What If We Had 31 Notes Instead of 12?
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- Опубликовано: 18 сен 2022
- How does music theory change if we had 31 notes instead of 12? Intro into 31EDO music theory! Ever wonder what kind of awesome chords and harmony we are missing out on by sticking to the rigid standards of 12 tone equal temperament? 12TET has had its time in the sun, now its time for it to step aside for 31TET! Join me in todays exploration of 31 tone equal temperament. Today I go over how to construct new chords like the neutral chord, the Subminor chord, and the supermajor 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.
Find me on TikTok, and Instagram. Follow the link to access my free sample pack: linktr.ee/levimcclainmusic
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/31edo
-Xenharmonic Wiki on 31 including interesting bits of music theory on the Neutral circle-of-fifths, Sagittal notation, and 31TET scales. 
Видеоклипы
![J.P., NLE Choppa - Bad Bitty (Remix) [Official Music Video]](http://i.ytimg.com/vi/rBDa6BCvw10/mqdefault.jpg)
Corrections:
The EDOstep notation is slightly off on this one:
0:48 should be: 0 10 18
1:05 should be: 0 8 18
2:02 should be: 0 11 18
The sub-minor chord made me feel like I've been hearing fake minor chords my whole life. Not exaggerating.
yeah, it's like if minor chords had the same in-tune feel that major chords do
Indeed! They sound very dark, and yet strangely “zippy” at the same time!
Its inversion, the supermajor sixth (fairly close to a 12:7 frequency ratio), also sounds very curious! That plus a M3 above the same root sounds interesting too.
@@MagentaFlavouredMusic that might be because a subminor chord is 6:7:9, where a major chord is 4:5:6 and a minor chord is 10:12:15--in a minor chord, all 3 intervals involved are simple, with 3:2, 6:5, and 5:4 involved, but as a totality the overtones don't triply line up very early, only doubly. with the subminor chord, you use more complicated septimal intervals, so the overtones line up doubly a bit later, but in return they line up triply much sooner.
@@mr88cet12/7 × 5/4 × 1/2 = 60/28 = 30/14 = 15/7
The supermajor chord could add so much depth to a song/film. I love the sound
I know right! Such a fantastic application. Really situated more film composers and sound designers don’t utilize it more consciously.
Can you imagine how ridiculously old fashioned older composers are going to look after society gets xenpilled?
And Superminor chord gave me strange emotion that unlocked memories from my childhood, or even dreams, so old that I have totally forgot about them. And for quite long I have a strong feeling that some familiar tunes sounded 50 or more cents flatter in my childhood. Possibly it may be due to my old tape player had slightly lower speed than it should be.
sounds like 5edo
@@nowandxenpodcast yes and no. It will be like looking at math pre-calculus. They were all enlightened, but limited in the tools available to them.
Xen's biggest obstacle is not marketing it to the masses. It's the difficulty that comes with creating it. You can't convince the masses to listen when there's barely any music out there to begin with. We need more accessible technology. I dream of a piano midi controller with an equal number of black and white keys. it could be made so incredibly cheap, but no one has tried to make it yet.
once artists can pump out microtonal stuff, the revolution will be slow, but steady. Then, it will just be a matter of time before mainstream labels smell profits in the water.
Hearing all these cool new chords makes me want to make a video game that uses these microtonal chords. Definitely gets my creativity flowing.
@EmeraldTeFoxit’s not microtonal. i believe it’s just tuned weird.
@EmeraldTeFoxThis is basically just a C# minor melody detuned +50¢
It's not counted
31 TET sounds surprisingly so deep and touching. I started to study by myself microtonals music. This will give me a lot of homeworks!
The most interesting thing in this video is not the microtonal. The most interesting thing is that 2-3 days ago I was thinking about it. Literally about how the chords will be built and what the theory will be if you break the octave into smaller intervals. I thought about it and didn't search for anything on the Internet and didn't tell anyone out loud. And RUclips helpfully slipped me this video. MYSTERIOUS
Does anyone find music just overwhelmingly awesome? Idk, man. I knew microtones existed, but in 1:37 my jaw dropped to the ground. The way music works is impressive and beautiful.
I know very little about music, but you made me think...
Tbh, that is all that really matters!
