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Could There Be A 13th Note?
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Күн бұрынBuild a website for free with Wix: wix.com/go/12tone
It's a question that's plagued theorists since time immemorial... Nah, just kidding, it's a goofy thing I decided to play around with to see what would happen. But still! What would happen if we added a 13th note to the octave? Can we do that? Would it work? Or would it be a pointless exercise in futility? Or maybe both, who knows. That's what I decided to find out, and the answer is... Well... Kinda both. I'm not really sure what we learned here, but the journey's a lot of fun.
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@12tone 5 жыл бұрын
Some additional thoughts/corrections: 1) Technically, it may be inaccurate to call this 13TET. Depending on whose definitions you subscribe to, calling it a temperament implies that something's being tempered out, effectively meaning that TET systems need to do a passable job at approximating some important ratios, whereas the broader term for any evenly-spaced system is "Equal Division of the Octave", or EDO. So maybe I should've called it 13EDO, but TET is more fun to say and I don't think the distinction's super necessary. 2) There's actually a couple different ratios for the subminor and supermajor 3rds. The ones I cited are the simplest, but really anything that exists in roughly that quartertone space could be considered one.
@leftaroundabout 5 жыл бұрын
The main reason I prefer EDO over TET is that there are also equal temperaments which don't start from the octave, in particular Bohlen-Pierce, which might in fact legitimately be called 13TET but is very different from 13EDO.
@captainbanaynays 5 жыл бұрын
It seems to me that when it comes to building n-TET scales that approximate the ratios of Just Intonation, the success of a scale depends on n's divisibility. For example, 12TET does such a good job at dividing into the octave because it is divisible by a large number of numbers - 1,2,3,4, and 6 - relative to its size. Because of its ease of divisibility, it will approximate those ratios better on average. On the other hand, 13 is prime, divisible by 1 and itself, creating many complex ratios between intervals and leading to a more difficult time constructing a scale which fits these simple ratios. I think that one will find is that if n is large and has many factors relative to its size, in other words is a "highly composite number", the better approximation of these ratios can be achieved. 6TET and 24TET are the ones closest to 12TET, but n can grow big. We use 60 to divide up time because it is divisible by so many numbers. 60TET should be a good candidate for approximating Just Intonation.
@Moinsdeuxcat 5 жыл бұрын
@@captainbanaynays No, it's not the reason. The reason why 12 works is that ln(3)/ln(2) is very close to 19/12 (you can formalize that with continued fractions to get the best rational approximations in a precise sense). This amounts to say that a 12-tone system will give a very good approximation of the fifth (the fact that we also have a good enough - although not very good - approximation of the major third is a gift from the sky). With that said, it's a real gift from the sky that 12 has so many divisors. It gives way to a lot of symmetric chords (tritone, diminished, augmented) and scales (half-whole, whole-tone), which wouldn't be possible with e.g. a prime number. When you realize how important e. g. diminished chords are for modulating thanks to their symmetry which blurs the tonality, it makes you think a real miracle has occurred for 12 to be such a good match). Another gift from the sky is that 12 seems like a good number for how many notes we want. 6 would have been very few, 30 would have been too much. 12 is large enough for many scales to hold in it, while letting us recognize individual intervals.
@ConvincingPeople 5 жыл бұрын
Ethan Meltzer Setting aside what was already said, a lot of far more accurate EDOs are prime: 19, 31, 41, 53, all represent things like just major third, septimal thirds and even 11- and 13-limit intervals better than 12. Not that 12 and, more importantly, its multiples are not highly versatile-72 is a fantastic scale-but divisibility is not the key factor. If so, 45 or 90 would be the holy grail, and that's... inaccurate.
@1234helloguy 5 жыл бұрын
@@captainbanaynays So this theory doesn't generally hold that true. Equal tempetaments that are particularly good at representing simple JI ratios include 19,31, and 53 which are both prime and very efficient in the range of intervals they represent and their accuracy relative to the tuning size. 60 tones for example isn't a particularly excellent tuning in general--it tunes the 3rd harmonic no better than 12, the 5th is 4c fkatm the 7th is pretty flat at 9 cents flat, the 11th falls evenly between two scale degrees pretty much (10c either way) and is therefor pretty much maximally bad for the size of the tuning, etc. This doesn't mean that divisibity makes equal tunings bad at representing JI--72 tones is a particular standout at sounding near-just through the 11 limit in most cases.
@rodrigoteresa7944 5 жыл бұрын
12 tone making vids on non 12 tone scales Top 10 anime betrayals
@commentfreely5443 5 жыл бұрын
what the hell do the pics have to do with what you are saying?
@thezipcreator 5 жыл бұрын
@@commentfreely5443 what pics??
@tjprosper7704 3 жыл бұрын
@@commentfreely5443 We'll never know about the pics, huh?
@deadman7624 5 жыл бұрын
Time to change the channel name to 13tone
@nugboy420 2 жыл бұрын
Still like the idr how many was it 31tone.
@Junebilation7900 Жыл бұрын
Yeaahhh 13tone doesn't have the same ring to it
@43615 5 жыл бұрын
What about 5040TET? Pythagoras: _excited greek noises_
@lonepilgrim83 4 жыл бұрын
What about Golden Meantone?
@witherblaze 4 жыл бұрын
5040, the perfect number to divide
@ordinaryshiba 4 жыл бұрын
well then each notes will be the 5040th root of 2 apart
@RealLifeKyurem 4 жыл бұрын
Ordinary Shiba So uselessly numerous? 1 cent ≔ 2^(1/1200). The human ear only hear differences of 5, that’s assuming it’s a sine wave. If I remember correctly, with timbre, the human ear can reliably differentiate differences of 10 cents. So let’s say it’s 10 cents. 10 cents = 2^(1/120) which is vastly larger than 2^(1/5040).
