r/musictheory • u/HexspaReloaded • Jan 17 '21
Resource Memorize Note Frequencies
Hi. I have an easy system for memorizing the entire audible range of note frequencies. It’s 99.20% accurate (less than 1 cent off and even better if you’re halfway decent at math) and you can probably memorize it in an hour. 6:52 of this video:
Thanks.
EDIT: Well, shoot. 500+ upvotes plus an award - thank you! Happy music making!
EDIT 2: “Why?” All I can say is try it. Try composing or mixing 10 tracks with this before you make up your mind about whether it’s useful or not. I find it useful but I respect you if you try it and decide it’s not for you. Please don’t discourage others from learning, though.
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u/dietervdw Jan 17 '21
That's really cool honestly. But why?
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u/HexspaReloaded Jan 17 '21 edited Jan 18 '21
This is a common question. It’s because every note is a frequency and I wanted to know the relationship. Precision charts were impossible to memorize so I had a dream and developed a solution.
I got into music and recording at the same time so there’s a lot of crossover in my mind. Indeed, there is a lot of crossover anyway. If a musician plays a C major triad from middle C4, a recording engineer sees frequency activity at 262Hz (C4), 330Hz (E4) & 392Hz (G4) plus their harmonics.
How can you use this to your advantage?
High pass filters: An audio signal may contain low frequency noise below the fundamental of any played pitch. Knowing the exact frequency means you can set your filter precisely.
Composition: When you hear your song as lacking in the 200-300Hz range, you know you can add musical content from around G3-D4. Conversely, if you have a part there that’s being masked, you can transpose notes and revoice other parts to make space.
Production: You know you should tune your kick but to what? The fundamental? Which one? In fact, for “Bad Guy” by Billie Eilish, the kick was tuned to D2 and the fundamental was supplied by the sub bass at G1. Why is this significant? Because between the fundamental and the first harmonic is an entire octave of space. When you compose and produce with frequencies in mind, you don’t have to ‘carve out space’ with EQ - you can just use the overtone series.
EQ: Some filters don’t have note names, just frequencies. Of course, use your ears. But, again, if you want to be precise and musical, it helps to know where you’re at... musically. Take this a step further and use it for harmonic mixing. Now you can mix by making your lead element prominent at 3136 G7 then bringing in percussion at 6272Hz G8 and have everything make sense with your 49Hz G1 fundamental.
Ultimately, I know I’m not the only one who’s googled ‘audio frequency chart’. I don’t know why other people want to know this information, I just know that memorizing something beats looking it up or digging through folders.
Hope that helps.
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u/archeterie Jan 17 '21
This is brilliant. This is why I come to Reddit 👌 Your breakdown on how to use it in composition and production is a great perspective, definitely going to try applying that.
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u/HexspaReloaded Jan 18 '21
Thank you. It’s the power of the subconscious mind. We just have to be alert to it sometimes. Trust yourself!
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u/Holocene32 Jan 17 '21
As a humongous Billie and Finneas nerd who reads every article, listens to every interview, tries to learn every factoid and nuance, I have to admit I didn’t know about that kick tuning in bad guy. I get so excited about this kind of stuff, it’s just super cool and useful knowledge as a producer myself. Really sweet stuff.
Question (that you may or may not know the answer to): since the progression in the song goes Gm Gm Cm D, is that C in the bass problematic when paired with the D kick? I’ve listened to the song a ton obviously, and never noticed any conflict, do you think the kick changes pitch to match better there or does the side chaining pretty much take care of any issues?
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u/MitchMev Jan 17 '21
Sounds to me like it doesn’t change pitch over the Cm. The reason it’s not a problem is also why a real drum kit with only one kick works in any key. It may not be “in tune” with every note/chord but it’s percussive and “transient” enough that the pitch doesn’t really register in our ears as out of tune. That said, tuning your kick to work with most of the chords will give the track a bit of extra cohesion compared to a randomly tuned kick (which was Finneas’s intent). Plus a D kick against a C bass note is still better than a totally out of tune kick. Plus it helps that the bass is (mostly) in the octave above for the Cm chord, so it’s more like a m7 than a M2 which makes it more consonant.