I feel "sold" on this idea, and after almost 40 years on trombone in 12edo It is refreshing to hear new things and maybe try them...I mean super major and sub minor are intriguing and the neutral chord is already accessible in blues. I wonder about the circle of fifths now. what harmonic language comes about? Look forward to more of your videos.
Two major thirds and one supermajor third makes one octave now.
Three minor thirds and one subminor third makes one octave also.
Three major seconds make a lesser (harmonic) tritone, same as a minor third plus a subminor third.
The "harmonic seventh" is now an augmented sixth, also called a subminor seventh.
@@henrikljungstrand2036 I am wondering about the context of these measurements. Many versions of intervals exist within different chords, and the best way, as a member of a trombone section or other chordal ensemble performed by individuals who can all listen and adjust is to iterate and learn by practical work. Then we try to contextualize what we have learned with finer detail knowledge of the "why" with math.
@@bontrom8 Yes the best way is to learn by practical work and listening for what sounds good and what works.
But many players soon find the new 7-limit consonances of 31equal, as well as the improved 5-limit consonances of 31equal, compared to 12equal.
You quickly find there is a difference between the diatonic semitone (16/15 = 15/14) and the harmonic "semitone"/thirdtone (25/24 = 21/20 = 28/27) in 31equal as well.
And then you probably find out about the "new" way augmented and diminished work.
finally another 31edo enjoyer. I genuinely enjoy using this microtonal scale, it's very trippy
I get the sentiment, but its not a scale...
@@panwaja yeah I agree, but it's just the terminology I see online
Really great explanation for beginners!
Thank you!
1:37 is perfect. Major feels happy, minor feels sad but neutral? It feels like nothing...
could be perfect for a horror soundtrack imo
Pythagoras is quaking in fear..
Ohhhhh THAT'S THE GOOD STUFF RIGHT THERE!!!
Thank you!!
I've been experimenting with deviding octave into 15 equal steps. It was fun!
For example there is two different tritones, which resolve differently.
That's was THE BEST video I saw about 31 tet untill now ! That's will be listed on my graduation conclusion work ! Great job man !
When you gave the superminor and supermajor chords I got deep Omori vibes
This actually broke me I am a travel king musician and have a major in music theory and this is a concept I didn’t even know was possible
Dyaxek. Same here. After studying western harmony quite intensely,I feel like those astrophysicists who has just been told the Big Bang theory is null and void after the discovery of ancient galaxies which were not supposed to be there.
now you can have a supermajor in music theory :)
i'm surprised nobody's thought of an equal temperament where two octaves have a ratio of 3:1
perfect intro!
Thanks!
Love your approach
Thank you! I’m really focused on making it as simple and direct as possible.
The supermajor chord sounds much happier than the major chord but at the same time it's kinda unsettling, although it could be because I'm not used to the sound of 31edo yet.
Took me 40 seconds to realize Im a big fan of your work LOL new subscriber alert
Nice buddy, thanks for giving me a starting point 🖖
Great video!!
never thought i would hear pleasing sounds outside of 12 et chromatic scale
thanks for this
i'll definitely be looking more into this
So good!!
🙏🙏🙏
I would really love a deeper explanation of these different harmonic structures--especially of supermajors and subminors, especially in the context of 19 tet/edo. And, I don't know much music theory!!
I'm imagining AGT or American Idol contestants
"I wasn't flat. I was singing in the neutral."
yes you and you alone BROKE MUSIC THEORY!!!!!!!!!!!!!!!!!!!!!! OMGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGARGD
😂😂😂
Anyone who's interested about music like this I would recommend listening to Ben Johnston's string quartets. Specifically quartets 7, 9 and 10, but really listen to all of them. His music goes even beyond 31 notes, it sometimes goes beyond 64 notes. His music is unbelievably beautiful.
These sounds sound,,, unreal
Like it's making me feel like I'm in the future
It's making me tear up
hugely interesting and inspiring ! but now i feel i have to make a choice that i didn't know i would ever have to make... to leap or not to leap, that is the question... argh...
😉
🙏
🌠
Nice 👌🏽
🙏🙏🙏
This is fun let's go
Is swear, neutral chords are so beautiful. I used a few in a song of mine, byt i feel like i could use them for some ambient music
I want to watch a 1 hour 30 minute video about 31EDO music theory
Hi Levi, great video. What software did you use to generate micro tonal scales? Thank you!
