24edo: Difference between revisions

The tunings supplied by [[72edo]] cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[k*N_subgroups|3*24 subgroup]] 2.3.125.35.11.325.17 [[just intonation subgroup]], making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11 and 17. Another approach would be to treat 24-EDO as a 2.3.11.17.19 [[Just intonation subgroup|subgroup]] temperament, on which it is quite accurate.  

=== Prime harmonics ===

{{harmonics in equal|24}}

=== William Lynch's notation ===

24edo breaks intervals into two sets of five categories. Infra - Minor - Neutral - Major - Ultra for seconds, thirds, sixths, and sevenths; and diminished - narrow - perfect - wide - augmented for fourths, fifths, unison, and octave.  

=== Interval alterations ===

The special alterations of the intervals and chords of 12edo can be notated like this:

==== Chord names ====

Naming chords in 24edo can be achieved by adding a few things to the already [[#|existing]] set of terms that are used to name 12edo chords.

'''Cons:''' Clutters a score easily, can get confusing when sight read at faster paces

{| class="wikitable"

'''Cons:''' Hard to write on a computer, doesn't fit with standard notation well

[[Sagittal notation]] works extremely well for 24edo notation as well as other systems.

=== Further discussion of 24edo notation ===

* [[24edo interval names and harmonies]]

* [[24edo Chord Names]]

* [[Ups and Downs Notation#Chords and Chord Progressions]].

24edo [[tempers out]] the following [[comma]]s. This assumes [[val]] {{val| 24 38 56 67 83 89 }}.  

<references />

*[[List of 24et rank two temperaments by badness]]

*[[List of edo-distinct 24et rank two temperaments]]

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''See [[24edo modes]].''

''See [[24edo tetrachords]]''.

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 a sort of super-extended chord structure of a major chord: 4:5:6:9:11:13.

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The ever-arising question in microtonal music, how to play it on instruments designed for 12edo, has a relatively simple answer in the case of 24edo: use two standard instruments tuned a quartertone apart. This [[Microtonal_Keyboards#twelvenoteoctavescales|"12 note octave scales"]] approach is used in a wide part of the existing literature - see below.

Hidekazu Wakabayashi tuned a piano and harp to where the normal sharps and flats are tuned 50 cents higher in which he called [[Iceface tuning]].

{{Wikipedia|List of quarter tone pieces}}