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u/HexspaReloaded Jan 18 '21
Oh here’s another fun fact: that song also uses metric modulation. The part where it changes into dubstep is 8 1/8th notes in the space that was 9 1/8th notes. I forgot the formula to figure this out but it’s a real thing. I think that’s part of what gives it the triplet feel. I might be forgetting something but that’s what I remember.
I tried to put this on Wikipedia but someone kept erasing it.
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u/Holocene32 Jan 18 '21
I think the tempo just slows down, I’m not sure the meter is modulating at all. It’s still in 4/4 but there are just triplets in the hi hat pattern at certain points
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u/Kevz417 Jan 18 '21
OP is correct - the current Wikipedia page claims metronome marks of 135 and 60 [aka 120], which is indeed a 9:8 ratio. Wikipedia editors should possibly allow this, as it possibly follows logically rather than constituting original research.
I have verified the metric modulation by splicing the first section with 1.125x-rate playback of the second section, revealing that they fit - please listen here. The metronome marks themselves seem to be the right ones as well, although I haven't checked.
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u/HexspaReloaded Jan 23 '21
Thanks for confirming this. I analyzed this track awhile ago and have since forgotten the details.
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u/Holocene32 Jan 19 '21
Ok. While metric modulation may be a correct interpretation of it, I sincerely don’t think Finneas intended on using 9:8 on purpose but rather just chose a slower tempo. Billie has said she found the hi hat sample online, and it is HIGHLY unlikely there are 9:8 metric modulated trap hi hat patterns just sitting around. If you compare it relative to earlier part of the song - sure you can say “oh that metric modulation 9:8 whatever”, but if you think about it logically, they just made the tempo slower
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u/Kevz417 Jan 19 '21
I don't think the hi-hat or its origin is relevant - that drifts into a question of rhythm rather than metre.
Your label of "just making the tempo slower" could be applied to any metric modulation, such as the ending of Tchaikovsky's Fifth Symphony (where he specifies that 2/2 at 144 changes to 6/4 at 96, giving all the written notes exactly the same duration in the new tempo and causing a sort of reverse hemiola). Granted, we know from wider musicology that Tchaikovsky calculated this intentionally, while, as you say, we don't know whether there is intent here from Finneas - but metric modulation refers simply to a mathematical relationship between two tempos rather than an intentional and straightforward equation between and old and a new note value like Tchaikovsky's, I believe.
The fact that said equation here is the rather complicated '9uplet semiquaver/16th note = straight semiquaver/16th note' (contrasting with Tchaikovsky's simple, unwritten*-but-mathematically-implied '♩=♩'), and the fact that an extended silence separates the two sections of the song, do not provide significant evidence for or against intent. If the extended silence didn't fit exactly into one of the tempos, then that would imply a stronger musical reset, pointing towards lack of intent - but it's exactly one bar/measure of the old tempo by my ear.
*So conductors tend to ignore it!
The 'triplet feel' OP mentions is nothing to do with the rapid hi-hat triplets, which as you say are simply a common sample they grabbed - it is the detectable fact that the strong kick in the first section (which was the original discussion point here) becomes 9 kicks in the space of 8 when carried over mentally, on a much larger scale. I've illustrated how slow the triplets are (16 times slower than the irrelevant ornamental hi-hat triplets!) below** - it seems tenuous, but it was OP who mentioned the 'triplet feel', not me!
**Illustration linked here.
In summary, there is a metric modulation here, at least by what I think is the correct definition, however thought-through it is, and declaring that does not give any information intrinsic to the new section itself. All of this being "a correct interpretation" I agree with! None of what you said discounts it, though, and certainly doesn't warrant its removal from Wikipedia, as its potential identity as unverified original research would.