The natural minor chord gives me a neutral feeling while the subminor chord gives a more dark or "sad" feeling.
Thanks for the good video. I offer five comments - with a question embedded in my second comment:
Anyone who likes or is more curious about non-12-EDO music should listen to Easley Blackwood's etudes for various EDOs. I don't think that he composed one for 31 EDO, but still, they are quite beautiful.
My approach to attempting composition in non-12-EDO systems is to first calculate what pitch class collections are relatively harmonious (i.e. "in-tune) for a low-limit just intonation, such as 5-limit or 7-limit, for the particular EDO system being considered. Then, I attempt to contrive harmonically functional chords from those pitch class collections. Then, I consider possible accidentals divided into two general categories, which are (1) those which progress the tonality harmonically along a closed circle of closely related keys and (2) contrapuntally useful passing tones and tendency tones for tonicizations and chromaticism. I've tried all of this - and it is very very difficult to find much that works well - at least for me. Perhaps this is why Blackwoods etude for 15-EDO is so haunting: The underlying mathematical structure all but demands chromatic mediants organized along the implied key centers of the augmented triads, of which one is common to both 15-EDO and 12-EDO. But this might also be why that particular etude does not sound very harmonically dynamic beyond those luscious but few useful chromatic mediants (in my opinion). QUESTION: DOES ANYONE HAVE A BETTER WAY TO APPROACH THIS? I AM ESPECIALLY INTERESTED IN LOWER-ORDER EDOs SIMPLY SO THAT I CAN USE SCORDATURA AND DIVISI TO ENABLE A TRADITIONALLY TRAINED STRING ORCHESTRA TO PERFORM THE MUSIC ON OPEN STRINGS, SOMETIMES WITH OCTAVE HARMONICS FOR SOFTER TIMBRE. Both my method and Blackwood's method seem quite limited! My best results, mathematically, are in 16-EDO, but the inherently intense symmetry yields little variety of sonorous triads - and this despite that I forego basic major and minor triads on favor of root-third-seventh triads. (On a related note: I wish that 24-EDO were more harmonically justifiable, as quarter-tone notation and playback is somewhat accessible on Sibelius and playable on actual piano pairs (per the hocket approach of Ives and Wyschnegradsky), but, unfortunately, it offers no advantage to 7-limit and 9-limit interval approximations beyond the 12-EDO system, which it contains, so its clear mathematical advantage for approximating the 11th harmonic, if attempted in actual music, tends to sound like a shocking invasion of a quarter-tone accidental into an essentially 12-EDO composition - not to mention that the 11th harmonic is so very high for tones with audible fundamentals that it is aurally irrelevant. I am well aware of Wyschnegradsky's quasi-tonic tetrachord, but it is terribly unconvincing to me as a listener. And all of this does not even address the awkwardness of wedging an 11th harmonic-based pitch into a tonally coherent polyphonic texture. It just doesn't work.)
12 has three prime factors (2, 2, and 3), whereas 31 is, itself, prime. Therefore, the symmetrical intervals and chords of 12 EDO have no symmetrical counterparts in 31 EDO. (whole-tone hexachord, fully diminished 7th chord, augmented triad, and tri-tone) This is not to say that some similar structures cannot be contrived in 31 EDO, but simply that they will not be symmetrical. A similar limitation can be said of the relatively popular 19 EDO, as 19 is also a prime number. This means that tonal modulations in 31 EDO and 19 EDO are more strictly (and conventionally, which is to say with less of the chromaticism of idioms such as Mannerism, Romanticism, and Atonality) tonal than those in 12 EDO, which can be oriented according to symmetrical divisions of the octave. Thus, a series of uniform modulations in 31 EDO or 19 EDO must cycle through the entire circle of 31 or 19 keys to return to the original key, as every multiple of chromatic tones besides 1 is co-prime with 31 (or 19). In contrast, in 12 EDO, uniform modulations can be made along intervals of 1, 2, 3, 4, and 6 chromatic steps. (In 12 EDO, the reason that the circles of fifths and fourths involve all 12 pitch classes is that perfect fifths have 7 chromatic steps and perfect fourths have 5 chromatic steps - and 7 and 5 are both co-prime with 12.) Of course, in any system, modulations can be made along the ascending or descending chromatic scale... but such are mathematically trivial.
