Anyway feel free to disagree but this method generally works for me.
I'll start by asking if you know what 12 Equal Temperament is. If you do, then great, if not then I'll tell you. The tuning used in the west, meaning the set of pitches that occur in music standardly is 12.
There are no other pitches on normal occasion. Think about it, the piano has 12 pitches on it and then the rest is just duplicates which we call "octaves." When I say pitches, I mean sounds, if you have absolute pitch you would only recognize 12 different notes as "real notes", anything else is out of tune to the majority of people with absolute pitch. Heck, even many musicians who do not have AP, many that do not even play be ear find out of tune notes a bother!
Now an enormous amount of music can be created with this system and it supported everything from Handel to Miley Cyrus. While there is SOME deviation in SOME styles, for the most part we simply consider these 12 notes to be the only way to do things in the universe. But this isn't true, music can be so much more and at this point, we should stop and ask ourselves: Is it really worth it to continually try to reuse the same system again and again? Why continue writing in the same tried notes over and over? I mean, really? We have created music in the same tuning system for ages, why can't we do something else? There is alot of issues such as instrument limitations, training requirements, cultural acceptance etc... But if you want to learn more about microtonality, keep reading. Enough of my ranting for now haha.
22 Notes in an octave
I don't wanna keep having to type "equal temperament" so we will refer to it with it's abbreviation from now on: "ET".
12 ET can be looked at as having 12 pitches to the octave. C C# D D# E F F# G G# A A# B then C which is just a duplicate of the bottom C. Each adjacent note has the same amount of space between them. C to C# is the exact same distance as E to F or F# to G etc.... Likewise, C to D is the same distance as F# to G# or D to E etc... What I'm getting at is it doesn't matter where the interval occurs in the scale, it's the same proportionally all around. All that matters is how many steps wide the interval is. C to E is a major third as well as F# to A# and they are exactly the same distance apart.
ET or Equal Temperament means that adjacent intervals are all the same distance apart.
ET or Equal Temperament means that adjacent intervals are all the same distance apart.
But more specifically, 22 ET now means there are 22 notes to the octave. That is, an octave would have 22 unique sounding pitches between it. Now that may seem like quite alot of notes but there are many reasons we don't just pick and choose any old division of the octave. And when I say
"reasons", I mean very technical reasons that I will not attempt to explain. That being said I encourage anyone to try a number of different small numbered ET's. For example, 16 ET is wonderful but has nothing resembling perfect fifths whatsoever. Back to 22 ET:
22 ET can be thought to have a much tighter grain than 12 ET. While 12 ET deals with half tones, 22 ET deals with quarter tones.
Just to make something clear, quarter tone is an approximate 1/4 of a 12 ET whole step.
It doesn't necessarily mean 24 ET and it doesn't necessarily mean an exact one-quarter of a 12 ET whole tone. It's more of a generalization for an approximate 1/4 of a tone.
21, 22, 23, 24, 25, 26 etc could all said to be quarter tonal tunings.
"reasons", I mean very technical reasons that I will not attempt to explain. That being said I encourage anyone to try a number of different small numbered ET's. For example, 16 ET is wonderful but has nothing resembling perfect fifths whatsoever. Back to 22 ET:
22 ET can be thought to have a much tighter grain than 12 ET. While 12 ET deals with half tones, 22 ET deals with quarter tones.
Just to make something clear, quarter tone is an approximate 1/4 of a 12 ET whole step.
It doesn't necessarily mean 24 ET and it doesn't necessarily mean an exact one-quarter of a 12 ET whole tone. It's more of a generalization for an approximate 1/4 of a tone.
21, 22, 23, 24, 25, 26 etc could all said to be quarter tonal tunings.
Moving on, 22 ET has 22 individual pitches to the octave which we will name using a special set of accidentals.
Accidentals
Naming notes in 12 is a piece of cake, but not so much in 22. There are alot of freaky enharmonic things that you need to learn if you wanna be a master at it. But honestly, you can get by just knowing basic notation. After all, it's not like you're reading 22 ET scores anytime soon. Not yet anyway hehe
In 12 ET we use # and b to represent a value of 1 step of 12 ET. C to C# is one step. D to Db is one step. Get it? In 22 though, # and b represent a value of 3 steps. This means C to C# is three steps apart and D to Db is three steps apart. It seems weird but we need the space to fit all the notes in the tuning. Think about it, we said 22 ET has notes closer together so while 1 step of 12 is a half step, 1 step of 22 is a quarter tone which is nearly half that size so it makes sense that there would need to be MORE notes between.
