If ghosts could speak, their speech would approximate this key (1778)(listsofnote.com)
listsofnote.com
If ghosts could speak, their speech would approximate this key (1778)
https://www.listsofnote.com/p/if-ghosts-could-speak-their-speech
57 comments
https://archive.ph/2Cd08
Keep in mind that under equal temperament, used ubiquitously today, all keys sound the same. The descriptions in the article probably only apply to a certain other tuning system. See https://en.wikipedia.org/wiki/Key_(music)#Key_coloration
Except for the fact that connotations inescapably persist through a long chain influences tracing all the way back to the relevant archaic tuning systems, treatises, church rituals, secular dances, and oral histories.
"D minor: Melancholy womanliness, the spleen and humours brood."
-Christian Schubart, 1778
"It's part of a trilogy, really-- a musical trilogy that I'm doing in d minor, which I find is the saddest of all keys. I don't know why, but it makes people weep instantly."
-Nigel Tufnel playing "Lick My Love Pump" in This is Spinal Tap[1], 1984
Also...
"C major: Completely pure. Its character is: innocence, simplicity, naïvety, children’s talk."
... will persist as long as C major consists of a) the white keys on the instrument of the piano and b) the key in modern notation that doesn't require any sharps or flats in its key signature.
1: FYI-- Christopher Guest appears to actually be playing in d minor for that moment in the movie.
"D minor: Melancholy womanliness, the spleen and humours brood."
-Christian Schubart, 1778
"It's part of a trilogy, really-- a musical trilogy that I'm doing in d minor, which I find is the saddest of all keys. I don't know why, but it makes people weep instantly."
-Nigel Tufnel playing "Lick My Love Pump" in This is Spinal Tap[1], 1984
Also...
"C major: Completely pure. Its character is: innocence, simplicity, naïvety, children’s talk."
... will persist as long as C major consists of a) the white keys on the instrument of the piano and b) the key in modern notation that doesn't require any sharps or flats in its key signature.
1: FYI-- Christopher Guest appears to actually be playing in d minor for that moment in the movie.
You need perfect pitch to be able to tell two keys apart with no reference tone. I'm pretty sure the key connotations are placebo by now
I don't have perfect pitch, but I play a fretless instrument and this means I can hear the distances and relations between notes very clearly.
I still however feel drawn to certain frequencies even without reference or other instrument playing and those frequencies I am drawn to are actual notes. I know 440 Hz is somewhat arbitrary sure, but 99% of the music we hear is somewhat referenced to it.
To me there is certainly a difference between playing a song with an fundamental A 440 Hz or an fundamental A# 466.16 Hz. Not even just when playing them next to each other, but also when you play them days apart. It happened more than once to me that some instrument had been detuned a semitone up or down and I noticed because the resulting music felt different. All of that of course playing solo with no reference to compare to.
Let's not forget, that our brain is not neutral towards frequencies. We can hear whether something is made of metal or wood, whether it is massive or hollow, whether it is controlled or uncontrolled. Deeper usually means bigger regardless of overtone structure. Higher can for example also mean faster (e.g. wind). Parents can hear in a slightly higher pitched noise their kid makes whether they have hurt themselves even if the noise is the same they make every day. Of people speak higher they are excited etc. A lot of that is about relative potch and overtone structures, but even if you take that away, some part that is absolute remains.
If you have a semitone of a difference in some physical vibrating object that can be a noticable difference in mass.
I am not saying transcendental statements like "key X is the most melancholic" are true, what I say is that even to those without perfect pitch hearing a semitone difference might feel different without reference (especially since our sound systems might be able to reproduce one bass fundamental better/punchier/clearer than another).
I still however feel drawn to certain frequencies even without reference or other instrument playing and those frequencies I am drawn to are actual notes. I know 440 Hz is somewhat arbitrary sure, but 99% of the music we hear is somewhat referenced to it.
To me there is certainly a difference between playing a song with an fundamental A 440 Hz or an fundamental A# 466.16 Hz. Not even just when playing them next to each other, but also when you play them days apart. It happened more than once to me that some instrument had been detuned a semitone up or down and I noticed because the resulting music felt different. All of that of course playing solo with no reference to compare to.
