SQRT(7):1 | Irrational Octave Microtones
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- เผยแพร่เมื่อ 30 ก.ย. 2024
- A murky theme in 12ed√7, also described as an octave ratio of √7:1. The tuning could also be described as ~8.549-TET (~8.549-EDO) or 140.368 cents per semitone.
Interestingly, the √7:1 octave ratio provides a more perfect 5th than 12-TET offers. The "5th" is just 0.116 cents off from the 3:2 just interval perfect 5th of 701.955 cents.
There are some other curious oddities with the Square Root of 7.
"On the reverse of the current US one-dollar bill, the 'large inner box' has a length-to-width ratio of the square root of 7, and a diagonal of 6.0 inches." - McGrath, Ken (2002). The Secret Geometry of the Dollar
en.wikipedia.o...
Composed and Produced by Shawn Michael
© 2023 Ambient Esoterica
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#experimentalmusic #microtonal #ambient #darkambient
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microtones really are an endless rabbit hole, the only limit is your creativity at this point
I just went down a rabbit hole searching quotes about rabbit holes to sound clever with this reply. 🐇
What's been your limit until this point?
-the thing about infinity is that on that scale everything's basically the same as everything else- [edit: opinion retracted - nobody needs to hear the little devil in my ear]
that said, this is some cool music. loving the harmonies!
@@SidShakalYou usually don't need any more complexity than that in 270edo (pure, stretched, or compressed octaves make little differences).
Often 198edo, 171edo, 118edo, or even such things as 94edo, 87edo, 72edo, 68edo or 53edo are quite enough. 41edo is also very nice.
This is for microtempered Just Intonation purposes.
You usually only need a small amount of the total notes of an equal temperament, perhaps about 50 notes or a bit less.
270edo is almost perfect in the 13-limit. 198edo or 342edo in the 11-limit. 171edo in the 7-limit, 118edo in the 5-limit, 53edo in the 3-limit. 94edo, 87edo, 72edo, 68edo, 41edo and a few others are noticable but small temperamental readjustments from Just Intonation.
These temperaments are good for finding lots of musical consonances, which you can restrict to smaller scales. If you want dissonances, you can use almost any scale and/or temperament.
270edo is a really nice 13-limit extension of the 7-limit Ennealimmal and 11-limit Semiennealimmal microtemperaments. If you stay in the 11-limit, then 342edo is pretty much a perfect tuning for Semiennealimmal (171edo only for Ennealimmal). But 342edo is worse than 270edo in the 13-limit. Talking about prime limits here. You almost never need higher primes than 13, such as 17, 19 or 23. So the primes 2, 3, 5, 7, 11 and 13 are quite enough for (almost) Just Intonation consonances.
Such things as 494edo, 612edo, 954edo, 2460edo and 8539edo might be useful for music theoretical purposes, but hardly for practical musical purposes. It is pointless to go beyond these, so we don't need infinite possibilities, only the near infinite possibilities of restricted scales of these edos or some smaller ones, plus higher rank temperaments supported by multiple equal temperaments out of these.
There is more info to be found on the xenwiki.
lovely pfp!
something abt this felt really nostalgic, reminds me of some long forgotten VHS recording from when i was a kid. kinda 60s sci fi maybe?
First landing on Mars.... They look around...Everything looks normal... except something is wrong...
Maybe it's the little self-playing organ in the middle of the crater, who knows...
One of the harmonics is close to the golden ratio, which was used a lot in 80's sci-fi.
The Residents have been making music like this for decades! 👁🙂👁
Works surprisingly well; I think the deep reverbs of the organ helps the different tones resonate together well.
Wow, this is something else. I have yet to venture into the world of irrational microtonal music. It's interesting how strangely nice some things can sound (like the chord at 2:40) even when it doesn't seem like it would sound that good from solely knowing that every interval is irrational. Math is riddled with patterns, and microtonality is just math with pitches. As stated by @phonetyx, the only limit is truly your creativity. That's one reason why I love all of this so much
"Math is riddled with patterns" Yes, and it speaks in the beautiful language of ratios.
