24edo/Interval names and harmonies: Difference between revisions

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Neutral intervals basically are right between the major and minor version of an interval in 12edo. For example, the neutral third is between the major and minor third. The name also suggests that the interval can function as either depending on how it is used. In addition, neutral intervals contain very special color to them that makes them unique.

=== ~~Ultra~~/~~infra~~ ===

=== Ultramajor/Inframior ===

~~Ultra~~ and ~~Infra~~ are used to describe intervals ~~that are borderline between two classes. For example, an ultra third borderlines~~ a ~~perfect fourth and can also be called a narrow fourth~~. Only seconds, thirds, sixths, and sevenths have ~~ultra~~ and ~~infra~~ classes~~, and the names are never used to describe fourths, fifths, or octaves.~~

Ultramajor and Inframinor are used to describe major and minor intervals which have been modified by a quartertone away from the neutral position. Only seconds, thirds, sixths, and sevenths have ultramajor and inframinor classes

=== ~~Narrow~~/~~wide~~ ===

=== Paramajor/Paraminor ===

~~Narrow~~ and ~~wide~~ are used to describe intervals that are ~~between~~ perfect and ~~diminished~~/~~augmented~~. ~~While they are not normally used~~ to ~~describe anything but fourths~~, ~~fifths~~, and ~~sometimes octaves~~, ~~they can be~~ used to ~~describe extreme altered intervals such as 350 cents being~~ a ~~narrow diminished fourth~~.

Paramajor and Paraminor are used to describe the quartertone intervals that are on either side of a perfect fourth or perfect fifth, with paramajor intervals being sharper than their perfect counterparts by a quartertone and paraminor intervals being sharper than their perfect counterparts by a quartertone. The terms "paramajor" and "paraminor" have their roots in the terms [[Wikipedia: Major fourth and minor fifth|"major fourth" and "minor fifth"]] as used by Ivan Wyschnegradsky. The reason the "para-" prefix (meaning "resembling" or "alongside"<ref>[[Wiktionary: para- #Etymology 1]]</ref>) has been added to the words "major" and "minor" as seen in Wyschnegradsky's original terms for these intervals is because the quartertone intervals surrounding the perfect fourth and perfect fifth relate to each other in a manner resembling the relationship between conventional major and minor for other scale degrees, except that this relationship occurs in a context where the note halfway between them is actually part of the base scale rather than the two notes in question.

=== Ultra-/Infra- ===

The terms "Ultra" and "Infra" themselves occur in prefix form when modifying Primes and Octaves, as well as when modifying Augmented and Diminished intervals, thus leading to the terms "Ultraprime", "Ultraoctave", "Infraoctave", "Infraaugmented", "Ultraaugmented", "Infradiminished" and "Ultradiminished"; however, the term "Infraprime" is not used since the perfect unison is already the smallest form of prime. Note, for example, that while an Infraaugmented Fourth is the enharmonically equivalent to a Paramajor Fourth in 24edo, this is not the case in systems where the [[rastma]] is not tempered out.

== Types of chords ==

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As mentioned above, 24edo contains all the types of chords contained in 12edo, so, for the sake of ease, only the most basic of those will be listed here. On the other hand, there are at least several new varieties of chord that are added.

=== ~~Ultra~~ ===

=== Ultramajor ===

This type of triad consists of the root, the 450¢ ~~ultra~~ third on top of that, and the 250¢ ~~infra~~ third on top of that. This triad, which is 24edo's version of the Tendo triad, has a rather bright but strange sound, and there are multiple types of tetrads which can be built on top of this chord.

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

=== Major ===

This type of triad is the same as the major triad found in 12edo. While there is nothing new about this triad structure in as of itself aside from the fact that it no longer the best substitute for the septimal supermajor chord, there are new potential set-ups and follow ups, as well as options for tetrads built on this type of triad. For instance, one can easily stack ~~infra~~ third on top of the major triad to make a triad that more closely approximates a harmonic seventh. Alternatively one can stack an ~~ultra~~ second on top of the Major triad to make a tetrad with functionalities reminiscent of the more traditional German sixth chord.

This type of triad is the same as the major triad found in 12edo. While there is nothing new about this triad structure in as of itself aside from the fact that it no longer the best substitute for the septimal supermajor chord, there are new potential set-ups and follow ups, as well as options for tetrads built on this type of triad. For instance, one can easily stack inframinor third on top of the major triad to make a triad that more closely approximates a harmonic seventh. Alternatively one can stack an ultramajor second on top of the Major triad to make a tetrad with functionalities reminiscent of the more traditional German sixth chord.

=== Neutral ===

This type of triad is halfway between the traditional ~~mjor~~ and minor chords, as the third is located at an even 350¢ above the tonic. It is more dissonant in sound than either the major or minor triads due to the third being located relatively far from harmonic entropy minima, but it is still viable in the right hands.

This type of triad is halfway between the traditional major and minor chords, as the third is located at an even 350¢ above the tonic. It is more dissonant in sound than either the major or minor triads due to the third being located relatively far from harmonic entropy minima, but it is still viable in the right hands.

=== Minor ===

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This type of triad consists of the root, the 250¢ ~~infra~~ third on top of that, and the 450¢ ~~ultra~~ 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.

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 ~~ultra~~ ===

=== Raised ultramajor ===

The raised ~~ultra~~ triad is a triad which consists of the root, the 450¢ ~~ultra~~ 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 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.

=== Raised major ===

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=== Raised 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¢ ~~major~~ third on top of that, and the 450¢ ~~ultra~~ 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 ~~ultra~~ triad.

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.