We will use ^ and v to represent a value of 1 step in 22 ET. These are your "Ups and Downs" which or whatever you want to call them really, there isn't a standard for 22 ET but this is what I use and many others as well. We then will use a combination of the two to indicate the 2 step values.
^ combined with b becomes b^ which is like saying a note is dropped by a value of 3 then put back up 1 meaning it's an "up-flat" which represents a value of lowering a note by 2.
v combined with a # becomes a #v or "down-sharp" which is raising a note by 2.
^ combined with b becomes b^ which is like saying a note is dropped by a value of 3 then put back up 1 meaning it's an "up-flat" which represents a value of lowering a note by 2.
v combined with a # becomes a #v or "down-sharp" which is raising a note by 2.
So far we have ^ v, ^b #v, and # b. There is more though we need for many chords and even just intervals to be notated correctly. We can use #^ or Up-sharp and bv or down-flat for values of +4 and -4.
For higher values, we will use the normal x and bb from 12 EDO to indicate +6 and -6 steps of 22 EDO. Therefore we can use xv or "Down-double sharp" and bb^ or "Up-double flat" to get a value of +5 and -5.
For higher values, we will use the normal x and bb from 12 EDO to indicate +6 and -6 steps of 22 EDO. Therefore we can use xv or "Down-double sharp" and bb^ or "Up-double flat" to get a value of +5 and -5.
22 ET Alphabet
Ok, so the thing is, the actual alphabet to use is debatable. Some think one single alphabet should be used for everything, others feel there should be different ones for different systems of basic scales. For the purpose of this, it's easiest to use the normal alphabet with the special accidentals. You can do anything you want but it makes it easy to translate from a background in 12 ET.
So we will use the same alphabet which written out ascending only is:
C C^ C#v C# D D^ D#v D# E F F^ F#v F# G G^ G#v G# A A^ A#v A# B and C
You'll notice that there is not pitch between E F and B C. In 24 EDO there would be but in 22, this allows a place for those two missing notes because 22 ET tunes the notes a tad further apart eliminating these two. I.E. 22 ET is 24 - 2 = 22 lol
Keep in mind there are alot of weird enharmonics but we do not need to know these for the sake of this basic guide.
A big thanks to Cryptic Ruse for coming up with this accidentals system.
Interval Names
Again very debatable, but this works for me so feel free to use it for the sake of this guide.
A huge thanks to Kite Giedratis for coming up with the color names for which this system is based on. I came up with a simpler system designed for 22 ET specifically, but you can read about the original system here: http://www.tallkite.com/misc_files/alt-tuner_manual_and_primer.pdf
A huge thanks to Kite Giedratis for coming up with the color names for which this system is based on. I came up with a simpler system designed for 22 ET specifically, but you can read about the original system here: http://www.tallkite.com/misc_files/alt-tuner_manual_and_primer.pdf
The system we use in 12 ET for intervals works very well for our sake. However, for 22 ET... Not so much, at least not without serious augmentation and no I don't mean an augmented chord.
An interesting concept with 22 ET is that is splits categories in new ways. 12 ET has a major third and a minor third, right? 22 ET however does something interesting in that it has not two, but four sizes of thirds. Meaning that these four color classes essentially replace major and minor.
The colors are blue, green, yellow, and red from low to high. Seconds, thirds, sixths, and sevenths all come in these four sizes. Fourths and fifths however only come in yellow, green, and WHITE in terms of how we name them. White is the color used in place of the normal term "perfect" so a white fifth is a perfect fifth.
Unisons and octaves are also white in this system. We will use the notation (x/22) to indicate how many steps of 22 an interval is in the system.
0/22 white unison
1/22 is a blue second or a yellow unison
2/22 is a green second, 3/22 is a yellow second, 4/22 is a red second
5/22 is a blue third, 6/22 is a green third, 7/22 is a yellow third, 8/22 is a red third
9/22 is a white fourth, 10/22 is a green fourth, 11/22 is a yellow fourth/green fifth, 12/22 is a yellow fifth
13/22 is a white fifth
14/22 is a blue sixth, 15/22 is a green sixth, 16/22 is a yellow sixth, 17/22 is a red sixth
18/22 is a blue seventh, 19/22 is a green seventh, 20/22 is a yellow seventh, 21/22 is a red seventh
and 22/22 is a white octave.
At first it may seem confusing to your ear to try and hear all these intervals as distinct. We're not used to hearing in four, only two categories. It may seem surprising but to a 22 tone musician, the red and yellow thirds are as different as major and minor are in 12 EDO to a trained musician. Same goes for blue and green. It's because they add up differently.