@mertatakan7591 25 күн бұрын
@@RealLifeKyuremThe human ear can hear 6 cents not 5
@juliangoulette7600 5 жыл бұрын
4:30 The modes of this 13tet "major" scale: "Ionian" LssLsLs -the default mode, contains its own negative harmony. "Dorian" ssLsLsL -the "darkest" mode. "Phrygian" sLsLsLs -symmetrical, has a similar feel to the Double Harmonic scale. "Lydian" LsLsLss -the "brightest" mode. "Mixolydian" sLsLssL -inverse of the default mode. "Aeolian" LsLssLs -the not-minor-anymore mode that is now ironically brighter than "major". "Locrian" sLssLsL -inverse of the not-so-minor-anymore mode.
@eboone 7 ай бұрын
the ol mosh
@LemakiMusik 5 жыл бұрын
1:09 That super major triad sounds SO GOOD! I wanna make music out of this!
@CorySherman 5 жыл бұрын
Yes! Such a unique sound. I also really like "large just minor 7th" at 6:08.
@ConvincingPeople 5 жыл бұрын
Technically in the quartertone system it's not merely supermajor but what some theorists call ultramajor: A near-just 13/10 ration, which in a triad forms a very neat 10:13:15. It's a strange sound but very harmonious.
@AlbySilly 5 жыл бұрын
If you wanna play around with microtonality, I'd recommend a program called "ZynAddSubFX"
@masicbemester 5 жыл бұрын
@@AlbySilly I use LMMS and I really like this synth
@wyattreed4024 5 жыл бұрын
Hell yeah. You can just hear the faintest hint of a sus chord in there!
@MarsLos10 5 жыл бұрын
I was disappointed that you didn't compose something using the 13tet system. Very interesting though
@fox-school-of-music 5 жыл бұрын
Sevish has one: kzfaq.info/get/bejne/pNSKrdhl2sebpps.html Xolta has a really pretty one too: kzfaq.info/get/bejne/jb2UlcdpnJ3GZWg.html
@aotmr1604 5 жыл бұрын
There's a lot of horrible EDOs (8, 10, 13 come to mind) but there's many more great ones (12, 19, 22, 31). I would love to hear your analysis of 19edo. 19edo is to 12edo as 12edo is to the diatonic scale: a useful superset that allows for greater flexibility in transposition and expression. While 19edo has a slightly flat fifth (7.2 c flat), it better approximates the major third (7.4 c sharp) and especially the minor third (0.15 c sharp). The notation is compatible with 12edo, except that previously enharmonic notes are different (C# and Db, for example are different notes); C#/Bb and E#/Fb are the only enharmonics. Basically, split the black keys in half and add an additional black key between C/B and E/F. This notation is compatible to the extent that one can basically play 12edo music on a 19edo keyboard, provided the notation doesn't abuse enharmonics.
@leftaroundabout 5 жыл бұрын
Right. Though 19edo does sound pretty anemic for Western music, because both of the flattish fifth and because the major third is actually _smaller_ than the JI one (same problem as here discussed for the 13edo major third). But, I really hope 12tone will discuss 19edo, 22edo and particularly 31edo (I personally think 31 will be necessary to actually replace 12edo, because meantone✓ fifths✓ thirds✓ ET✓ microtonal✓).
@aotmr1604 5 жыл бұрын
@@leftaroundabout For typical, triad-based western music, sure. But 19edo has much smoother 7th chords--in fact, 7th (and even higher-extended) might even be the fundamental 19edo chord[1], as the triad is to 12edo. [1] en.xen.wiki/w/19edo
@alsatusmd1A13 5 жыл бұрын
@@aotmr1604 31 has even smoother 7th chords than 19 (4:5:6:7 within 5.986 cents of just vs. 10:12:15:18 within, but 2:3 and 5:9 jarringly rough contrasted against essentially pure 5:6). And you mean this article: en.xen.wiki/w/Chord_progressions_in_19edo-family_scales
@e8heterotic649 5 жыл бұрын
17 EDO is very underrated. It's quite useful, and it only has 5 more notes than 12 EDO. Indeed, you can use the exact same notation for 17 EDO as 12 EDO as long as you forget the enharmonic equivalence of F# to Gb, G# to Ab, etc.. The only enharmonic equivalences that remain are B# = C, Cb = B, E# = F, and Fb = E. Basically, each of the black keys gets split into 2 separate keys.
@JAzzWoods-ik4vv 5 жыл бұрын
We need 60 notes. That way you can nail every ratio
@1234helloguy 5 жыл бұрын
Cool video. I don't think I've ever heard anyone try to describe 11/8 as a minor 5th in the microtonal community. Aside from referencing it mathematically, it's usually called a harmonic 11th, and this is implied in how it's ordinary notated in Johnston notation, Sagittal, and Ellis-Sabat, which all would notate it as a 4th plus a upward arrow. The inversion of 11/8 (or its utonal version depending on how you look at it) I'd probably call probably a subfifth or something, or to extend the above idea, a subharmonic 5th. Minor in my mind is an approximate half step from a major interval. I think that, aside from acknowledging 13EDO's accuracy in representing 11/8, 10/9, and 7/6, you kind of miss the primary appeal of 13EDO. would say it's complete inability to approximate 3/2 and the diatonic scale are it's strengths. It has enough reasonable consonances (the above, plus the flat 5/4, and some 13 limit ratios) that you can build systems of consonance dissonance, admittedly with somewhat novel intervals, but it supports some structurally bizarre scales built from moments of symmetry. I Because 13 is prime, any interval can be used as a generator for a moment of symmetry, with the most often used being 2/13 and 5/13, which form a 6L1S scale and a 5L3S scale respectively, which sound weird as all getout but hold together well. If you're going to throw a microtonal scale out, it might be good to link to a few examples. kzfaq.info/get/bejne/hLaKqcZy3qq9aIE.html is the classic from Blackwood's microtonal etudes.
