24edo/Interval names and harmonies: Difference between revisions

Line 92:

This type of triad consists of the root, the 250¢ inframinor third on top of that, and the 450¢ ultramajor third on top of that. This triad, which is 24edo's version of the Arto triad, has a rather dark and bluesy sound, and there are multiple types of tetrads which can be built on top of this chord.

=== ~~Raised~~ ultramajor ===

=== Cocytic ultramajor ===

The ~~raised~~ ultramajor triad is a triad which consists of the root, the 450¢ ultramajor third on top of that, and the 300¢ minor third on top of that. When this triad is built on the note located 650 cents above the tonic, it can act as a set-up for either a lowered major triad or lowered neutral triad built on the root located a semitone below it. In addition, it can also be followed up by a lowered major or lowered minor triad built on the tonic, which in turn can lead to modulations.

The cocytic ultramajor triad is a triad which consists of the root, the 450¢ ultramajor third on top of that, and the 300¢ minor third on top of that. When this triad is built on the note located 650 cents above the tonic, it can act as a set-up for either a lowered major triad or lowered neutral triad built on the root located a semitone below it. In addition, it can also be followed up by a lowered major or lowered minor triad built on the tonic, which in turn can lead to modulations.

=== ~~Raised~~ major ===

=== Cocytic major ===

~~One of four chords named for a similar type of chord found in [[oneirotonic]] scales, the raised~~ major triad is a bright but tense triad which consists of the root, the 400c major third on top of that, and the 350c neutral third on top of that. When built on the tonic, it can lead into modulations.

The cocytic major triad is a bright but tense triad which consists of the root, the 400c major third on top of that, and the 350c neutral third on top of that. When built on the tonic, it can lead into modulations.

=== ~~Raised~~ neutral ===

=== Cocytic neutral ===

The ~~raised~~ neutral triad is a triad which consists of the root, the 350¢ neutral third on top of that, and the 400¢ major third on top of that. It can also set up either a major triad or a lowered major triad built on the root located a major third below it, and can also lead into either a major or minor triad on the same root.

The cocytic neutral triad is a triad which consists of the root, the 350¢ neutral third on top of that, and the 400¢ major third on top of that. It can also set up either a major triad or a lowered major triad built on the root located a major third below it, and can also lead into either a major or minor triad on the same root.

=== ~~Raised~~ minor ===

=== Cocytic minor ===

~~One of four chords named for a similar type of chord found in oneirotonic scales, the raised~~ minor triad is a triad which consists of the root, the 300¢ minor third on top of that, and the 450¢ ultramajor third on top of that, though it can also be conceived as being the result of stacking two 750¢ fifths. It is likely to arise in counterpoint under certain circumstances. Like a raised neutral triad, it can set up either a major triad or a falling major triad built on the root located a major third below it. However, in addition to this, has some of the same set-ups and follow-ups as the raised ultramajor triad.

The cocytic minor triad is a triad which consists of the root, the 300¢ minor third on top of that, and the 450¢ ultramajor third on top of that, though it can also be conceived as being the result of stacking two 750¢ fifths. It is likely to arise in counterpoint under certain circumstances. Like a raised neutral triad, it can set up either a major triad or a falling major triad built on the root located a major third below it. However, in addition to this, has some of the same set-ups and follow-ups as the raised ultramajor triad.

=== ~~Lowered~~ major ===

=== Dusthumic major ===

~~One of four chords named for a similar type of chord found in oneirotonic scales, the~~ lowered major triad is a bright but tense triad which consists of the root, the 400¢ major third on top of that, and the 250¢ inframinor third on top of that. When this triad is built on the note located 550 cents above the tonic, especially with octave reduplication of the root, it can easily be followed up with with the same tonic's traditional V7 chord. In modulation, this same triad can also be followed up with a dominant seventh chord built on the same root, leading to the tonicization of the neutral seventh. Regardless, the use of this chord requires the proper harmonic and melodic set-ups, with one of the most reliable set-ups early on being the 0¢-550¢-700¢ suspension chord, though the IIImin and Imaj triads also work later on.

The dusthumic lowered major triad is a bright but tense triad which consists of the root, the 400¢ major third on top of that, and the 250¢ inframinor third on top of that. When this triad is built on the note located 550 cents above the tonic, especially with octave reduplication of the root, it can easily be followed up with with the same tonic's traditional V7 chord. In modulation, this same triad can also be followed up with a dominant seventh chord built on the same root, leading to the tonicization of the neutral seventh. Regardless, the use of this chord requires the proper harmonic and melodic set-ups, with one of the most reliable set-ups early on being the 0¢-550¢-700¢ suspension chord, though the IIImin and Imaj triads also work later on.