The video states to the effect that the major triad is more in tune (i.e. to 5-limit just intonation) in 31 EDO than in 12 EDO. It is true that the major 3rd and minor 3rd that are stacked to form the major triad are each much more in-tune in 31 EDO than in 12 EDO. However, their sum, which is the perfect 5th, is about 60% more out-of-tune in 31 EDO as in 12 EDO. Fortunately, this 60% greater of such a small intonation discrepancy is also a small intonation discrepancy, so the perfect 5th is decent in both EDOs - and much better than the awfully howling perfect 5th in 19 EDO. (The same applies to the derivative perfect 4th.) With most string, woodwind, brass, and vocal live acoustic 31 EDO instruments (were they to exist and were musicians trained to play them), this intonation discrepancy would surely be obfuscated by ordinary vibrato, but I wonder whether for some instruments with fixed resonators (e.g. pipe organs and synthesizers) the beating of the third harmonic (i.e. a perfect 12th above the fundamental) with a simultaneously played pitch that is a perfect 5th or perfect 12th above would be annoying. (I especially imagine a synthesized clarinet timbre with its strong 3rd harmonic and electronic pitch stability.)
Theories of pitch organization that depend upon symmetries (e.g. pertaining to Bartok and Messiaen) would be undermined by prime EDOs such as 31 EDO and 19 EDO. One theory (by whom I forget) posits that in 12 EDO, key centers along an ascending chromatic scale correspond to the cyclical sequence of tonic, dominant, and sub-dominant. As this sequence has 3 elements (i.e. tonic, dominant, and sub-dominant) and 3 is a factor of 12, this renders a one-for-one correspondence of key centers to these three general harmonic regions. Thus, for example, in C-major or minor, the chords of C-major or minor, E-flat major or minor, F-sharp major or minor, and A-major or minor are all facets of the same essential tonic region. Etcetera for other symmetrically-spaced quartets of major or minor chords regarding dominant and sub-dominant regions. (This might explain why some of my own canons with four voices at multiples of minor 3rds sound somewhat monotonous despite their intense chromaticism, whereas some of my canons with three voices at multiples of major 3rds sound harmonically refreshed throughout.) All of this would be lost in 31 EDO or 19 EDO. On the other hand, we could enjoy the challenge of composing a 31 voice or 19 voice canon with every voice entering one chromatic step away from the previous... and maybe on my lunchbreak on the 32nd day of some month, I'll squeeze one out. But seriously, I've done this quite successfully with a 12 voice canon at successive semitones in 12 EDO... but even for 12 voices, there is no way for the listener to cognitively parse the independent voices, so I'm doubtful of the point in attempting this with an even greater degree of polyphony for a higher EDO.
Of course, my comments go beyond the scope of the video, but they are worth considering for context, depending upon one's compositional goals - and perhaps some kind and knowledgeable person can answer (for my benefit) the question that I embedded in my second comment.
Nice
Some of my Synthesizer can be modulated into Microtones which is very interesting. I tuned the Synth to an 24 Tone Equal Temperament and its so cool to try out new things with it. You have so much more possibilites. What do you think about Microtonal Music in general?
these subminor, supermajor, and neutral chords make me (impatiently) eager to hear 31TET doom metal or 31TET tech-death. or even just some neat impressionist music
As someone with absolute pitch, i hate this so much and want to try writing something with this right now
Oh no I'm already failing the TET 12 ear training xD
I have taught all levels of undergraduate theory at a major Ivy League University, and I have extensive professional-level experience with contemporary music, especially with the avant-garde period of the 20th century. All these posts about microtonal music seem to ignore facts. No one has ever demonstrated a consistent harmonic system (or even a monophonic one) in which microtones are of structural significance - the way the "dominant" is significant in Gregorian chant or the way a "leading tone" is structurally significant in harmony of the Common Practice period. Many styles include microtonal ornaments, but every such style is still based on a 12-note division of the octave. Even when using the standard scales, it is very difficult for a composer to establish an artistically unified harmonic system that is completely non-standard (cf. Bartok) except when the materials used are very extremely limited (cf. Stravinsky). Now, there IS one type of presentation where a microtonal environment is established (is it Henry Cowell? I forget) by using two keyboard instruments tuned a 1/4-tone apart. But even those never establish what might be called a significant internal system of harmony (where "harmony" is understood in the broad sense) that dependes on new relations made possible by the additional resources of a 24-note octave division. Microtones in North-Indian raga are, in fact, used motivically, but every such motive remains a matter of ornamenting a standard 5-th-based scale system ( C G D A E B F# etc. generating the entire 12-note octave.) Gamelans are often tuned in a way that is contrasted with Western music, but they also never establish a consistent structure that depends on the extra notes in the octave. These facts are a testament to the artistic rejection of microtonal environments by almost everyone, at every time, on Earth.
