#1
For simplicity, let's look at melody before harmony.

One thing that I think is real is resolution. You can get a definite sense that a melody has ended at its tonic or key note. Whether this is intrinsic in music or culturally-based / learned doesn't matter at this stage.

What about major / minor? The quality of the interval a third above the tonic does have a big effect. But a melody could be made that used the minor third and the major third in equal amounts. It might sound odd, but to me this indicates that the third is just like any other interval. It's just more common to stick to one or the other throughout a piece of music. Does this justify there 'really' being major keys and minor keys, or is it just a compositional convention?

As for modes and scales, aren't these all just examples of favouring some intervals more than others?

As I see it, only the tonal centre has any reality outside of convention and nomenclature. Things such as mode names, scale names, and even major / minor are just short-hand ways of describing the intervals used in the piece of music in relation to the tonic.

Most tunes don't use all possible intervals; the subset that are actually used will flavour the melody. When you use mode names, scale names etc. you aren't forbidding any deviation from a strict set of notes but simply describing overall flavour. Nothing more meaningful than that, so no need to get too pedantic about it.

This point of view would surely render many of the arguments we see in MT forum invalid, or at least purely semantic.
#2
mt arguments purely invalid, pointless and semantic?

you get banned for spreading libelous rumours like that m8
#3
Quote by Jehannum

As for modes and scales, aren't these all just examples of favouring some intervals more than others?

I really like this idea of thinking. It helps to make this aspect of music feel more inclusive, rather than prescriptive.
it's all just coming back
it's all coming back

it's all coming back to me
#4
This topic has been researched rather extensively. There are a dozen or so things which have been shown to have an emotional impact regardless of social or cultural conditioning. The only one I remember offhand is a series of descending fifths coming to rest.
#5
The harmonic series is really what all these associations come from. The octave, being the first harmonic, comes across so loud and consonant that we consider it to be the same note, the second harmonic is the 5th, also very loud and consonant. The whole major scale is based on the harmonic series and this is why it has such a pure sound. In fact, Just Intonation is based off of the harmonic series as well. 12TET intonation is just an altered version of that that allows key changes to sound ok.

The harmonic series is also what makes up the timbre of different instruments. In different instruments the volume of the harmonics (relative to other instruments) will be different.

http://en.wikipedia.org/wiki/Harmonic_series_%28music%29
Last edited by The4thHorsemen at Oct 21, 2014,
#7
There isn't a real clear response on this question yet. Historically, most cultures have agreed upon the "pleasing" quality of perfect fourths, fifths, and the octave. Ancient music of all cultures generally create scales out of these intervals in one way or another. At least in the Western world, Pythagorean tuning established these intervals as acceptable consonances. In terms of why it is pleasing, at least on some level it's because these intervals form superparticular ratios in either multiples (x * N) or ([N+1]/N) for frequency ratios. Generally speaking these intervals sound more pleasing to the ear and that is probably why they have been acceptable for so long. Likewise, instruments with more pure harmonics generally sound "cleaner" or more "pure". Dissonance so defined just defined an arbitrary distance away from the fundamental in the harmonic series.

So in this sense if you mean "real" then we can say that everyone at least agrees that these intervals sound pleasing. As for major/minor thirds, they were not considered acceptable consonances into the middle ages with the advent of mean tone temperament tuning systems that solved some of the initial tuning problems that Pythagoras encountered when trying to tune his instruments using scales constructed purely out of perfect fourths and fifths.

It's actually pretty difficult to write music that is purely atonal though. Even a lot of dissonant metal still has a pretty well-established tonal center or one that is changing constantly. Our ears have been trained to accept tonal centers and the V - I chord relationships mostly because the diatonic scales and their associated chords are built around it. Similarly, if you try to construct chord progressions out of the Greek Modes you will often find them collapsing into major or minor. All this to say that the chords used in functional harmony were constructed out of satisfying a certain set of ideas and they intrinsically sound good to us.

However, it's been seen historically that anyone can be trained to find dissonances more pleasing. Some of it might be from the effect of the unexpected rather than finding it pleasing to the ear. I like dissonance but not because I think it's beautiful necessarily. In the same way, deviating from a scale as you pointed out is not forbidden and this is because breaking the rules, delving into the unexpected creates interest. In a sense, the fact that the rules and conventions exist mean you can transgress them and that's where the fun in writing music often lies. Would it necessarily be as interesting if there was no established norm? This is open to debate.