=== ~~Lowered~~ neutral ===

=== Dusthumic neutral ===

The ~~lowered~~ neutral triad is a triad which consists of the root, the 350¢ neutral third on top of that, and the 300¢ minor third on top of that. It is one of two triads that can be considered to sound like a xenharmonic version of a diminished triad. Like with a lowered major triad, it can easily be followed up with the same tonic's traditional V7 chord.

The dusthumic neutral triad is a triad which consists of the root, the 350¢ neutral third on top of that, and the 300¢ minor third on top of that. It is one of two triads that can be considered to sound like a xenharmonic version of a diminished triad. Like with a lowered major triad, it can easily be followed up with the same tonic's traditional V7 chord.

=== ~~Lowered~~ minor ===

=== Dusthumic minor ===

~~One of four chords named for a similar type of chord found in oneirotonic scales, the lowered~~ minor triad is a triad which consists of the root, the 300¢ minor third on top of that, and the 350¢ neutral third on top of that. It is also one of two triads that can be considered to sound like a xenharmonic version of a diminished triad.

The dusthumic minor triad is a triad which consists of the root, the 300¢ minor third on top of that, and the 350¢ neutral third on top of that. It is also one of two triads that can be considered to sound like a xenharmonic version of a diminished triad.

=== ~~Lowered~~ inframinor ===

=== Dusthumic inframinor ===

The ~~lowered~~ inframinor triad is a triad which consists of the root, the 250¢ inframinor third on top of that, and the 400¢ major third on top of that. Like the lowered major triad, when this triad is built on the note located 550 cents above the tonic, especially with octave reduplication of the root, it can easily be followed up with the same tonic's traditional V7 chord. However, the use of this chord also requires the proper set-ups in terms of both melody and harmony, especially the 0¢-550¢-700¢ suspension chord early on, though the bVImaj triad and the Imin triad also work later on.

The dusthumic inframinor triad is a triad which consists of the root, the 250¢ inframinor third on top of that, and the 400¢ major third on top of that. Like the lowered major triad, when this triad is built on the note located 550 cents above the tonic, especially with octave reduplication of the root, it can easily be followed up with the same tonic's traditional V7 chord. However, the use of this chord also requires the proper set-ups in terms of both melody and harmony, especially the 0¢-550¢-700¢ suspension chord early on, though the bVImaj triad and the Imin triad also work later on.