@mertatakan7591 25 күн бұрын
You're right when you say that 11/8 shouldn't be a "minor fifth", but harmonic eleventh makes less sense cuz 11/8 is not an eleventh. It's a fourth. It's called the (undecimal) superfourth/semiaugmented fourth, harmonic fourth, etc. By the xenharmonic wiki, there's also wide fourth and its inversion, 16/11 would be narrow fifth. Also you didn't need to write an article
@TheGymSavant 5 жыл бұрын
When I read the title, I thought you meant a 13-tuplet. Lmao.
@masicbemester 5 жыл бұрын
I thought of 13th note as a 6th but an octave higher
@DPowerOfRock 5 жыл бұрын
I'm very annoyed that you didn't write us any melodies in "13TET"
@Stephen-Fox 5 жыл бұрын
Really fun video, I do enjoy your occasional deep theory dives like this. Since you weren't sure what we learnt today according to your description, what I got from this was that Western musical tradition is mostly arbitrary, ears can adjust to anything given enough exposure, and that equally valid systems exist but when approached from 12tet lens their strengths are going to be minimized. I'm not convinced this was the best way of illustrating that, but reading your description that isn't what you were aiming to do anyway.
@karawethan 4 жыл бұрын
Every musical system looks arbitrary in hindsight. But in reality, musical systems are shaped by very non-arbitrary pressures. For example, material technology. Cultures that prioritize idiophones (struck metal, wood, bamboo, rock, etc.) tend to develop different tuning systems than those that prioritize string or wind instruments. There are acoustic reasons for this that have to do with harmonic vs inharmonic timbres. That's just one example. There are also aesthetic pressures, cognitive pressures (like whether the music is written down or not), economic/political/religious pressures etc etc that influence the development of musical systems. Most tuning systems appear poor when viewed through a 12tet lens. The exception is tuning systems that have a historical basis in Western music; 19tet, 31tet, various "well temperaments." That's because they all support the same sort of chordal harmony. The problem is that chordal harmony is not universal; it's actually the exception rather than the rule in terms of all musical traditions.
@AnAmericanComposer 5 жыл бұрын
Here I thought you were going to discuss Julian Carrillo's microtonal music theory text _Sonido 13_ Shame!
@12tone 5 жыл бұрын
Whoops, I completely forgot about Sonido 13! Good catch, I probably should've at least name-checked it in the quartertone section. Sorry about that!
@AustralopithecineXen 3 жыл бұрын
That was also my first thought upon clicking.
@bob-rogers 5 жыл бұрын
ET exists on keyboards, but violinists play with way more than 12 notes already. There is a considerable difference between C# and Db when a violinist plays them. PS> I liked the use of the butterfly in the graphic!
@mertatakan7591 21 күн бұрын
Also there is a difference between Bb and Bb a syntonic comma apart.
@aheendwhz1 5 жыл бұрын
4:30 I really like this scale, it's so bluesy! Actually, I think this scale is 13tet's true strength.
@elmostachojuanoh 5 жыл бұрын
The 12 equal tones try to approach something that already exists, the natural harmonics. They sound "good" to us cause they are mathematically close intervals like 2 to 3 or so, and the 12 equal notes approach mostly all of the simple/small ones. I thought you would approach the 13th by adding another ratio/harmonic that were not already into the standard. Anyways a very interesting video as always
@DrMackSplackem 5 жыл бұрын
This is the comment I was looking for. I once graphed it out and was satisfied that 12 notes made the most sense, and was not some arbitrary choice.
@mertatakan7591 25 күн бұрын
31edo is better, cuz it has better (major) thirds. In 12edo major thirds are 13,687 cents sharp, which is a lot really. In 31edo, it's 0,783 cemts sharp, basically nothing. The fifths are eh, not that good but the difference is still inaudible. They're 5,181 cents flat exactly. The most out of tune interval I can think of is the major second, which is the perfect fifth stacked, hecne 5,181 × 2 = 10,362 cents. Still, it's pretty close.
@mertatakan7591 21 күн бұрын
The 11th harmonic: 💅👁👄👁💅
@dominikkozub7934 5 жыл бұрын
Understanding (don't fear) the reaper, please that would be great.
@user-om9jl5jv5y 5 жыл бұрын
More like "(Not Fearing) The Reaper", ha ha
@aakashchakrabarty4262 5 жыл бұрын
Could you please make video/(s) on microtuning scale 🙂
@whiskymylove 4 жыл бұрын
From a musical dyslexic, you out things very easy to understand. I appreciate you and your work, you have helped me rap my mind around a free concepts that have vexed for some time, and for that i give you my thanks and gratitude
@xenontesla122 5 жыл бұрын
13edo was used in one of my favorite microtonal songs, Sean’s Bits by Sevish. It uses the whole tone scale to get surprisingly natural sounding melodies.
@dnaroseandthewolves Жыл бұрын
ooOOh ooOOh
@SaintOfIdiocy 5 жыл бұрын
4:30 I love that scale. It may not have been what you were looking for, but that does't mean it sounds useless or uninteresting
@Alexander-mw1ek 5 жыл бұрын
You should do a whole video on “unjust” tuning systems. I’m really interested in them because I want to know what all these ratios you describe would sound like if they weren’t off by a few cents, and what some good starting places would be. I’ve never been a fan of the major 6th interval of pretty much any mode of the major scale, and in my electronic compositions, I purposely bend that note to be about 20¢ sharp sometimes because it seems to sound really good in some contexts. I don’t really do this with other notes because those intervals all sound pretty nice to me, mainly just major 6ths. Anyways, please do a video on this topic.