what's the lowest number EDO that gives you reasonably in-tune notes, and access to sub/neutral/super triads? Is it 31?
"I broke music theory."
I'm pretty sure they came up with this in the 1600s, so, no, it wasn't you.
True indeed 😂
@@LeviMcClain Made me click and watch.
bruh the xylophone dude mate did it too bruh manne
What did you use to make the sounds?
Very very fascinating
I've got 3 question:
1. Why exactly 31? I know you could divide an octave with every number, but is there a reason?
2. How /or does this work with normal sheet notation, because you got so many new notes?
3. Are there others likewise different notations with more /less tones, like for example based on the natural series or something?
Because equal temperaments are approximations of the "perfect" pitch ratios. If you sing in a choir, or play in a band, you'll often have to lower or raise parts of a chord to get them in tune. If you want an instrument that can both play in multiple keys and have equally spaced notes, you'll have to reach a compromise. This is where our 12 note system came from, mostly because of the perfect forth and the perfect fifth. The reason 31 was the specific number chosen was because equally dividing an octave 31 times got notes closer to those "perfect" pitch ratios which we are always trying to approximate. It just happened to line up. Other popular divisions are 41, 43, and 53
I could also be wrong, im still learning as well, feel free to reply and correct my dumbassery if so
@@kell_0741 thanks a lot, however now I've actually already informed myself with several RUclips videos. Damn it is pretty cool. I still don't completely understand why stacking (perfect) fifths won't ever result in a perfect octave but I found a graphic imagination: the notes in the 12 note system are established with the tweltht root of 2. And the root of 2 is always (unless the second) an irrational number so something that never can equal frequencies multiplied or divided by normal numbers (like with the natural series). So it is impossible to create an equal spaced system with perfect natural series frequencies
One reason for 31 is because 31 equal division of the octave provides a very close approximation to the (1/4-comma variety of) meantone temperament -- which has absolutely pure major thirds and was the normal tuning system for keyboards around 400 years ago when our present system of notation became standardized. If you limit it to the normal major and minor sorts of triads, it gives you a sort of what-you-see-is-what-you get system: E flat makes a minor third in the C minor chord, but D sharp is a different (lower) pitch that makes a major third in the B major chord -- and so on around the rest of the scale.
@@juliusschaller The underlying mathematical reason why stacking purely tuned perfect fifths won't ever arrive at an exact octave is that no matter how many threes you multiply together you will never get an even number. Odd times odd always gives odd.
Thus, every time multiply 3/2 (the ratio of the just-intonation perfect fifth) by itself to stack up another fifth, you always get a fraction that will have an odd number on top and an even number on the bottom. It can never divide out to be exactly a power of two, which is what it would need to do to hit an exact number of octaves.
In the animation you highlighted the number 0 when referring to the fundamental. Shouldn't this be the number 1? Cause in the diagram, by having scale degrees 1-31 plus a scale degree 0, there are suddenly 32 notes, not 31.
Why didn’t you play the notes and chords on an easily digestible instrument sound?
0:34-0:36 my favorite
My calcified old brain has to work hard not to hear these microtonal chords as "out of tune,"--I can appreciate them and hear them for what they are, but it takes effort to do so. But I wonder what they would sound like to children raised on this music?
I need a saxophone that has a key pad for each of those 31 notes
the subminor chord sounds so much darker than a regular one.
How would the keyboard look like in 31 TET?
there's the fokker organ, the archicembalo, and the lumatone, all of which have 31 notes, go look them up!
I just want to listen music that use that system.
