- Home

The new tonal music system

This HP mainly deals with the definition of tonality. However, my definition on tonality is quite different from that of western music system in that tonality here means color. In other words, my music system deals with the elements of sounds that make people feel color such as brightness, darkness and so forth. I am pretty sure that this is a brand new idea and you have never heard of the similar kind of music system. However, I do not intend to reveal my secret here but I would like to mention how this system works by showing some examples.

In my music system, tonality can be classified into only three parts, that is, major, minor and others. And there is no atonality in my music system. Even though quarter tones are used, still they are in the realms of tonalities though they produce bizarre effects. In my opinion, no matter what composers do, it is physically impossible to escape from the boundary of tonalities. Moreover, the characteristic of each tonality is that while major and minor can have the end, other tonalities cannot have the end and moreover, while major and minor are consonant, other tonalities are dissonant. There are reasons for those claims but I would like to avoid explaining their reasons since they have something to do with my secret. Instead, I show you how this concept on tonality can be applied to constructing chords and chord progressions.

My HP mainly deals with how to make chords and chord progressions. They should be produced mathematically, namely, by computer calculation. Otherwise, it is often too difficult for humans to create good chords or chord progressions.

The ultimate purpose of this music system is to construct the computer-based music system which can deal with all kinds of music by analyzing frequencies of sounds and translating them into the music language, and thus provides composers with the maximum possibilities of chord progressions which can be placed on melodies.

Giant chords

You can listen to some examples here.

Look at this score. Obviously, this chord is chaotic, what I mean is that this chord contains lots of tonal elements in an irregular way. From a western music point of view, this chord can be classified as atonal. However, this chord contains lots of elements of the minor tonality which make people perceive dark and pathetic color. So, change the position of each tone in a way that elements other than minor are hidden and the elements of minor tonality come up.

Then, I get this chord. This chord cannot be played backward, if you do so, this chord becomes chaotic. For this reason, I will explain later.

Likewise, this is a chaotic chord but it contains lots of elements of minor tonality. Extract the elements of the minor tonality from it.

Then, that chord changes to a minor chord. It cannot be played backward too.

In the same way, change the position of each tone

to this. Then, It changes to a reasonably consonant minor chord.

This is my favorite chord. Change the position of each tone

to this. This minor chord function as Dominant and tends to move to Em.

New video

Thus, even though chords are not dependent upon major/minor scales, it is possible to make chords as consonant as chords based upon major/minor scales. The above examples imply the fact that even though the instrument is played randomly, it is possible to reconstruct it and make consonant chord progressions out of it by computer calculation. By the way, the reason why I made minor chords many more than major chords is that elements of the minor tonality are more abundant than those of major chords and therefore easier to make. The minor tonality is richer in color and varieties. With regard to the major tonality and the minor tonality, it is often assumed that the major tonality is based upon the natural harmonic series and therefore natural. On the other hand, the minor tonality cannot be derived from the natural harmonic series and therefore artificial. However, supposing that the minor tonality is artificial, it is impossible to explain the fact that the minor tonality, irrespective of people's culture and language, gives people pathetic impressions. In my opinion, the frequencies of sounds which should be categorized as the minor tonality, along with the major tonality, are abundant in nature. Normally, people cannot notice those frequency to be the minor tonality, however, if they are extracted like the above examples, they can change to reasonably consonant minor chords. You may think that the minor tonality has something to do with minor scales, but minor scales are just part of the much bigger system "the minor tonality". (The minor tonality here means completely different from what is called the minor tonality in the western music system sense.) And it is possible to make zillions of those beautiful chords out of the abstract concept of "tonality".

Incidentally, is it possible to make consonant motions by using all twelve tones? Well, still it is possible to make consonant motions. Look at this. This is a major arpeggio. Because all dissonant elements and elements of the minor tonality are excluded, though this arpeggio contains all twelve tones, this sounds consonant.
However, this arpeggio should not be played fast, if you do so, dissonant elements will come to surface and this arpeggio sounds no longer consonant.

This is an interesting comparison. If this scale is played slowly, this does not sound consonant at all. However, if this scale is played fast, this sounds even more consonant than a major scale despite the fact that this scale contains all tweleve tones. This scale gives people the impression that each tone sounds clearer and brighter than C major scale.

You can check how those arpeggio and scale sound from the below.

Another chord which includes all twelve tones is here.　The last chord is the one. It is so consonant that without being told you can hardly notice that fact I suppose. However, in the last chord I made a small mistake that is against the rule of dissonance. Never mind.

In contrast to those chords, the arpeggio or the scale, this chord is close to a pure minor chord which contains few elements other than minor and therefore this chord can be played backward.