All this to say that at the very least, the majority of people agree that certain intervals sound good. But drawing the line of when dissonance sounds good is mostly arbitrary and at best cultural or social in nature.
#8
All harmony comes from the harmonic series. The third partial in the harmonic series is the 5th. Thats why V-I is so strong. When you play V, you are evoking the 5th found in the harmonic series of I and your brain wants to hear what that note is the 5th of. The 5th partial is the major third. The 7th partial is the b7. So in the first 7 partials, you get a V7 chord. No wonder V7 is such an important chord!

Youll find that as you go up the partials, all the prime numbers represent harmonies of the tonic. You can find every note of the chromatic scale in this series, and more. Harmonics closer to the 1st partial are what we consider "consonant" and further from it are "dissonant."

If you ask me, harmony is just exploring the tonal possibilities of the first note you played

Also, dont forget that pitch is really rhythm, since its dictated by the speed at which the air pressure beats against your ear. Rhythms sped up dramatically may look like and sound like wave forms of notes with a harmonic series


^I have this problem with atonal to. If your still in 12edo, is it really atonal?
#9
Everyone has already mentioned the harmonic series.

The first six harmonics in the harmonic series are fundamental, octave, P5th, octave, M3rd, P5th

I'm pretty sure that the minor third doesn't occur in the harmonic series. The tritone definitely doesn't.

The pentatonic scale is five notes and is built from fifths
C -> G -> D -> A -> E

This makes it a somewhat natural scale. There is a lot of stuff around about the prevalence of the pentatonic scale in the traditional songs across diverse cultures from around the world.

I've also read somewhere that every cultures higher music systems tend to break the octave down differently. Apparently almost all of them favour the octave and the perfect fifth.

The scales and musical modes we use are a result of our history and acquired cultural tastes. But they are also based on our ability to recognize and appreciate some physical properties of pitched sound frequencies.

Some music theorists suggest that there are laws that govern tonal music.

As for your search for "reality" in music? It's one of those cases where perception is reality.
Si
#10
At the 19th harmonic we get a 19:16, which is just slightly flat (2.5 cents) from a 12TET minor 3rd.
#11
Quote by bassalloverthe
^I have this problem with atonal to. If your still in 12edo, is it really atonal?


In the context that the word is generally used, atonal refers to the perceived lack of a tonal center in the writing (or if you prefer, as Schoenberg did, all tones are equally considered to be the tonal center). Since it was proposed in the context of 12edo it is generally used to refer to our modern tuning system.

Atonality is still important in other tuning systems but because you have such a huge variety of chords in some systems, tonality is much more complex and atonality is much more difficult to do well IMO.
#12
Quote by 20Tigers
Everyone has already mentioned the harmonic series.

The first six harmonics in the harmonic series are fundamental, octave, P5th, octave, M3rd, P5th

I'm pretty sure that the minor third doesn't occur in the harmonic series. The tritone definitely doesn't.

The pentatonic scale is five notes and is built from fifths
C -> G -> D -> A -> E

This makes it a somewhat natural scale. There is a lot of stuff around about the prevalence of the pentatonic scale in the traditional songs across diverse cultures from around the world.

I've also read somewhere that every cultures higher music systems tend to break the octave down differently. Apparently almost all of them favour the octave and the perfect fifth.

The scales and musical modes we use are a result of our history and acquired cultural tastes. But they are also based on our ability to recognize and appreciate some physical properties of pitched sound frequencies.

Some music theorists suggest that there are laws that govern tonal music.

As for your search for "reality" in music? It's one of those cases where perception is reality.


Well now 3 people mentioned the HM then

Minor thirds and tritones both occur in the HM. Theres also the TT between the 5 and 7 partial which is what most people are talking about when they say JI TT. Someone already pointed out 19:16 is b3 and I may be talking out my ass, but Im pretty sure 49:48 is a generally accepted tritone. The problem with the tritone is: where you you draw the halfway point on a logarithmic scale?

^

>mfw how can you consider serial music atonal. Its probably the most tonal system there is, considering 100% of the pitch material is derived from the same notes in the same order

Yes I know that as a naming convention, its referred to as atonal. Which was stupid if you ask me...
Last edited by bassalloverthe at Oct 21, 2014,
#13
Quote by bassalloverthe
Well now 3 people mentioned the HM then

Minor thirds and tritones both occur in the HM. Theres also the TT between the 5 and 7 partial which is what most people are talking about when they say JI TT. Someone already pointed out 19:16 is b3 and I may be talking out my ass, but Im pretty sure 49:48 is a generally accepted tritone. The problem with the tritone is: where you you draw the halfway point on a logarithmic scale?

