7 ms·

It's worth mentioning that stacking fifths this way creates something pretty close to an octave, but it's still noticeably different from an octave. The differe

It's worth mentioning that stacking fifths this way creates something pretty close to an octave, but it's still noticeably different from an octave. The difference between an octave and 12 fifths is called "Pythagorean comma", it's about 23.46 cents and it'll be obvious to all humans who don't have a speech/hearing impediment, even if you were never musically trained. (It's believed humans are sensitive to small intervals like this because it's required to process spoken human language). Traditionally, it's considered anything more than a synctonic comma (i.e. 21.51 cents) will feel different to even untrained ears. (but of course, this is just the theory, in reality there is some small variance between humans, background, culture etc). https://en.wikipedia.org/wiki/Pythagorean_comma https://en.wikipedia.org/wiki/Pythagorean_comma This is pretty significant to mention, because even though 12 fifths are "very close" to an octave [1], they're far apart enough that no one will feel an octave. In music, near misses like this are very significant since they cause the feeling of harmonic "dissonance". Since 12 fifths is a very dissonant interval (since it's so close to an octave but still noticeably out-of-tune) Western music developed techniques (such as well-temperament, equal temperament etc) to make sure this "error" is blend in. We achieve this by changing other notes ("tempering") ever so slightly so that critical intervals like fifths (or in other cases thirds etc) are stable. Other cultures, such as classical Indian music, have their own way dealing with Pythagorean comma! Since music is a universal phenomena found in all cultures, but it doesn't manifest the same way in all cultures (e.g. not all cultures give the same kind of emphasis to pitch or harmony Western music gives) various cultures developed their own different and interesting ways to work around this "error". [1] To be precise, we're referring to the difference between 12 fifths and 7 octaves. Since an octave is so consonant, sounds N octave(s) apart feel "equal" albeit with different timbre.

jacquesm 4y ago
Somewhere there is a perfect universe where 12 fifths form an octave.
- CobrastanJorji 4y ago
  You don't need a new universe. You just need a species that hears sounds a little differently. We won't like listening to their music, but it'll be really great for them.
  - gnulinux 4y ago
    This may or may not be true. In fact, it seems unlikely to me your claim is true. In nature, sounds produce harmonics i.e. when two objects collide they usually create waves of frequency f, 2f, 3f, 4f... in various (usually exponentially decreasing) weights. It's very rare to find pure sounds (i.e. only f frequency) in nature. The interval between f and 2f is an octave apart (1:2 ratio); the interval between 2f and 3f is a perfect fifth (2:3 ratio). So, when you actually hear a sound, you actually hear an octave and a fifth too, and how dominant this octave and fifth changes the "timbre" of the sound. This way, you know the source of the sound independent of the frequency. For example, both a violin and a piano can produce the note A4 at 440Hz, but anyone can easily determine if it's a piano or violin. The reason is, when a piano produces A4, it sounds not only just 440Hz but also 880Hz and 1320Hz etc... too and the relative volume of 880Hz and 1320Hz will be different than that of violin. Your brain automatically interprets these volume weights as "timbre" and the fundamental frequency 440Hz as "pitch". Consequently, in order for your brain to be able to process the timbre of a sound it needs to find octaves and fifths between each fundamental note it hears. This means there might be something universal about octave and fifth (and other decreasingly consonant intervals such as major third etc...). Maybe we "understand" music because our brain is hard-wired to search for octaves and fifths in all sounds, in order to analyze timbre and in order to process spoken language. If this hypothesis is true, maybe an alien species could have octave/fifth/major third based music too! (if they have music at all, of course)
    - jacquesm 4y ago
      There is also the shape of the individual waveforms to take into account a piano has a more or less sinusoidal wave and a violin is more of sawtooth (due to the stickslip of the bow moving across the string(s)).
- deleted 4y ago
  [deleted]
- thaumasiotes 4y ago
  That would have to be a universe in which the fundamental theorem of arithemetic was false. Otherwise, the only way to cross an interval that is an integer number of octaves is to take steps that are also octaves.
  - coldtea 4y ago
    What the parent proposed doesn't require different math. Just a species that hears out current slightly offset divisions in 12-tet as perfect, as opposed to only hearing integral ratios as perfect.
    - thaumasiotes 4y ago
      Viewing sound waves that don't synchronize with each other as being better matched than sound waves that do synchronize is less plausible than violating the fundamental theorem of arithmetic. There's no element of coincidence in whether two frequencies harmonize. That hypothetical species wouldn't recognize two notes an octave apart as being similar, so there would be no reason to imagine a circle of fifths in the first place.
      - coldtea 4y ago
        >Viewing sound waves that don't synchronize with each other as being better matched than sound waves that do synchronize is less plausible than violating the fundamental theorem of arithmetic Actually it's perfectly plausible. People couldn't imagine others enjoying hearing a tritone -- and nobody in 1800 would imagine we'd enjoy listening to punk, hip hop, or Death Metal, and yet, millions do. We can surely consider a race that doesn't require intervals to absolutely synchronize. >That hypothetical species wouldn't recognize two notes an octave apart as being similar, so there would be no reason to imagine a circle of fifths in the first place. Note how I said that this imagined alien race would consider the "divisions in 12-tet as perfect". Note how those do include a perfect octave, that we already recognize as such. The alien race wouldn't change that, they'd just need to also consider perfect the slightly off ratios in 12-tet.
- inopinatus 4y ago
  I've heard there is a secret chord, that prophets play to please their lords. But if you care for music less than algebra, just know it goes like this; the fourth, the fifth: the minor falls, the major lifts.
  - navi0 4y ago
    Well played
  - formerkrogemp 4y ago
    But, you don't really care for music; do ya?
- femto 4y ago
  That would be a non-Euclidian (ie. curved) universe? Maybe it is possible to construct a non-Euclidean universe for sound, by modifying properties of the propagation medium as a function of space or time?
posterboy 4y ago
I'm not comfortable with this first refering to a natural human tendency and then a western harmony, which is pretty much accquired, as if it were a natural consequence. A simpler way to go about this is using the chromatic scale, drawing multiples of C0 upto C8 so that C7 to C8 spans an octave, and then fixing F according to a table of equal temperament.
- coldtea 4y ago
  >I'm not comfortable with this first refering to a natural human tendency and then a western harmony, which is pretty much accquired, as if it were a natural consequence. Well, western harmony is based on a set of natural human tendencies formalized. There are other ethnic music practices, also based on natural human tendencies. The parts that are acquired are built on top. But most/all music practices (western or otherwise) start with natural human tendencies, as their foundations.

