24edo/Interval names and harmonies - Revision history

Aura at 17:53, 3 February 2025

2025-02-03T17:53:56Z

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	=== Fifths ===		=== Fifths ===
	24edo contains five distinct sizes of fifths: the diminished fifth (600{{c}}), paraminor fifth (650{{c}}), [[3/2\|perfect fifth]] (700{{c}}), paramajor fifth (750{{c}}), and augmented fifth 800¢. The sound of the paraminor and paramajor fifths are often ~~considerd~~ to be 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.		24edo contains five distinct sizes of fifths: the diminished fifth (600{{c}}), paraminor fifth (650{{c}}), [[3/2\|perfect fifth]] (700{{c}}), paramajor fifth (750{{c}}), and augmented fifth 800¢. The sound of the paraminor and paramajor fifths are often considered to be 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 dusthumic triad. The paramajor fifth is a good representation of [[17/11]] and is easily used as the fifth of a cocytic triad.

	=== Sixths ===		=== Sixths ===

Aura: Fixed another instance of the same missing word

2025-02-03T17:49:48Z

Fixed another instance of the same missing word

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	=== Semi-augmented tone ===		=== Semi-augmented tone ===
	In addition to all the other tones, 24edo has a semi-augmented tone, which is 250{{c}} in size; this generally has a more metallic sound than the whole tone as well as a moodier character compared to the brightness of the natural whole tone, and some would say that it's a cross between a step and a leap. In context of a major chord, the semi-augmented tone brings a much colder flavor to the major chord than the whole tone which enhances the brightness of the major chord. The semi-augmented from the root clashes heavily with minor chords as the minor third and the semi-augmented tone are only a quarter tone apart. Diatonic chords tend to move naturally by semi-augmented tone movement such as moving an Am chord to a Gd major chord, and other chords can do the same. The semi-augmented tone is too small to be considered an accurate [[7/6]] and too large to be considered an accurate [[8/7]]; as such, it fits more as being described as a [[15/13]]. Within scale context, the semi-augmented tone can be represented by an uppercase "S". An example of semi-augmented tone is C–D{{demisharp2}}, or enharmonically, C–E{{sesquiflat2}}.		In addition to all the other tones, 24edo has a semi-augmented tone, which is 250{{c}} in size; this generally has a more metallic sound than the whole tone as well as a moodier character compared to the brightness of the natural whole tone, and some would say that it's a cross between a step and a leap. In context of a major chord, the semi-augmented tone brings a much colder flavor to the major chord than the whole tone which enhances the brightness of the major chord. The semi-augmented tone from the root clashes heavily with minor chords as the minor third and the semi-augmented tone are only a quarter tone apart. Diatonic chords tend to move naturally by semi-augmented tone movement such as moving an Am chord to a Gd major chord, and other chords can do the same. The semi-augmented tone is too small to be considered an accurate [[7/6]] and too large to be considered an accurate [[8/7]]; as such, it fits more as being described as a [[15/13]]. Within scale context, the semi-augmented tone can be represented by an uppercase "S". An example of semi-augmented tone is C–D{{demisharp2}}, or enharmonically, C–E{{sesquiflat2}}.

