24edo/Interval names and harmonies: Difference between revisions

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24 EDO or 24 ET divides the octave into 24 equal parts and is also a multiple of twelve, therefore, 24 EDO contains all of the original harmonies found in 12 EDO. This page

24 EDO or 24 ET divides the octave into 24 equal parts and is also a multiple of twelve, therefore, 24 EDO contains all of the original harmonies found in 12 EDO. This page seeks to explore the new harmonies available in a 24 Tone system.

seeks to explore the new harmonies available in a 24 Tone system.

=Tone Sizes=

While 12 EDO contains only two tone sizes: the whole tone at 200 cents, and the semitone at 100 cents,

While 12 EDO contains only two tone sizes: the whole tone at 200 cents, and the semitone at 100 cents, 24 EDO contains five being that it has three additional new tone sizes. Generally, as it divides the octave into 24 parts, it's a good idea to approach 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.

24 EDO contains five being that it has three additional new tone sizes. Generally, as it divides the octave into 24 parts, it's a good idea

to approach 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===

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===Whole Tones===

24 EDO there are not one, but two distinct sizes of larger tones. The wide whole tone usually called "wide tone" at 250 cents, and the natural whole tone, usually called "whole tone" at 200 cents, therefore the natural whole tone is exactly the same interval that appears in 12 EDO as a whole tone. The wide whole tone generally has a more metallic sound than the narrow 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

24 EDO there are not one, but two distinct sizes of larger tones. The wide whole tone usually called "wide tone" at 250 cents, and the natural whole tone, usually called "whole tone" at 200 cents, therefore the natural whole tone is exactly the same interval that appears in 12 EDO as a whole tone. The wide whole tone generally has a more metallic sound than the narrow 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 an Gd major chord. The wide tone is fairly unique to 24 EDO as in it's too small to be considered a good 7/6 and 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 to D and a wide tone is C to Dt or enharmonically C to Edb.

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 an Gd major chord. The wide tone is fairly unique to 24 EDO as in

it's too small to be considered a good 7/6 and 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 to D and a wide tone is C to Dt or enharmonically C to Edb.

===Semitones===

Like whole tones, there are two distinct sizes of semitones in 24 EDO: The narrow semitone at 100 cents and the wider semitone at 150 cents called "neutral". While the narrow semitone is exactly the same as the 12 EDO semitone, the neutral tone is unique. The neutral tone is called so because it represents both a narrow whole tone and a wide semitone depending on how it's used. It is heavily used in persian, turkish, and other forms of eastern music as well as some east asian scales though normally is slightly sharp or flat from 24 ET. 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. If fact, the dialing tone in the US is fairly close to a 150 cent neutral tone so I guess you could call it a "dial tone" hehe.

Like whole tones, there are two distinct sizes of semitones in 24 EDO: The narrow semitone at 100 cents and the wider semitone at 150 cents called "neutral". While the narrow semitone is exactly the same as the 12 EDO semitone, the neutral tone is unique. The neutral tone is called so because it represents both a narrow whole tone and a wide semitone depending on how it's used. It is heavily used in persian, turkish, and other forms of eastern music as well as some east asian scales though normally is slightly sharp or flat from 24 ET. 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. If fact, the dialing tone in the US is fairly close to a 150 cent neutral tone so I guess you could call it a "dial tone" hehe. An example of a narrow semitone is C to C# or enharmonically, C to Db. An example of a wide semitone is C to Dd.

An example of a narrow semitone is C to C# or enharmonically, C to Db. An example of a wide semitone is C to Dd.

==Seconds==

Within a theory context, the above tone sizes will normally be referred to as seconds of the following names from great to small:

Within a theory context, the above tone sizes will normally be referred to as seconds of the following names from great to small: Infra Second 50c - Minor Second 100c - Neutral Second 150c - Major Second 200c - Ultra Second 250c. Therefore an Infra second is the same as a Quarter Tone, a Minor second is the same as a semitone, a Neutral second is the same enharmonically as a neutral tone/wide semitone/narrow whole tone, a Major second is the same as a whole tone, and an Ultra second is the same as a Wide tone.

Infra Second 50c - Minor Second 100c - Neutral Second 150c - Major Second 200c - Ultra Second 250c. Therefore an Infra second is the

same as a Quarter Tone, a Minor second is the same as a semitone, a Neutral second is the same enharmonically as a neutral tone/wide semitone/narrow whole tone, a Major second is the same as a whole tone, and an Ultra second is the same as a Wide tone.