Let's not forget, that our brain is not neutral towards frequencies. We can hear whether something is made of metal or wood, whether it is massive or hollow, whether it is controlled or uncontrolled. Deeper usually means bigger regardless of overtone structure. Higher can for example also mean faster (e.g. wind). Parents can hear in a slightly higher pitched noise their kid makes whether they have hurt themselves even if the noise is the same they make every day. Of people speak higher they are excited etc. A lot of that is about relative potch and overtone structures, but even if you take that away, some part that is absolute remains.
If you have a semitone of a difference in some physical vibrating object that can be a noticable difference in mass.
I am not saying transcendental statements like "key X is the most melancholic" are true, what I say is that even to those without perfect pitch hearing a semitone difference might feel different without reference (especially since our sound systems might be able to reproduce one bass fundamental better/punchier/clearer than another).
> It happened more than once to me that some instrument had been detuned a semitone up or down and I noticed because the resulting music felt different.
I suspect this is you having some amount of absolute pitch? It's pretty common! What's rare is reliably and quickly identifying pitches without a reference, though even this can often be learned with practice.
I suspect this is you having some amount of absolute pitch? It's pretty common! What's rare is reliably and quickly identifying pitches without a reference, though even this can often be learned with practice.
I just might. Although I also have a deep love for microtonal or otherwise non-equal tempered music (even accidenrally detuned instrument can sound very great and interesting at times).
> (especially since our sound systems might be able to reproduce one bass fundamental better/punchier/clearer than another).
Yes, especially in that bass range, the absolute value of the frequencies really come into play. A low C at 55Hz might be fully audible on a typical home system, but 2 notes down a ~41Hz A note might dissapear because it's getting harder to play that frequency on a smaller set of speakers.
Yes, especially in that bass range, the absolute value of the frequencies really come into play. A low C at 55Hz might be fully audible on a typical home system, but 2 notes down a ~41Hz A note might dissapear because it's getting harder to play that frequency on a smaller set of speakers.
We grow up hearing “tuned” musical notes. It’s possible we learn these familiar frequencies so that at least some of us can tell the difference as you do. I’m not sure I could.
Experiments on the development of the visual system in cats revealed that seeing only vertical edges and not horizontal edges while kittens made their perceptions of horizontal edges as adults less sensitive. I suppose that there is similar development of sensitivity to a certain frequencies in humans.
Experiments on the development of the visual system in cats revealed that seeing only vertical edges and not horizontal edges while kittens made their perceptions of horizontal edges as adults less sensitive. I suppose that there is similar development of sensitivity to a certain frequencies in humans.
Perfect pitch can most definitely be learned. The parent comment echos a common belief that mentally prevents people from distinguishing key signatures (even under equal temperament), which not insignificantly has a knock-on effect in music education.
>Perfect pitch can most definitely be learned.
Rick says no...
https://m.youtube.com/watch?v=816VLQNdPMM
Rick says no...
https://m.youtube.com/watch?v=816VLQNdPMM
Rick is making that claim in a similar manner to how adult language learners may never develop a perfect local accent. There is truth to that, but it is not an absolute.
I emphasise that the common belief echoed here in this discussion perpetuates to children who can learn perfect pitch but often do not for lack of encouragement.
It is similar to illiteracy that is often perpetuated by parents to their offspring, which incidentally is often the case with music notation. There are different languages of music notation but most children never learn to read or write.
I emphasise that the common belief echoed here in this discussion perpetuates to children who can learn perfect pitch but often do not for lack of encouragement.
It is similar to illiteracy that is often perpetuated by parents to their offspring, which incidentally is often the case with music notation. There are different languages of music notation but most children never learn to read or write.
Synesthetes with perfect pitch and strong associations to musical keys report associations consistently. The associations aren’t universal, though/not everyone would agree with Shubart.
This list is probably intended for someone playing under well temperament: https://en.wikipedia.org/wiki/Well_temperament
Also this is only the case for the differences they describe between different root notes (A vs G); major versus minor is still totally a thing.
Also this is only the case for the differences they describe between different root notes (A vs G); major versus minor is still totally a thing.
I'm not sure what you mean by "sound the same", but just by comparing a simple change from major to minor is quite a dramatic change:
https://www.youtube.com/watch?v=_CTYymbbEL4
https://www.youtube.com/watch?v=10CQAjCrYPY
Same thing with a more recent pop tune: https://www.youtube.com/watch?v=A9HZH_P_5qM
There's also a reason that in electronic music A minor is used significantly more: https://www.edmprod.com/beatport-analysis/
It probably has a lot to do with how well that key suits club speakers.
https://www.youtube.com/watch?v=_CTYymbbEL4
https://www.youtube.com/watch?v=10CQAjCrYPY
Same thing with a more recent pop tune: https://www.youtube.com/watch?v=A9HZH_P_5qM
There's also a reason that in electronic music A minor is used significantly more: https://www.edmprod.com/beatport-analysis/
It probably has a lot to do with how well that key suits club speakers.