	== Types of intervals ==		== Types of intervals ==

Aura: fixed missing word

2025-02-03T17:48:51Z

fixed missing word

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	=== Semi-augmented tone ===		=== Semi-augmented tone ===
	In addition to all the other tones, 24edo has a semi-augmented tone, which is 250{{c}} in size; this generally has a more metallic sound than the whole tone as well as a moodier character compared to the brightness of the natural whole tone, and some would say that it's a cross between a step and a leap. In context of a major chord, the semi-augmented tone brings a much colder flavor to the major chord than the whole tone which enhances the brightness of the major chord. The semi-augmented from the root clashes heavily with minor chords as the minor third and the semi-augmented are only a quarter tone apart. Diatonic chords tend to move naturally by semi-augmented tone movement such as moving an Am chord to a Gd major chord, and other chords can do the same. The semi-augmented tone is too small to be considered an accurate [[7/6]] and too large to be considered an accurate [[8/7]]; as such, it fits more as being described as a [[15/13]]. Within scale context, the semi-augmented tone can be represented by an uppercase "S". An example of semi-augmented tone is C–D{{demisharp2}}, or enharmonically, C–E{{sesquiflat2}}.		In addition to all the other tones, 24edo has a semi-augmented tone, which is 250{{c}} in size; this generally has a more metallic sound than the whole tone as well as a moodier character compared to the brightness of the natural whole tone, and some would say that it's a cross between a step and a leap. In context of a major chord, the semi-augmented tone brings a much colder flavor to the major chord than the whole tone which enhances the brightness of the major chord. The semi-augmented from the root clashes heavily with minor chords as the minor third and the semi-augmented tone are only a quarter tone apart. Diatonic chords tend to move naturally by semi-augmented tone movement such as moving an Am chord to a Gd major chord, and other chords can do the same. The semi-augmented tone is too small to be considered an accurate [[7/6]] and too large to be considered an accurate [[8/7]]; as such, it fits more as being described as a [[15/13]]. Within scale context, the semi-augmented tone can be represented by an uppercase "S". An example of semi-augmented tone is C–D{{demisharp2}}, or enharmonically, C–E{{sesquiflat2}}.

	== Types of intervals ==		== Types of intervals ==

Aura: Attempted to separate different sections and fix a few things- I also removed some information that I didn't quite understand, and I'll later re-add said information in more understandable terms

2025-02-03T17:36:51Z

Attempted to separate different sections and fix a few things- I also removed some information that I didn't quite understand, and I'll later re-add said information in more understandable terms

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	While 12edo contains only two sizes of seconds, thirds, sixths, and sevenths, 24edo has three additional new tone sizes, giving it five different kinds. Generally, as it divides the octave into 24 parts, it is a good idea to approach [[interval]]s 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 sizes of seconds, thirds, sixths, and sevenths, 24edo has three additional new tone sizes, giving it five different kinds. Generally, as it divides the octave into 24 parts, it is a good idea to approach [[interval]]s 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~~ ===		=== Quartertone ===
	The [[~~quarter tone~~]] is the smallest tone size in 24edo. At only 50{{cent}} in size, 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 very 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–C{{demisharp2}}, or enharmonically, C–D{{sesquiflat2}}.		The [[quartertone]] is the smallest tone size in 24edo. At only 50{{cent}} in size, 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 somewhat similar to the way a semitone does in 12edo but it tends to sound very different as it is such a small interval, and in addition, there are functional differences between the quartertone and the nearby semitone in terms of voice-leading characteristics. Due to the high [[dissonance]], this interval is challenging to make it sound good as a chord tone 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 quartertone 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, however, there are more options for this interval, as the quartertone is one of the most versatile intervals that 24edo has to offer in terms of voice-leading. Within scale context, the quartertone is represented by a lowercase "q". An example of quartertone is C–C{{demisharp2}}, or enharmonically, C–D{{sesquiflat2}}.

