum in which they are found, there may be many valid and desirable schemes reflecting the diversity of viewpoints and styles to be found in world musics. What I describe here is merely one possible solution, and one influenced by my own musicmaking experience and philosophy which seeks an equitable and inclusive balance between intervals at or near simple integer ratios, and those having a more complex or active nature.~~"''~~

: In naming categories of intervals, or regions of the spectrum in which they are found, there may be many valid and desirable schemes reflecting the diversity of viewpoints and styles to be found in world musics. What I describe here is merely one possible solution, and one influenced by my own musicmaking experience and philosophy which seeks an equitable and inclusive balance between intervals at or near simple integer ratios, and those having a more complex or active nature.

Schulter proposes the following categories and gives a tentative range of cents values for intervals that fall within those categories. In ''Regions'', she points out, "A main caution is that the borders are inevitably 'fuzzy,' so that one region shades into another and suggested values in cents are more illustrative than definitive."

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~~See: [[Interval_size_measure|interval size measure]], [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]~~

<pre>Pure unison (1:1) 0 cents

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Pure octave (2:1) 1200 cents</pre>

== See also ==

* [[Mike Sheiman's Alternative Interval Categorizations]]

* [[SKULO interval names]]

* [[Interval size measure]]

* [[Gallery of just intervals]]

[[Category:Interval region| ]]

[[Category:Classification]]

[[Category:Distance measure]]

@@ Line 1: / Line 1: @@
-It is well-known that there are infinite possible intervals, even if one confines one's view to a single octave. This includes the rational intervals of [[just intonation]] and the irrational intervals of [[EDO]]s, [[edonoi]]s, and other systems. However, it is helpful to consider '''interval categories''', which there may be a finite number to consider.
+It is well-known that there are infinite possible intervals, even if one confines one's view to a single octave. This includes the rational intervals of [[just intonation]] and the irrational intervals of [[EDO]]s, [[edonoi]]s, and other systems. However, it is helpful to consider '''interval regions''' (or '''interval categories'''), which there may be a finite number to consider.
-==The Schulter System==
+== Extended-diatonic interval names ==
+{{Main|Extended-diatonic interval names}}
+Many interval naming systems extend the diatonic interval names by adding new [[interval qualities]] to the usual set. While some systems preserve the fifth-based structure entirely, other systems define regions based on the proximity to the intervals associated with the diatonic intervals, which are then divided into finer subregions.
-[[Margo_Schulter|Margo Schulter]] describes her system for categorizing intervals in [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum], which begins:
+== Schulter system ==
+[[Margo Schulter]] describes her system for categorizing intervals in ''[http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum]'', which begins:
-''"In naming categories of intervals, or regions of the spectrum in which they are found, there may be many valid and desirable schemes reflecting the diversity of viewpoints and styles to be found in world musics. What I describe here is merely one possible solution, and one influenced by my own musicmaking experience and philosophy which seeks an equitable and inclusive balance between intervals at or near simple integer ratios, and those having a more complex or active nature."''
+: In naming categories of intervals, or regions of the spectrum in which they are found, there may be many valid and desirable schemes reflecting the diversity of viewpoints and styles to be found in world musics. What I describe here is merely one possible solution, and one influenced by my own musicmaking experience and philosophy which seeks an equitable and inclusive balance between intervals at or near simple integer ratios, and those having a more complex or active nature.
 Schulter proposes the following categories and gives a tentative range of cents values for intervals that fall within those categories. In ''Regions'', she points out, "A main caution is that the borders are inevitably 'fuzzy,' so that one region shades into another and suggested values in cents are more illustrative than definitive."
@@ Line 236: / Line 239: @@
 | | 1200
 |}
-See: [[Interval_size_measure|interval size measure]], [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]
 <pre>Pure unison (1:1)           0 cents
@@ Line 348: / Line 349: @@
 Pure octave (2:1)        1200 cents</pre>
+== See also ==
+* [[Mike Sheiman's Alternative Interval Categorizations]]
+* [[SKULO interval names]]
+* [[Interval size measure]]
+* [[Gallery of just intervals]]
 [[Category:Interval region| ]] <!-- main article -->
 [[Category:Classification]]
 [[Category:Distance measure]]