24edo: Difference between revisions
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=== Ups and down notation === | === Ups and down notation === | ||
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<references/> | <references /> | ||
In many other edos, 5/4 is downmajor and 11/9 is mid. To agree with this, the term mid is generally preferred over down or downmajor. | In many other edos, 5/4 is downmajor and 11/9 is mid. To agree with this, the term mid is generally preferred over down or downmajor. | ||
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=== William Lynch's notation === | === William Lynch's notation === | ||
24edo breaks intervals into two sets of five categories. Infra | 24edo breaks intervals into two sets of five categories. {{dash|Infra, Minor, Neutral, Major, Ultra|s=space|d=med}} for seconds, thirds, sixths, and sevenths; and {{dash|diminished, narrow, perfect, wide, augmented|s=space|d=med}} for fourths, fifths, unison, and octave. | ||
For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth. | For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth. | ||
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| width="40px" |[[File:HeQu1.svg|21px|center]] | | width="40px" | [[File:HeQu1.svg|21px|center]] | ||
| A "semisharp" accidental comprising one half of a regular musical sharp symbol. | | A "semisharp" accidental comprising one half of a regular musical sharp symbol. | ||
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| width="40px" |[[File:HeQu3.svg|32px|center]] | | width="40px" | [[File:HeQu3.svg|32px|center]] | ||
| A "sharp and a half" or "sesquisharp" accidental, comprising the above half-sharp symbol connected to the right side of a normal sharp. | | A "sharp and a half" or "sesquisharp" accidental, comprising the above half-sharp symbol connected to the right side of a normal sharp. | ||
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| width="40px" |[[File:HeQd1.svg|22px|center]] | | width="40px" | [[File:HeQd1.svg|22px|center]] | ||
| A "semiflat" accidental, comprising a flat symbol mirrored horizontally so that the lobe is facing left. | | A "semiflat" accidental, comprising a flat symbol mirrored horizontally so that the lobe is facing left. | ||
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| width="40px" |[[File:HeQd3.svg|36px|center]] | | width="40px" | [[File:HeQd3.svg|36px|center]] | ||
| A "flat and a half" or "sesquiflat" accidental, comprising the above half-flat symbol and a regular flat symbol placed back to back. | | A "flat and a half" or "sesquiflat" accidental, comprising the above half-flat symbol and a regular flat symbol placed back to back. | ||
|} | |} | ||
'''Pros:''' Familiar, fairly easy to learn | '''Pros:''' Familiar, fairly easy to learn | ||
[[Category:IMPORTDEBUG - Change External Images]] | [[Category:IMPORTDEBUG - Change External Images]] | ||
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====Persian accidentals ==== | ====Persian accidentals ==== | ||
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'''Cons:''' Hard to write on a computer, doesn't fit with standard notation well | '''Cons:''' Hard to write on a computer, doesn't fit with standard notation well | ||
====Sagittal notation==== | ==== Sagittal notation ==== | ||
[[Sagittal notation]] works extremely well for 24edo notation as well as other systems. | [[Sagittal notation]] works extremely well for 24edo notation as well as other systems. | ||
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[[File:24edo Sagittal.png|800px]] | [[File:24edo Sagittal.png|800px]] | ||
=== Further discussion of 24edo notation === | |||
===Further discussion of 24edo notation=== | |||
* [[24edo interval names and harmonies]] | * [[24edo interval names and harmonies]] | ||
* [[24edo Chord Names]] | * [[24edo Chord Names]] | ||
* [[Ups and Downs Notation#Chords and Chord Progressions]]. | * [[Ups and Downs Notation#Chords and Chord Progressions]]. | ||
==Regular temperament properties== | == Regular temperament properties == | ||
