Omniconsonant scale: Difference between revisions

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== Theory ==

Omniconsonant scales have do be defined in the relation to what a particular system defines as ~~"consonance".~~

Omniconsonant scales have to be defined in the relation to what a particular system defines as “consonance”.

For example, in the standard 5-limit theory of Western music and it's diatonic and Pythagorean backing, 12edo is not an omniconsonant temperament - P4 and P5 are consonandissonance does exist in JI, which is once again relative.

== Examples ==

~~ces~~, thirds, sixths less so, and seconds and sevenths are dissonant, with the lowest consonance being semitone and tritone. However, if taken in 2.3.7.17.19 subgroup, tritone gets to be 7/15 or 10/7, a semitone 17/16, two thirds being 19/15 and 19/16, making all 12 notes pairwise consonant.

For example, in the standard 5-limit theory of Western music and it's diatonic and Pythagorean backing, 12edo is not an omniconsonant temperament - P4 and P5 are consonances, thirds, sixths less so, and seconds and sevenths are dissonant, with the lowest consonance being semitone and tritone. However, if taken in 2.3.7.17.19 subgroup, tritone gets to be 7/15 or 10/7, a semitone 17/16, two thirds being 19/15 and 19/16, making all 12 notes pairwise consonant.

It is therefore possible to say that any EDO is omniconsonant in regards to a particular JI choice, since every irrational number has infinitely many close rational numbers around it.

It's possible to argue that [[just intonation]] is omniconsonant by definition - as all the intervals form the basis of what is considered "harmonious", harmony by definition coming from ratios of integers, they define also what consonance means and thus are themselves all by definition consonant. However, JI practitioners such as Kyle Gann would argue that

It's possible to argue that [[just intonation]] is omniconsonant by definition - as all the intervals form the basis of what is considered "harmonious", harmony by definition coming from ratios of integers, they define also what consonance means and thus are themselves all by definition consonant. However, JI practitioners such as Kyle Gann would argue that dissonance does exist in JI, which is once again a relative statement. A comma-step interval is dissonant relative to the interval which it differs from such as 40/27 against 3/2, however if one were to be as elaborate as to make a system involving thousands of pitches and commas as individual steps, then an interval like 40/27 can assume the role of the consonance.

'''5edo'''

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== Links ==

* [https://www.kylegann.com/JIreasons.html Kyle Gann - Reasons for Using Just Intonation]

* [[Runoff]] scales - a related concept

* [~~https~~:~~//www.kylegann.com/JIreasons.html Kyle Gann - Reasons for Using Just Intonation~~]

[[Category:Scales by family]]

@@ Line 4: / Line 4: @@
 == Theory ==
-Omniconsonant scales have do be defined in the relation to what a particular system defines as "consonance".
+Omniconsonant scales have to be defined in the relation to what a particular system defines as “consonance”.
-For example, in the standard 5-limit theory of Western music and it's diatonic and Pythagorean backing, 12edo is not an omniconsonant temperament - P4 and P5 are consonandissonance does exist in JI, which is once again relative.
 == Examples ==
-ces, thirds, sixths less so, and seconds and sevenths are dissonant, with the lowest consonance being semitone and tritone. However, if taken in 2.3.7.17.19 subgroup, tritone gets to be 7/15 or 10/7, a semitone 17/16, two thirds being 19/15 and 19/16, making all 12 notes pairwise consonant.
+For example, in the standard 5-limit theory of Western music and it's diatonic and Pythagorean backing, 12edo is not an omniconsonant temperament - P4 and P5 are consonances, thirds, sixths less so, and seconds and sevenths are dissonant, with the lowest consonance being semitone and tritone. However, if taken in 2.3.7.17.19 subgroup, tritone gets to be 7/15 or 10/7, a semitone 17/16, two thirds being 19/15 and 19/16, making all 12 notes pairwise consonant.
 It is therefore possible to say that any EDO is omniconsonant in regards to a particular JI choice, since every irrational number has infinitely many close rational numbers around it.
-It's possible to argue that [[just intonation]] is omniconsonant by definition - as all the intervals form the basis of what is considered "harmonious", harmony by definition coming from ratios of integers, they define also what consonance means and thus are themselves all by definition consonant. However, JI practitioners such as Kyle Gann would argue that
+It's possible to argue that [[just intonation]] is omniconsonant by definition - as all the intervals form the basis of what is considered "harmonious", harmony by definition coming from ratios of integers, they define also what consonance means and thus are themselves all by definition consonant. However, JI practitioners such as Kyle Gann would argue that dissonance does exist in JI, which is once again a relative statement. A comma-step interval is dissonant relative to the interval which it differs from such as 40/27 against 3/2, however if one were to be as elaborate as to make a system involving thousands of pitches and commas as individual steps, then an interval like 40/27 can assume the role of the consonance.
 '''5edo'''
@@ Line 24: / Line 22: @@
 == Links ==
+* [https://www.kylegann.com/JIreasons.html Kyle Gann - Reasons for Using Just Intonation]
+* [[Runoff]] scales - a related concept
-* [https://www.kylegann.com/JIreasons.html Kyle Gann - Reasons for Using Just Intonation]
+[[Category:Scales by family]]