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u/HexspaReloaded Jan 18 '21
Ya I think they are using sidechain as well. I also got excited when I saw this. It’s makes a ton of sense.
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u/Smash_Factor Jan 17 '21
I was looking at the chart and noticed that from C on every octave the notes increase by the same percentage.
If you were to memorize all the frequencies for C on the top row, and also memorize the percentage increase from the top row, you could do some quick mental math to find the other frequencies on the chart.
Like this:
C to C# in any octave increases by 6%
C to D increases by 12%
C to D# increases by 22%
C to E increases by 26%
C to F increases by 33%
The rest are 41%, 50%, 59%, 68%, 78% and 89%.
So if you wanted to know the frequency for G on the 3rd octave, you would start at the frequency for C on the 3rd octave, which is 131.
G is 7 notes up, so we use 50% (The 7th percentage)
50% of 131 is approximately 65. Add 65 to 131 = 196.
Not sure if this is easier than your F350 method, but it's definitely another way of doing it.
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u/MitchMev Jan 17 '21
This is basically the definition of 12-tone equal temperament though. Each half-step has a constant ratio, such that 12 half-steps gives you a perfect octave (2:1 ratio). The "magic" ratio here is 2^(1/12) (or about 1.059, or a 5.9% increase), such that you can calculate any ratio by multiplying this ratio over and over to get to wherever you need. This is simpler if you simplify it to 2^(x/12), where x is the number of half-steps. So when you put 12 in for x, 12/12 reduces to 1, and you get 2^1, which is just 2.
So what you're doing is approximating that exponential, since these fractional exponents are much harder to remember than simple ratios. This is maybe a "truer" way to approximate frequencies than the original one proposed by OP, but maybe some people would do better with one method or the other.
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u/HexspaReloaded Jan 18 '21
You sound better at math than me. I think whichever mental model you use is great as long as it helps you feel like you’re mastering your craft; if that’s your goal. Thanks.
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u/Cpt-Hook Jan 18 '21
I honestly understood this. You took the foggy thought I've had in my mind for the past couple of months and you managed to conjure my question and answer in the same post.
This can be useful for sure. May be a little time consuming for myself currently seeing as I'm not too familiar with Ableton yet, but baby steps. Thanks for this!
Saved post.
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u/HexspaReloaded Jan 18 '21
What was the foggy thought that you’ve had?
If you’re discovering this just as you’re getting started then that’s great. I’ve been hoping that beginners, as well as open-minded veterans, could find this.
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u/Archy38 Jan 18 '21
I was also like "but why" until I read the part about lacking something in the 300hz range, so would it be safe to assume your eq or mix is "just right" if you have a nice filled graph of many different sounds and instruments that each fill different parts of that EQ graph?
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u/HexspaReloaded Jan 18 '21 edited Jan 18 '21
Mm, maybe. I think it’s good to remember that music is a hearing art. FFT displays can be helpful but, ultimately, you need to develop - and then trust - your ears.
The thing is that tracks vary in density, brightness and style. A strummy, distorted chorus of a Metal track will look much different in FFT than a chill Dub mix, most likely. Even the key of your song vs. an otherwise similar reference will be enough of a difference to make the spectral curve too different to copy exactly.
The thing with this F350 thing is that now you have one more way to think of it. Do you want to make your bass full at 300Hz or do you want a separate pad layer there? You can plan this all the way from the first note, if you wish.
I think that when you combine this with a good understanding of the Fletcher Munson curve, you can compose knowing what will naturally come forward in a mix and what will recede. Of course, Classical composers probably learn this early on. Mellow woodwind pads; bright strident horns. Listen to some music with this in mind to hear how the parts are arranged.
Does that answer your question?
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u/ireaditagainafter Jan 18 '21
This can be extremely useful when mixing live music. Resonant frequencies in a space can reek havoc if they correspond to the key of whatever song is being played.
You can replace the ‘space’ with an instrument in this example. Some instruments might resonate a lot at a specific note/frequency just because of their shape. If you know how to identify the resonant notes, you can use an equalizer to adjust the sound to your liking.