>I'm not sure what you mean by "sound the same", but just by comparing a simple change from major to minor is quite a dramatic change
That's because OP is not talking about the differences between scales (major vs minor) but keys (C major vs A major). With equal temperament all keys of the same scale have the exact same intervals between the notes. They are simply shifted up or down by a constant amount. Before equal temperament that was not the case.
That's because OP is not talking about the differences between scales (major vs minor) but keys (C major vs A major). With equal temperament all keys of the same scale have the exact same intervals between the notes. They are simply shifted up or down by a constant amount. Before equal temperament that was not the case.
There definitely can be instrument-specific differences though, even under equal temperment. For example, the black keys on a piano sound distinctly different than the white keys; and on stringed instruments, some keys lend themselves to voicings containg more open strings, which AFAIK leads to a brighter/fuller sound (though I don't play stringed instruments, so don't quote me on that). There's also the practical matter that some things are easier or harder to play in some keys.
And of course, playing a song in a higher or lower key means you’re playing it higher or lower. A couple semitones can make a subtle difference in the character of a piece; transposing half an octave can be drastic. This combines with instrument-specific differences too, as most instruments just sound different in different octave ranges. I once had to play a piece written that was written originally in A major for a Rhodes electric piano, but I had to transpose to D major to accommodate a vocalist. This was incredibly awkward; transposing downwards sounded way too muddy, but transposing upwards sounded annoyingly chimey.
And of course, playing a song in a higher or lower key means you’re playing it higher or lower. A couple semitones can make a subtle difference in the character of a piece; transposing half an octave can be drastic. This combines with instrument-specific differences too, as most instruments just sound different in different octave ranges. I once had to play a piece written that was written originally in A major for a Rhodes electric piano, but I had to transpose to D major to accommodate a vocalist. This was incredibly awkward; transposing downwards sounded way too muddy, but transposing upwards sounded annoyingly chimey.
> "For example, the black keys on a piano sound distinctly different than the white keys"
Can you elaborate on that? One thing that I noticed is that sometimes it can be hard to make the black keys sound the same as the white keys just because of their different geometry. They are shorter and therefore the lever length is shorter. You have to actively work to get timing and intensity right but you learn that early.
Apart from that I cannot think of a reason why they should be different from the white keys.
Can you elaborate on that? One thing that I noticed is that sometimes it can be hard to make the black keys sound the same as the white keys just because of their different geometry. They are shorter and therefore the lever length is shorter. You have to actively work to get timing and intensity right but you learn that early.
Apart from that I cannot think of a reason why they should be different from the white keys.
Okay, full disclosure: I’m not entirely sure what the physical reason is, and I don’t have a source beyond just my own experience.
However, I can definitely tell a difference, and it’s not subtle at all. If you play a note on the piano for me while my eyes are closed I can reliably tell whether it’s a black key or a white key. If I’m playing on a (high-quality sampled) synth piano that’s accidentally set to transpose -1 or +1 semitones I notice right away that it sounds like a black key where I played a white key or vice versa. Something about the black keys seems to sound a bit harsher/sharper/tangier to my ears; maybe a slightly sharper attack and/or slightly brighter harmonics in the upper-mid range.
I suppose it’s possible that I’ve just learned to distinguish the pitches — I don’t have perfect pitch, but I’ve been playing piano for quite literally longer than I remember, so maybe my brain just internalized the C major scale, or something. But I’m sure I can hear a difference :)
However, I can definitely tell a difference, and it’s not subtle at all. If you play a note on the piano for me while my eyes are closed I can reliably tell whether it’s a black key or a white key. If I’m playing on a (high-quality sampled) synth piano that’s accidentally set to transpose -1 or +1 semitones I notice right away that it sounds like a black key where I played a white key or vice versa. Something about the black keys seems to sound a bit harsher/sharper/tangier to my ears; maybe a slightly sharper attack and/or slightly brighter harmonics in the upper-mid range.