Red thirds and blue thirds can be reached quickly by stacking white fifths. However, yellow and green thirds are quite far out in a chain of fifths. They are better reached by stacking yellow seconds.
The colors are blue, green, yellow, and red from low to high. Seconds, thirds, sixths, and sevenths all come in these four sizes. Fourths and fifths however only come in yellow, green, and WHITE in terms of how we name them. White is the color used in place of the normal term "perfect" so a white fifth is a perfect fifth.
Unisons and octaves are also white in this system. We will use the notation (x/22) to indicate how many steps of 22 an interval is in the system.
0/22 white unison
1/22 is a blue second or a yellow unison
2/22 is a green second, 3/22 is a yellow second, 4/22 is a red second
5/22 is a blue third, 6/22 is a green third, 7/22 is a yellow third, 8/22 is a red third
9/22 is a white fourth, 10/22 is a green fourth, 11/22 is a yellow fourth/green fifth, 12/22 is a yellow fifth
13/22 is a white fifth
14/22 is a blue sixth, 15/22 is a green sixth, 16/22 is a yellow sixth, 17/22 is a red sixth
18/22 is a blue seventh, 19/22 is a green seventh, 20/22 is a yellow seventh, 21/22 is a red seventh
and 22/22 is a white octave.
At first it may seem confusing to your ear to try and hear all these intervals as distinct. We're not used to hearing in four, only two categories. It may seem surprising but to a 22 tone musician, the red and yellow thirds are as different as major and minor are in 12 EDO to a trained musician. Same goes for blue and green. It's because they add up differently.
Red thirds and blue thirds can be reached quickly by stacking white fifths. However, yellow and green thirds are quite far out in a chain of fifths. They are better reached by stacking yellow seconds.
Compare first the Yellow then the Red Thirds:
Compare the Green then the Blue thirds:
Listen to the intervals and compare: Fourths and Fifths
The full list of intervals:
w1 - b2 - g2 - y2 - r2/b3 - g3 - y3 - r3 - w4 - g4 - y4/g5 - y5 - w5 - b6 - g6 - y6 - r6 - b7 - g7 - y7 - r7 - P8
Chords
So now that we have established a grounding of intervals, note names and other jazz; let's talk chords. Now obviously there are hundreds of possible chords in 22 ET, but this system is a naming system I use which again is largely based on Kite's color notation.
We can translate the exact same chord names to 22 ET from 12 ET as long as we use the color names.
Triads:
There is no one major chord in this system of notating 22 ET, there are two types: Red and Yellow. And if you understand interval logic then it should be obvious what a Red triad and yellow triad are.
If not then listen well:
In 12 ET, major chord means there is a major third and a perfect fifth from the root. Minor chord means there is a minor chord from the root and a perfect fifth also from the root.
In 12 ET: C E G is a c major chord, C Eb G is a minor chord.
In 22 ET, it works the same except now we have four qualities to think about.
A Red triad has a Red third from the root as well as a white fifth. C E G
A Blue triad has a Blue third from the root as well as a white fifth. C Eb G
A Yellow triad has a Yellow third from the root and a white fifth. C Ev G
A Green triad has a Green third from the root and a white fifth. C Eb^ G
But something also is happening here. A major triad has a minor third between the third and fifth of the chord right? C E G so E G is a minor third. But in 22, a red triad C E G has some kind of third also between E G but what is it? Well, it's blue. How do I know this? Because Red and Blue are related as well as Green and yellow. They are opposite pairs and if you want to get technical, Red and blue are equivalent to septimal intervals while green and yellow are more like 5-limit intervals.
So it's not only that there is four qualities of intervals, but that there actually two pairs of related colors. Red/Blue and Green/Yellow.
Listen to the four triad types here listening for different flavors of each one:
Yellow then Red then Blue then Green.
If not then listen well:
In 12 ET, major chord means there is a major third and a perfect fifth from the root. Minor chord means there is a minor chord from the root and a perfect fifth also from the root.
In 12 ET: C E G is a c major chord, C Eb G is a minor chord.
In 22 ET, it works the same except now we have four qualities to think about.
A Red triad has a Red third from the root as well as a white fifth. C E G
A Blue triad has a Blue third from the root as well as a white fifth. C Eb G
A Yellow triad has a Yellow third from the root and a white fifth. C Ev G
A Green triad has a Green third from the root and a white fifth. C Eb^ G
But something also is happening here. A major triad has a minor third between the third and fifth of the chord right? C E G so E G is a minor third. But in 22, a red triad C E G has some kind of third also between E G but what is it? Well, it's blue. How do I know this? Because Red and Blue are related as well as Green and yellow. They are opposite pairs and if you want to get technical, Red and blue are equivalent to septimal intervals while green and yellow are more like 5-limit intervals.