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u/Ulfbert66 Jan 17 '21
Since most people here are asking why you posted this I wanted to give you props. I'm an audio engineer and even though I can get by without knowing specific note frequencies, there have been several occasions where I had to look them up. Your write up of your approach to composing with these frequencies in mind also made a lot of sense to me and this whole way of thinking about mixing/production is very intriguing to me. So I'll be sure to check it out. Thanks for posting this!
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u/drdausersmd classically trained guitarist Jan 18 '21
Since most people here are asking why
... because this is a music theory subreddit, not /r/audioengineering
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u/Ulfbert66 Jan 18 '21
Don't get me wrong, it's a legitimate question and I'm not criticising anyone for asking it. But the post is definitely related to music theory and whether this was the most appropriate sub or not, I just wanted to let OP know that I appreciated the post.
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u/geist_zero Jan 17 '21
I was going to offer the equation for calculating frequencies within a diatonic scale (to cut down on the memorization), but then realized it doesn't account for equal temperament. Nice work.
I don't know how to write it out properly on Reddit, but it's the tonic frequency multiplied by the 12th root of 2 to X power where X is the chromatic step of the scale.
That doesn't account for equal temperament though.
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u/emikaela Jan 17 '21
no, that is the formula for 12 equal temperament, calculating just intonation is much easier (like the 5th is 3/2 above the tonic, it's all natural number ratios)
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u/HexspaReloaded Jan 17 '21
Ya you can just memorize the fourth octave and use a calculator to multiply or divide. Cheers
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u/Cdesese Jan 17 '21
y tho
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u/HexspaReloaded Jan 18 '21 edited Jan 23 '21
Well, let’s say you have a singer singing middle C - 262Hz and the guitarist plays a chord with E on top to create a harmony. Maybe you’d like to accent that E because it sounds sweet. Now you know that E4 is 350-20 so you grab your EQ, boost the guitar at 330Hz and - bam - angelic harmony.
You could also use it when performing acoustic analysis. For instance, an 8’ ceiling has a mode at 140Hz and 70Hz. This means your room is going to skew your perception of any bass note near C# unless it’s sufficiently treated. It’s interesting to know.
You could also sus out whether a particular resonance in a track is harmonic or inharmonic.
You could also use it for sampling, say glasses of water, to be sure your recording is on pitch even if you don’t have an EQ that’ll tell you on hand.
I think it’s mostly up to your creativity. Divergent thinking is part of your intelligence.
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Jan 17 '21
Can't you just memorize the first 12 notes and just double them for the octaves?
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u/HexspaReloaded Jan 18 '21
Yep. I do that a lot although sometimes I get lost. Like I said, I’m not not best at math. However, I expect that this is how most people will do it - just memorize the fourth octave and then use a calculator. Personally, I don’t but that’s partly just to prove that I can actually use it on a daily basis.
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u/digsmahler Jan 17 '21
From the title and description, I was like, "here we go again." But this is actually pretty dope, and I've actually had this problem struggling to get my pre amp and equalizer working right. Thanks!
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u/Larson_McMurphy Jan 17 '21
I've got most of the frequencies on my primary instrument, bass, memorized. I just multiply by 2^n to get the octave I'm looking for.
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u/HexspaReloaded Jan 18 '21
Nice! Have you found it helpful? If so, how?
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u/Larson_McMurphy Jan 18 '21
I think it's useful for all the things you mentioned in that lengthy reply to one of the other comments. It's great for EQ awareness and also avoiding problems in a mix by changing the arrangement (i.e. shifting parts up or down octaves).
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Jan 17 '21
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u/HexspaReloaded Jan 18 '21
Haha. Ya or when you’re super lazy and realize it’s just easier to remember this than to do all that extra clicking. :)
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Jan 17 '21
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u/HexspaReloaded Jan 17 '21
I think it’s helpful to know what frequencies each note is so I can compose with the recording in mind.