I suppose it’s possible that I’ve just learned to distinguish the pitches — I don’t have perfect pitch, but I’ve been playing piano for quite literally longer than I remember, so maybe my brain just internalized the C major scale, or something. But I’m sure I can hear a difference :)
It probably relates to the tuning you're used to. Piano strings do not have perfectly linear overtones, and thus piano tuning is never 100% equitemperal (I've tried; it sounds quite off). So the tuner has to make concessions across the scale, and most likely, there are more of them in the black keys since they are typically used less and you'd typically start with the pure intervals from A anyway.
Of course, since you hear this effect even when played one by one, this assumes you are unconciously comparing them to some reference pitch. (I'm not aware of anything in manifacturing of piano strings that would somehow make black strings be produced different, so unless I'm missing something, it would have to either be in terms of key mechanics, hammer wear, or tuning.)
Of course, since you hear this effect even when played one by one, this assumes you are unconciously comparing them to some reference pitch. (I'm not aware of anything in manifacturing of piano strings that would somehow make black strings be produced different, so unless I'm missing something, it would have to either be in terms of key mechanics, hammer wear, or tuning.)
I've noticed this too, on the upright piano I grew up with. There's a definite "thunkiness" to the sound of black keys. I've only played digital pianos since, and haven't noticed it, which is not surprising given that most digital pianos use the same sample for at least 2-3 adjacent pitches.
I also do not know the reason, but I suspect it might have to do with body resonances/geometry.
I also do not know the reason, but I suspect it might have to do with body resonances/geometry.
Here's a test you could do: take a recording of piano and play it back at 1.06x. Do the black keys start sounding like white keys? This distinguishes between something about the way a piano is constructed/played vs whether you have learned something about specific pitches.
Maybe you have instrument specific perfect pitch without being aware of it?
Which keyboard/samples do you use where the difference is not subtle? I'd like to do the black key vs. white key test without looking. Maybe there is something to it I'd never noticed.
Which keyboard/samples do you use where the difference is not subtle? I'd like to do the black key vs. white key test without looking. Maybe there is something to it I'd never noticed.
[deleted]
I agree to everything you have written, except
> the black keys on a piano sound distinctly different than the white keys
I never noticed that and it doesn't seem plausible to me. The mechanics of black and white keys are identical, no?
> the black keys on a piano sound distinctly different than the white keys
I never noticed that and it doesn't seem plausible to me. The mechanics of black and white keys are identical, no?
The do have a shorter lever arm.
To say more, since people are asking: equal temperment means that you take an octave and divide it into 12 pitches, so that the ratio of each pitch to the next is the same (the 12th root of 2). When you play in a major key, you pick a particular set of 7 of those 12, with a particular set of "skips". You can get from one major scale to another one by multiplying all the frequencies by the same scaling (some power of the 12th root of 2). Notice that in that major scale, for instance, the frequency between notes 1 and 7 is close to, but not exactly 3/2. It's in some sense out of tune. Back in the day it was more common for pianos to not be in equal temperment. One advantage might be that you could, in some key, have notes 1 and 7 be closer to a ratio of 3/2. But this means that the same scale in different keys would have different ratios of frequencies! That's how they would sound different.
A key is just a transposition for the notes as they appear on the music sheet to actual notes on an instrument. Each key is a different transposition. Good keyboards have a transpose feature where you get to pick a key, then you play a piece as you remember or read the music, then do the same thing in a different key, and even though you played the same keys, in the same order, with the same timing, the sound will be quite different.
Play the same piece in different keys, and you'll see that the feelings you get will be different for each key.
Play the same piece in different keys, and you'll see that the feelings you get will be different for each key.
The original comment was about historical tunings with unequal spacing between each note, optimized for perfect ratios between certain notes. This has a drawback of being quite incompatible with some transpositions.
Modern tuning with 12-TET is not perfect, but good enough, and doesn't yield very dramatic differences when transposed.
Modern tuning with 12-TET is not perfect, but good enough, and doesn't yield very dramatic differences when transposed.
> doesn't yield very dramatic differences when transposed
What differences are you thinking it does yield when transposed?
What differences are you thinking it does yield when transposed?
If you use perfect tuning the 5ths are a slightly larger interval than the way modern instruments are tuned. If you were to tune a piano to perfect tuning based on the key of C, the key of G would be slightly higher than what we hear today. The leading tone back to C would be slightly higher and "lean into" C a bit more. But if you decided to try to play in a distantly related key (say C# or something like that) the spacing between the notes would be so far off that you'd probably need to retune the piano.