==Thirds==

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==Sixths==

24 EDO contains five distinct sizes of sixths: Infra Sixth 750c - Minor Sixth 800c - Neutral Sixth 850c - Major Sixth 900c - Ultra Sixth - 950c. The Infra sixth is enharmonically the same as the wide fifth. The neutral sixth is a decent approximation of 13/8, the thirteenth harmonic, however not quite as good as how well 24 approximates 11/8; The interval may more closely approximate 18/11. The Neutral sixth is though to be the sweetest sounding neutral interval in the tuning.

24 EDO contains five distinct sizes of sixths: Infra Sixth 750c - Minor Sixth 800c - Neutral Sixth 850c - Major Sixth 900c - Ultra Sixth - 950c. The Infra sixth is enharmonically the same as the wide fifth. The neutral sixth is a decent approximation of 13/8, the thirteenth harmonic, however not quite as good as how well 24 approximates 11/8; The interval may more closely approximate 18/11. The Neutral sixth is though to be the sweetest sounding neutral interval in the tuning. The Ultra sixth approximates the interval 26/15 very closely but also can be considered a rather poor 7/4, yet can functionally harmonize in the same manner.

The Ultra sixth approximates the interval 26/15 very closely but also can be considered a rather poor 7/4, yet can functionally harmonize in the same manner.

==Sevenths==

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==Special Enharmonics==

24 EDO contains certain enharmonics that are good to keep in mind, the list is as follows:

* An ultra second and infra third are both 250 cents.

An ultra second and infra third are both 250 cents.

* An ultra third and narrow fourth are both 450 cents.

* A wide fifth and infra sixth are both 750 cents.

An ultra third and narrow fourth are both 450 cents.

* An ultra sixth and infra seventh are both 950 cents.

A wide fifth and infra sixth are both 750 cents.

An ultra sixth and infra seventh are both 950 cents.

=Interval Class Categories=

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==Narrow/Wide==

Narrow and wide are used to describe intervals that are between perfect and diminished/augmented. While they aren't 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.

[[category:todo:cleanup]]