Dide you have some reference ???
hear between the lines, zhea erose, benyamind :]
Definitely check those musicians! if you want to hear other systems though, there are plenty other great artists! like sevish, brendan byrnes, the mercury tree, and others! definitely check them out if you’re interested
On band camp check out freenoterecords and hansford rowe (steel blue, no other). And Robert Rich (Neurogenesis, Filaments, Electric Ladder). Hjertmann - Visitors
Was going to come here to recommend, but it seems everyone recommended what I was going to recommend hahaha
Xotla has a bunch of stuff in 31, and many other tunings. :)
The music industry is falling apart and I feel like if someone were able to pull this off in a palatable way they would change music forever. Im tempted to try.
you're already making the mistake of conflating commercial music with actual culture. They're very intertwined, but there's a distinction between art and a product.
0:07 Are they really 12 equally spaced? I remember their frequency distance wasn’t the same for all notes…
it's called *equal* temperament for a reason
24 is Andalusian (Arab) , they use 1/4 steps.
the neutral and subminor chords are just chromatic alterations of the minor chord. A minor third is a minor third, whether or not it's 12 cents lower or something
By that logic, the minor chord is just a badly tuned major chord. They are different intervals in the harmonic series.
@@rafexrafexowski4754 neither the minor third nor the neutral third are in the harmonic series. Both are a lowered form of a major third.
There's no noticable difference between a minor third or a neutral third jnless they're played subsequent to each other, my comment was poorly phrased. There's nothing special about the neutral third, it's no different from any other modified interval.
@@Whatismusic123 That is, again, incorrect. The major third is the 5:4 ratio, the minor one is the 6:5 ratio and the neutral third is the 11:9 ratio. If you are arguing that there is no audible difference between the neutral and minor thirds, you are either tone deaf, have zero musical ear training, or have perfect pitch (which hinders listening to microtonal music). Or I have misinterpreted what you have said, and you are arguing that physically there is a close relation between all thirds in the harmonic series. If that is the case, you could argue that a minor third is just a rearranged major third, just like how you can argue that a major second is a kind of fifth, but a neutral third is so removed from any kind of third in all but name that a comparison of them is practically impossible, let alone calling the neutral third an out of tune minor third. You could say that the neutral third is a kind of undecimal superfourth (11:8), which is commonly considered the fundamental 11-limit ratio, but it is no way related to any 5-limit thirds.
@@rafexrafexowski4754 the "ratios" have absolutely nothing to do with the quality of a chord. It's just a fun coincidence.
A minor third, has to do with specifically, a lowered version of the 4th harmonic. That's also why augmented seconds exists, and double diminished fourths. They're all different intervals, despite having the same pitch.
A minor third is a major third, lowered by 100 cents, a neutral third is a major third lowered by 50 cents. That's all there is to it, of course they're different, but in most musical examples, they're nothing except different tunings.
When playing a perfect fourth, you're playing a halfsharp fourth, but 49 lowered by 49 cents, as the 10th harmonic is a fourth which is 49 cents sharper than is heard in the harmonic series.
It's very easily verifiable what I said, as there's plenty of musical examples proving it. In the harmonic series, Bb and Fhalf# are pitches of the fundamental note C. Thus, when you raise and lower them to B and F, they hold functions reflecting that, B had a leading effect upwards, F has a leading effect downwards, such exists for every chromatically altered note, D# leads up, Eb leads down, they don't need to resolve that way, but it's a very obvious connection, to recognize that all chromatically altered notes, have a corresponding function.
@@Whatismusic123 Holy sh*t, there's so much wrong with this comment.
Ratios fully determine the quality of a chord. Our brain just equates the out of tune intervals in 12EDO to the corresponding ratios in JI. That's why we differentiate augmented fourths and diminished fifths for example. We think of them as having different "roles", but that is because our brain interprets them as different ratios (45:32 and 64:45 respectively), and thus different intervals.
How is the minor third a lowered fourth harmonic in any way? It is the difference between the sixth and the fifth harmonic (that's why it's a 6:5 ratio).
The minor third (6:5), the augmented second (75:64) and the double-diminished fourth (768:625) are completely different intervals in JI. If you were to replace a minor third with a double-diminished fourth in JI, you would get extremely strong beating, as the difference between the two is quite small, but very much audible on its own.