@seiph80 5 жыл бұрын
Of all the channels I'm subscribed to, you're the first to ever mention Ivan Wyschnegradsky. Not a household name, but I've read about him for years; too bad his ideas didn't go mainstream, but interesting nonetheless. Thank you, 12tone!
@stephenweigel 5 жыл бұрын
Two of the best pieces of music I've ever heard in 13-tone equal temperament are Easley Blackwood's microtonal etude (Sostenuto), and Ernst Krenek's Spiritus Intelligentiae Sanctus (op. 152), both of which are on KZfaq.
@mememem 5 жыл бұрын
You are messing with powers far beyond your comprehension, mortal.
@KohuGaly 5 жыл бұрын
Do you mean powers of 2 to the power of one 13th? Because that is precisely what he's messing with :-D
@noahrubio2939 5 жыл бұрын
13 vibration. Golden ratio of the pyramid within.
@Stargazer1312 5 жыл бұрын
Damn, my favorite shitpost channel in the comments of my favorite music channel
@oldtimetinfoilhatwearer 4 жыл бұрын
S-sauce on pfp
@gngrblls2thwall 4 жыл бұрын
Random idea: a duet with one instrument using 13 tet and the other using 12. Have the 13 tet instrument focus on the intervals that that temperament excels at and the same for the 12 tet instrument. Also analyze to see what intervals you can get harmonizing the 12 tet notes with the 13 tet notes, and focus on the sweet ones. Has this been done? 2 temperaments dancing with each other?
@qantuum7567 Жыл бұрын
I'm really enjoying all these intros to xenharmonic music you have done! lots of stuff to explore thanks a lot.
@ohwhen7775 5 жыл бұрын
If it's not my imagination, JI was used for those triads at 3:40.
@therealandrew185 5 жыл бұрын
I've been thinking this needed to happen for a while. Two days ago I started looking for a way to make the difference in hz between notes prettier to my base10 mind. I did not know about this "cents" system and I'm glad I watch your videos. I really hope some new system like this 13tet one catches on, I think it would help us make a lot of progress in the field of music theory (that we've really only scratched the surface of). I'd also love to try and make music with the 13tet system
@buxeessingh2571 3 жыл бұрын
When I was learning violin, I was taught that we cheat on 12TET so that we play consonant ratios of frequencies in harmony, but relative to the context, such as the key of the section of the piece. So the same note in the score may be played slightly differently depending on the part and what else is happening around you. For instance, a properly tuned violin has its open strings exactly a 5th apart, whence you can compute the exact frequency each string vibrates at if A= 440 Hz.
@ValkyRiver 3 жыл бұрын
2:57 This is almost exactly 135:128, which is the interval between 16:9 and 15:8. Just approximation for 13-TET: 1:1 19:18 10:9 20:17 21:17 17:13 11:8 16:11 26:17 34:21 17:10 9:5 36:19 2:1
@timh.6872 5 жыл бұрын
I actually tried to explore this space of alternate octaves once. I noticed that the Just Intonation ratios for certain intervals had power of 2 denominators, and ran with that idea instead. I arranged notes in a lopsided binary tree, where the left branch's left branch was the same as the right branch, up to the leaf nodes. Expanding this tree in every direction gives a whole slew of note positions. Pick a node along the left "spine" as unity. Its parent is an octave up, its left child is an octave down. Its right child is the average of itself and its parent, giving 3:2. What ends up happening is that the odd numbers are arranged sequentially left to right, top to bottom within an octave, while each row of the tree has the same power of 2 denominator. The recursive construction giving the lopsided tree (because human hearing is logarithmic), however, wants there to be 13 notes, the "new" one nestled between unison and the minor second. I never really got around to exploring that harmonic space, though.
@DrBartosz 5 жыл бұрын
You used sampled piano sounds to illustrate your new intervals. The problem with it is that a single piano sound contains (among others) a very prominent perfect fifth in its overtone series, which clashes with your modified scale steps. I bet the new intervals wouldn't sound as bad if you used pure tones. You could also try synthesizing new sounds using modified overtone series, or use instruments like bells or marimbas that have weird overtone series.
@An_Amazing_Login5036 5 жыл бұрын
Okok Dumb idea time: Have anyone made the literal worst approximation of JI intervals? Like if we space out 12 tones in an octave such that we get no gap bigger than a whole-tone, how can we make sure we miss all the nice clean ratios as much as possible? I need that tuning system for erm... ”recreational purposes”. Ok you got me I just wanted to program all-star in a truly tone-deaf system, is that so wrong?!
@karawethan 5 жыл бұрын
You will always be close to *some* JI intervals, because the range of JI intervals is continuous. But in terms of missing the most simple/consonant intervals, 11tet and 13tet are pretty gnarly. Or for a non-equal scale you can look at a harmonic dissonance curve and just pick intervals from the peaks.
@KilloZapit 5 жыл бұрын
It probobly isn't the worst approximation of JI intervals out there, but allow me to introduce you to a little something called the Bohlen-Pierce scale: Okay, so you know how 13TET (and most other microtonal scales) is based around how many notes are in an octave? An octave is just another random ratio after all, it just means each octave is double the frequency of the last one, or a ratio of 2:1. So what if we didn't do that at all. What if we made a scale based on something else. Maybe a ratio of 3:1, where each "octave" (or in case it's often called a "tritave") is triple the frequency of the last one? The result? Well... kzfaq.info/get/bejne/qcphlZx9zZ7NdnU.html “Sounds-possibly musical-heard in the night from other worlds or realms of being.” ― H. P. Lovecraft
@farissaadat4437 5 жыл бұрын
One way to quantify how good or bad a number is for rational number approximation (sounding good) is continued fractions. Using this we find that the golden ratio ((1+√5)/2) is the worst interval, I am not sure about the general case as it gets quite elaborate. If you wanna dive real deep you can look up Arnold Tongues (which I barely understand).