=== Augmented ===

@@ Line 92: / Line 92: @@
 This type of triad consists of the root, the 250¢ inframinor third on top of that, and the 450¢ ultramajor third on top of that. This triad, which is 24edo's version of the Arto triad, has a rather dark and bluesy sound, and there are multiple types of tetrads which can be built on top of this chord.
-=== Raised ultramajor ===
+=== Cocytic ultramajor ===
-The raised ultramajor triad is a triad which consists of the root, the 450¢ ultramajor third on top of that, and the 300¢ minor third on top of that. When this triad is built on the note located 650 cents above the tonic, it can act as a set-up for either a lowered major triad or lowered neutral triad built on the root located a semitone below it. In addition, it can also be followed up by a lowered major or lowered minor triad built on the tonic, which in turn can lead to modulations.
+The cocytic ultramajor triad is a triad which consists of the root, the 450¢ ultramajor third on top of that, and the 300¢ minor third on top of that. When this triad is built on the note located 650 cents above the tonic, it can act as a set-up for either a lowered major triad or lowered neutral triad built on the root located a semitone below it. In addition, it can also be followed up by a lowered major or lowered minor triad built on the tonic, which in turn can lead to modulations.
-=== Raised major ===
+=== Cocytic major ===
-One of four chords named for a similar type of chord found in [[oneirotonic]] scales, the raised major triad is a bright but tense triad which consists of the root, the 400c major third on top of that, and the 350c neutral third on top of that. When built on the tonic, it can lead into modulations.
+The cocytic major triad is a bright but tense triad which consists of the root, the 400c major third on top of that, and the 350c neutral third on top of that. When built on the tonic, it can lead into modulations.
-=== Raised neutral ===
+=== Cocytic neutral ===
-The raised neutral triad is a triad which consists of the root, the 350¢ neutral third on top of that, and the 400¢ major third on top of that. It can also set up either a major triad or a lowered major triad built on the root located a major third below it, and can also lead into either a major or minor triad on the same root.
+The cocytic neutral triad is a triad which consists of the root, the 350¢ neutral third on top of that, and the 400¢ major third on top of that. It can also set up either a major triad or a lowered major triad built on the root located a major third below it, and can also lead into either a major or minor triad on the same root.
-=== Raised minor ===
+=== Cocytic minor ===
-One of four chords named for a similar type of chord found in oneirotonic scales, the raised minor triad is a triad which consists of the root, the 300¢ minor third on top of that, and the 450¢ ultramajor third on top of that, though it can also be conceived as being the result of stacking two 750¢ fifths. It is likely to arise in counterpoint under certain circumstances. Like a raised neutral triad, it can set up either a major triad or a falling major triad built on the root located a major third below it. However, in addition to this, has some of the same set-ups and follow-ups as the raised ultramajor triad.
+The cocytic minor triad is a triad which consists of the root, the 300¢ minor third on top of that, and the 450¢ ultramajor third on top of that, though it can also be conceived as being the result of stacking two 750¢ fifths. It is likely to arise in counterpoint under certain circumstances. Like a raised neutral triad, it can set up either a major triad or a falling major triad built on the root located a major third below it. However, in addition to this, has some of the same set-ups and follow-ups as the raised ultramajor triad.
-=== Lowered major ===
+=== Dusthumic major ===
-One of four chords named for a similar type of chord found in oneirotonic scales, the lowered major triad is a bright but tense triad which consists of the root, the 400¢ major third on top of that, and the 250¢ inframinor third on top of that. When this triad is built on the note located 550 cents above the tonic, especially with octave reduplication of the root, it can easily be followed up with with the same tonic's traditional V7 chord. In modulation, this same triad can also be followed up with a dominant seventh chord built on the same root, leading to the tonicization of the neutral seventh. Regardless, the use of this chord requires the proper harmonic and melodic set-ups, with one of the most reliable set-ups early on being the 0¢-550¢-700¢ suspension chord, though the IIImin and Imaj triads also work later on.
+The dusthumic lowered major triad is a bright but tense triad which consists of the root, the 400¢ major third on top of that, and the 250¢ inframinor third on top of that. When this triad is built on the note located 550 cents above the tonic, especially with octave reduplication of the root, it can easily be followed up with with the same tonic's traditional V7 chord. In modulation, this same triad can also be followed up with a dominant seventh chord built on the same root, leading to the tonicization of the neutral seventh. Regardless, the use of this chord requires the proper harmonic and melodic set-ups, with one of the most reliable set-ups early on being the 0¢-550¢-700¢ suspension chord, though the IIImin and Imaj triads also work later on.
-=== Lowered neutral ===
+=== Dusthumic neutral ===
-The lowered neutral triad is a triad which consists of the root, the 350¢ neutral third on top of that, and the 300¢ minor third on top of that. It is one of two triads that can be considered to sound like a xenharmonic version of a diminished triad. Like with a lowered major triad, it can easily be followed up with the same tonic's traditional V7 chord.
+The dusthumic neutral triad is a triad which consists of the root, the 350¢ neutral third on top of that, and the 300¢ minor third on top of that. It is one of two triads that can be considered to sound like a xenharmonic version of a diminished triad. Like with a lowered major triad, it can easily be followed up with the same tonic's traditional V7 chord.
-=== Lowered minor ===
+=== Dusthumic minor ===
-One of four chords named for a similar type of chord found in oneirotonic scales, the lowered minor triad is a triad which consists of the root, the 300¢ minor third on top of that, and the 350¢ neutral third on top of that. It is also one of two triads that can be considered to sound like a xenharmonic version of a diminished triad.
+The dusthumic minor triad is a triad which consists of the root, the 300¢ minor third on top of that, and the 350¢ neutral third on top of that. It is also one of two triads that can be considered to sound like a xenharmonic version of a diminished triad.
-=== Lowered inframinor ===
+=== Dusthumic inframinor ===
-The lowered inframinor triad is a triad which consists of the root, the 250¢ inframinor third on top of that, and the 400¢ major third on top of that. Like the lowered major triad, when this triad is built on the note located 550 cents above the tonic, especially with octave reduplication of the root, it can easily be followed up with the same tonic's traditional V7 chord. However, the use of this chord also requires the proper set-ups in terms of both melody and harmony, especially the 0¢-550¢-700¢ suspension chord early on, though the bVImaj triad and the Imin triad also work later on.
+The dusthumic inframinor triad is a triad which consists of the root, the 250¢ inframinor third on top of that, and the 400¢ major third on top of that. Like the lowered major triad, when this triad is built on the note located 550 cents above the tonic, especially with octave reduplication of the root, it can easily be followed up with the same tonic's traditional V7 chord. However, the use of this chord also requires the proper set-ups in terms of both melody and harmony, especially the 0¢-550¢-700¢ suspension chord early on, though the bVImaj triad and the Imin triad also work later on.
 === Augmented ===