I was taught in musical college that temperaments with less than 12 notes per octave are technically called macrotonal and not microtonal (like 5edo 7edo 9edo for example). So those are called macrotones
Love your experiments btw ;)
Valid. Makes sense and seems a more proper way to designate the
(edited out the spelling mistake)
@@ambientesoterica Checked the xenharmonic wiki, it agrees with this term, so you can change it in the title 🙃
@@ambientesotericaSo it's some kind of macrotonal edonoi, right? Did you divide the √7:1 interval into 12 equal parts (logarithmic scale) or am I getting it wrong?
@@NonsenseTreasureyes that's exactly what was done. It is still 12 equal semitones, but the "octave" is an expanded width in comparison to the standard 2:1.
For me it's really just a fancy mathematical slight of hand way to have fun with certain significant numbers.
id love to see some details about how a keyboard arrangement/any other method of displaying notes would look with effectively a non integer number of notes in an octave
Yeah, the 5ths sounded really good. The rest of it also sounded good though.
@ambient esoterica I really dig this sound, thanks for sharing! I've made a system called Tonus Veritatis that uses 10-tones (about 165 cents per step) based on Solfeggio tones with metric math, so 9 scales (174, 285, 396...etc) and 10% up or down per step. you get some really wild sounds with T.V. I am very interested in what you're doing with these also! I have my Scala files shared if you would like to try them.
Interesting concept. I like it. Is the 10% up or down arbitrary, or is it following a pattern?
@@ambientesoterica following simple mathematical pattern to create 10-tone scales, 10% up or down each way 🙂
this has a completely different and also alien character when the overtones of the individual notes are √7 intervals as well, very metallic almost like a tubular bell, but the tuning as a result overall becomes stable and self-resonant, stretching or compressing just intonation intervals as opposed to an equal temperament into the irrational octave is interesting for this also
This is a brilliant and gifted way of explaining it. Thank you for this.
The equal-tempered mathematics causes stability and self-resonance no matter the interval. The irrationality at a certain decimal point reaches beyond human aural detection.
I thought the description was confusing. I did the math to conclude what it's saying. This is 12-ed-sqrt(7).
Yes, exactly correct. I believe was still learning / researching how to name tunings that were not 2:1 octaves.
*will update the description. Thanks for the reminder.
@@ambientesoterica
Oh, I think I get it from his description. So, any note is sqrt(7) times the same note in the previous octave.
@@vapourmile YES, you got it 😎. Instead of the octaves being 'twice as high' in frequency, they are sqrt(7) as high.
@@ambientesoterica
Cool. That's fine then so the note series can be produced with the formula base_frequency*sqrt(7)^(n/12) where n is the number of semitones from the base frequency.
Yes, exactly. Cheers 🍻.
Next vid/aud (scheduled approx 90 mins from now) is in the 'fifth root of 100' octave. Turns out to be just a fraction more than 9Edo.
I hope you enjoy. 🫠
YES 🔥🔥🔥
how did you make this
The sound or the visuals?
audio
Why is this giving me Allan Holdsworth vibes?
damn thats a cool tuning
May i Ask how you create Microtonal music?😊
I mostly use custom Google sheets to perform the calculations for the tuning scripts, then import them into Native Instruments' Kontakt VSTs.
@@ambientesoterica thanks! Just figured out how to make microtonal music with pigments. I really love the idea of melodies that no one has ever made before, and new feelings that no one has ever shown through music before. You wouldnt happen to know anyone who makes pro microtonal music? All microtonal music ive heard to now has had bad mixing and often weird drum patterns
@@TheoShahh I found some of the more lofi diy projects present the oddities of experimental intervals better. That being said, I'm not a big fan of name dropping, as I will always inevitably leave people out. . . . Check out:
www.youtube.com/@Sevish
www.youtube.com/@mannfishh
www.youtube.com/@nowandxenpodcast
www.youtube.com/@stephenweigel
www.youtube.com/@uraniidumbra5219
. . . and many more I'm sure I neglected to mention from the top of my head.
@@ambientesoterica thanks for the help!
Wow, there's so much consonance in this tuning!
That was my reaction. It convinced me that irrational intervals could make more sense that rational ones, considering that ET is irrational anyway.
Maybe I have absolute hearing but this sounds aweful, I can't imagine hearing anything good come out of microtones, to be honest.
