24edo/Interval names and harmonies: Difference between revisions

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== Tone sizes ==

While 12edo contains only two tone sizes: the [[whole tone]] at 200 cents, and the semitone at 100 cents, 24edo contains five being that it has three additional new tone sizes. Generally, as it divides the octave into 24 parts, it is a good idea to approach [[Interval|intervals]] and tones with this mindset of there being a new wider or narrower version of the previous intervals. These tone sizes are mainly used in context of scale steps and sometimes modulation but not usually in context of a chord or scale degrees.

While 12edo contains only two tone sizes: the [[whole tone]] at 200 [[cents]], and the semitone at 100 cents, 24edo contains five being that it has three additional new tone sizes. Generally, as it divides the octave into 24 parts, it is a good idea to approach [[Interval|intervals]] and tones with this mindset of there being a new wider or narrower version of the previous intervals. These tone sizes are mainly used in context of [[scale]] steps and sometimes modulation but not usually in context of a [[chord]] or scale degrees.

=== Quarter tone ===

The quarter tone is the smallest tone size in 24edo. At only 50 cents, it is a highly [[Consonance and dissonance|dissonant]] interval and has a characteristic washy, beating sound to it and is reminiscent of tuning instrument. Melodically it can function similar to the way a semitone does in 12edo but it tends to sound really different as it is such a small interval. Due to the high dissonance, this interval is challenging to make it sound good in a chord within the context of tonal music but can work quite well for composers who wish to explore the dissonance of 24edo. Through chord changes, the quarter tone is very effective in creating a sound of a record player going in and out of pitch. It can be a nice effect in smooth jazz progressions or post-modal music to simply move a diatonic chord from 12edo up a quarter tone as quarter tone root movement is quite novel in sound. Within scale context, the quarter tone is represented by a lowercase q. An example of quarter tone is C to Ct or enharmonically C to Ddb.

The [[quarter tone]] is the smallest tone size in 24edo. At only 50 cents, it is a highly [[Consonance and dissonance|dissonant]] interval and has a characteristic washy, beating sound to it and is reminiscent of tuning an instrument. Melodically it can function similar to the way a semitone does in 12edo but it tends to sound really different as it is such a small interval. Due to the high [[dissonance]], this interval is challenging to make it sound good in a chord within the context of tonal music but can work quite well for composers who wish to explore the dissonance of 24edo. Through chord changes, the quarter tone is very effective in creating a sound of a record player going in and out of pitch. It can be a nice effect in smooth jazz progressions or post-modal music to simply move a [[diatonic scale|diatonic]] chord from 12edo up a quarter tone as quarter tone root movement is quite novel in sound. Within scale context, the quarter tone is represented by a lowercase q. An example of quarter tone is C to Ct or enharmonically C to Ddb.

=== Whole tones ===

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=== 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 [[triad]]s.

=== Fifths ===

24edo contains five distinct sizes of fifths: diminished fifth 600¢ – paraminor fifth 650¢ – [[3/2|perfect fifth]] 700¢ – paramajor fifth 750¢ – augmented fifth 800¢. The sound of the paraminor and paramajor fifths are very cool and extremely different from 12et sounds. The paraminor fifth, which is considered to be the most dissonant interval in 24et next to the ultramajor seventh, is a fantastic representation of the 11th [[subharmonic]] ([[16/11]]). The paraminor fifth, sometimes mistakenly called a "wolf fifth", can be used to create dynamic texture and voice leading but has a rough character that can be challenging to incorporate into the music well, though of course there is the option using it as the fifth of a lowered triad. The paramajor fifth is a good representation of [[17/11]] and is easily used as the fifth of a raised triad.

24edo contains five distinct sizes of fifths: diminished fifth 600¢ – paraminor fifth 650¢ – [[3/2|perfect fifth]] 700¢ – paramajor fifth 750¢ – augmented fifth 800¢. The sound of the paraminor and paramajor fifths are very cool and extremely different from 12et sounds. The paraminor fifth, which is considered to be the most dissonant interval in 24et next to the ultramajor seventh, is a fantastic representation of the 11th [[subharmonic]] ([[16/11]]). The paraminor fifth, sometimes mistakenly called a "[[Wolf interval|wolf fifth]]", can be used to create dynamic texture and voice leading but has a rough character that can be challenging to incorporate into the music well, though of course there is the option using it as the fifth of a lowered triad. The paramajor fifth is a good representation of [[17/11]] and is easily used as the fifth of a raised triad.

=== Sixths ===

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=== 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", "Infra-Augmented", "Ultra-Augmented", "Infra-Diminished" and "Ultra-Diminished"; however, the term "Infraprime" is not used since the perfect unison is already the smallest form of prime. Note, for example, that an Infra-Augmented Fourth is the enharmonically equivalent to a Paramajor Fourth in 24edo because the [[rastma]] tempered out.

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

== Types of basic chords ==

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=== 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 [[7-limit|septimal]] supermajor chord, there are new potential set-ups and follow ups, as well as options for [[Tetrad|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.

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 [[7-limit|septimal]] supermajor chord, there are new potential set-ups and follow ups, as well as options for [[Tetrad|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 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.

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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=== Dusthumic minor ===

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.

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.

