# Need help from someone who knows physics and music theory



## sammyooba

My questions might be a bit weird or difficult, but if you know, please share your knowledge. Also, I'm not good at explaining things especially explaining my question as I am so into atonal music that I am not coherent, so please ask for clarifications on the confusing areas.
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I realize that in music, there are keys to want to resolve to other keys. For example, In C major, the first chord (if it is a major chord)
is C-E-G. C, E, ...and G are the stable keys. If I were to play D,F,A, or B, it would sound unstable and want to resolve to one of the
stable keys - c, e , or g. For the minor version of that chord, it would be C-Eb-G, and those would be the stable keys.

I remembered, very faintly, from my physics class, (not exactly sure how to term this, maybe wave intereference?) waves happen on every other levels. 
I think this picture might have to do with what I faintly remember lol. http://en.wikipedia.org/wiki/File:Double-slit_experiment_results_Tanamura_2.jpg

Do you think that this wave property has to do with the unstable and stable keys we see in music?
I believe those stripe patterns, where the electrons hit, are the stable points.

So -

If there is, What is the mathematical point of view on these stable and unstable points in music? I want to calculate which hertz, from the root, 
is the most stable points.

And I think those stable points are the "bridge" of a chord which brings me to another question that I think is related to the above.

What is the scientific definition of a chord? Or the mathematical method of creating a chord. I know this one might be somewhat subjective but by chord, I mean harmonically stable chords, meaning playing only the stable keys from the root (4 mini steps, 3 mini steps for major chords from the root position)(3 mini steps, 4 mini steps for minor chords from the root position) 
--
I think the general concept of a chord is - playing every 2 steps from the root to play the chord,
but something that has always bugged me is the 7 chord in major or 2 chord in minor. 
It is diminished which sounds very unstable compared to all the other chords. Most likely, this chord is the worst place chord to end a music with because it won't sound like it ends.
I wonder if this is an error in how the scale is tuned or if there is a better rule to follow than the
'playing every 2 steps from root' rule.

For that reason, instead of using that method to create chords, I just, from the root point, play the stable pitches.

What I am looking for, if there is, is the 4th stable point of a chord. For example, for the chord C-E-G-?, what's the next stable point?

I know that most would say B, but I think there might be something better than B since B wants to resolve to C, and for my case, I'm looking for harmonically stable chords. Harmonically as in, peaceful and peaceful things are not wobbly (unstable) but rather - stable, and beautiful, like every chords are except for the 7 in major and 2 in minor.

Usually, my chords follow the following pattern (C) ROOT (E) 25% from root (G)50% from root (C)100% from root.
--
I'm thinking 2 cases - either there's no 4th stable point (but then, what is with the huge gap between 50% and 100%?) or standard piano tuning cannot play the correct hertz to play the 4th stable point. 
--

Well, the next % in the pattern is 75% which would A# is closest and in this case; however, when played, it sounds like nature or asian music which doesn't sound perfect enough to me. And it doesn't sound perfect enough to me because E-G-A# create a diminished sound within that chord. Also, A# doesn't sound too stable, at least to me.

However, if someone knows more about physics and the math of these concepts, please share what you know and how, if there is, we can calculate where the 4th stable point is, or just how these stable points are affected by differently pitched waves. Or any ideas on how wave intereferences may affect the creation of scales 
root and root times 2 gives us an octave, with an infinite number of pitches in between; however, we only play a limited number of keys to create a scale. How can physics explain this better?


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## Argus




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## mmsbls

I'm not sure I fully understand everything you are asking, but I can try to give you some of the physics behind notes, intervals and chords.

Sounds are simply changes in the air pressure. They consist of waves of regularly increasing and decreasing pressure. Water waves are similar in that at any given point the water surface will rise and fall periodically. All sounds are made up of these periodic waves of air pressure. The number of times the air pressure increases and decreases (oscillates) every second is called the frequency.

A musical note is a very regular set of sound waves made up of the lowest frequency wave and higher harmonics. The harmonics are just waves with frequencies that are integral multiples of the lowest frequency (i.e. two, three, four etc. times the lowest frequency). The A above middle C has a frequency of 440 oscillations a second (or Hz). Its harmonics have frequencies of 880, 1320, 1760, etc. Hz. When an A is played, you hear all of these harmonic waves as well as the lowest frequency wave.

The most consonant interval (2 notes) is the octave or A plus the next higher A. Two notes an octave apart have frequencies exactly a factor of 2 apart. The A two above middle C has a frequency of 880 Hz. The relationship between their frequencies is very simple. In fact, every harmonic of the A two above middle C is also a harmonic of the A above middle C. All the waves "match" very well.

