6 ms·

This article did not mention overtones: https://en.wikipedia.org/wiki/Overtone https://en.wikipedia.org/wiki/Overtone https://en.wikipedia.org/wiki/Harmonic_s

This article did not mention overtones: https://en.wikipedia.org/wiki/Overtone https://en.wikipedia.org/wiki/Overtone https://en.wikipedia.org/wiki/Harmonic_series_(music) https://en.wikipedia.org/wiki/Harmonic_series_(music) Combinations of frequencies that form simple integer ratios are naturally perceived as being consonant, no culture or upbringing needed. As the ratios begin to involve higher integers and become more complex, the intervals they produce are considered more dissonant. For instance, in ancient Greece, the scales were constructed by combining intervals where the integer ratios have a prime number no higher than 3. The result is a very consonant but almost bland music. Something you could easily fall asleep to. The major and minor scales from which classical music is composed are made by combining intervals with a prime no higher than 5. This adds more dissonance and makes things a bit more interesting. Scales based around higher prime numbers (7,11,13,..) are outside the scope of mainstream music although jazz is said to approximate the scales that could be built off the '7-limit' intervals, which explains its more dissonant nature (heavy use of tritone which has a ratio of 7:5, and the 'minor seventh' approximates the interval with a ratio of 7:4). That covers consonance, but it doesn't explain emotional affect. I think one example that is at least a part of the explanation can be seen in the distinction between the overtones and undertones. The major scale (and more specifically the major chord) of today's western music is generally considered to be happy, confident, uplifted, etc. The major chord appears naturally in the harmonic series of overtones (any 3 notes played together whose frequency ratio is 4:5:6). The minor chord, on the other hand, appears naturally in the undertone series which is just an inversion of the overtones (1/4:1/5:1/6). It also occurs in nature like the overtones, although less frequently. I may have flubbed some details as I'm writing off the top of my head mostly but I think it covers the gist of how harmony can contribute to the perception of music. There is of course also the rhythm and the sense of expectations/irony involved in writing as well.