Bach wrote the Well Tempered Clavier with a fugue and prelude in every major and minor key. It was a celebration of tempered tuning which meant you could play in every key without needing to retune the instrument when switching to play a piece in a different key.
Put simply, well tempered tuning means that if you walk up the circle of 5ths starting at C, then G, then D, etc. When you eventually get back to C, it will be an even doubling of where you started. With perfect tuning when you get back to C, you'll be higher than that.
Bach wrote the Well Tempered Clavier with a fugue and prelude in every major and minor key. It was a celebration of tempered tuning which meant you could play in every key without needing to retune the instrument when switching to play a piece in a different key.
Put simply, well tempered tuning means that if you walk up the circle of 5ths starting at C, then G, then D, etc. When you eventually get back to C, it will be an even doubling of where you started. With perfect tuning when you get back to C, you'll be higher than that.
But my parent was talking about 12 tone equal temperament?
I replied using a comparison of 12-TET, to scales with unequal steps. The post I replied to, used only the perspective of modern keyboards when talking about transposing music.
You wrote "Modern tuning with 12-TET is not perfect, but good enough, and doesn't yield very dramatic differences when transposed" and I was trying to figure out what differences you were referring to as still being there in 12-TET. As in, why write "very dramatic" instead of "any"?
Isn't equal temperament only possible for some instruments?
A bugle can't do equal temperament, so yes, but are there any standard orchestral instruments that can't be made to do equal temperament?
Obviously a string quartet doesn't normally play equal temperament, but they could if they wanted to, I think, if we ignore the playing of harmonics, which is a fairly unusual technique.
Obviously a string quartet doesn't normally play equal temperament, but they could if they wanted to, I think, if we ignore the playing of harmonics, which is a fairly unusual technique.
Just because an instrument can do equal temperament doesn't mean that is necessarily the best choice. Although absolute pitch can't be heard by most, relative pitch can, and so when playing any interval, such as a fourth, it will sound off in equal temperament, yet sound perfect when you put it "out of tune". There's some pretty interesting music theory that comes out of the traditional 12 tones not being able to be equally subdivided to then be arranged into those perfect intervals
> Obviously a string quartet doesn't normally play equal temperament
This seem to refute the assertion by arxanas that "all keys sound the same (unless you have perfect pitch)".
This seem to refute the assertion by arxanas that "all keys sound the same (unless you have perfect pitch)".
Assuming that well-tempered would be the primary alternative here, does it enable one to differentiate between keys? Asking as someone with very little experience / knowledge of music theory.
It's an interesting history, better explained here: https://en.wikipedia.org/wiki/12_equal_temperament but in short, prior tuning systems were more mathematically correct, but an instrument would be tuned for a particular key and playing in other keys would sound (to us, anyway) like the instrument was out of tune.
But if a piece was written for a specific key and the instrument was tuned to that key for that piece, that would be both more mathematically correct and also matching the original intent of the composer? What is the rationale for equal temperament?
"In a key" means using the indicated scale. If you mean "all keys sound the same" literal, you're wrong: key changes are audible.
Key _changes_ are audible, but you can't tell a key on its own in equal temperament (except if you have perfect pitch)
While most people can't give a name to the key they are hearing, I'm not sure that proves they can hear no difference. A painter may look at a landscape and identify all the individual colors they are seeing where a common person may mostly ignore or tune out much of what they see, but it doesn't mean they aren't experiencing it in some lesser way even if they can't fully articulate it like a painter can
Yes, of course. The claim that all keys sound the same is neither objectively nor subjectively true. Objectively, the root notes are at different frequencies, and the other notes similarly feature a unique combination of frequencies.
Subjectively, I - and I presume many others - get a particular feel even from individual notes, and when I compose something I often start by picking a root note that suits what I want, and then choose the key based on that. Otherwise why have keys in the first place? I’ve had conversations with other musicians about what particular key we’re into lately, for instance, for a long time I’ve really enjoyed Bb minor.
Subjectively, I - and I presume many others - get a particular feel even from individual notes, and when I compose something I often start by picking a root note that suits what I want, and then choose the key based on that. Otherwise why have keys in the first place? I’ve had conversations with other musicians about what particular key we’re into lately, for instance, for a long time I’ve really enjoyed Bb minor.
There are some differences, though. For example, the resonance of the open G strings on the violins is sometimes audible, and this may make different keys sound different.
Body resonance also -- which provides most of the color of an instrument's sound. For example, middle C on an electric bass guitar (which sounds at 130.8 Hz) often sounds "honky" or "thunky" -- this is due to a null in the body resonance. (Not all bass guitars exhibit this.)