=== Lowered major ===

@@ Line 54: / Line 54: @@
 Neutral intervals basically are right between the major and minor version of an interval in 12edo. For example, the neutral third is between the major and minor third. The name also suggests that the interval can function as either depending on how it is used. In addition, neutral intervals contain very special color to them that makes them unique.
-=== Ultra/infra ===
+=== Ultramajor/Inframior ===
-Ultra and Infra are used to describe intervals that are borderline between two classes. For example, an ultra third borderlines a perfect fourth and can also be called a narrow fourth. Only seconds, thirds, sixths, and sevenths have ultra and infra classes, and the names are never used to describe fourths, fifths, or octaves.
+Ultramajor and Inframinor are used to describe major and minor intervals which have been modified by a quartertone away from the neutral position. Only seconds, thirds, sixths, and sevenths have ultramajor and inframinor classes
-=== Narrow/wide ===
+=== Paramajor/Paraminor ===
-Narrow and wide are used to describe intervals that are between perfect and diminished/augmented. While they are not normally used to describe anything but fourths, fifths, and sometimes octaves, they can be used to describe extreme altered intervals such as 350 cents being a narrow diminished fourth.
+Paramajor and Paraminor are used to describe the quartertone intervals that are on either side of a perfect fourth or perfect fifth, with paramajor intervals being sharper than their perfect counterparts by a quartertone and paraminor intervals being sharper than their perfect counterparts by a quartertone.  The terms "paramajor" and "paraminor" have their roots in the terms [[Wikipedia: Major fourth and minor fifth|"major fourth" and "minor fifth"]] as used by Ivan Wyschnegradsky.  The reason the "para-" prefix (meaning "resembling" or "alongside"<ref>[[Wiktionary: para- #Etymology 1]]</ref>) has been added to the words "major" and "minor" as seen in Wyschnegradsky's original terms for these intervals is because the quartertone intervals surrounding the perfect fourth and perfect fifth relate to each other in a manner resembling the relationship between conventional major and minor for other scale degrees, except that this relationship occurs in a context where the note halfway between them is actually part of the base scale rather than the two notes in question.
+=== Ultra-/Infra- ===
+The terms "Ultra" and "Infra" themselves occur in prefix form when modifying Primes and Octaves, as well as when modifying Augmented and Diminished intervals, thus leading to the terms "Ultraprime", "Ultraoctave", "Infraoctave", "Infraaugmented", "Ultraaugmented", "Infradiminished" and "Ultradiminished"; however, the term "Infraprime" is not used since the perfect unison is already the smallest form of prime.  Note, for example, that while an Infraaugmented Fourth is the enharmonically equivalent to a Paramajor Fourth in 24edo, this is not the case in systems where the [[rastma]] is not tempered out.
 == Types of chords ==
@@ Line 66: / Line 70: @@
 As mentioned above, 24edo contains all the types of chords contained in 12edo, so, for the sake of ease, only the most basic of those will be listed here. On the other hand, there are at least several new varieties of chord that are added.
-=== Ultra ===
+=== Ultramajor ===
 {{Main| Arto and Tendo Theory }}
-This type of triad consists of the root, the 450¢ ultra third on top of that, and the 250¢ infra third on top of that. This triad, which is 24edo's version of the Tendo triad, has a rather bright but strange sound, and there are multiple types of tetrads which can be built on top of this chord.
+This type of triad consists of the root, the 450¢ ultramajor third on top of that, and the 250¢ inframinor third on top of that. This triad, which is 24edo's version of the Tendo triad, has a rather bright but strange sound, and there are multiple types of tetrads which can be built on top of this chord.
 === Major ===
-This type of triad is the same as the major triad found in 12edo. While there is nothing new about this triad structure in as of itself aside from the fact that it no longer the best substitute for the septimal supermajor chord, there are new potential set-ups and follow ups, as well as options for tetrads built on this type of triad. For instance, one can easily stack infra third on top of the major triad to make a triad that more closely approximates a harmonic seventh. Alternatively one can stack an ultra second on top of the Major triad to make a tetrad with functionalities reminiscent of the more traditional German sixth chord.
+This type of triad is the same as the major triad found in 12edo. While there is nothing new about this triad structure in as of itself aside from the fact that it no longer the best substitute for the septimal supermajor chord, there are new potential set-ups and follow ups, as well as options for tetrads built on this type of triad. For instance, one can easily stack inframinor third on top of the major triad to make a triad that more closely approximates a harmonic seventh. Alternatively one can stack an ultramajor second on top of the Major triad to make a tetrad with functionalities reminiscent of the more traditional German sixth chord.
 === Neutral ===
-This type of triad is halfway between the traditional mjor and minor chords, as the third is located at an even 350¢ above the tonic. It is more dissonant in sound than either the major or minor triads due to the third being located relatively far from harmonic entropy minima, but it is still viable in the right hands.
+This type of triad is halfway between the traditional major and minor chords, as the third is located at an even 350¢ above the tonic. It is more dissonant in sound than either the major or minor triads due to the third being located relatively far from harmonic entropy minima, but it is still viable in the right hands.
 === Minor ===
@@ Line 86: / Line 90: @@
 {{Main| Arto and Tendo Theory }}
-This type of triad consists of the root, the 250¢ infra third on top of that, and the 450¢ ultra 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.
+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 ultra ===
+=== Raised ultramajor ===
-The raised ultra triad is a triad which consists of the root, the 450¢ ultra 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 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.
 === Raised major ===
@@ Line 102: / Line 106: @@
 === Raised 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¢ major third on top of that, and the 450¢ ultra 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 ultra triad.
+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.
 === Lowered major ===