24edo/Interval names and harmonies: Difference between revisions

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=== Thirds ===

Like seconds, 24edo contains five sizes of thirds which are in order: inframinor third 250¢ – minor third 300¢ – neutral third 350¢ – major third 400¢ – ultramajor third 450¢. Obviously, the inframinor third is enharmonically the same as the ultramajor second but appear differently on the staff and function differently. In a chord such as C E G Dt or 0-400-700-250, 250¢ is functioning as an ultramajor ninth but in a chord such as 0-250-700-950, we could say that it is probably functioning as an inframinor third. The inframinor third is thought to represent 15/13, the neutral third is 11/9 and the ultra third is 13/10.

Like seconds, 24edo contains five sizes of thirds which are in order: inframinor third 250¢ – minor third 300¢ – neutral third 350¢ – major third 400¢ – ultramajor third 450¢. Obviously, the inframinor third is enharmonically the same as the ultramajor second but appear differently on the staff and function differently. In a chord such as C E G Dt or 0-400-700-250, 250¢ is functioning as an ultramajor ninth but in a chord such as 0-250-700-950, we could say that it is probably functioning as an inframinor third. The inframinor third is thought to represent [[15/13]], the neutral third is [[11/9]] and the ultra third is [[13/10]].

=== Fourths ===

24edo contains five distinct sizes of fourths: diminished fourth 400¢ – paraminor fourth 450¢ – [[4/3|perfect fourth]] 500¢ – paramajor fourth 550¢ – augmented fourth 600¢. The paramajor fourth is a great representation of the eleventh harmonic 11/8, while the paraminor fourth is enharmonically the same as an ultramajor third. The 11/8 is a fantastic addition to major triads, while the 13/10 can sound good with minor triads.

24edo contains five distinct sizes of fourths: diminished fourth 400¢ – paraminor fourth 450¢ – [[4/3|perfect fourth]] 500¢ – paramajor fourth 550¢ – augmented fourth 600¢. The paramajor fourth is a great representation of the eleventh harmonic [[11/8]], while the paraminor fourth is enharmonically the same as an ultramajor third. The 11/8 is a fantastic addition to major triads, while the 13/10 can sound good with minor triads.

=== Fifths ===

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=== Sixths ===

24edo contains five distinct sizes of sixths: inframinor sixth 750¢ – minor sixth 800¢ – neutral sixth 850¢ – major sixth 900¢ – ultramajor sixth 950¢. The inframinor sixth is enharmonically the same as the paramajor fifth. The neutral sixth is a decent approximation of [[13/8]], the thirteenth harmonic, however not quite as good as how well 24 approximates [[11/8]]; The interval may more closely approximate [[18/11]]. The neutral sixth is though to be the sweetest sounding neutral interval in the tuning. The ultramajor sixth approximates the interval [[26/15]] very closely but also can be considered a rather poor [[7/4]], yet can functionally harmonize in the same manner.

24edo contains five distinct sizes of sixths: inframinor sixth 750¢ – minor sixth 800¢ – neutral sixth 850¢ – major sixth 900¢ – ultramajor sixth 950¢. The inframinor sixth is enharmonically the same as the paramajor fifth. The neutral sixth is a decent approximation of [[13/8]], the thirteenth harmonic, however not quite as good as how well 24 approximates 11/8; The interval may more closely approximate [[18/11]]. The neutral sixth is though to be the sweetest sounding neutral interval in the tuning. The ultramajor sixth approximates the interval [[26/15]] very closely but also can be considered a rather poor [[7/4]], yet can functionally harmonize in the same manner.

=== Sevenths ===

@@ Line 23: / Line 23: @@
 === Thirds ===
-Like seconds, 24edo contains five sizes of thirds which are in order: inframinor third 250¢ – minor third 300¢ – neutral third 350¢ – major third 400¢ – ultramajor third 450¢. Obviously, the inframinor third is enharmonically the same as the ultramajor second but appear differently on the staff and function differently. In a chord such as C E G Dt or 0-400-700-250, 250¢ is functioning as an ultramajor ninth but in a chord such as 0-250-700-950, we could say that it is probably functioning as an inframinor third. The inframinor third is thought to represent 15/13, the neutral third is 11/9 and the ultra third is 13/10.
+Like seconds, 24edo contains five sizes of thirds which are in order: inframinor third 250¢ – minor third 300¢ – neutral third 350¢ – major third 400¢ – ultramajor third 450¢. Obviously, the inframinor third is enharmonically the same as the ultramajor second but appear differently on the staff and function differently. In a chord such as C E G Dt or 0-400-700-250, 250¢ is functioning as an ultramajor ninth but in a chord such as 0-250-700-950, we could say that it is probably functioning as an inframinor third. The inframinor third is thought to represent [[15/13]], the neutral third is [[11/9]] and the ultra third is [[13/10]].
 === Fourths ===
-edo contains five distinct sizes of fourths: diminished fourth 400¢ – paraminor fourth 450¢ – [[4/3|perfect fourth]] 500¢ – paramajor fourth 550¢ – augmented fourth 600¢. The paramajor fourth is a great representation of the eleventh harmonic 11/8, while the paraminor fourth is enharmonically the same as an ultramajor third. The 11/8 is a fantastic addition to major triads, while the 13/10 can sound good with minor triads.
+edo contains five distinct sizes of fourths: diminished fourth 400¢ – paraminor fourth 450¢ – [[4/3|perfect fourth]] 500¢ – paramajor fourth 550¢ – augmented fourth 600¢. The paramajor fourth is a great representation of the eleventh harmonic [[11/8]], while the paraminor fourth is enharmonically the same as an ultramajor third. The 11/8 is a fantastic addition to major triads, while the 13/10 can sound good with minor triads.
 === Fifths ===
@@ Line 35: / Line 35: @@
 === Sixths ===
-edo contains five distinct sizes of sixths: inframinor sixth 750¢ – minor sixth 800¢ – neutral sixth 850¢ – major sixth 900¢ – ultramajor sixth 950¢. The inframinor sixth is enharmonically the same as the paramajor fifth. The neutral sixth is a decent approximation of [[13/8]], the thirteenth harmonic, however not quite as good as how well 24 approximates [[11/8]]; The interval may more closely approximate [[18/11]]. The neutral sixth is though to be the sweetest sounding neutral interval in the tuning. The ultramajor sixth approximates the interval [[26/15]] very closely but also can be considered a rather poor [[7/4]], yet can functionally harmonize in the same manner.
+edo contains five distinct sizes of sixths: inframinor sixth 750¢ – minor sixth 800¢ – neutral sixth 850¢ – major sixth 900¢ – ultramajor sixth 950¢. The inframinor sixth is enharmonically the same as the paramajor fifth. The neutral sixth is a decent approximation of [[13/8]], the thirteenth harmonic, however not quite as good as how well 24 approximates 11/8; The interval may more closely approximate [[18/11]]. The neutral sixth is though to be the sweetest sounding neutral interval in the tuning. The ultramajor sixth approximates the interval [[26/15]] very closely but also can be considered a rather poor [[7/4]], yet can functionally harmonize in the same manner.
 === Sevenths ===