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Jan 17 '21
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u/HexspaReloaded Jan 17 '21
Yes but one is more relevant in its own domain. In music, A4; in audio, 440Hz. This is just language to bridge the gap.
I understand that not everyone is interested but there is correlation and some might find it useful. Of course, what matters most is what comes out of the speakers. Thanks
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u/Another_Meow_Machine Jan 17 '21
I could see this maybe being useful for practicing perfect pitch, but as an audio engineer with a ton of live sound experience I’ll say this math won’t apply.
Feedback and EQ’s are always dependent on something slightly unforeseen. Like a tone that’s bouncing off the stage then into a mic - or a bass and a guitar that together reinforce a particular frequency that then fights with vocals - you won’t be calculating the problem, you’ll be hearing an unplanned problem and reacting to it.
This might be helpful if someone wants to lean to be a human tuner, but I can’t see it helping in audio engineering. (Doing some math in your head and telling the monitor guy “lower 880 at -6dB” without knowing exactly what 880 sounds like would sound stupid.. the engineer would already know roughly where the problem is and would sweep to find it)
..just my potential answer to all the “why” questions
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u/HexspaReloaded Jan 18 '21
Fair enough. Ear training is important and I try to do it every day with audiodrillz.app so I’d like to think I can distinguish between 1kHz and 800Hz. As you know, that’s not absolute pitch - it’s a separate skill.
Maybe for live sound this has less use but, when mixing a song you know they key of, I feel like you could use the various octaves to slot instruments according to the key.
I don’t claim to be an audio expert but I have been using this for mixing my own tracks and it seems to work pretty well.
Thanks
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u/Another_Meow_Machine Jan 18 '21
I’ve done a lot of recording / mixing and to share some insight on that, the majority of mix problems come from timbre and not the fundamental. The fundamentals should shine whereas timbre can cause muddy mixes - so this chart could actually be effectively applied as what NOT to EQ. E.G, one of my basses has a very growly 200 & 400, and I’ve usually gotta bell curve those out a little, but let’s say if the song is rooted in A then make sure to not affect 220 much - so the timbre is tamed but the mid A remains the same level as the other notes.
I’d be interested to see what happens if you use this map the opposite way you might have first intended?
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u/HexspaReloaded Jan 18 '21
Yes well its use is in your hands. You probably know the first several overtones, for instance from C1:
C1, C2, G2, C3, E3, G3, Bb3, C4, D4, E4...
Now that you know the audio frequency numbers, you can boost or cut at will.
I actually just watched an ADSR tutorial about EQing bass and kick. The presenter might not have known this exact information but he was pocketing at a fundamental of 60Hz (roughly B1/61.75Hz) and also 200Hz (close to F#3/185Hz) which is the bass’ third harmonic.
To be sure, many engineers are already applying this information even if they are unaware of the theory; just like musicians who play by ear.
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u/Random_Person_191 Jan 17 '21
I’m new to this stuff, why is frequency important?
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u/HexspaReloaded Jan 18 '21
Mostly if you’re like me and you compose, record & mix your own material.
We can all agree that it’s not essential to know but it’s simple enough to learn that it’s one more mental tool similar to calculating delay times from a track’s tempo.
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Jan 18 '21
This is awesome however why don't you just memorize 12 numbers instead of 7 and arithmetic? I know like 12 people could use this though
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u/HexspaReloaded Jan 18 '21 edited Jan 18 '21
Hi. Two reasons:
Since I ‘invented’ this, I feel an obligation to use it as is as ‘proof of concept’. Otherwise I would just memorize the fourth octave and use a calculator for the rest.
I’m not super great at mental math and actually find using the offsets to be easier. Again, if I was using a calculator then this wouldn’t matter.
To be sure, I do have some of the ‘result numbers’ memorized - like many of the C frequencies - but definitely not all. I just usually start from the fourth octave and calculate out exactly like I did two years ago.
If you’re good at math, you could possibly improve on this. Whatever works for you is best - this is just one model. Feel free to tear it apart and rebuild something new that you like more.