If the above minor chord is inverted, it changes to a major chord like this. Thus, it is possible to say that the structure of minor chords is paralell to major chords and vice-versa.

As you can see, if you invert a minor chord, you can make a major chord and vice-versa. (But not always!)
But be careful. Although major and minor are structurally paralell, dissonant elements are not. Here are examples.
This is a minor chord and the place where dissonance occurs is C#.

Retrograde this chord, then, there is no place where dissonance occurs. However, elements of the major tonality affect the chord and therefore the entire chord becomes unstable.

Moreover, invert this chord, then, we get a major chord and the place where dissonance occurs changes to C.

Furthermore, invert and retrograde the original chord, then, it changes to a major chord and there is no place where dissonance occurs.

Thus, unlike elements of major/minor tonalities, tonalities outside major and minor do not have the parallel structure. As I claimed above, all chords can be categorized into three tonalities (major, minor and others) and there is no place where chords are categorized as other than those three. Although the proof is necessary regarding why all chords can be categorized so, (There is the mathematical reason for that) because it has something to do with my secret I cannot show you its proof here.

To summerize what I have discussed above, regarding the structure of each tonality, they are as follows:

1) If major chords are inverted, they become either minor chords or chaotic chords.
2) If minor chords are inverted, they become either major chords or chaotic chords.
3) If tonal chords other than major and minor are inverted, they become chaotic chords.

Additionally, "chaotic" here means chords that have all kinds of tonal elements in an irregular way.

Supposing that the above hypothsis is correct, it is possible to prove that in terms of sound, atonal songs are completely chaotic and not different from playing the piano at random. For this reason, with the method of tweove tone technique, it is simply impossible to exclude the elements that should be defined as major and minor tonalities. If that technique is used, its tone row, in most cases, will contain all tonal elements in a chaotic way. And that is the reason why there are very few atonal pieces which are considered to be a master piece. Atonality means nothing. Indeed, it succeeded in escaping from the boundary of tonality in terms of concept in the sense of the western music system. However, what if concept on harmony that dodecaphonism is based upon is not correct? In my opinon, dodecaphonism is the biggest mistake of composition in 20th century music. How can theories that cannot explain the minor tonality well (though there are some theories to explain minor chords theoritically such as Neo-Riemannian theory but not successful) deal with things more complicated than the major tonality and the minor tonality?

By the way, if there are tonalities outside major and minor, is it possible to use those to write a song. My answer is "yes". And to my surprise, songs written by tonalites other than major and minor are beautiful (though this depends on people's taste) and not chaotic like so called "atonal songs".

However, the drawbacks of using tonalities other than major and minor are that if songs are written by tonalities outside major and minor, songs are completely lacking in the dynamism. How do they sound? Well, if you image a whole tone scale or a diminished chord where each tone sounds equally, you can guess how they sound. Image what if a song is written just by the whole tone scale or the diminished chord only. That is one drawback to write a song by tonalities outside major and minor. If so, why can major and minor have the dynamism? Well, it has something to do with the reason why major and minor can end a song but other tonalities cannot.

The other drawback is that controlling tonalites other than major and minor is very difficult. For that reason, the influence of the major tonality and the minor tonality is so strong that it is a feat to escape from those influence. Although it appears that dodecaphonism has succeeded in escaping from the boundary of the major tonality and the minor tonality, the fact is that in terms of sound, it never achieves that goal. I can see that songs which are written by twelve tone technique contain plenty of elements that should be categorized as the major tonality and the minor tonality. In other words, in terms of sound, songs written by tweleve tone method sounds exactly the same as playing the piano at random. I leave its judgement on whether my claim is correct of not to readers. Please judge so by listening to chords and chord progressions based upon my tonal concept.

Moreover, the other difficulty to control tonalities outside major and minor is that it seems that without taking quater tones into account, it is impossible to control tonalities outside major and minor due to the method of the instrument tunning. It is only the computer that can achieve that feat but human mind can never do. Unfortunately, tonalities outside major and minor are my biggest secret and I cannot show you examples. Sorry about that.

So much for harmony, I would like to move to music modulations.

Unfortunately, with the advent of atonality, the major tonality and the minor tonality have tended to be thought of as "obsolate" or even "valgur". However, natural and beautiful music modulations can be made by avoiding tonalities other than major and minor. Therefore, to deal with beautiful music modulations is the same as dealing with tonalities other than major and minor, in other words, dissonant elements. Thus, dealing with the major tonality and the minor tonality is neither out of date nor valgur. Now, let's move to the music modulations

Regarding music modulations

Regarding dissonance, it is, in my opinion, the matter of comparison. What I mean is that if the progression from C to C#m is compared with the progression from C to F, it is obvious that the former one is more dissonant. If somebody claims that both progressions are equally beautiful, its claim is the same as claiming that minor 2nd is as consonant as perfect fifth. Then, the entire music system theoritically starts to collapse. Therefore, in order to create a good music system, it is necesarry to defince consonance and dissonance in a strict way.