	=== ~~Neutral second~~ ===		=== Middle tone ===
	While the ~~minor second~~ and ~~major second,~~ at 100 and 200{{c}}, respectively, are the same as that of 12edo, 24edo also has another kind of second halfway between the two, called a ~~"neutral" second~~. This can serve as both a narrow whole tone and a wide semitone depending on how it is used. It is heavily used in [[Arabic, Turkish, Persian]], and other forms of Eastern music as well as some east Asian scales though normally is slightly sharp or flat from 24et. The character of the ~~neutral~~ tone resembles the sound of bells, a car horn, and other sounds that are normally considered "non-musical" which can be a valuable asset to those trying to impressionistically compose music to mimic sounds such as trains and car horns. In fact, the ~~dialling~~ tone in the US is fairly close to a 150{{c}} ~~neutral~~ tone so one could potentially (and humorously) call it a "dial tone". In addition to all this, the ~~neutral~~ tone is surprisingly useful in chord progressions. An example of a ~~neutral second~~ is C–D{{demiflat2}}.		While the semitone and whole tone at 100{{c}} and 200{{c}} respectively, are the same as that of 12edo, 24edo also has another kind of second halfway between the two, called a middle tone. This can serve as both a narrow whole tone and a wide semitone depending on how it is used. It is heavily used in [[Arabic, Turkish, Persian]], and other forms of Eastern music as well as some east Asian scales though normally is slightly sharp or flat from 24et. The character of the middle tone resembles the sound of bells, a car horn, and other sounds that are normally considered "non-musical" which can be a valuable asset to those trying to impressionistically compose music to mimic sounds such as trains and car horns. In fact, the dialing tone in the US is fairly close to a 150{{c}} middle tone so one could potentially (and humorously) call it a "dial tone". In addition to all this, the middle tone is surprisingly useful in chord progressions. Within scale context, the middle tone can be represented by either a lowercase "m" or an uppercase "M" depending on how it's used. An example of a middle tone is C–C{{sesquisharp2}}, or, enharmonically, C–D{{demiflat2}}.

			=== Semi-augmented tone ===
			In addition to all the other tones, 24edo has a semi-augmented tone, which is 250{{c}} in size; this generally has a more metallic sound than the whole tone as well as a moodier character compared to the brightness of the natural whole tone, and some would say that it's a cross between a step and a leap. In context of a major chord, the semi-augmented tone brings a much colder flavor to the major chord than the whole tone which enhances the brightness of the major chord. The semi-augmented from the root clashes heavily with minor chords as the minor third and the semi-augmented are only a quarter tone apart. Diatonic chords tend to move naturally by semi-augmented tone movement such as moving an Am chord to a Gd major chord, and other chords can do the same. The semi-augmented tone is too small to be considered an accurate [[7/6]] and too large to be considered an accurate [[8/7]]; as such, it fits more as being described as a [[15/13]]. Within scale context, the semi-augmented tone can be represented by an uppercase "S". An example of semi-augmented tone is C–D{{demisharp2}}, or enharmonically, C–E{{sesquiflat2}}.

			== Types of intervals ==
			While the previous section mainly covered the new tone sizes from a voice-leading perspective and from an acoustic perspective, this section will cover those same intervals from another perspective, plus the additional intervals that 24edo offers.

	=== Seconds ===		=== Seconds ===
	In the 5-limit, 24edo has one whole tone ~~(major second) representing~~ both [[9/8]] and [[10/9]], like other [[meantone]] temperaments; at 200{{c}}, it is exactly the same interval that appears in 12edo as a whole tone. ~~However~~, it ~~also~~ has ~~an "ultramajor" second, which is 250{{c}} in size; this generally has a more metallic sound than the whole tone~~ as well as a more moody character compared to the brightness of the natural whole tone. In context of a major chord, the wide tone brings a much colder flavor to the major chord than the whole tone which enhances the brightness of the major chord. The wide tone from the root clashes heavily with minor chords as the minor third and the wide tone are only a quarter tone apart. Diatonic chords tend to move naturally by wide tone movement such as moving an Am chord to a Gd major chord, and other chords can do the same, such as moving a D semi-augmented chord to a Et diminished chord—the latter type of motion in particular being useful in modulations. The ultramajor second is fairly unique to 24edo in that it is too small to be considered an accurate [[7/6]] and ~~too large to be considerd an accurate [[8/7]]; as such, it fits more as being described as a~~ [[15/13]]. ~~The major whole tone~~ is ~~represented by a lowercase w while to wide whole~~ tone ~~is represented by an uppercase W~~. ~~An example of a whole tone is C–D and a wide tone is C–D{{demisharp2}}, or enharmonically, C–E{{sesquiflat2}}.~~		In the 5-limit, 24edo has one whole tone which serves as both [[9/8]] and [[10/9]], like other [[meantone]] temperaments; at 200{{c}}, it is exactly the same interval that appears in 12edo as a whole tone. Similarly, it has one semitone serving as both [[16/15]] and [[256/243]]. What's new in this category is the additional three tone sizes mentioned above. Within a theory context, the tone sizes will normally be referred to as seconds of the following names from small to large: inframinor second (50{{c}}), minor second (100{{c}}), neutral second (150{{c}}), major second (200{{c}}), and ultramajor second (250{{c}}). Therefore, an inframinor second is the same as a quarter tone, a minor second is the same as a semitone, a neutral second is the same as a middle tone, a major second is the same as a whole tone, and an ultramajor second is a semi-augmented tone.