So it's not only that there is four qualities of intervals, but that there actually two pairs of related colors. Red/Blue and Green/Yellow.
Listen to the four triad types here listening for different flavors of each one:
Yellow then Red then Blue then Green.
To me red chords are pastel like, pungent, metallic, and cold sounding
Yellow chords are warm, sunny and rich
Green chords are cool and soft
Blue chords are metallic, thick and grungy
But different people hear these things differently and the perceptions change depending on the new context created in the unique new tuning system. Obviously this is merely a naming convenience as well as a starting point, 22 ET doesn't have to be harmonized with basic triads as these, but it's an easy way to start taking in the whole tuning and does work quite well anyway.
Seventh Chords
Seventh chords work pretty much the same way in 22 ET as they do in 12. You simply use an initial color to indicate the triad quality then a second for the seventh. Obviously if the colors are the same in both the third and seventh, you only right the color name of both ONCE followed by "7".
r7 such as C E G B would consist of a Red third, white fifth, and red seventh
g7 such as G Bb^ D F^ would consist of a Green third, white fifth, and green seventh.
And so on, it's pretty simple if you know 12 ET jazz chords.
we use a second color if the seventh or sixth is of a different color than the third.
r7 such as C E G B would consist of a Red third, white fifth, and red seventh
g7 such as G Bb^ D F^ would consist of a Green third, white fifth, and green seventh.
And so on, it's pretty simple if you know 12 ET jazz chords.
we use a second color if the seventh or sixth is of a different color than the third.
rg7 is a red triad with a green seventh.
yb7 is a yellow triad with a blue seventh.
yb7 is a yellow triad with a blue seventh.
List of all fifth based triads with sevenths are:
y7, yr7, yb7, yg7, gy7, gr7, gb7, g7, r7, ry7, rg7, rb7, bb7, bg7, br7, by7
As you can see you get four types of triads r, y, b and g and it produces a whopping sixteen possible seventh chord types all with one of the fifth based triads on the root!
y7, yr7, yb7, yg7, gy7, gr7, gb7, g7, r7, ry7, rg7, rb7, bb7, bg7, br7, by7
As you can see you get four types of triads r, y, b and g and it produces a whopping sixteen possible seventh chord types all with one of the fifth based triads on the root!
Altered chords
We also use the color names to indicate if the fifth has been altered. Yg5 is a yellow triad with a green fifth for instance such as C E Gb^. If we want the fifth to be raised higher than a white fifth, we will use the suffixes "Huge" and "Tiny" with color names.
Huge indicated with "+" means raising an interval by three steps of 22 ET while Tiny indicated with "-" means lowering three steps. We are getting into some enharmonic territory here but it's needed to notate chord types such as augmented in 22 ET if you want to use the same scheme as those chords to in 12 ET.
A huge green fifth is enharmonically the same as a blue sixth
A huge yellow fifth is enharmonically the same as a green sixth
A huge white fifth is enharmonically the same as a yellow sixth
Thus there isn't one single "augmented chord" in 22 ET but a few possible types due to the larger harmonic palette available.
C E G#v is a y+y5 or a "yellow huge yellow five" chord which may be the closest in sound to the 12 ET augmented chord.
Extended harmony with 11's, 13'ths, 15's whatever, works the same, just use the color name.
Examples yb7y9 Yellow triad with a blue seventh and a yellow ninth
r9g13g5 A Red triad with a possible red seventh, a red ninth, a green thirteenth and a green fifth.
I hope this guide has taught you enough about 22 ET to start to understand it a bit. Obviously playing in the scale will help you to really get it. I recommend starting out with some seven note scales which I will be writing about on this site as well.
Now that you have a basic idea of the system I use, check out some other helpful posts here:
Reading and Notating Music in 22 Equal Temperament
Porcupine Music System
Superpyth Music System
Decatonic Scale System
Have fun enjoying microtonality!
I hope this guide has taught you enough about 22 ET to start to understand it a bit. Obviously playing in the scale will help you to really get it. I recommend starting out with some seven note scales which I will be writing about on this site as well.
Now that you have a basic idea of the system I use, check out some other helpful posts here:
Reading and Notating Music in 22 Equal Temperament
Porcupine Music System
Superpyth Music System
Decatonic Scale System
Have fun enjoying microtonality!
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