[[File:24ed2.svg|250px|thumb|right|none|alt=alt : Your browser has no SVG support.|Selected 19-limit intervals approximated in 24edo]] | [[File:24ed2.svg|250px|thumb|right|none|alt=alt : Your browser has no SVG support.|Selected 19-limit intervals approximated in 24edo]] | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
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==Scales | == Scales and modes == | ||
''See: [[24edo scales]] and [[List of MOS scales in 24edo]].'' | ''See: [[24edo scales]] and [[List of MOS scales in 24edo]].'' | ||
==Tetrachords== | == Tetrachords == | ||
''See [[24edo tetrachords]]''. | ''See [[24edo tetrachords]]''. | ||
==Chord types== | == Chord types == | ||
24edo features a rich variety of not only new chords, but also alterations that can be used with regular 12edo chords. For example, an approximation of the ninth, eleventh, and thirteenth harmonic can be added to a major triad to create 4:5:6:9:11:13, a sort of super-extended major chord. | 24edo features a rich variety of not only new chords, but also alterations that can be used with regular 12edo chords. For example, an approximation of the ninth, eleventh, and thirteenth harmonic can be added to a major triad to create 4:5:6:9:11:13, a sort of super-extended major chord. | ||
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The tendo chord can also be spelled 1 ^3 5 ^6. Due to convenience, the names Arto and tendo have been changed to Ultra and Infra. | The tendo chord can also be spelled 1 ^3 5 ^6. Due to convenience, the names Arto and tendo have been changed to Ultra and Infra. | ||
==Counterpoint== | == Counterpoint == | ||
24edo is the first edo to have both a [[sqrt(25/24)]] distinct from [[25/24]] and a correct [[5-odd-limit]]. It is thus the first edo which allows to lead the two voices of a major third to a minor third by [[strict contrary motion]]. And vice versa. | 24edo is the first edo to have both a [[sqrt(25/24)]] distinct from [[25/24]] and a correct [[5-odd-limit]]. It is thus the first edo which allows to lead the two voices of a major third to a minor third by [[strict contrary motion]]. And vice versa. | ||
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24edo can also be played on the Lumatone: see [[Lumatone mapping for 24edo]] | 24edo can also be played on the Lumatone: see [[Lumatone mapping for 24edo]] | ||
==Music== | == Music == | ||
{{Wikipedia|List of quarter tone pieces}} | {{Wikipedia|List of quarter tone pieces}} | ||
{{Main|Music in 24edo}} | {{Main|Music in 24edo}} | ||
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** [[196608edo]] (14mu tuning) | ** [[196608edo]] (14mu tuning) | ||
==External links== | == External links == | ||
* [http://tonalsoft.com/enc/q/quarter-tone.aspx Tonalsoft Encyclopedia | ''quarter-tone / 24-edo / 24-ed2''] [https://www.webcitation.org/5xeFMH6cd Permalink] | * [http://tonalsoft.com/enc/q/quarter-tone.aspx Tonalsoft Encyclopedia | ''quarter-tone / 24-edo / 24-ed2''] [https://www.webcitation.org/5xeFMH6cd Permalink] | ||
* [http://www.96edo.com/24_EDO.html About 24-EDO] by Shaahin Mohajeri [https://www.webcitation.org/5xeFBNdQW Permalink] | * [http://www.96edo.com/24_EDO.html About 24-EDO] by Shaahin Mohajeri [https://www.webcitation.org/5xeFBNdQW Permalink] | ||
* [https://docs.google.com/file/d/0Bzrl-iLY6DeEVkl1VjBGdEJlOTg/edit Notation and Chord Names for 24-EDO] by William Lynch | * [https://docs.google.com/file/d/0Bzrl-iLY6DeEVkl1VjBGdEJlOTg/edit Notation and Chord Names for 24-EDO] by William Lynch | ||
* [http://www.tonalsoft.com/sonic-arts/darreg/dar8.htm The place of QUARTERTONES in Today's Xenharmonics] by [[Ivor Darreg]] | * [http://www.tonalsoft.com/sonic-arts/darreg/dar8.htm The place of QUARTERTONES in Today's Xenharmonics] by [[Ivor Darreg]] | ||
{{Todo| cleanup }} | |||
[[Category:Meantone]] | [[Category:Meantone]] | ||
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[[Category:Subgroup temperaments]] | [[Category:Subgroup temperaments]] | ||
[[Category:Twentuning]] | [[Category:Twentuning]] | ||
[[Category:Lists of intervals]] | [[Category:Lists of intervals]] | ||