This part angered me the most: you are saying that all thirds are the same interval, except differently tuned. Holy sh*t, by that logic, every interval is an out of tune unison. Extending all minor thirds into major ones upwards would definitely destroy any piece of music. Also physics as well as your brain doesn't care about the number of cents, it cares about frequency and ratios. Cents are only used to divide an octave, not to determine the quality of the interval. And that is exactly what ratios do.
No, when playing a 4:3 fourth, I am not playing a flattened halfsharp fourth, because that interval is unrelated using ratios. When it comes to tuning a piano, then yes, but those intervals are not to be equated in music theory.
I don't understand what you were trying to prove with your last paragraph. It seems totally unrelated to the rest of your comment.
I think I know why this conversation is going wrong: your thesis is different from what you are proving using your arguments. Your thesis is that your brain hears a neutral third as an out of tune minor third, not as its own interval. Your arguments only prove that a 31EDO neutral third is a 31EDO minor third sharpened by 39 cents, not that the brain hears them that way. If your thesis was true, all intervals would be heard as an out of tune unison.
If you and you can make this music where is it i would like it
Check out my latest long form video!
idk why I got scared @ 1:46 ☹
Hear Between the Lines is awesome for this stuff. I can't wait for their album. No, 12 aren't enough: ruclips.net/video/B1sdMP3Ne74/видео.html
My piano is microtonal in a 12 note way
How do u play microtones
Lots of ways! You can retune pianos, zithers, dulcimers, and most mallet percussion instruments to accommodate subsets of 31 pretty well. I play fretless bass and you can get microtonal fretboards if you’re a guitarist. String players can hit microtones as well since they are without frets. If you make music in a daw, there is a bunch of virtual synths which support microtonal tunings too. Alternatively you can retune nearly any instrument in post!
When watching a video longer than 1 minute in vertical feels weird.
>TFW finding out neutral intervals
19 doesnt have the neutral but yeah ut got the sub n super third lol
I think we should stop at 118 tet ...let me not explain why
1:41
You can achieve the same result by playing an out of tune piano. The 12EDO was finally found in China and in Italy at the same time in the 16th century. Antonio Galilei, father of Galileo was the Italian musician and mathematician that SOLVED the problem that from ancient greek to Galileo we were struggling against. Odd tunings that sounds... Out of tune.
And now there is this novelty of microtonal subdivision (I saw a 53TET video). I noticed though, that will there are tons of video about this "theory", there are very few (not to say none) videos people playing actual music.
Why 31 and not 47 or 129?
31 TET is basically the maximum you can go while still being playable on an instrument (most commonly, the lumatone) while still giving viable approximations for common intervals like the fifth; major and minor third; the half and whole tone; and the tritone; and offering new flavours that the commonly used 12 TET cannot offer. These flavours can be, by example, the ones mentioned on this video and the harmonic 7th (lower than the minor seventh by 39 hundredths of a semitone, and just one of the many new intervals 31 TET can offers). This is not to talk about the insane modulations, chord progressions, consonance and dissonance, and infinitude of things that just would not be possible on our current common system
31 equal divisions of the octave is a meantone tuning system, like 12. This means that stacking four fifths results in a 5th harmonic. Much of the harmony we are familiar with is based on this property. Meantone systems include 12, 19, 31, 43, 50, 55... Among all of these, 31 is particularly interesting because not only it has a more accurate 5th harmonic than the other ones, but also contains a very accurate 7th harmonic, which allows to use all sorts of new consonances we are not familiar with while keeping the ones we already know.
31 isn’t quite as high and unwieldy as those, and it’s interesting you said 47, as it’s actually well known in the microtonal community as being one of the worst options for a higher equal temperament. It has no perfect fifth, with two notes both almost exactly equally off, and very poor approximations of most harmonics. additionally, it fails to have interesting rank 2 temperaments, and the commas it tempers don’t tend to be useful, and the lack of any perfect fifth is a big issue. 129 is far too large for most uses, and it also lacks a good fifth, and only exists to expand 43et, which is already a pretty fringe and less common meantone equal temperament, that tends to be less useful that 19, 31, or 50.
You might want to check out the music of Niccola Vicentino! Microtonality is not new in Western music.