jacquesm 4y ago

Somewhere there is a perfect universe where 12 fifths form an octave.

CobrastanJorji 4y ago
You don't need a new universe. You just need a species that hears sounds a little differently. We won't like listening to their music, but it'll be really great for them.
- gnulinux 4y ago
  This may or may not be true. In fact, it seems unlikely to me your claim is true. In nature, sounds produce harmonics i.e. when two objects collide they usually create waves of frequency f, 2f, 3f, 4f... in various (usually exponentially decreasing) weights. It's very rare to find pure sounds (i.e. only f frequency) in nature. The interval between f and 2f is an octave apart (1:2 ratio); the interval between 2f and 3f is a perfect fifth (2:3 ratio). So, when you actually hear a sound, you actually hear an octave and a fifth too, and how dominant this octave and fifth changes the "timbre" of the sound. This way, you know the source of the sound independent of the frequency. For example, both a violin and a piano can produce the note A4 at 440Hz, but anyone can easily determine if it's a piano or violin. The reason is, when a piano produces A4, it sounds not only just 440Hz but also 880Hz and 1320Hz etc... too and the relative volume of 880Hz and 1320Hz will be different than that of violin. Your brain automatically interprets these volume weights as "timbre" and the fundamental frequency 440Hz as "pitch". Consequently, in order for your brain to be able to process the timbre of a sound it needs to find octaves and fifths between each fundamental note it hears. This means there might be something universal about octave and fifth (and other decreasingly consonant intervals such as major third etc...). Maybe we "understand" music because our brain is hard-wired to search for octaves and fifths in all sounds, in order to analyze timbre and in order to process spoken language. If this hypothesis is true, maybe an alien species could have octave/fifth/major third based music too! (if they have music at all, of course)
  - jacquesm 4y ago
    There is also the shape of the individual waveforms to take into account a piano has a more or less sinusoidal wave and a violin is more of sawtooth (due to the stickslip of the bow moving across the string(s)).
deleted 4y ago
[deleted]
thaumasiotes 4y ago
That would have to be a universe in which the fundamental theorem of arithemetic was false. Otherwise, the only way to cross an interval that is an integer number of octaves is to take steps that are also octaves.
- coldtea 4y ago
  What the parent proposed doesn't require different math. Just a species that hears out current slightly offset divisions in 12-tet as perfect, as opposed to only hearing integral ratios as perfect.
  - thaumasiotes 4y ago
    Viewing sound waves that don't synchronize with each other as being better matched than sound waves that do synchronize is less plausible than violating the fundamental theorem of arithmetic. There's no element of coincidence in whether two frequencies harmonize. That hypothetical species wouldn't recognize two notes an octave apart as being similar, so there would be no reason to imagine a circle of fifths in the first place.
    - coldtea 4y ago
      >Viewing sound waves that don't synchronize with each other as being better matched than sound waves that do synchronize is less plausible than violating the fundamental theorem of arithmetic Actually it's perfectly plausible. People couldn't imagine others enjoying hearing a tritone -- and nobody in 1800 would imagine we'd enjoy listening to punk, hip hop, or Death Metal, and yet, millions do. We can surely consider a race that doesn't require intervals to absolutely synchronize. >That hypothetical species wouldn't recognize two notes an octave apart as being similar, so there would be no reason to imagine a circle of fifths in the first place. Note how I said that this imagined alien race would consider the "divisions in 12-tet as perfect". Note how those do include a perfect octave, that we already recognize as such. The alien race wouldn't change that, they'd just need to also consider perfect the slightly off ratios in 12-tet.
inopinatus 4y ago
I've heard there is a secret chord, that prophets play to please their lords. But if you care for music less than algebra, just know it goes like this; the fourth, the fifth: the minor falls, the major lifts.
- navi0 4y ago
  Well played
- formerkrogemp 4y ago
  But, you don't really care for music; do ya?
femto 4y ago
That would be a non-Euclidian (ie. curved) universe? Maybe it is possible to construct a non-Euclidean universe for sound, by modifying properties of the propagation medium as a function of space or time?

posterboy 4y ago

I'm not comfortable with this first refering to a natural human tendency and then a western harmony, which is pretty much accquired, as if it were a natural consequence. A simpler way to go about this is using the chromatic scale, drawing multiples of C0 upto C8 so that C7 to C8 spans an octave, and then fixing F according to a table of equal temperament.

coldtea 4y ago
>I'm not comfortable with this first refering to a natural human tendency and then a western harmony, which is pretty much accquired, as if it were a natural consequence. Well, western harmony is based on a set of natural human tendencies formalized. There are other ethnic music practices, also based on natural human tendencies. The parts that are acquired are built on top. But most/all music practices (western or otherwise) start with natural human tendencies, as their foundations.