Regarding dissonance occuring in chord progressions, it seems that musicians tend to think that dissonance in chord progressions has something to do with distance in each tonality. However, in my opinion, that assumption is wrong. The reason why the chord progressions such as C to C#m are more dissonant than chord progressions such as C to F is not because of the distance of each tonality but because of the effect of tonalities other than major and minor. The same thing can be true of well known dissonance in chord progressions such as consecutive perfect eighth and consecutive fifth.

If so, supposing that inserting one chord which does not cause tonal sound other than major and minor into between C and C#m, it is, in theory,  possible to find chords which combine C with C#m in the most consonant way.

Thus, its equation is as follows:


                                                                                   C ----------- X-----------C#m

You can see the list of all chords which can be placed in X in NEXT PAGE. Each tone is described by the number like C=0, C#=1, D=2 and so forth.

Let a computer (I use MATLAB for this calculation) choose the most consonant chord which can combine C with C#m amongst the list of all chourds above, then, a computer chose the following chords as the most consonant ones. You can listen to the actual sound from here. Btw, "CM to F#M" is my mistake. "CM7 to F#M7" is correct. Sorry about that.

This is a bit similar chord. In this case, it is impossible to omit D# because D# creates M7. If you do so, you get a progression more dissonant than M7 (><)

And two more similar chords produced by MATLAB. You may notice that all chords here are just the derivatives of the chord below.

This progression is inferior a bit.

They are the most consonant chord progressions in the case of the modulation from C to C#m according to my own calculation. If you would like to prove my music system to be wrong or just pseudoscience, all you have to do is to find a better one amongst the list of chords. However, I am afraid that you cannot do so.

However, just as there are not always solutions in mathematical equations, so are not always good solutions in music modulations.

For instance, regarding the following equation

C#m-------X---------C

There is no good solution though there are several possibilities.
This is one of the chords my computer (MATLAB) chose.

Athough in terms of dissonance this chord has almost no problem, it is simply lacking in the force to move to C. This fact means that
there is simply no good solution. In that case, there are three other solutions.

1) Let tonalities other than major and minor occur in the modulation in a way that dissonant elements are not so conspicuous.

2) To find suitable chords amongst chaotic chords which can be changeable to consonant chords like the above examples.

3) To extend the modulation.

I choose 3 as a solution here. Unfortunately, 2 is a kinf of transcendental way of music modulation and my computer programming cannot deal with that so far.
(But of course theoritically that transcendental way of music modulation is possible. It is just the matter of calculation)

In that case, the easiest one is C#m----D-----G-----C. However, this is a progression that anybody can come up with. Moreover, that chord progression is not so stable due to its context. So, I would like to show you an unusual and good one that composers can hardly come up with.

Here is one of the solutions that my computer creates.

Because MATLAB calculates all possibilities to combine two chords, it often comes up with the bizarre ideas that human mind can hardly do. These may be good examples.

Those are just examples of how my modulation system works. It is possible to make thousands of similar chords. You want to know how to make those chord progressions? Sorry, it is a secret. And even though I reveal my secret here, without a computer programming, it is very difficult and painstaking. As for me, I, the innovator of this system, took 3 hours to come up with just one modulation from C to C#m. And to be frank with you, I made so many stupid mistakes before my friend made a computer programming for me. Now, it is time to show you more examples.

The above example is about how my system works. But in practice abusing modulation is not a good idea at all, because although each connection is consonant, as a whole, music becomes chaotic like the above. So, if you want to compose a consonant song, just use, though this is very boring, chord progressions based upon major/natural minor scales like old classic music.
(But be careful. chord progressions based upon a major scale are not always consonant. A good example is C to Em.)

Consonance and dissonance by context

It is the well-known fact that music context affects whether people feel consonant or dissonant. I show you some examples. Although C# to G is a dissonant progression, if you play C-C#-G-C, C# to G no longer makes you feel dissonant. On the other hand, although C to C# is not too dissonant, if you play G-C-C#, C-C# becomes dissonant. Because C# to G is in the C major realm, it becomes consonant? Well, kind of. But its reason is more complicated than you think. For example, C# augment is a kind of the combination of C# and F. So, if F or C# is substituted with C#aug, is that progression consonant? Well, let's play it.

You know, that sounds (>_<) What I mean is that dissonance is not so simple, especially the above case.

About how to end the progression

In blues, (though I am not familiar with blues at all) , an unusual progression which is forbidden in the western
harmonic system is often used. That is C-G-F-C like this.