@Anonymous-df8it 2 жыл бұрын
@@karawethan It's not continuous. There are gaps, like literally every irrational number ever.
@charlesrosenbauer3135 5 жыл бұрын
A video mentioning subminor, supermajor, and neutral chords? Finally! I've been waiting for this for a while. Halfway through the video I thought "the only way this could be better is if he mentions the 11th harmonic". Then suddenly you start talking about a note between the tritone and 5th. This is the video I've been waiting for! For those interested in the ideas from this video, here's some cool stuff: Subminor music (subminor chords/scales are actually really good for making things sound creepy): kzfaq.info/get/bejne/q5pymburnsetqac.html kzfaq.info/get/bejne/msWWjMWZzLqth40.html Brendan Byrnes has this classic video on 22tet, with a microtonal music theory lesson at the end. He uses the 11th harmonic heavily: kzfaq.info/get/bejne/p654qZae3LC4nJs.html He also has tons of other cool stuff in 22tet with the 11th harmonic. This piece is great too: kzfaq.info/get/bejne/aZuKh9motq2Rn3U.html I also found this, which is in 13tet: kzfaq.info/get/bejne/aqqWZ5CW1NKxqnk.html
@themathhatter5290 5 жыл бұрын
I think that the reason we don't use this scale or say the Bohlen-Pierce scale is that they're just not particularly nice to our ears. We don't have one of the most fundamental ratios, 3:2, and without that relaxing and calm sound, there is no relaxing in general. You can play around with some crazy ratios in the Major scale, but you almost always come back to 2:1, 3:2, and 4:3. Without those homes, your ear doesn't like the new sights you're throwing at it because it all feels alien.
@stephenweigel 5 жыл бұрын
I've heard plenty of nice chords that aren't anywhere remotely near JI. The gamelan tradition, which is centuries old, would disagree with you.
@kristofwynants 5 жыл бұрын
I LOVE the cat drawing for "ignore", yes I've been paying attention. Very very interesting stuffffffff
@spielersubliminals8025 5 жыл бұрын
I'm going to build a 13-TET piano now.
@EASReviewer 4 жыл бұрын
Good luck my friend :)
@deldarel 5 жыл бұрын
I have a very good case for why 9TET is actually the way to go.
@averykral9654 5 жыл бұрын
Let's hear it
@TheSquareOnes 5 жыл бұрын
I am also interested, although I am skeptical that significantly lowering the melodic and harmonic possibilities would ever be good for a new "standard" tuning given how played out most aspects of 12TET are already. Personally I think quarter tones are the ideal next "standard" thing since it wouldn't require reinventing the wheel and would thus be much easier for most people to get used to hearing and writing with. Historically ease of use has been more important than mathematical arguments.
@RizalBudiLeksono 5 жыл бұрын
9tet is beautiful scale. If you numbered te tones with 1 2 3 4 5 6 7 8 9, we would have Javanese pentatonic scale called Pelog scale if we choose 1 2 3 6 7 (pelog nem), or 2 3 6 7 8 (pelog barang). You can add the number 5 or 8 for accidental tones in pelog nem, or 5 and 1 for accidental tones in pelog barang.
@dsws2 5 жыл бұрын
How about some xentonality? You could presumably construct a timbre that would work reasonably well with 13TET. And you would presumably have something to temper out, since the timber would be a compromise between fitting well with 13 equal divisions of the octave and having the sound cohere well into a recognizable pitch.
@pissnips8903 5 жыл бұрын
12tet is 12th roots of 2 (x by 440). To do 13tet just do 13th roots, you can do this for any number
@bruce9421 5 жыл бұрын
Well, this video tells what happens when using the 13th root of two
@argenteus8314 4 жыл бұрын
My favorite tuning is 36-EDO, AKA the 33.333 cents tuning. It fully contains 12-EDO, so it's good for more "normalish" music, but it's also got lots of fun and (in my opinion) musically useful intervals of its own. Its sixthtones are also easy to think about if you're used to 12-EDO; basically in addition to each 12-EDO note you have a blue note that's 33.333 cents lower and a red note that's 33.333 cents higher. Also, this isn't all that important, but it nicely approximates the golden ratio. It's only 0.24 cents off, which shouldn't be distinguishable by humans. I find this a musically pleasing interval; it sounds sweet yet teasing to me.
@AlbySilly 5 жыл бұрын
Oh yess, finally some proper microtonality. 13 might not be my favorite, but it's better than nothing
@wizard1370 5 жыл бұрын
Equal temperament is not for me. I use 13-limit just intonation (2^a*3^b*5*c*7^d*11^e^13^f) where b,c,d,e,f have to add up to 2 and a has to be between -3 and 3 in order to fit the notes into an octave. If I chose to fit all of the notes into the octave there would be way too many notes. I also wanted to make every prime number have an equal chance at getting noticed so instead of using the euler gradus function, I used the equal version that I made up which is when you just ignore multiplying the exponents by p minus 1. Here is my scale: 1/1 ,14/13,13/12,12/11,11/10,9/8,8/7,7/6,13/11,6/5,5/4,14/11,13/10,4/3,11/8,7/5,10/7,3/2,20/13,11/7,8/5,13/8,5/3,22/13,12/7,7/4,20/11,11/6,24/13,13/7,15/8. Anybody interested?
@knasigboll 5 жыл бұрын
The theory behind tuning is wildly fascinating! This makes me think about how etheral and cool the well tuned piano sounds is.