chimeracoder 8y ago
> Combinations of frequencies that form simple integer ratios are naturally perceived as being consonant, no culture or upbringing needed. As the ratios begin to involve higher integers and become more complex, the intervals they produce are considered more dissonant. This is only true for a definition of "consonant" and "dissonant" that is literally tautological. Yes, one can distinguish between consonant and dissonant, but the assignment of those as "pleasurable" and "not pleasurable" (which is the topic of the article) are incredibly culturally contextual. That is, you can construct a distinction between harmonies that one might label as consonant and dissonant, but the interpretation of that distinction is not universal. In fact, the relevance or applicability of that distinction is not even universal, because there are plenty of musical traditions where this wouldn't apply at all, and therefore couldn't be used to distinguish "pleasurable" and "not pleasurable" music. In reality, in the grand scheme of musical traditions, the classical European model of consonant, simple integer ratios is an outlier.
- crazynick4 8y ago
  I'm curious, which musical traditions favor music built on scales from dissonant intervals? Do you mean music which is more percussion oriented?
  - TheOtherHobbes 8y ago
    Balinese gamelan is played on metal instruments which don't have the same concept of consonance and whose overtones and scales have almost no relationship with Western music. Some eastern european folk uses minor-like scales but harmonies feature a major second, which is certainly not considered a consonant interval. In the West there's also jazz, which is based rather loosely on conventional Western harmony but uses unusually remote and dissonant chords. And the entire serial and post-classical academic tradition, which is self-consciously and deliberately anti-tonal and dissonant. In fact extremely consonant music is the exception.
    - crazynick4 8y ago
      Ok I see what you are saying. I guess I didn't really get this across but I'm not saying that more consonance always means more listening pleasure. As with the Pythagorean tunings, all consonance and no dissonance can become bland. Dissonant intervals are also a part of the harmonic series as you go further up. The major second that you mentioned is a 16:15 ratio. As far as Jazz chords, many are not as dissonant as you would think. The dominant seventh which makes up the entirety of the blues progression is generally considered dissonant because of the flat 7th, the most 'out of tune' note in western tuning. It actually is an attempt to approximate the interval formed between the 7th and 4th overtones which are a strong consonance. Dissonance is definitely a part of what makes music interesting. I wasn't trying to say that consonant intervals are the only reason for listening pleasure, just pointing out that there's some natural phenomena (harmonic series) that we're approximating or emulating with our music that can explain why we perceive music the way we do or why it sounds beautiful to us. I'm not familiar with gamelan but I found this interesting quote on the page regarding one of its tunings: > ..where instruments are played in pairs which are tuned slightly apart so as to produce interference beating. The beating is ideally at a consistent speed for all pairs of notes in all registers, producing stretched octaves as a result. This contributes to the very "agitated" and "shimmering" sound of gamelan ensembles. In the religious ceremonies that contain gamelan, these interference beats are meant to give the listener a feeling of a god's presence or a stepping stone to a meditative state. So in a way, even though the tuning system goes 'outside' the harmonic series, it doesn't completely ignore it but rather 'stretches' some of its intervals, which is what gives the music its otherworldly or mystical feeling.
gwn7 8y ago
Thank you for mentioning overtones. I think it's a very important factor that makes it possible to talk about a universal musical aesthetics, even if a very basic one. > For instance, Greek music is composed by combining intervals where the integer ratios have a prime number no higher than 3 to form the scales. You mean the classical Greek music, right? I think the system you describe is called the Pythagorean tuning.
- crazynick4 8y ago
  Yeah that's what I meant, I edited my post to clarify.
vagab0nd 8y ago
For people who are not familiar, there are 12 steps in an octave. The frequency of the note doubles for each octave. Thus, each "step" increase the frequency of the note by 2^(1/12) times. So you have the frequencies of each semitone as roughly: 1.00 1.06 1.12 1.19 1.26 1.33 1.41 1.50 1.59 1.68 1.78 1.89 This is the reason why "Do/Mi/So" (1/1.26/1.5, ~4/5/6) or "Do/Fa/La" (1/1.33/1.68, ~3/4/5) sound good to the ear. Incidentally, the way the piano is tuned is different from guitar, where piano tuning is more precise (closer to the 2^(1/12) steps), and guitar more close to the integer relations.
yesenadam 8y ago
jazz is said to approximate the scales that could be built off the '7-limit' intervals, which explains its more dissonant nature (heavy use of tritone which has a ratio of 7:5 That all sounds pretty baseless to me. is said to? By who? (Those people who find endless patterns in the measurements of the Egyptian pyramids, maybe.) I've never heard or read that. A tritone doesn't "have a ratio of 7:5", not in the equal temperament we use nowadays - 2^(6/12)=sqrt(2), or in its most literal/basic form of going up 6 perfect fifths i.e. (3/2)^6.
- crazynick4 8y ago
  Quoting David Doty from Just Intonation Primer (highly recommended if you can find a copy): "7:4, 7:5, and 7:6 can be identified with the flatted seventh, fifth, and third beloved of blues and jazz musicians". He may not be the most well known person to write about music theory but his understanding of the fundamentals of music/tuning/harmony is solid. Anyway, it is fairly self evident that the blues scale would not sound the way it does if it didn't have these three intervals (the others just being the fourth, fifth, and octave, which is about as basic as you can get) As an aside, the flat third certainly has a different representation in 5-limit tuning (6:5) but both this as 7:6 are approximated by the same interval in twelve tone equal temperament. Also: https://en.wikipedia.org/wiki/7-limit_tuning https://en.wikipedia.org/wiki/7-limit_tuning In the section 'Approximation using equal temperament' you can see the tritone represented as 7:5. To be more accurate with my wording, its not that the 'tritone is 7:5', but rather what we call a tritone in 12 tone equal temperament is really an approximation of the interval 7:5. Look at the 7th and 5th notes in a harmonic series, which interval do they most closely resemble? The most basic and literal form of an interval is always the smallest possible whole integer ratio that can be used to represent that interval, in this case, 7:5. As you mention, you can arrive at something similar by going up 6 perfect fifths, but the ratio ends up being 729:64 -> 89:64, if you take out the octave. The only way this would have musical significance is if its used as an approximation for 7:5. Scales that are built by stringing perfect fifths do not produce a clean 'tritone', hence its relative shunning in classical music (and its absence in 5-limit tuning where the interval you mention is more of a byproduct). It sounds like you are writing from the point of view of twelve tone equal temperament tuning as the standard by which intervals are defined, whereas I'm starting from the concept that the harmonic series is the basis of harmony and (most) tuning systems are just attempts to emulate it.

chimeracoder 8y ago

> Combinations of frequencies that form simple integer ratios are naturally perceived as being consonant, no culture or upbringing needed. As the ratios begin to involve higher integers and become more complex, the intervals they produce are considered more dissonant. This is only true for a definition of "consonant" and "dissonant" that is literally tautological. Yes, one can distinguish between consonant and dissonant, but the assignment of those as "pleasurable" and "not pleasurable" (which is the topic of the article) are incredibly culturally contextual. That is, you can construct a distinction between harmonies that one might label as consonant and dissonant, but the interpretation of that distinction is not universal. In fact, the relevance or applicability of that distinction is not even universal, because there are plenty of musical traditions where this wouldn't apply at all, and therefore couldn't be used to distinguish "pleasurable" and "not pleasurable" music. In reality, in the grand scheme of musical traditions, the classical European model of consonant, simple integer ratios is an outlier.