The next most consonant interval is the fifth. The ratio of frequencies between the notes of a fifth is 3/2. The ratio of frequencies of a fourth (also very consonant) is 4/3. The third's ratio of frequencies is 5/4. An octave has a ratio of 2/1 (or 2). Note that all these have frequency ratios that are fractions made up of small integers (i.e. not 113/34). Notes that are related to each other by the simplest (in the sense above) ratios of frequencies will sound "nice" together. The C E G chord is made up of a third and fifth which both sound "nice". The reason they sound "nice" is related to your point below.



sammyooba said:


> I remembered, very faintly, from my physics class, (not exactly sure how to term this, maybe wave intereference?) waves happen on every other levels.
> I think this picture might have to do with what I faintly remember lol.
> Do you think that this wave property has to do with the unstable and stable keys we see in music?
> I believe those stripe patterns, where the electrons hit, are the stable points.


The picture you mention is a standard example of wave interference (unusual to some because it implies that electrons are actually waves, which is somewhat true). When two or more waves meet they will interfere. The amplitude (e.g. height of a water wave) of the waves will add together. If one wave is at its maximum and another at its minimum, they will cancel each other as along as the amplitudes of the waves are the same (this is the principle behind noise suppression headphones). If the two maxima meet, they will enforce each other.

The important point is that waves with ratios of frequencies made up of small integers will have an interference pattern that repeats much more frequently than waves with ratios of frequencies made up of larger integers. In this sense they are more "stable" and less varying. This makes them sound "nicer". This point is difficult to describe in words, but this website has some nice video along with sound http://www.animations.physics.unsw.edu.au/waves-sound/interference/. See especially 7.3 and 7.4 on the right hand side where it says "play".


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## petrarch

sammyooba said:


> I realize that in music, there are keys to want to resolve to other keys. For example, In C major, the first chord (if it is a major chord) is C-E-G. C, E, ...and G are the stable keys. If I were to play D,F,A, or B, it would sound unstable and want to resolve to one of the stable keys - c, e , or g. For the minor version of that chord, it would be C-Eb-G, and those would be the stable keys.


You can't really speak of "stable" keys. As mentioned by mmsbls, it's all a question of how distant the ratio between base frequencies of two notes is ("distant" here in the sense of how simple the ratios are). You can more or less talk about consonance and dissonance, but it is all relative. Consonance (or degrees thereof) are mostly a convention and tradition more than anything else. There was a time when thirds were considered dissonant.

More generally, music is about tension and release. In tonal music, there usually is a frame of reference that is established from the outset (e.g. C major); the piece then moves to other degrees, more or less distant from the first one through modulation; and at the end it typically returns to the same one that opened the piece. This creates an arc, a sense of closure and consistency.

This movement is based on the exact same principles that make up a chord. The most stable point is unison (1/1), followed by octave (2/1), followed by fifth (3/2), etc. However, too much stability is boring. The music becomes uninteresting.



sammyooba said:


> What is the scientific definition of a chord? Or the mathematical method of creating a chord. I know this one might be somewhat subjective but by chord, I mean harmonically stable chords, meaning playing only the stable keys from the root (4 mini steps, 3 mini steps for major chords from the root position)(3 mini steps, 4 mini steps for minor chords from the root position)
> --
> I think the general concept of a chord is - playing every 2 steps from the root to play the chord,
> but something that has always bugged me is the 7 chord in major or 2 chord in minor.
> It is diminished which sounds very unstable compared to all the other chords. Most likely, this chord is the worst place chord to end a music with because it won't sound like it ends.
> I wonder if this is an error in how the scale is tuned or if there is a better rule to follow than the
> 'playing every 2 steps from root' rule.


The rule "playing every 2 steps from the root" is a bit of a simplification. There are rules (rather, conventions) for more complex chords and that involve all degrees of the scale. There are also rules on how to "end a music"; sometimes composers really want to leave things in suspension.



sammyooba said:


> For that reason, instead of using that method to create chords, I just, from the root point, play the stable pitches.
> 
> What I am looking for, if there is, is the 4th stable point of a chord. For example, for the chord C-E-G-?, what's the next stable point?
> 
> I know that most would say B, but I think there might be something better than B since B wants to resolve to C, and for my case, I'm looking for harmonically stable chords. Harmonically as in, peaceful and peaceful things are not wobbly (unstable) but rather - stable, and beautiful, like every chords are except for the 7 in major and 2 in minor.
> 
> Usually, my chords follow the following pattern (C) ROOT (E) 25% from root (G)50% from root (C)100% from root.
> --
> I'm thinking 2 cases - either there's no 4th stable point (but then, what is with the huge gap between 50% and 100%?) or standard piano tuning cannot play the correct hertz to play the 4th stable point.
> --
> 
> Well, the next % in the pattern is 75% which would A# is closest and in this case; however, when played, it sounds like nature or asian music which doesn't sound perfect enough to me. And it doesn't sound perfect enough to me because E-G-A# create a diminished sound within that chord. Also, A# doesn't sound too stable, at least to me.


You see, when you have a chord built from root, and then 25%, 50% and 100% from root what you have is really a dominant seventh chord. In fractions, you built a chord stacking up notes every 1/4, i.e. root (1/1 = 4/4), third (5/4), fifth (3/2 = 6/4) and minor seventh (7/4). The next 1/4 is the octave (2/1 = 8/4). Such a chord typically resolves to the root a fifth below, according to common practice. In other words, C-E-G-Bb resolves to F-A-C (voice leading considerations aside).