@abacussssss 5 ай бұрын
the original idea of having 12EDO + an extra pitch class is something that genuinely happens in extratone, although i don't know if anyone's ever actually taken advantage of that
@tehcanadian4653 4 жыл бұрын
"This is SUPER simple..." Proceeds to then speak Enchantment table language
@JohnWilliams-uk2hf 4 жыл бұрын
I know that this video is old, but I want to tell one thing that is very important to know about 12 notes scales; The 12 notes scales actually increase via mathematical rules that we set there, and we know that we can't have perfect number tuning, which makes the notes actually irrationally tuned and such. 12tone should've used the 13th root of 2, so you could have the perfect 13 scale, though it wont be "perfect" to our ears. Though this video is old, this is only a corrector for this video, and as a corrector here, I'd like to see a newer result with the 13th root for tuning, where the unison (lets say 3rd octave) first note was 440 hz, the last one will still be close to the 880 hz. Though, here's how it would've gotten for increasing; (0/13) 440, (1/13) 464.09, (2/13) 489.51, (3/13) 516.32, (4/13) 544.59, (5/13) 574.42, (6/13) 605.88, (7/13) 639.06, (8/13) 674.06, (9/13) 710.98, (10/13) 749.91, (11/13) 790.98, (12/13) 834.30, (13/13) 880. I know this might not work very well, but hey, its the rules to calculating it!
@Chris-cf2kp 3 жыл бұрын
I just had this thought after studying the ancient Mayans recently, and their incredibly precise calendar based on multiples of cycles of 13 and also 20 which equals 260; which end up accounting for cycles of the sun and moon's rotation almost exactly and even human gestation periods in pregnancy. Fascinating! Each day in the 13 cycle is considered to be a 'tone' of resonance that applies to the day and anyone born on that day, and the cycle of 20 which coincides with it, makes each cycle of 13 unique and no same combination of day repeats once until about every 53 years or so. So then I thought hang on, western music only recognizes 12 tones, but we fundamentally compose in a way to represent nature with chaos vs order and that is all based on the Fibonacci sequence, which is a ratio of 13, so we must be missing one more piece to our musical alphabet. Surely we can have music more attuned to nature with 13 tones? Western 12-tone music is entirely arbitrarily established as a result of equal temperament, surely? Very interesting inquiry. I think a good place to go looking for the 13th note is exploring the overtone series outside of equal temperament then incorporating it into modern instruments. It would probably make pianos have an even ratio of black and white keys, 3 by 3 black keys instead of 2 by 3 by 2.
@testerbleck 2 жыл бұрын
4:32 I find it cool how you managed to generate a Hijaz tetrachord while trying to get a major scale.
@mistershaf9648 4 ай бұрын
I love to explore different temperaments! THANKS SO MUCH!
@DoctorLazertron 2 жыл бұрын
I just want a plugin that will apply just intonation to what chord I’m playing or at least what key I’m in. I don’t know if or how it would work but those perfect triads are just gorgeous.
@naomisalama430 4 жыл бұрын
I really like the change from a neutral triad to super major. I'll have to use that in a song some day.
@ChasMusic 4 жыл бұрын
I really appreciate your willingness to experiment.
@aanon1342 5 жыл бұрын
I wanna see this video again but for 5 to 53 equal divisions, or at least all the cool ones.
@Oopaack 5 жыл бұрын
Love the channel! Here's a question..Would building your new system in 15edo work better? Instead of having a half step equal 92.3 steps. which just seems clunky AF, you're now using 80 cents per step, a much rounder... wait...That can of worms I'm about to open looks huge...what we call a major third in 12tet would be a fourth because the amount of cents between is the same, 400, right?Or would that be building a different chord entirely? If not, the fifth, which is 700 cents higher than the root, there is no exact, precise way to get to that tone in 15edo, so the closest tone would be... 25 cents short of the ninth tone in our now 15 note equal temperament system... Dammit, I'm gonna be awake I dunno how long tryna work out a way to do this without simply doubling. And trying to figure out if using sharps and flats makes sense or should I just use numbers, or just use A through O... Can't do 18edo, can we? Should we? How and why did 12tet come about in the first place? DANG BRUH!
@JbfMusicGuitar 5 жыл бұрын
We should ask David about this note, maybe he put it in his chord? You know, the secret one?
@ottolehikoinen6193 5 жыл бұрын
Next up - 53edo video that's 4 times longer than this one. Thanks for starting with this.
@RockStarOscarStern634 3 жыл бұрын
The 41 Tone Equal Temperament is really interesting cause you can every note to be in tune
@lenypapas 5 жыл бұрын
I've always thought that in another universe without our laws of physics could be more notes up or down without the necessity to return an octave or adjusting the frecuencies.
@redlightclinicdrummer 5 жыл бұрын
I've been thinking something similar for months! Theres something big people are trying to connect! I learned the other day the human brain actually produces bass notes that by physics can't actually exist. If these bass waves were to actually exist in the real world it would shatter gravity. I think it in a way points towards spirit being another form beyond the real world. These unwordly notes are inside us we just need to learn how to scale them
@bro748 5 жыл бұрын
With instruments that can adjust their pitch a bit (e.g. wind and string instruments) they often don't play in equal temperament, but use just intonation. I've also heard that some pop/techno music uses just intonation to make it sound extra satisfying. so, uh, 12 tone equal temperament is not always 'just what we do.'
@groovinhooves 3 жыл бұрын
A fascinating idea, but how to configure a necessary 13TET keyboard, one that can be played by touch with as much facility? Non-keyboard players may be tempted to suggest adding a sixth black key, equalizing the groupings, but that's how we keyboard-savvy players who like to touch the score with our eyes and read the keyboard with fingers get around-by our fingers being able to see and accept that inequality as the price of order and harmony. Why 12TET in the meanwhile? Why and how did we fixate on that? Mathematics and pragmatism for the most part. The even temperament semitone is an interval accessible to most would-be musicians, especially prospective members of the choir at your chosen house of worship, e.g. Twelve (and its multiples) is so nicely evenly divisible by so many integers smaller than itself, either symmetrically or asymmetrically, as for example Slonimsky neatly demonstrates. There's a lot going for 12, very fundamentally, that is seldom considered.