	Within a theory context, the tone sizes will normally be referred to as seconds of the following names from ~~great~~ to ~~small~~: inframinor second (50{{c}}), minor second (100{{c}}), neutral second (150{{c}}), major second (200{{c}}), and ultramajor second (250{{c}}). Therefore, an inframinor second is the same as a quarter tone, a minor second is the same as a semitone, a neutral second is ~~halfway in betwen~~ a tone ~~and semitone~~, a major second is the same as a whole tone, and an ultramajor second is a ~~quarter tone wider than a whole~~ tone.

	=== Thirds ===		=== Thirds ===
	Like seconds, 24edo contains five sizes of thirds which are in order: the inframinor third (250{{c}}), minor third (300{{c}}), neutral third (350{{c}}), major third (400{{c}}), ~~andultramajor~~ third (450{{c}}). The inframinor third is enharmonically the same as the ultramajor second, but it appears differently on the staff and functions differently. In a chord such as C–E–G–D{{demisharp2}} (0-400-700-250), 250{{c}} 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 represents [[15/13]], the neutral third is [[11/9]], and the ultramajor third is [[13/10]].		Like seconds, 24edo contains five sizes of thirds which are, in order: the inframinor third (250{{c}}), minor third (300{{c}}), neutral third (350{{c}}), major third (400{{c}}), and ultramajor third (450{{c}}). The inframinor third is enharmonically the same as the ultramajor second, but it appears differently on the staff and functions differently. In a chord such as C–E–G–D{{demisharp2}} (0-400-700-250), 250{{c}} 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 represents [[15/13]], the neutral third is [[11/9]], and the ultramajor third is [[13/10]].

	=== Fourths ===		=== Fourths ===
	24edo contains five distinct sizes of fourths: the diminished fourth (400{{c}}), paraminor fourth (450{{c}}), [[4/3\|perfect fourth]] (500{{c}}), paramajor fourth (550{{c}}), and augmented fourth (600{{c}}). The paramajor fourth is an extremely accurate representation of the eleventh harmonic ([[11/8]]), while the paraminor fourth is enharmonically the same as an ultramajor third. 11/8 is often ~~considerd~~ to be a fantastic addition to major ~~triads~~, while the 13/10 can sound good with minor ~~[[triad]]s~~.		24edo contains five distinct sizes of fourths: the diminished fourth (400{{c}}), paraminor fourth (450{{c}}), [[4/3\|perfect fourth]] (500{{c}}), paramajor fourth (550{{c}}), and augmented fourth (600{{c}}). The paramajor fourth is an extremely accurate representation of the eleventh harmonic ([[11/8]]), while the paraminor fourth is enharmonically the same as an ultramajor third. The 11/8 is often considered to be a fantastic addition to major [[triad]]s, while the 13/10 can sound good with minor triads, and both can easily be used as suspensions.

	=== Fifths ===		=== Fifths ===
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	=== Ultra-/Infra- ===		=== Ultra-/Infra- ===
	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.		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]] is tempered out.

	== Types of basic chords ==		== Types of basic chords ==

ArrowHead294: /* Types of basic chords */

2025-01-23T15:18:34Z

Types of basic chords

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	== Types of basic chords ==		== Types of basic chords ==
			{{See also\| Arto and tendo theory }}

	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.		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.