Using ratios like this gives you a good sense of the relative consonance and dissonance of an interval. However, you have to keep in mind that equal temperament doesn't use these perfect ratios (though they are a good approximation) and that typical acoustic music instruments have more complex harmonic spectra--in other words, any one note from an instrument is itself a "chord", a superimposition of several pure frequencies, so that when you play many notes simultaneously you are actually reinforcing certain harmonics of the instrument's own timbre.


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## haydnfan

To the OP, the discreteness of notes has very little to do with the double slit experiment.

The discreteness of notes is due to the discrete frequencies allowed for standing sound waves in a pipe, that is what you're thinking of. The wave travels through the pipe, reflects and comes back. If you want the open end to be a node (where the pressure wave is zero) only certain frequencies allow this (it has to do with how long the wave is before it repeats, you want it to repeat in the same place after going through the pipe and back).

Read this link for a detailed explanation: http://hep.physics.indiana.edu/~rickv/Standing_Sound_Waves.html

Violin strings work in a mathematically analogous manner.


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## sammyooba

Thanks for the inputs. I figured out at last what tonality really is, probably.

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"Its harmonics have frequencies of 880, 1320, 1760, etc. Hz. When an A is played, you hear all of these harmonic waves as well as the lowest frequency wave.

The most consonant interval (2 notes) is the octave or A plus the next higher A. Two notes an octave apart have frequencies exactly a factor of 2 apart. The A two above middle C has a frequency of 880 Hz. The relationship between their frequencies is very simple. In fact, every harmonic of the A two above middle C is also a harmonic of the A above middle C. All the waves "match" very well.

The next most consonant interval is the fifth."
----

I continued this pattern adding 440s and seeing which music notes show up most frequent. Most frequent was Root(A), then 5th(E), third(C#), then G, B, etc..

I then convert them so that their in the same octave and I get pretty much the major scale but not as precise in the decimal areas. 

Is there a pattern similar to this that would create a minor sounding pattern? For example, the 3rd from the root A would be C and not C# kind of pattern.

And are minor chords/relationships just as stable as major chords are?

--

And concerning whether a chord is a major or minor in a scale,
- How do we determine what 'emotion' the chord has? For example, why is the third chord in major a minor chord or why is the 7 chord diminished. Did someone just say so or was this based on some mathematical property?

I think I have the answer and it has to do with stability. Playing the black keys would result in frequencies out of range of what are within the harmonics of the root; and consequently, losing tonality or stability; but in return, gaining tension to keep the music alive and not dead with 0 tension/dissonance. So even when the 3 chord in a major scale by itself wants to naturally resolve to a major chord, it actually resolves to a minor chord in the context of a major scale to maintain stability and tonality, I think?

---
And..
Is there a reason why the A key on the piano is the only key whom's frequency is a whole number while every other note has decimals and fat numbers? Was the layout on the piano based on the note, A?


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## Vor Gott

This all does have to do with waves and interference, but of course not the wave-particle duality that is the cause of that specific experiment's result. For instance, C and another C an octave higher are related in the ratio of 1:2 in their frequencies. This means that, ideally, the lower C would reinforce the higher C's wave every other time. In reality, there is a regular repetition of _some_ pattern (e.g., a wave at the end of another every other time). The mathematics behind pitches is this equation (note that 440Hz is to account for the arbitrary absolute frequencies that we use):

f = 2^(n/12) x 440 Hz

where n is steps from A4 (negative if downward). Therefore the relationship between the notes in a C major chord (actually any major chord, but only after simplifying) is the ratio:

2^(-9/12) : 2^(-5/12) : 2^(-2/12)

for middle C and simplified a major chord gives the ratio:

(^12√2) : 5(^12√2) : 8(^12√2)

(the twelve root of two, etc.). There is nothing surprising about this mathematically when we look at it this way, but the steps as values are more unique: 1, 5, and 8. C to E is four, and E to G is three. What becomes apparent is that the middle key is on the higher of the two middle pitches in a major chord, but on the lower for a minor chord. They are related in how they approximate the trisection of a set of eight pitches.

However, if you want to treat the relationship as a function, then the next note could be two steps above G - the note A. Perhaps it is one four steps above G: the seventh, B. I believe that the simplest answer would be the seventh, but because the cords seem simply to skip every other note in their respective keys. The scales themselves are seemingly arbitrary: whole whole half whole whole whole half (for major keys). You can see that the dominant is the only other place in the key where the chord follows the same pattern. Interesting, but not what you were talking about.

This just occurred to me: the double-slit experiment has to do with individual things interfering with each other even after the previous one has stopped. Perhaps hearing these notes at different times could produce the same effects when the brain reflects upon the previous phrase as a coherent whole. This might not be what you initially meant, but it certainly reflects the experiment in question!


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