^

>mfw how can you consider serial music atonal. Its probably the most tonal system there is, considering 100% of the pitch material is derived from the same notes in the same order

Yes I know that as a naming convention, its referred to as atonal. Which was stupid if you ask me...


The tritone in 12edo is slightly off from the harmonic series but it's close. The minor third only shows up if you use the theoretical undertone series. But it's "implied" by the overtone series.

As for the naming convention, Schoenberg actually wanted to use "pantonal" which is probably closer to the truth.
#14
I question whether some of these paradigms and ideas concerning the harmonic series and comparisons of elements within it to elements within various tuning and interval systems across cultures are more a posteriori than a priori in presentation. On the pentatonic scale, for instance: is it because the relative pitches of the scale can be unwrapped into a sequence of fifths that it sounds good to varied ears? or because the relative pitch distances of the compressed scale are sufficiently apart in apparent pitch-distance to be easily singable on the one hand, and that the qualitative-experiential effects of the intervals are somehow potent on the other? This is to say: the pentatonic scale is not often played as stacked fifths, be it in harmony or melody. The Lydian-Chromatic Dealio® also extends the recurrent fifths idea to the diatonic scale, but that also doesn't present frequently in the skeletal fashion of repetitive fifths. Where do the bones become the body? Stacked, for instance, major thirds (though detuned a bit in 12ET and such) produce the augmented scale, which many - at least Western - ears don't take well to at the drop of a hat. I mean, it's a neat occurrence that a number of important features of the primary Western musical system for the past few hundred years coincide in the way they do, but it doesn't really answer anything without showing how one actually makes the other, if any such thing happens at all.


To answer Jehannum:

Almost every non-practical-problem discourse in MT is about the definition of one thing or another, to various tiers of abstract.

["What is music?"
|
["What are music's properties?"
|
["What does it matter the answer to either?"

There are positivists, structuralists, reductionists, a few nihilists... But what unfolds here is never really anything new. The particular points of contention may change or even be as-yet untouched every so often, but the forms and aesthetics are relatively constant. All of the arguments here are pointless and invalid except for showing what we think.
You might could use some double modals.
#15
Quote by AETHERA
I question whether some of these paradigms and ideas concerning the harmonic series and comparisons of elements within it to elements within various tuning and interval systems across cultures are more a posteriori than a priori in presentation. On the pentatonic scale, for instance: is it because the relative pitches of the scale can be unwrapped into a sequence of fifths that it sounds good to varied ears? or because the relative pitch distances of the compressed scale are sufficiently apart in apparent pitch-distance to be easily singable on the one hand, and that the qualitative-experiential effects of the intervals are somehow potent on the other? This is to say: the pentatonic scale is not often played as stacked fifths, be it in harmony or melody. The Lydian-Chromatic Dealio® also extends the recurrent fifths idea to the diatonic scale, but that also doesn't present frequently in the skeletal fashion of repetitive fifths. Where do the bones become the body? Stacked, for instance, major thirds (though detuned a bit in 12ET and such) produce the augmented scale, which many - at least Western - ears don't take well to at the drop of a hat. I mean, it's a neat occurrence that a number of important features of the primary Western musical system for the past few hundred years coincide in the way they do, but it doesn't really answer anything without showing how one actually makes the other, if any such thing happens at all.


I am not quite sure what you mean by apriori or aposteriori in this context. There is certainly empirical evidence that shows that the majority of the population finds superparticular ratios pleasing. If you are asking how we know that this was the reason they constructed scales using it, we don't. But it's a reasonable assumption. I don't think there is any way to get a real answer to the question in the way you want so we may as well speculate.

Regarding my answer, I hoped that I conveyed that idea that it is not that the scales themselves unwrap into the harmonic series in our heads (or that our brains equate them as being the same thing) but that the cultures that created these scales had those intervals in mind when constructing them. This is definitely true as we have records of how these scales were made and it was through measurements using 2/1, 3/2, or 4/3 ratios.

You are right to point out that we often digress from these patterns which is why I said that it is largely cultural and that variation adds interest. Rigidity is boring.