@@ Line 1: / Line 1: @@
-EDO or 24 ET divides the octave into 24 equal parts and is also a multiple of twelve, therefore, 24 EDO contains all of the original harmonies found in 12 EDO. This page
+EDO or 24 ET divides the octave into 24 equal parts and is also a multiple of twelve, therefore, 24 EDO contains all of the original harmonies found in 12 EDO. This page seeks to explore the new harmonies available in a 24 Tone system.
-seeks to explore the new harmonies available in a 24 Tone system.
 =Tone Sizes=
-While 12 EDO contains only two tone sizes: the whole tone at 200 cents, and the semitone at 100 cents,
+While 12 EDO contains only two tone sizes: the whole tone at 200 cents, and the semitone at 100 cents, 24 EDO contains five being that it has three additional new tone sizes. Generally, as it divides the octave into 24 parts, it's a good idea to approach 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.
-EDO contains five being that it has three additional new tone sizes. Generally, as it divides the octave into 24 parts, it's a good idea
-to approach 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===
@@ Line 16: / Line 8: @@
 ===Whole Tones===
-EDO there are not one, but two distinct sizes of larger tones. The wide whole tone usually called "wide tone" at 250 cents, and the natural whole tone, usually called "whole tone" at 200 cents, therefore the natural whole tone is exactly the same interval that appears in 12 EDO as a whole tone. The wide whole tone generally has a more metallic sound than the narrow 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
+EDO there are not one, but two distinct sizes of larger tones. The wide whole tone usually called "wide tone" at 250 cents, and the natural whole tone, usually called "whole tone" at 200 cents, therefore the natural whole tone is exactly the same interval that appears in 12 EDO as a whole tone. The wide whole tone generally has a more metallic sound than the narrow 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 an Gd major chord. The wide tone is fairly unique to 24 EDO as in it's too small to be considered a good 7/6 and 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 to D and a wide tone is C to Dt or enharmonically C to Edb.
-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 an Gd major chord. The wide tone is fairly unique to 24 EDO as in
-it's too small to be considered a good 7/6 and 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 to D and a wide tone is C to Dt or enharmonically C to Edb.
 ===Semitones===
-Like whole tones, there are two distinct sizes of semitones in 24 EDO: The narrow semitone at 100 cents and the wider semitone at 150 cents called "neutral". While the narrow semitone is exactly the same as the 12 EDO semitone, the neutral tone is unique. The neutral tone is called so because it represents both a narrow whole tone and a wide semitone depending on how it's used. It is heavily used in persian, turkish, and other forms of eastern music as well as some east asian scales though normally is slightly sharp or flat from 24 ET. 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. If fact, the dialing tone in the US is fairly close to a 150 cent neutral tone so I guess you could call it a "dial tone" hehe.
+Like whole tones, there are two distinct sizes of semitones in 24 EDO: The narrow semitone at 100 cents and the wider semitone at 150 cents called "neutral". While the narrow semitone is exactly the same as the 12 EDO semitone, the neutral tone is unique. The neutral tone is called so because it represents both a narrow whole tone and a wide semitone depending on how it's used. It is heavily used in persian, turkish, and other forms of eastern music as well as some east asian scales though normally is slightly sharp or flat from 24 ET. 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. If fact, the dialing tone in the US is fairly close to a 150 cent neutral tone so I guess you could call it a "dial tone" hehe.  An example of a narrow semitone is C to C# or enharmonically, C to Db. An example of a wide semitone is C to Dd.
-An example of a narrow semitone is C to C# or enharmonically, C to Db. An example of a wide semitone is C to Dd.
 ==Seconds==
-Within a theory context, the above tone sizes will normally be referred to as seconds of the following names from great to small:
+Within a theory context, the above tone sizes will normally be referred to as seconds of the following names from great to small: Infra Second 50c - Minor Second 100c - Neutral Second 150c - Major Second 200c - Ultra Second 250c. Therefore an Infra second is the same as a Quarter Tone, a Minor second is the same as a semitone, a Neutral second is the same enharmonically as a neutral tone/wide semitone/narrow whole tone, a Major second is the same as a whole tone, and an Ultra second is the same as a Wide tone.
-Infra Second 50c - Minor Second 100c - Neutral Second 150c - Major Second 200c - Ultra Second 250c. Therefore an Infra second is the
-same as a Quarter Tone, a Minor second is the same as a semitone, a Neutral second is the same enharmonically as a neutral tone/wide semitone/narrow whole tone, a Major second is the same as a whole tone, and an Ultra second is the same as a Wide tone.
 ==Thirds==
@@ Line 44: / Line 26: @@
 ==Sixths==
-EDO contains five distinct sizes of sixths: Infra Sixth 750c - Minor Sixth 800c - Neutral Sixth 850c - Major Sixth 900c - Ultra Sixth - 950c. The Infra sixth is enharmonically the same as the wide fifth. The neutral sixth is a decent approximation of 13/8, the thirteenth harmonic, however not quite as good as how well 24 approximates 11/8; The interval may more closely approximate 18/11. The Neutral sixth is though to be the sweetest sounding neutral interval in the tuning.
+EDO contains five distinct sizes of sixths: Infra Sixth 750c - Minor Sixth 800c - Neutral Sixth 850c - Major Sixth 900c - Ultra Sixth - 950c. The Infra sixth is enharmonically the same as the wide fifth. The neutral sixth is a decent approximation of 13/8, the thirteenth harmonic, however not quite as good as how well 24 approximates 11/8; The interval may more closely approximate 18/11. The Neutral sixth is though to be the sweetest sounding neutral interval in the tuning. The Ultra sixth approximates the interval 26/15 very closely but also can be considered a rather poor 7/4, yet can functionally harmonize in the same manner.
-The Ultra sixth approximates the interval 26/15 very closely but also can be considered a rather poor 7/4, yet can functionally harmonize in the same manner.
 ==Sevenths==
@@ Line 53: / Line 33: @@
 ==Special Enharmonics==
 EDO contains certain enharmonics that are good to keep in mind, the list is as follows:
+* An ultra second and infra third are both 250 cents.
-An ultra second and infra third are both 250 cents.
+* An ultra third and narrow fourth are both 450 cents.
+* A wide fifth and infra sixth are both 750 cents.
-An ultra third and narrow fourth are both 450 cents.
+* An ultra sixth and infra seventh are both 950 cents.
-A wide fifth and infra sixth are both 750 cents.
-An ultra sixth and infra seventh are both 950 cents.
 =Interval Class Categories=
@@ Line 72: / Line 48: @@
 ==Narrow/Wide==
 Narrow and wide are used to describe intervals that are between perfect and diminished/augmented. While they aren't 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.
+[[category:todo:cleanup]]