User:Vector/Vector's intro to 22edo/Notation

While 22edo is intuitive in many different ways, notating it is somewhat complicated. While many people try to use the diatonic scale as a basis for notation, I personally find it more illuminating to understand 22edo as not adding any new accidentals to the standard 12-note system, but instead adding three new ordinals in the first place. However, that is more of an advanced subject, so I'll still in this section be providing the standard diatonic notation for 22edo, which takes as a basis the Pythagorean diatonic scale (4-4-1-4-4-4-1) and uses the standard accidentals # and b to raise and lower by 3 edosteps respectively, and the accidentals ^ and v to raise and lower by a single edostep.

The following section echoes the format of https://31et.com/page/notation.

4-4-1-4-4-4-1 Diatonic Notation

Note names in 22edo

22edo consists of 22 equally spaced notes in the octave. As a result, all intervals correspond to a number of steps of 22edo. One step of 22edo is a quartertone. The basic way to understand the notation of 22edo in the standard Pythagorean diatonic manner is to understand 22edo's intervals. As such, I will provide a list of 22edo intervals.

In 22edo, the space between each of the notes that is separated by 2 steps in 12edo is instead 4 steps; notes separated by a single step remain that way. As a result, each sharp or flat can be split into three distinct notes. It is important to understand the usage of enharmonic equivalence here; unlike in systems such as 31edo where each note has an easily derivable "canonical" notation, it is important to understand the many faces of each of 22edo's pitches (which is, to me, the biggest downside of using the Pythagorean system).

D
Eb	^D
^Eb	vD#
vE	D#
E

Accidentals

22edo's accidentals, as mentioned and demonstrated previously, consist of sharps and flats, as well as up and down accidentals. A sharp moves up three steps, a flat moves down three steps, and as a result ups and downs have a nice sequence to them when combined with multiple sharps and flats. A sharp is one step less than a whole tone, meaning that the diatonic and chromatic semitones straddle the true "semitone" of 22edo.

Accidental	Steps	Interval
vbb		Pentamajor Third
bb		Pentaminor Third
^bb		Subminor Third
vb		Supermajor Second / Whole Tone
b		Pentamajor Second
^b		Pentaminor Second
v		Subminor Second
Natural		Unison
^		Subminor Second
v#		Pentaminor Second
#		Pentamajor Second
^#		Supermajor Second / Whole Tone
vx		Subminor Third
x		Pentaminor Third
^x		Pentamajor Third

Example: The C Major Scale

The scale consists of diatonic semitones and whole tones. The diatonic semitones are between E and F, as well as between B and C. Meanwhile, the remaining steps in the scale are whole tones.

Note that the true "semitone" of 22edo (which evenly divides the whole tone) is not the diatonic semitone being used here. The diatonic semitone is the same size as a quarter-tone, and the complementary chromatic semitone is a 3/4-tone. So, in 22edo, a "semitone" may refer to any interval smaller than a whole tone.

The enharmonic equivalents of 22edo are not the same as in 12edo. Eb is lower than D# by a perfect semitone - larger than a 12edo semitone! However, ^Eb and vD# are the same pitch.