You do realize that 12 edo was only put in place as the standard for western music in the 19th century and that there are numerous cultures who use various microtonal systems with histories much longer than western 12 edo, right? Saying you can’t imagine anything good coming from microtones is saying you dismiss all of this cultural music and all pre 19th century western music as “not good”.
@@123unknownsoldier126 welp
Basically 17 TET
(Removing every other note from 17) Good point.
Huh, so it's 24-ED7? Neat! I once did an experiment like this with 17-ED17 which I still have yet to release. The result was basically just a bunch of almost perfectly just 13/11s strung together, which hits that weird place where it's not really a scale but not really a chord either? Very strange effect, great for spooky spacey music.
It's a beautiful thing to experiment with numbers and ratios just to see what happens. I like 17ED17 conceptually matching the number of division with the octave ration. That's cool idea.
me to the emotion I get from this piece:
[Lie] I know what you really are.
how does this not sound as bad as how an out of tune piano sounds
reverb 😜 jk . . .
Like much of what I do, just wanted to hear what it would sound like. . . . and faith in the mathematics of frequency and ratio.
Your ear's been stretched by metamodern music.
❤😂So irre ist das gar nicht! Mit den sauberen tonalen gefakten Tunings musste ich mir auch 60 Jahre Pop bis Classic reinziehen.O.Sala hat es vorgemacht und die subharmonische macht es schön vor🙄💖🤦🎹😏💚
Danke. Nichts ist verrückt oder irrational, wenn es um estoerische Stimmungen geht 👁🌿♍🔥
Ich bin halt nun alt und krank,aber aus 55 Jahren Klavier und Keyboardspiel/Reparatur blieb über die Zeit viel im Kopfbereich hängen✌️🙋🎹🤦💚💚💚💖
@@matthiaswilhelm9813 Diese Tastaturen fühlen sich geehrt, Ihre Fähigkeiten zu haben
What DAW do you use, also plugin for xenharmonic temparements? This is awesome and I wish to create xenharmonic music too
Thank you. 😊 The DAW is Cubase. The microtones are created by importing custom tuning scripts into Native Instruments' Kontakt. The tuning scripts I create using spreadsheets to perform the calculations.
@@ambientesotericaI guess no easy way to produce this as a scala tuning?
@@fotgjengeren you could use Sevish's Scale Workshop and export as a Scala File. I added the data for a SQRT7 to this URL. Should only need to chose an export option.
sevish.com/scaleworkshop/?n=SQRT7%3A1%20Octave&l=3w.sdj&version=2.1.0
@ambientesoterica oh wow, thanks a lot. I might actually try this out in something just because there's probably not much music in this tuning, I particularly like tunings based around other intervals besides octaves. As a follow-up question, I'm wondering how you generated this. You inputted the cent value of each step, right?
@@fotgjengeren it being an Equal Temperament means the cents / semitone is constant between the notes.
The math part comes in to play to determine what that cents value would be. With the square root of 7 octave in 12 equal parts the ratio from note-to-note becomes: the twelve root of the square root of 7
I nerd out hard with Google sheets to run calculations for all this stuff.
A question here: why using 12-TET keyboard to visualize a piece if it is written in ~8.549-TET?
Instead of a regular 2:1 Octave, the piece uses an √7:1 octave, so that after going up 12 keys the frequency increases by √7.
The 8.549 number means that the distance between two consecutive keys is equivalent to that of 8.549-TET.
@@simonsama5857 this is it exactly. Great explanation
@@simonsama5857Thanks for your explanation. I always think that an octave should be 2:1 because of the overtone series.
@@airazure2050 You may be interested in checking out xentimbres, in which the overtones of the timbre are designed to fit a specific tuning. It's pretty interesting.
@airazure2050 any interval can be used in place of an octave, therefore a tuning can result in no octaves, with Bohlen-Pierce or 13edt, based around 3/1 or a tritave (octave+5th) being the most widespread example of that. The tuning of this track would also not feature a 2:1 pure interval as you ascend or descend. It's 12ed/7 (imagine a square root there and not "/")
5ed3/2..?
Actually, it's quite close to that!. . . by a difference of ~0.02325 cents/semitone.
@@ambientesoterica cool
Sounds amazing!
reminds me of the residents, it's great !
What a cool concept and well realized
thank you!
Pretty cool!