@andrekim9597 5 жыл бұрын
Dude, does the E half sharp remind you of the first note of "Pain it, black" by the Rolling Stones?
@Copperhell144 4 жыл бұрын
Probably because the first note of Paint it Black is F
@theexcelsior_0024 5 жыл бұрын
Understanding "Paranoid Android - Radiohead" in the future perhaps?
@GRUNGETIME1 5 жыл бұрын
I really love your content ! Gets on point what I am really interested in
@markholdahl6511 5 жыл бұрын
Maybe it would sound better with A4 tuned to 432Hz? I'll let myself out...
@tf5624 5 жыл бұрын
I vote this the most music theory wonk 12tone entry ever!
@HeadCannon19 3 жыл бұрын
This is like trying to understand non-euclidean geometry
@Lucius_Chiaraviglio 7 ай бұрын
If you don't confine yourself to equal divisions of the octave, you can find systems in which adding a 13th note is a good thing -- namely, with quarter-comma meantone, if you have only 12 notes per octave, you have to choose between G♯ and A♭, but if you go to 13 notes per octave by way of a split flat/sharp key, you can have both, as can be found on a small subset of harpsichords and organs from the Renaissance and early Baroque. Some of these also had a split flat/sharp key for D♯ and E♭, and a small number of harpsichords (and Nicol Vicentino's arciorgano, but as far as I know no other pipe organs until recent times) went to 19, 24, 31, or even 36 notes per octave, although 36 notes per octave (Nicola Vicentino's arcicembalo and arciorgano) was split onto 2 manuals, causing a practical restriction in what notes could be played at the same time, as you can see from KZfaq videos of replicas of such instruments . With 31 notes per octave, you could get them all onto one manual for better simultaneous playability and in principle saving a second manual for different timbre, although as far as I know no one actually made a 2 * 31 note per octave instrument until the Fokker Organ in 1951, which also has a 31 notes per octave pedalboard, but unfortunately sounds terrible unless blended with other instruments/voices.
@PaulC13 5 жыл бұрын
Wow! generally I understand everything you discuss and this makes my ears and brain hurt in a good way. Well done! now for that scene in scanners....lol Also how drastic would it be to take something like this and do it in 432 or anything other then 440? does that even make a difference?
@Thehammerofwhat 5 жыл бұрын
where can i find music that is written in different tuning systems?
@chrishuggett3697 11 ай бұрын
Thanks for an interesting video. Just a comment that when you don't allow spaces in between your talking then it can be very stressful for the listener as it's quite unnatural. I know you don't wanna loose people with a short attention span but honestly you have great material so I wouldn't worry about it. Anyway, just a thought.
@PieceOfDuke 3 жыл бұрын
It'd be great to see your analysis of connection between the tuning and the timbre. Some instruments made out of metal (bells in orthodox christian churches) resonate better to each other when in "out of tune" tunings because of their distorted harmonic series...
@BlueBlob 5 жыл бұрын
this video triggers my perfect pitch
@roceb5009 5 жыл бұрын
It seems like a scale should be built around leading tones and functional Harmony and such. Whatever the most harmonious interval is, build a chord and then figure out leading tones and such and there's your major scale. It's probably going to end up pentatonic at best
@tymime 5 жыл бұрын
How do you make those microtonal/xenharmonic sounds with your keyboard? I always wanted to compose music using that sort of thing (like Bohlen-Pierce), but I haven't had any luck finding the technology to do it. I use a MIDI keyboard and virtual instruments, so there's that limitation to work with.
@gwyneth2869 5 жыл бұрын
the minor fifth : just the chord metal needed
@yitzharos Жыл бұрын
I propose there is only 11. Based on the octave being the repeating category: beginning the 1st note of each Octave+10 more semitones. I believe we decided on 12 for symmetry reasons.
@Gnurklesquimp 4 жыл бұрын
I'd love to hear all the equally distributed tuning systems, to a reasonable extent. (Aside from the ones the 6, or the 24 note one that just sounds like it's fundamentally the 12 note one with some quirks)
@jhhl 2 жыл бұрын
Scales are intimately tied to timbres. This is, like, chapter 1 of William A. Setharis' Tuning, Timbre, Spectrum, Scale. So you can make up any system of scales, but if the purpose of the scale is to make consonant and dissonant intervals and chords and have strategies for transitioning from one to the other, then you have to start with the timbres. Having a temperament is a compromise on natural consonance, and also allows interoperability of different timbres inherent in different instruments. Equal temperament is about something else: the theory that transposing intervals doesn't really change the music, which is not really true. Just drop a tune 2 octaves or more to test that theory. When that happens, timbre makes high harmonics now audible and now must be accommodated in concepts of consonance. Which brings back the eternal struggle of melody vs. harmony.
@xcheesyxbaconx 5 жыл бұрын
For a 13 note scale, how about replacing the Tritone with the augmented fourth and diminished fifth? This was pretty common with Just Intonation.
@BaieDesBaies 5 жыл бұрын
Wy not just take the 13th odd number harmonic of the root ? I mean, our notes were built by taking harmonics (adding fifth or taking odd numbers : 3 for fifth, 5 for third, 9 for second...).
@SodomySnake 4 жыл бұрын
In my quest for new levels of earbleed-inducing dissonance, I made a 13EDO guitar today. Well, I "made" a "13EDO" guitar by moving the bridge so that the octave is at the 13th fret instead of the 12th, which does a reasonable job of approximating 13EDO. As a bonus, the scale length in now about 27", so good for down-tuning. The lack of a proper fifth is somewhat an issue, since heavy metal guitar is entirely based on power chords, i.e. fifths, but it's fun to play around with. There's a surprising lack of xenharmonic heavy metal out there, although given how guitar-unfriendly it is (or any other fixed-pitch instrument for that matter), I can see why. Also, with careful note selection, 13EDO can sound quite nice.