crazynick4 8y ago
I'm curious, which musical traditions favor music built on scales from dissonant intervals? Do you mean music which is more percussion oriented?
- TheOtherHobbes 8y ago
  Balinese gamelan is played on metal instruments which don't have the same concept of consonance and whose overtones and scales have almost no relationship with Western music. Some eastern european folk uses minor-like scales but harmonies feature a major second, which is certainly not considered a consonant interval. In the West there's also jazz, which is based rather loosely on conventional Western harmony but uses unusually remote and dissonant chords. And the entire serial and post-classical academic tradition, which is self-consciously and deliberately anti-tonal and dissonant. In fact extremely consonant music is the exception.
  - crazynick4 8y ago
    Ok I see what you are saying. I guess I didn't really get this across but I'm not saying that more consonance always means more listening pleasure. As with the Pythagorean tunings, all consonance and no dissonance can become bland. Dissonant intervals are also a part of the harmonic series as you go further up. The major second that you mentioned is a 16:15 ratio. As far as Jazz chords, many are not as dissonant as you would think. The dominant seventh which makes up the entirety of the blues progression is generally considered dissonant because of the flat 7th, the most 'out of tune' note in western tuning. It actually is an attempt to approximate the interval formed between the 7th and 4th overtones which are a strong consonance. Dissonance is definitely a part of what makes music interesting. I wasn't trying to say that consonant intervals are the only reason for listening pleasure, just pointing out that there's some natural phenomena (harmonic series) that we're approximating or emulating with our music that can explain why we perceive music the way we do or why it sounds beautiful to us. I'm not familiar with gamelan but I found this interesting quote on the page regarding one of its tunings: > ..where instruments are played in pairs which are tuned slightly apart so as to produce interference beating. The beating is ideally at a consistent speed for all pairs of notes in all registers, producing stretched octaves as a result. This contributes to the very "agitated" and "shimmering" sound of gamelan ensembles. In the religious ceremonies that contain gamelan, these interference beats are meant to give the listener a feeling of a god's presence or a stepping stone to a meditative state. So in a way, even though the tuning system goes 'outside' the harmonic series, it doesn't completely ignore it but rather 'stretches' some of its intervals, which is what gives the music its otherworldly or mystical feeling.

gwn7 8y ago

Thank you for mentioning overtones. I think it's a very important factor that makes it possible to talk about a universal musical aesthetics, even if a very basic one. > For instance, Greek music is composed by combining intervals where the integer ratios have a prime number no higher than 3 to form the scales. You mean the classical Greek music, right? I think the system you describe is called the Pythagorean tuning.

crazynick4 8y ago
Yeah that's what I meant, I edited my post to clarify.

vagab0nd 8y ago

For people who are not familiar, there are 12 steps in an octave. The frequency of the note doubles for each octave. Thus, each "step" increase the frequency of the note by 2^(1/12) times. So you have the frequencies of each semitone as roughly: 1.00 1.06 1.12 1.19 1.26 1.33 1.41 1.50 1.59 1.68 1.78 1.89 This is the reason why "Do/Mi/So" (1/1.26/1.5, ~4/5/6) or "Do/Fa/La" (1/1.33/1.68, ~3/4/5) sound good to the ear. Incidentally, the way the piano is tuned is different from guitar, where piano tuning is more precise (closer to the 2^(1/12) steps), and guitar more close to the integer relations.

yesenadam 8y ago

jazz is said to approximate the scales that could be built off the '7-limit' intervals, which explains its more dissonant nature (heavy use of tritone which has a ratio of 7:5 That all sounds pretty baseless to me. is said to? By who? (Those people who find endless patterns in the measurements of the Egyptian pyramids, maybe.) I've never heard or read that. A tritone doesn't "have a ratio of 7:5", not in the equal temperament we use nowadays - 2^(6/12)=sqrt(2), or in its most literal/basic form of going up 6 perfect fifths i.e. (3/2)^6.

crazynick4 8y ago
Quoting David Doty from Just Intonation Primer (highly recommended if you can find a copy): "7:4, 7:5, and 7:6 can be identified with the flatted seventh, fifth, and third beloved of blues and jazz musicians". He may not be the most well known person to write about music theory but his understanding of the fundamentals of music/tuning/harmony is solid. Anyway, it is fairly self evident that the blues scale would not sound the way it does if it didn't have these three intervals (the others just being the fourth, fifth, and octave, which is about as basic as you can get) As an aside, the flat third certainly has a different representation in 5-limit tuning (6:5) but both this as 7:6 are approximated by the same interval in twelve tone equal temperament. Also: https://en.wikipedia.org/wiki/7-limit_tuning https://en.wikipedia.org/wiki/7-limit_tuning In the section 'Approximation using equal temperament' you can see the tritone represented as 7:5. To be more accurate with my wording, its not that the 'tritone is 7:5', but rather what we call a tritone in 12 tone equal temperament is really an approximation of the interval 7:5. Look at the 7th and 5th notes in a harmonic series, which interval do they most closely resemble? The most basic and literal form of an interval is always the smallest possible whole integer ratio that can be used to represent that interval, in this case, 7:5. As you mention, you can arrive at something similar by going up 6 perfect fifths, but the ratio ends up being 729:64 -> 89:64, if you take out the octave. The only way this would have musical significance is if its used as an approximation for 7:5. Scales that are built by stringing perfect fifths do not produce a clean 'tritone', hence its relative shunning in classical music (and its absence in 5-limit tuning where the interval you mention is more of a byproduct). It sounds like you are writing from the point of view of twelve tone equal temperament tuning as the standard by which intervals are defined, whereas I'm starting from the concept that the harmonic series is the basis of harmony and (most) tuning systems are just attempts to emulate it.