Love Vincentino’s work!
Victor Wooten said that there is 31 notes I think, not 12.
Gosh music theory goes completely over my head. But yeah, no Western music theory is underrated in it's theory, or rather, lack thereof.
Welcome to Hindustani classical music. Peace.
this whole video feels like you just picked 31 arbitrarily
Check out all the other 31 videos on my channel. Not arbitrary in the slightest!
Why 31 specifically?
Basically you want to have access to pure 3rds (approximating 5:4 frequency ratio) and 5ths (3:2 frequency ratio) because these intervals are perceived as the most consonant and they form the basis of many chords. Outside traditional 12-note subdivision, 19 and 31 happen to approximate these intervals with enough precision (in fact better than our standard 12-tone equal temperament system). Also because 19 and 31 are prime numbers, repeating any fixed interval in these scales cycles through all possible notes.
In short, mathematical coincidence. Triadic harmony developed in the context of 1/4-comma meantone (in popular use from roughly 1500 to 1700), a temperament where four slightly flattened fifths add up to a just major third of 384 cents. It just so happens that if you extend 1/4-comma meantone out to enough places, it ALMOST forms a closed circle. The difference between this extended meantone and 31edo is so small as to be imperceptible, in fact. So 31edo accurately reproduces what was considered "ideal" harmony in the 16th and 17th centuries without the problems that come with conventional meantone (like certain keys sounding extremely out-of-tune). And since we still "speak" the basic language of meantone today despite using 12edo, 31edo is directly applicable to contemporary music as well, unlike some of the more exotic edos.
@@baze3SC Indeed. I's all about consonant ratios.
ok but i'm still gonna simp for 14tet
Hell yeah!
I can't play those
Why 31 tho?
It approximates thirds better, as well as upper limit intervals :)
When it says 1 10 18 and not 0 10 18
it would make it so much harder to sing in tune
that's true for people who have listened to 12-tone music their entire lives, it's actually easier to sing some 31-tone intervals over their 12-tone counterparts (by ear), most notably the major third and the minor (harmonic/dominant) seventh
but yeah more notes = harder to conceptualize
great ideas but the effects on the synth are too much.
i would love to hear this video with no “special effects” to interfere with understanding the sound.
it has a decay, reverb and vibratto plus a goofy underlying sound.
real physical strings would be best.
1:37 sounds Arabic
The perfect fifth in standard tuning is 1.498 times the frequency of the root, a little less than 0.1% of a 3:2 harmonic. Not a coincidence!
Standard tuning is the way it is because it's closely related to pythagorean tuning. The circle of fifths in music theory is basically how the pythagorean scale is built.
If you ask me, you're better off learning to master standard tuning. Maybe microtunings have some value to the artist, but you're going to have a hard time finding an audience. Your audience's ear probably isn't really picking up on cents, they're picking up on octaves and fifths - because they're harmonics.
A subminor third actually appears a lot quicker in the harmonic series than any type of tritone, so you can get used to it a lot more quickly. Standard 12edo tuning is also in no way the best, it was just the one that happened to be the most popular for classical musicians and composer in the late 19th century. Most older composer before that time used well temperaments, which were arguably better.
@@rafexrafexowski4754 In physics, the perfect fifth is the third harmonic, the second harmonic is the octave.
A 7:6 subminor third is further down the list.
I don't know exactly what you mean by "a lot quicker", but I assume it has something to do with actual harmonic series (that your ear drums, cilia, and perceptive mechanisms in your brain are picking up on).
The thing with music theory, is it makes a different kind of sense when you understand the physics and the psychology of the situation.
You're defining a palette in music theory, and a way to communicate to other musicians about what to play. That is all.
Nature has its own music theory.
Do you have an explanation for why two notes separated by an octave should be considered the same note?
Clearly they're not the same frequency... So what's special about octaves?
laughing in oriental music
Sounds like a train horn
"I broke music theory" That's weird... You don't look like Adrian Fokker at all. You don't look like Harry Partch either.
You are correct, I am neither of those people 😂
Yeah. Obviously.
@@cletusyesk Thank you for your input Cletus.
But he undeniably sounds more like Fokker than he does like Partch. 🙂
failed short
How do I listen to Orwell 9? I cannot find it anywhere. @LeviMcClain