Microtonal Music Theory: 31 EDO & the Importance of the Diesis
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- Опубликовано: 15 сен 2024
- How does music theory change if we had 31 notes instead of 12? Lets figure that out by reconstructing the interval that has been lost to history, the Diesis! The Diesis, or 5th tone is a very small interval that divides the whole tone into 5 evenly spaced notes. The diesis step in what helps us form the chromatic scale of 31 tone equal temperament. In this video we dive into some of the history behind the diesis, from the music writings of Plutarch, Aristotle, and Ptolemy, to the music writings of St. Thomas Aquinas & Johannes Tinctoris . 31 EDO is such a wonderful microtonal and xenharmonic tuning system that allows us to create hauntingly beautiful chords, buzzy, dreamlike harmony and chords of new colors, like the septimal/subminor chord, the supermajor chord, and the neutral chord. These microtonal chords gives us so much freedom when it comes to building unique harmony, microtonal chord progressions, and unique xenharmonic music. I hope this microtonal music lesson gives you the tools to allow you to easily start making microtonal and xenharmonic music for yourself.
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Shoutout to Bill Coates book, "Diesis, An Introduction to the Temperament of 31 Notes to Each Octave" from which a lot of the research for this theory video was sourced.
Here are some 31EDO or 31TET resources:
31et.com
- Awesome microtonal resource for 31 notes, includes a standalone 31TET keyboard, list of intervals in 31 equal temperament, and notes on enharmonic equivelants, ambiguous harmony and how to do notation with 31 EDO
en.xen.wiki/w/...
-Xenharmonic Wiki on 31 including interesting bits of music theory on the Neutral circle-of-fifths, Sagittal notation, and 31TET scales.
In Italian, "Diesis" is the only translation of "sharp" (the musical term). We call D sharp Re Diesis, C sharp Do Diesis etc.
You could also define the diesis by how much 3 major thirds undershoot the octave (lesser diesis, ≈ a 31 TET step) or by how much 4 minor thirds overshoot it (greater diesis, ≈ a 19 TET step)
Does 53 edo have both
@@LeReubzRic Yes; 53 Edo's best approximation of 5/4 is 17 steps, so 3 of those leaves you with 51, 2 steps shy, which we could call the lesser diesis. Its best minor third is 14 steps, so 4 of those leaves you with 56, or 3 steps over the octave which we could call the greater diesis.
@@YourAverageLink ok
Playing on my 31EDO guitar i found the importance of diesis myself. It makes two notes (witch are the same in 12EDO) with different functions sounds realy different. Different cases - when you move into target note, from it, or oscillate around it - requare slightly different pitches. This work as attraction/repulsion. You dont need to know any theory to hear it. Just play simple diatonic melodies on 31EDO instrument. Here i was talking only about single voice melody, not about ratios and chords, it is another story. When i play melody i always want to enlarge/decrease some intervals. Everyone can refret cheap guitar into 31EDO, it is not so dificult.
When talking about 31EDO, everyone talks about the harmony. And only in video the author remember about melody. Its great!
Any chance you could do some kind of composition based around the concept? Some sort of context would be really interesting to hear.
I like the way you think! I just uploaded a composition short demonstrating some of these concepts. Feel free to check it out 🤘
Amazing
Monteverdi played that organ!
Wait, like that exact one? 😮
I'm from Sri lanka 🇱🇰
Why do most keyboards with split black keys have the keys for C♯/D♭ and F♯/G♭ not split although other black keys are split?
Stylistic, ergonomic, construction, and economic reasons were probably all at play. Organs are exceedingly expensive to begin with. More pipes for additional keys across the octaves just adds on to the cost. Since the music that would generally be played on the organ probably didn't call for those keys, they were left out. On the other keyboard instruments, more strings for additional split keys would make the instrument harder to play, more expensive, as well as posing construction problems due to the added tension to the body, so only the notes necessary for playing in the most popular keys were added.
From what I've seen, A# is also missing on many keyboards, like the one in the video. That means no B major or, more problematically, relative B harmonic minor in D major, presuming that all notes are tuned in the meantone temperament. The major keys that are available in this configuration with their relative minors are thus Eb, Bb, F, C, G, A, E, + D major. That's seven major+minor keys, and that was probably deemed sufficient. Adding A# would allow for playing in B, adding Db would unlock Ab major, and adding Gb further provides for Db major. The further you want to go in the sequence of fifths, the more notes are needed.
What does that last chord mean in words?
C subminor 11 half sharp 5
are there any examples of this in a song i can listen to?
Sevish is my go to recommendation for people just diving into this stuff. I also just uploaded a short composition that is basically just the example version of this!
7 dieses in 19 octaves gives 1/31 of an octave
Wait, if you subdivide each whole tone in 5 dieses, then you should get 30 tones, not 31, right?
The tone that's being divided in 31 EDO is a bit smaller than in 12 EDO, so six of them fall short of the octave by a diesis. Or, in other words, five steps of 31 EDO, which are close in size (though a bit smaller) to the diesis, make for a slightly smaller tone.
This makes it so that two of these flatter tones, at ~194 cents, when added together form a very consonant major third, which needs to be around 14 cents flatter than on the piano in order to be pure. You can also consider that 31 EDO is an approximation of the 1/4-comma meantone temperament, where the major thirds are tuned pure and then split into two tones of equal size. Here's where the actual diesis comes in: it's the interval by which three pure major thirds fall short of the octave. Since the major thirds are all split into two tones, the octave consists of 6 tones + 1 diesis.
diesis is 49/48
What does "sin" mean in the final chord?
Subminor. Meaning the minor third and the minor seventh are both lowered by a diesis. 🐧
@@silentgloria Interesting abbreviation I must say
Where did you find that video if the last chord?
It's his
The last chord and graphics are mine. Just whipped them up for this video
@@LeviMcClain, bro… please just drop like a compilation of chords. I would love that.
Enharmonic equivalence is terrible music theory. Making A# and Bb seperate pitches is equally stupid.