	=== Ultramajor ===		=== Ultramajor ===
	~~{{Main\| Arto and Tendo Theory }}~~

	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.		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.

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	=== Inframinor ===		=== Inframinor ===
	~~{{Main\| Arto and tendo theory }}~~

	This type of triad consists of the root, the 250{{c}} inframinor third on top of that, and the 450{{c}} 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.		This type of triad consists of the root, the 250{{c}} inframinor third on top of that, and the 450{{c}} 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.

ArrowHead294: /* Neutral second */

2025-01-21T16:25:46Z

Neutral second

← Older revision		Revision as of 16:25, 21 January 2025
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	=== Neutral second ===		=== Neutral second ===
	While the minor second and major second, at 100 and 200{{c}}, respectively, are the same as that of 12edo, 24edo also has another kind of second halfway between the two, called a "neutral" second. This can serve as both a narrow whole tone and a wide semitone depending on how it is used. It is heavily used in [[Arabic]], [[Persian~~]], [[Turkish maqam music temperaments\|Turkish~~]], and other forms of Eastern music as well as some east Asian scales though normally is slightly sharp or flat from 24et. The character of the neutral tone resembles the sound of bells, a car horn, and other sounds that are normally considered "non-musical" which can be a valuable asset to those trying to impressionistically compose music to mimic sounds such as trains and car horns. In fact, the dialling tone in the US is fairly close to a 150{{c}} neutral tone so one could potentially (and humorously) call it a "dial tone". In addition to all this, the neutral tone is surprisingly useful in chord progressions. An example of a neutral second is C–D{{demiflat2}}.		While the minor second and major second, at 100 and 200{{c}}, respectively, are the same as that of 12edo, 24edo also has another kind of second halfway between the two, called a "neutral" second. This can serve as both a narrow whole tone and a wide semitone depending on how it is used. It is heavily used in [[Arabic, Turkish, Persian]], and other forms of Eastern music as well as some east Asian scales though normally is slightly sharp or flat from 24et. The character of the neutral tone resembles the sound of bells, a car horn, and other sounds that are normally considered "non-musical" which can be a valuable asset to those trying to impressionistically compose music to mimic sounds such as trains and car horns. In fact, the dialling tone in the US is fairly close to a 150{{c}} neutral tone so one could potentially (and humorously) call it a "dial tone". In addition to all this, the neutral tone is surprisingly useful in chord progressions. An example of a neutral second is C–D{{demiflat2}}.

	=== Seconds ===		=== Seconds ===

ArrowHead294 at 16:23, 21 January 2025

2025-01-21T16:23:40Z

Show changes

ArrowHead294: ArrowHead294 moved page 24edo interval names and harmonies to 24edo/Interval names and harmonies: Change to subpage format

2025-01-21T15:59:54Z

ArrowHead294 moved page 24edo interval names and harmonies to 24edo/Interval names and harmonies: Change to subpage format

← Older revision	Revision as of 15:59, 21 January 2025
(No difference)

BudjarnLambeth: Links

2024-12-24T06:05:07Z

Links

← Older revision		Revision as of 06:05, 24 December 2024
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	== Tone sizes ==		== 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 ===		=== 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 ===		=== Whole tones ===
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	=== Fourths ===		=== 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 ===		=== 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 ===		=== Sixths ===
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	=== Ultra-/Infra- ===		=== 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 ==		== Types of basic chords ==
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	=== Major ===		=== 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 ===		=== 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 ===		=== Minor ===
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	=== Dusthumic minor ===		=== 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 ===		=== Dusthumic inframinor ===

Aura at 17:01, 29 July 2024

2024-07-29T17:01:40Z

← Older revision		Revision as of 17:01, 29 July 2024
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	=== Paramajor/Paraminor ===		=== Paramajor/Paraminor ===

	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.		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" that were 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- ===		=== Ultra-/Infra- ===