What is problematic from a point of view of the western harmonic system is why this progression, despite the fact that Tonic and Dominant are put opposite, makes people feel the end of the progression a little bit. Well, its reason is easy.
In my opinion, it is not just accident that people prefer to use that progression. There is the reason for that. However, it has nothing to do with the assumption that something like Reverse Overtone Series which is likened to Imaginary numbers occurs to our mind and thereby people feel F-C to be the end, and moreover minor chord has something to do with that. Does this mean that when we listen to major chords, we hear the actual sound and when we listen to minor chords, we hear imaginary things though it is true that minor chords and major chords are kind of opposite in terms of structure? So what makes the above progression special?

It is, in my opinion, context that makes you feel end the progression. I can show you a progression that has the similar effect of C-G-F-C. That is, C-G-B-C-G (Just ignore consecutive fifth)

That is my answer regarding why C-G-F-C is musically acceptable. But the difficulty to treat the above things is that it is very difficult for a computer to recognise those phenomena.

Harmonization

How do we use those chords or chord progressions in composition? Well, for instance, this is the first phrase of "Melody" composed by Kajiura Yuki.

Harmonize it, then, I get this. This is a sort of crazy example. You can listen to it from here.

Another crazy harmonization. This melody is, of course, E minor but a chord starts with G#m. However, because it modulates to E minor quickly along with its melody, this does not sound too bad I think.

The limitation of this system

Although this system is quite good at dealing with things that everybody shares irrespective of their background, this system cannot deal with things that people do not always share. (Though it is very difficult to define the boundary beween what everybody, regardless of their background, always share and what everybody does not always share.) For instance, this system can never tells you why some people like Bartok's dissonance whereas others do not. What this system can do is just to calculate enormous amount of numbers for several minutes and indicates that the degree of dissonance in this progression is high/low and so forth. In other words, this system can never appreciate great composers' works. Therefore, although you can produce many beautiful chords with my music system, just making thousands of consonant progressions never guarantees you to create a good song at all. (That is the main reason why I cannot put my song in my HP. I am a kind of person whose mind never produces good melodies and therefore desparately try in vain to rely on numbers to compose something. I supposed that if I could only construct a good music system, I could be a Chopin. But I have to admit that it was my biggest mistake (>_<) Terrible~! ) If you rely on this system too much, even though this system enables you to make thousands of consonant chord progressions, chord progressions that you made sound like the same, especially when you stick to consonance, and that bores people. Although my music system is a sort of good gyroscope to help you to lead to the place where you want to go in the deep sea of 12 tone world, it is you who have to decide where to go.

Incidentally, I do not regard my music system as merely a tool for composition. This is my art that can connect numbers to human feelings.

Further development

In my opinion, my music system can be likened to Wright Brothers'plane. What I mean is that my system is very rudimentary. It requires much more development.

This system has huge potential. What sort of potential does this system has?

1) New music. In theory, this system can be applicable to any scale/harmony. But of course it is necesarry to change music system according to the frequencies of sounds. My music system I present here is, of course, set according to 12 tone-based music system and therefore not applicable to others. Supposing that I would like to use 13 scales in two octaves, I have to completely change my system though the basis must be remaind as the same. In all probabilities, it is possible to create a much bigger calculation system which is applicable to any scale/chord, in short, Great Unified music system.

2) New Music software. This is definitely possible. However, my music system is not sophisticated enough mathematically to put good harmonies on melodies as music arrangers can do due to the complexity of the relationship amongst harmonies, melodies and mentality. I need further development here.

3)Applying this system to twelve tone method. But how? To put consonant/dissonant elements in a way to make people feel that there is a regurality in consonance/dissonance along with strictly following the rules of twelve tone methods. Then, it is, I think, possible to avoid chaotic sound peculiar to dodecaphonism. But 3) is not my interest at all because my concept on tonality conflicts that of the western music system.
What is my concept on tonality anyway? Well, it is a secret. Please guess. I have already given you lots of clues!

Unfortunately, I am neither engineer nor psychologist and further development seems to be beyond my head. However, I strongly believe that this system is not something that will be completely forgotten and lost with me though it seems to be very tough to find an able one who can appreciate something that appears completely new and bizzare to him/her. (><) However, my dream is that this music system has been passed from generation to generation and many composers are willing to use this system when they compose songs. And what I need is the help of people who can appreciate my music system!

Lastly, although I completely avoid explaining how to compute to create the above chords/chord progressions because of a business reason, because they were created by strictly following the law of consonance, dissonance and 'root', I hereby would like to make what I have written here together with things I posted on YouTube the proof that I am the very first person who discovered that law that has something to do with consonance, dissonance and 'root'.

That is all. Thank you very much for your time to read my HP.