=== Dusthumic inframinor ===

@@ Line 3: / Line 3: @@
 == Tone sizes ==
-While 12edo contains only two tone sizes: the [[whole tone]] at 200 cents, and the semitone at 100 cents, 24edo contains five being that it has three additional new tone sizes. Generally, as it divides the octave into 24 parts, it is a good idea to approach [[Interval|intervals]] and tones with this mindset of there being a new wider or narrower version of the previous intervals. These tone sizes are mainly used in context of scale steps and sometimes modulation but not usually in context of a chord or scale degrees.
+While 12edo contains only two tone sizes: the [[whole tone]] at 200 [[cents]], and the semitone at 100 cents, 24edo contains five being that it has three additional new tone sizes. Generally, as it divides the octave into 24 parts, it is a good idea to approach [[Interval|intervals]] and tones with this mindset of there being a new wider or narrower version of the previous intervals. These tone sizes are mainly used in context of [[scale]] steps and sometimes modulation but not usually in context of a [[chord]] or scale degrees.
 === Quarter tone ===
-The quarter tone is the smallest tone size in 24edo. At only 50 cents, it is a highly [[Consonance and dissonance|dissonant]] interval and has a characteristic washy, beating sound to it and is reminiscent of tuning instrument. Melodically it can function similar to the way a semitone does in 12edo but it tends to sound really different as it is such a small interval. Due to the high dissonance, this interval is challenging to make it sound good in a chord within the context of tonal music but can work quite well for composers who wish to explore the dissonance of 24edo. Through chord changes, the quarter tone is very effective in creating a sound of a record player going in and out of pitch. It can be a nice effect in smooth jazz progressions or post-modal music to simply move a diatonic chord from 12edo up a quarter tone as quarter tone root movement is quite novel in sound. Within scale context, the quarter tone is represented by a lowercase q. An example of quarter tone is C to Ct or enharmonically C to Ddb.
+The [[quarter tone]] is the smallest tone size in 24edo. At only 50 cents, it is a highly [[Consonance and dissonance|dissonant]] interval and has a characteristic washy, beating sound to it and is reminiscent of tuning an instrument. Melodically it can function similar to the way a semitone does in 12edo but it tends to sound really different as it is such a small interval. Due to the high [[dissonance]], this interval is challenging to make it sound good in a chord within the context of tonal music but can work quite well for composers who wish to explore the dissonance of 24edo. Through chord changes, the quarter tone is very effective in creating a sound of a record player going in and out of pitch. It can be a nice effect in smooth jazz progressions or post-modal music to simply move a [[diatonic scale|diatonic]] chord from 12edo up a quarter tone as quarter tone root movement is quite novel in sound. Within scale context, the quarter tone is represented by a lowercase q. An example of quarter tone is C to Ct or enharmonically C to Ddb.
 === Whole tones ===
@@ Line 27: / Line 27: @@
 === 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 [[triad]]s.
 === Fifths ===
-edo contains five distinct sizes of fifths: diminished fifth 600¢ – paraminor fifth 650¢ – [[3/2|perfect fifth]] 700¢ – paramajor fifth 750¢ – augmented fifth 800¢. The sound of the paraminor and paramajor fifths are very cool and extremely different from 12et sounds. The paraminor fifth, which is considered to be the most dissonant interval in 24et next to the ultramajor seventh, is a fantastic representation of the 11th [[subharmonic]] ([[16/11]]). The paraminor fifth, sometimes mistakenly called a "wolf fifth", can be used to create dynamic texture and voice leading but has a rough character that can be challenging to incorporate into the music well, though of course there is the option using it as the fifth of a lowered triad. The paramajor fifth is a good representation of [[17/11]] and is easily used as the fifth of a raised triad.
+edo contains five distinct sizes of fifths: diminished fifth 600¢ – paraminor fifth 650¢ – [[3/2|perfect fifth]] 700¢ – paramajor fifth 750¢ – augmented fifth 800¢. The sound of the paraminor and paramajor fifths are very cool and extremely different from 12et sounds. The paraminor fifth, which is considered to be the most dissonant interval in 24et next to the ultramajor seventh, is a fantastic representation of the 11th [[subharmonic]] ([[16/11]]). The paraminor fifth, sometimes mistakenly called a "[[Wolf interval|wolf fifth]]", can be used to create dynamic texture and voice leading but has a rough character that can be challenging to incorporate into the music well, though of course there is the option using it as the fifth of a lowered triad. The paramajor fifth is a good representation of [[17/11]] and is easily used as the fifth of a raised triad.
 === Sixths ===
@@ Line 64: / Line 64: @@
 === 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", "Infra-Augmented", "Ultra-Augmented", "Infra-Diminished" and "Ultra-Diminished"; however, the term "Infraprime" is not used since the perfect unison is already the smallest form of prime.  Note, for example, that an Infra-Augmented Fourth is the enharmonically equivalent to a Paramajor Fourth in 24edo because the [[rastma]] tempered out.
+The terms "Ultra" and "Infra" themselves occur in prefix form when modifying [[Prime]]s and Octaves, as well as when modifying Augmented and Diminished intervals, thus leading to the terms "Ultraprime", "Ultraoctave", "Infraoctave", "Infra-Augmented", "Ultra-Augmented", "Infra-Diminished" and "Ultra-Diminished"; however, the term "Infraprime" is not used since the perfect unison is already the smallest form of prime.  Note, for example, that an Infra-Augmented Fourth is the enharmonically equivalent to a Paramajor Fourth in 24edo because the [[rastma]] tempered out.
 == Types of basic chords ==
@@ Line 77: / Line 77: @@
 === 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 [[7-limit|septimal]] supermajor chord, there are new potential set-ups and follow ups, as well as options for [[Tetrad|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.
+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 [[7-limit|septimal]] supermajor chord, there are new potential set-ups and follow ups, as well as options for [[Tetrad|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 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.
+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 118: / Line 118: @@
 === Dusthumic minor ===
-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.
+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.
 === Dusthumic inframinor ===