Another problem is that you are talking purely about melody. The harmonic movements of a 3-limit just intonation system are implied in diatonic chord movements which is why they are "pleasing". There are additional studies that show that children who have not been exposed to music before naturally sing just intervals an these intervals become less consonant (toward 12tet) as time progresses. This suggests to me that there is something innate in the brain wiring that "likes" superparticular ratios but that this can be overridden or built upon by culture. Furthermore, very dissonant intervals and overtones can sometimes resemble panic calls/screams and there are some studies showing that such tones can activate elements of the HPA axis in the brain suggesting stress response.

So overall I would argue that there is an innate culture liking for 3-limit ratios and more consonant superparticular ratios that are close to the fundamental but this does not mean that the system cannot be built upon or added to.
#16
I look at it like this:

I use the major scale pattern a lot. It holds meaning to me. Any note of that could be a tonic around which pieces/sections are centered.

I discovered this on my own. It is there. It is not a fabrication. It does only exist, really, by virtue of our beings, like the subjects of any of our senses, but it is a pattern of pitches which is meaningful to a number of humans.

Theory is built from our real observations of these things. First we noticed the pattern, then we named it. It is at least real to some people. It is real to me.

However, many of the naming systems, and chosen ways of organizing theory are arbitrary, or more suited for certain approaches/styles, than others, and imo are not worth debating. I know I approach theory in some ways which are different than the consensus of academia. I know that has implications for communication, but I don't care that much. For me, the priority is being able to play music how I like to play music, and to the best of my ability.
#17
hello all. two things to say

1) the Greeks did not actually use the "Greek modes". never invoke antiquity.

2) my primary area of study as a mathematician is the harmonic series. it is not so mysterious as it's made out to be. it's an abstraction of models of constructive and destructive interference in periodic phenomenon (jiggly air). this is all besides the point though. the beauty of the harmonic series is in it's growth and that has nothing to do with music (thankfully) or any physical garbage

take care
i don't know why i feel so dry
#18
Quote by bassalloverthe
Well now 3 people mentioned the HM then

Minor thirds and tritones both occur in the HM. Theres also the TT between the 5 and 7 partial which is what most people are talking about when they say JI TT. Someone already pointed out 19:16 is b3 and I may be talking out my ass, but Im pretty sure 49:48 is a generally accepted tritone. The problem with the tritone is: where you you draw the halfway point on a logarithmic scale?

^

>mfw how can you consider serial music atonal. Its probably the most tonal system there is, considering 100% of the pitch material is derived from the same notes in the same order

Yes I know that as a naming convention, its referred to as atonal. Which was stupid if you ask me...


Yeah it depends how you define the tritone. The tritone in 12TET however is a wavelength that never coincides with the fundamental over however many cycles you want. The halfway point in a logarithmic scale would be the frequency X multiplied by 2 to the power of 1/2. That's how the 12TET system works - multiply the fundamental frequency by 2^(s/12) where s=the number of semitones.

The 12TET system is flawed in that it doesn't really nail a few of the intervals but is a close enough approximation that the benefits outweight the costs. If your goal is the halfway point in a logarithmic scale though, then that is one thing the 12TET does better than any other tuning system. It pretty much nails it.

Even in just intonation the point at which these particular intervals (compared with the P5 and M3) are so far down the line they are practically irrelevant. Though I certainly wasn't clear about that.
Si
#19
Quote by sn7221
The tritone in 12edo is slightly off from the harmonic series but it's close. The minor third only shows up if you use the theoretical undertone series. But it's "implied" by the overtone series.

As for the naming convention, Schoenberg actually wanted to use "pantonal" which is probably closer to the truth.


Wrong on the first three counts. The first "tritone" is exactly half way between 12edo 4 and #4. The next octave contains a TT very close to 12edo. I believe thats also the octave the minor third appears in. What you have to understand is, the HS literally goes on forever. Every 12TET and other other distance from the octave is within it

Also, the undertone series is not theoretical. Certain dunes and desert landscapes will produce an undertone series via the wind blowing across the land scape. Robin Hayward plays a tuba which plays 1/64th tones chromatically, and the fingerings are based on both under and over tones

^Not irrelevant though. For instance, the music of Wolfgang von Schweinitz
Last edited by bassalloverthe at Oct 22, 2014,
#20
Quote by bassalloverthe
Wrong on the first three counts. The first "tritone" is exactly half way between 12edo 4 and #4. The next octave contains a TT very close to 12edo. I believe thats also the octave the minor third appears in. What you have to understand is, the HS literally goes on forever. Every 12TET and other other distance from the octave is within it