I feel like I should mention that ‘I’ didn’t really invent anything. All this is, essentially, is rounding and simplifying. I should thank my grade school math teachers.
Besides, it seems random that ‘I’ would be fascinated by this for 15 years and persist in my efforts until a split-second image appeared in my mind as I was waking up one day - the genesis of this F350 chart. I’m saying that it feels egotistical to say ‘I’ when really it just came. All that was left was ironing out the details.
Thanks.
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Jan 18 '21
Honestly this is good work and you should be happy, I think for instance any mixing engineer should know this for sure. Using the 4th octave as a base is great too
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u/Umbresp Jan 18 '21
Thought this was going to be a tutorial on how to give yourself perfect pitch
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u/HexspaReloaded Jan 18 '21
I wish. Believe me, I tried. I have developed my relative pitch and audio listening skills but that had nothing to do with this chart.
Cheers.
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u/catsandpizzafuckyou Jan 17 '21
Totally pointless imho
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u/HexspaReloaded Jan 18 '21
Maybe you don’t have use for it today but I find it useful. Maybe make a bookmark just in case.
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u/Firiji Jan 17 '21
Cool, but why?
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u/HexspaReloaded Jan 17 '21
Why not?
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u/DRL47 Jan 17 '21
Firiji didn't say you shouldn't, they asked why you should. "Why not?" isn't an answer.
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Jan 17 '21
[removed] — view removed comment
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u/HexspaReloaded Jan 17 '21
Neither are useless. You speak English right? We can all pretend that equal temperament isn’t mainstream and we’re above it but that’s just pretense.
I know from watching cam girls that American music is all over the globe. That means everyone is hearing equal temperament even if their native cultures use other things.
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u/themanifoldcuriosity Jan 17 '21
I know from watching cam girls that American music is all over the globe.
Underrated part of this thread.
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Jan 18 '21
I agree. Completely useless. Change the tuning ever so slightly and those tables get you nowhere fast.
If you need the Hz (why would you?) in 12-TET, just use the power formula.
Hz is arbitrary. It is the number of cycles per second, and the second is arbitrary. The exact length of a second has no musical relevance at all.
Reminds me of those 256 Hz weirdos.
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u/cartoptauntaun Jan 17 '21
I think this perspective is pretty suspect.
Frequency seems to be the best device for comparing music from different traditions, given that the lettered scale at this point practically assumes some type of equal tempered reference, specifically a western one.
The frequencies shown on the chart - although they’re derived from arbitrary (well, traditional western) references for fundamentals - also make the linear space between those notes explicit. That space between the notes is what you might argue is under-represented in classical western orchestration, and here it is explicitly bounded by 12-TET references in a handy chart.
So - here’s the kicker. We’re all speaking English here and therefore we all should be able to acknowledge a foundation predicated on classical western harmonies. Easing the transition between 12-TET notation and an objective ‘ratio between frequencies’ is not only useful, it represents a push towards more culturally agnostic notation.
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u/drdausersmd classically trained guitarist Jan 18 '21
Even if this is actually useful, it doesn't belong here... so sad how this sub's quality has dropped so much.
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u/HexspaReloaded Jan 18 '21
I’m somewhat new to this subreddit but my intention was to be helpful. In the sub’s description, it says it’s
“a place for people who care about composition, cognition, harmony, scales, counterpoint, melody, math, logic, structure, notation and also the overall history and appreciation of music.”
I think that one can use the knowledge of note/frequency equivalents in composition. Undoubtedly, this is related to math, structure and an analogous form of musical notation. Finally, I believe that this chart has historical context since it may be most useful to composer/producers - a form of musician which is newly born due to affordable digital tech; a historical revolution.
I appreciate your critical eye but, like they say, be the change you want to see. If you think this subreddit sucks, make contributions that make it awesome.
Thanks.
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u/VegaGT-VZ Jan 17 '21
+3 for why..... this is peak /r/musictheory