24edo/Interval names and harmonies: Difference between revisions

=== Quarter tone ===

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}}.

=== 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, 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}}.

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}}.

 

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.

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]].

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 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.

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.