I suppose techniques like vibrato (which you can't do on an open string) and harmonics (which you can normally only do on an open string) make a clear distinction and give a composer an incentive to use a particular key (or give a player an incentive to use a non-standard tuning).
If you tune the violin down to a historical A=415, the open G string will still sound resonant even though in concert pitch it's now Gb.
Here is some context behind musical tuning systems, and how harmony works:
Musical harmony in Western music is based on physical properties of the way materials vibrate. When you vibrate something resonant through plucking, striking, forcing air through, etc, it vibrates at a fundamental frequency, and integer multiples of that fundamental frequency. So for instance 400 Hz, 800 Hz, 1200 Hz, etc.
The power of two multiples sound like the same note in a higher octave. Human hearing is logarithmic, and the same note one octave higher is double the frequency.
The non power of 2 multiples do NOT sound like the same note. These notes are what "sounds good" with the base frequency, and generally the lower frequency multiple it comes from the better it sounds. So for instance, starting with 400 Hz, 400 x 3 = 1200. Divide that back down below 800 to 600 to put it in the same "octave", and you have the interval called a 5th. 400 Hz x 5 = 2000, divide it back down to 500 Hz. That's a major 3rd? I think? It might be a 4th, I don't remember.
Notice that these frequencies are defined by exact ratios to each other, not by consistent logarithmic increases which can be repeated in a pattern (a scale). So, how can you split up an octave in the way that most closely appoximates these exact ratios? Turns out dividing an octave into 12 steps is much better than any number before or after until you get to 24. Thus the 12 note system of western music.
All the different tuning systems mentioned by others are trying to tune these 12 notes for different purposes. Older pre-modern systems usually tuned to C most exactly, and left small errors in every other key. These small errors gave different character to different keys in music of the time. Newer tuning systems (equal temperament), have the key errors balanced out evenly across every key, so every key now sounds the same in character.
Musical harmony in Western music is based on physical properties of the way materials vibrate. When you vibrate something resonant through plucking, striking, forcing air through, etc, it vibrates at a fundamental frequency, and integer multiples of that fundamental frequency. So for instance 400 Hz, 800 Hz, 1200 Hz, etc.
The power of two multiples sound like the same note in a higher octave. Human hearing is logarithmic, and the same note one octave higher is double the frequency.
The non power of 2 multiples do NOT sound like the same note. These notes are what "sounds good" with the base frequency, and generally the lower frequency multiple it comes from the better it sounds. So for instance, starting with 400 Hz, 400 x 3 = 1200. Divide that back down below 800 to 600 to put it in the same "octave", and you have the interval called a 5th. 400 Hz x 5 = 2000, divide it back down to 500 Hz. That's a major 3rd? I think? It might be a 4th, I don't remember.
Notice that these frequencies are defined by exact ratios to each other, not by consistent logarithmic increases which can be repeated in a pattern (a scale). So, how can you split up an octave in the way that most closely appoximates these exact ratios? Turns out dividing an octave into 12 steps is much better than any number before or after until you get to 24. Thus the 12 note system of western music.
All the different tuning systems mentioned by others are trying to tune these 12 notes for different purposes. Older pre-modern systems usually tuned to C most exactly, and left small errors in every other key. These small errors gave different character to different keys in music of the time. Newer tuning systems (equal temperament), have the key errors balanced out evenly across every key, so every key now sounds the same in character.
Could I get some clarification?
> Divide that back down below 800 to 600
Do you mean "keep dividing 1200 by 2 until it is less than 400 times 2"? So, if I have a starting frequency N and some multiple frequency KN then the process is "find i such that (KN >> i) < 2N"?
> Divide that back down below 800 to 600
Do you mean "keep dividing 1200 by 2 until it is less than 400 times 2"? So, if I have a starting frequency N and some multiple frequency KN then the process is "find i such that (KN >> i) < 2N"?
Yes, because remember, humans hear frequency doubling as an octave pitch change. So 1200 divided or multiplied by any multiple of 2 sounds like the same note. You are finding the note in between N and 2N, to find the version of the note in the same octave, to approximate your scale note to.
Does this only apply to piano, brass, and woodwind? Seems like with choral or string music, high level performers would naturally adjust the tuning of their particular note to match the context of the chord. Like I can't imagine someone singing a 5th and NOT falling into a perfect tuning.