@taticatnineland 5 жыл бұрын
I love this type of video; thank you! 💕
@bullitosaladino 5 жыл бұрын
Which tuning software do you use?
@sophiastargazer 4 жыл бұрын
This is very pedantic, but instead of "modern music", you should probably say "modern European music", because otherwise it sounds like you're implying that the European music system of heptatonic scales divided into twelve halftone steps is the only one that (still) exists today, which is not the case. There are numerous other tone systems which are still used today like pentatonic scales or scales involving a lot more microtonal intervals like the quartertone you mentioned, like scales with 22 intervals between one octave. I know this channel mostly discusses music composed in the European heptatonic system, but I find it important to point this out, because most discussion about music and music theory is still heavily eurocentric, which modern musicologists are trying to push past, at least at my university.
@VOLKOV9 5 жыл бұрын
"Who says... ?" Physics says. The harmonic series comes up all over the physics of vibration, from taught strings to the human voice. Anharmonic overtones result in aperiodic tones, i.e. tones with no defined frequency. It's no mere cultural accident that we like how two notes with frequency ratios 3:2 sound - their harmonic series line up and avoid dissonance. It's therefore unsurprising that most cultures that come to different musical traditions still agree 3:2 is important and good. This is not an argument that Western 12-note scales are best, but that they are more than a mere accident, and the likelihood of changing something fundamental on a whim resulting in something as consonant is low. Still interesting - thank you for the thought-provoking video! I'd love to hear someone try to write music (or even just the 14-note chromatic scale).
@BradsGonnaPlay 5 жыл бұрын
Thank you! I don’t have the eloquence to make this point but that part of the video irked me for how much time he spends talking about the importance of the ratios in other videos. These are great thought experiments but I am still waiting to be compelled by any piece written using any of these ideas
@markop.1994 5 жыл бұрын
I prefer thinkin of ur "minor fifth" as a sort of harmonic 4th. Like u said it's the 11 of the harmonic series. And Although I think of the harmonic series I would probably use this interval melodically as like a neighbor or passing tone like the 4th between major 3 and P5 to make a janky lydian sound. Or maybe flatten the 2 and the 6 of a Dorian scale to make (what I call) a maybe Dorian maybe natural minor maybe phrygian scale.
@rattusprat 5 жыл бұрын
I was worried you were going to be searching for the note between B and C - Howard's note. That way lies madness, and is possibly cruel to the crab. But it does have a nice oaky timbre.
@brucedavis191 5 жыл бұрын
why not build on the 12tet not start on the c. go down a half step and end on the same note. i don't think that sub dividing the one gets us any where. sub divide the 1.25/1.5?. why not 9 notes in the octive and ennea-tonic (9 notes ) scale. cause 12 notes divided by 8 in the octave we get 1.5 and 9 notes divided by the 13 notes we get 1.4444 ect. that is close.
@joshuaharvey3631 5 жыл бұрын
But... here's the thing. 13 is a nasty prime number. Maybe try 16 or 18, those have much nicer mathematical factors and I bet they'd make much more pleasing scales.
@e8heterotic649 5 жыл бұрын
16 EDO is actually extremely dissonant. Believe it or not, many of the nicest sounding EDO scales are prime: 17, 19, 29, 31, 41, 43, and 53 are all quite nice. Of course, so is 22, but that's not prime.
@liraven7676 Жыл бұрын
Exactly.. I love Lou Reed😂😂 7:38
@samuelmincarelli5051 4 жыл бұрын
You’ve heard of the 12 tone system, but what about the 13 note system? Arnold Schoenberg has left the chat
@0live0wire0 5 жыл бұрын
Paul Hindemith proposed adding a separate tone for a #4 and b5 - basically two tritones. He managed to bring all the other intervals to sound natural by using the harmonic series up to the 7th overtone. Quarter tones are an abomination created by the practical idea of the 12ET (which obviously works, but is very flawed and shouldn't be used for the basis of other tunings). Hindemith's is the best system ever conceived yet - a somewhat small compromise yielding great results.
@wanderingrandomer 3 жыл бұрын
I dunno about anyone else, but to me, quarter tones sound really 'wobbly', like they're straining to get back to the nearest semitone, and the sound is changing pitch. I'm sure it's an illusion, but I feel like I can hear a whole spectrum of notes in there.
@QuikVidGuy 5 жыл бұрын
I think the tones of the primary triads being chromatic opens up some interesting things, but I don't know enough to actually put it into practice
@lonepilgrim83 4 жыл бұрын
12tone, what are your feelings about Golden Meantone? Is there something special about it, or is there no real point in going beyond 31 EDO?
@dlwatib 5 жыл бұрын
"Who says that tuning systems need to try to approximate simple frequency ratios anyway?" Our ears, that's who! Our ears (actually our auditory system) is programmed to be pleased with simple frequency ratios. They're what we call "harmonious". Just as we find certain odors pleasant and certain other odors unpleasant, we find certain (simple) frequency ratios harmonious and pleasant, and others inharmonious and unpleasant. Dogs can't distinguish between pleasant and unpleasant odors and sounds, but humans can. Our instincts in this regard are really quite strong. Musicians have experimented with inharmonious systems before, and none have ever become at all popular. It's a sure-fire way to make sure a musical composition remains obscure, rarely heard and largely unplayed.
@be7th 5 жыл бұрын
Oh my god. The (dis)appearing ghost from the set.
@Ujvi89721 4 жыл бұрын
Great vid. I like how you think about 13tet, it might be great if you meet it at his own terms
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