Also, the undertone series is not theoretical. Certain dunes and desert landscapes will produce an undertone series via the wind blowing across the land scape. Robin Hayward plays a tuba which plays 1/64th tones chromatically, and the fingerings are based on both under and over tones

^Not irrelevant though. For instance, the music of Wolfgang von Schweinitz


Maybe I just didn't convey what I meant exactly. I meant that nothing in the overtone series is exactlyequal to the tritone, even at very high harmonics. The equal-tempered tritone would have a frequency of 2^1/2. The square root of two is irrational and therefore has no fractional representation. So no possible ratio generated by the overtone series could ever by the same frequency as the tritone in 12edo. The Pythagorean tritones come close as do two other 5-limit tritones. These are 45/32 and 64/45, neither of which are in the second octave.

The overtone series may go on forever, but there is no representation of an irrational number using a ratio of two other numbers by definition. It doesn't matter how far you extend the series.

I only said the undertone series is theoretical because there are some well-respected people in academia as well as musicians who have made this claim. It's not universally accepted and people are still arguing about it.
Last edited by sn7221 at Oct 23, 2014,
#21
Quote by sn7221
Maybe I just didn't convey what I meant exactly. I meant that nothing in the overtone series is exactlyequal to the tritone, even at very high harmonics. The equal-tempered tritone would have a frequency of 2^1/2. The square root of two is irrational and therefore has no fractional representation. So no possible ratio generated by the overtone series could ever by the same frequency as the tritone in 12edo. The Pythagorean tritones come close as do two other 5-limit tritones. These are 45/32 and 64/45, neither of which are in the second octave.

The overtone series may go on forever, but there is no representation of an irrational number using a ratio of two other numbers by definition. It doesn't matter how far you extend the series.

I only said the undertone series is theoretical because there are some well-respected people in academia as well as musicians who have made this claim. It's not universally accepted and people are still arguing about it.


My point is that there is a TT close to 12TET tritone in one of the lower octaves though. And my other point is that 12TET is an adjustment of the HS, not the other way around
#22
Quote by bassalloverthe
My point is that there is a TT close to 12TET tritone in one of the lower octaves though. And my other point is that 12TET is an adjustment of the HS, not the other way around


Fair enough, I'm just being pedantic at this point
#24
I tend to be into feel music.

That is all the musicians that are playing are listening closely to one another and playing tastefully.
#25
Quote by Jehannum
For simplicity, let's look at melody before harmony.

One thing that I think is real is resolution. You can get a definite sense that a melody has ended at its tonic or key note. Whether this is intrinsic in music or culturally-based / learned doesn't matter at this stage.

What about major / minor? The quality of the interval a third above the tonic does have a big effect. But a melody could be made that used the minor third and the major third in equal amounts. It might sound odd, but to me this indicates that the third is just like any other interval. It's just more common to stick to one or the other throughout a piece of music. Does this justify there 'really' being major keys and minor keys, or is it just a compositional convention?

As for modes and scales, aren't these all just examples of favouring some intervals more than others?

As I see it, only the tonal centre has any reality outside of convention and nomenclature. Things such as mode names, scale names, and even major / minor are just short-hand ways of describing the intervals used in the piece of music in relation to the tonic.

Most tunes don't use all possible intervals; the subset that are actually used will flavour the melody. When you use mode names, scale names etc. you aren't forbidding any deviation from a strict set of notes but simply describing overall flavour. Nothing more meaningful than that, so no need to get too pedantic about it.

This point of view would surely render many of the arguments we see in MT forum invalid, or at least purely semantic.


Different strokes for different folks. I'm sure lots of people will disagree.

But I agree with you. This is how I think (if I'm, consciously thinking about) when writing a melody. It just makes sense to me to neither over-analyse, nor restrict. I am aware of what kind of basic flavour I want to impart (to mainly guide note choice), but I'm definitely not wedded to absolutely sticking with a given scale 100%, unless that suits the music I'm writing, or is too out of place for the genre being written for.

But I also think consciously, and a lot, about melodic phrasing, or rather what phrase(s) I want to use first (as in humming a rhythym), and then later populate it with notes ... this breaks me out of some old habits and cliches, and helps me find more structure to the tune.

cheers, Jerry
Last edited by jerrykramskoy at Oct 30, 2014,