# New Scale, not based on the Octave concept.



## Domingo Gomez

Hi all,
I hope this video could be of interest to you:
It is about a new Musical Scale not based on the Octave concept.

---English Subtitles. HD---


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## pianozach

Oh, I don't have the patience to wade through all that. 

With all the charts and graphs it seems like he's trying to throw a conspiracy theory at us. 

Anyone else able to decipher this and boil it down to a paragraph or two?


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## Guest

pianozach said:


> Oh, *I don't have the patience to wade through all that*.
> With all the charts and graphs it seems like he's trying to throw a conspiracy theory at us.
> Anyone else able to decipher this and boil it down to a paragraph or two?


_*Verdad, macho!*_ I speak Spanish (it's my second native language) and the video is like treading through treacle.
I think there is one poster (recently banned/unbanned) who can probably give us a succint summary.


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## aritmo

**********************************************************************************************
*Video Description:*

*Time: 0:00 - 17:28 *
Brief description on all the myths and capricious decrees that supported "music theory" since the time of Pythagoras up to now, (of course, if we may use the words "music theory", because for consonance ideas to become a true Theory they must be founded on a solid scientific base, which has not been the case since the creation of the first musical scale).
Any musical scale must be constructed by the agency of a true Consonance Theory.
Difference between the pleasant effect of the Consonance of chords, and our particular preference for some melody and/or rhythm.
This video deals only with Consonance of chords which is a measurable physical phenomenon.

*Time: 17:28 - 21:14*
The importance of the interval 1-3 when compared to the Octave interval, when considering how to divide the whole dominion of sounds.

*Time: 21:15 - 28:37*
Description of the Modulator-Carrier equation for any two-sound chord.
Comparison between the chords 2:1 and 3:1.
How to estimate the number amplitude peaks of the resultant wave of any two-sound chord. 
More amplitude peaks and amplitude variations mean more effort and an unpleasant sensation for the ears.
Some brief comments on the Temporal Resolution and the Temporal Modulation Function. 
Comments on the Modulator-Carrier equation for chords with any number of sounds.

*Time: 28:38 - 33:34*
Brief description on the creation of a Dissonance Index based on the Modulator-Carrier equation, the number of peaks and amplitude variations (including the Modulation effect), as previously described.
Determination of the most consonant two-sound chords within the interval 1-3

*Time: 33:35 - 35:04*
The new Scale: El Tríplice.

*Time: 35:05 - End*
Final comments on other contents of the Book: 'Aulos. La Otra Luz. El Haz en Fuga'
End
**********************************************************************************************


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## aritmo

A new website with all the maths background for the new Music Scale, not based
on ancient myths and royal decrees but just on Consonance.

https://numbermusicrevolution.com
(Secured Site SSL)


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## BabyGiraffe

aritmo said:


> A new website with all the maths background for the new Music Scale, not based
> on ancient myths and royal decrees but just on Consonance.
> 
> https://numbermusicrevolution.com
> (Secured Site SSL)


The scale from your video exists in 31 equal division of octave (and others) (way more efficient size than corresponding divisions of tritave (3/1) that contain it). For example, you can stack in 31 equal a chain of major seconds or minor thirds or major thirds to get less than 31 tone subset that contains your scale.


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## aritmo

BabyGiraffe said:


> The scale from your video exists in 31 equal division of octave (and others) (way more efficient size than corresponding divisions of tritave (3/1) that contain it). For example, you can stack in 31 equal a chain of major seconds or minor thirds or major thirds to get less than 31 tone subset that contains your scale.


31 parts? 
why not 41, or 51, or 2631 parts?

I mean, If one divides the Octave in an infinite number of parts then one will span all the possible scales in this world, no matter the consonance of the sounds, however, that does not make any point, at all.

The point is that the new scale is based on a Consonance Index of two sounds as detailed in the video and the website, and can be expanded to span the Consonance Index of more than two sounds by using the corresponding Modulator-Carrier wave equation. This new scale is not based on any interval criteria, nor on any ancient myth or beliefs on the octave concept.
A music scale must be based just on Consonance as explained in the video.

The ancient concept on the division of the whole realm of sounds by using the octave is just a capricious myth, an ancient primitive belief that comes from ancient tribes including the european tribes. The primitive creed that a note is equal to its double is the most bizarre thing that happened to music since the beginning.

The interval 1-3 is the true perfect interval as scientifically explained in the video, the octave is just another modulated wave which is not perfect, at all.

2500 years of crude primitive myths, beliefs, creeds and royal decrees are not enough?

It is certainly the right time to release the music from all those old chains once and for all.


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## mikeh375

...all well and good aritmo, but is there any music we can listen to that uses this 'new music scale?'


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## BabyGiraffe

aritmo said:


> 31 parts?
> why not 41, or 51, or 2631 parts?
> 
> I mean, If one divides the Octave in an infinite number of parts then one will span all the possible scales in this world, no matter the consonance of the sounds, however, that does not make any point, at all.
> 
> This new scale is not based on any interval criteria, nor on any ancient myth or beliefs on the octave concept.
> .


The error is higher in 41, that's why. 51 is roughly the same as 31, so: no point.
53 (which is basically very well tuned Pythagorean scale) is even better than 31.
58 and 68 are roughly the same as 53.
72 is very close, I doubt anyone can hear any difference in practice.

Anyway, your musings about divisions of octave are funny.
Music is based on tempered scales for many reasons, but the most important ones are probably - transpositions (no need to retune the instrument, if you are going to modulate) and ease of performance. In addition, each equal division has its own topology, dictating the logic of chord changes and melodic motion.
Optimal divisions of octave are well known, so any scale that you generate with your equations will be well approximated as a subset in many of them (the smaller, the better, of course, for practical music composition and performance). Even division of octave for scales, optimal for inharmonic timbres (bell, marimba etc), can be easily found (still, again these timbres are problematic, counterpoint with such sounds will sound chaotic and they won't blend in a texture).

If you don't believe in the octave, you go into polytonal music territory, which is very dubious direction - mammalian auditory system is inherently biased towards octave-equivalence.


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## MarkW

Yes, but how does it actually sound?


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## Bwv 1080

MarkW said:


> Yes, but how does it actually sound?


Like that matters?

It is theoretically perfect, listening to it would only be a disappointment. All you would do is sit around and grieve that Beethoven or Bach were stuck with 12 more or less equal tempered half steps rather than the One Trve Scale


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## aritmo

Now I realized that there were some responses to my post that I have not seen, no problem, the truth has not rush, it remains always there like the drop of water that hits the rock. 
I am replying this particular post, however it spans all the others, it is not just oriented to a specific poster, and for that reason it is quite long, like “walking on grease”.:lol:

Apparently, you did not realize the meaning of my response.

You insist in arguing that the new Scale: Tríplice, is just another division of the Octave, or at least, it is contained by some known division of the Octave. 
And you are convinced of that , because you believe that any note is equal to its double, however, that is absolutely false , there is not any trace of scientific fundament on that.

Notice, that you shouldn’t consider this as a personal attack, at all, because that is not your fault, and I do not blame you for thinking in such a wrong way, not only because I am aware of the whole story on false statements, myths, creeds, decrees, crude primitive beliefs, and errors that have –in most cases intentionally-- plagued the music since its beginnings, 
say, since the times of the Sumerian tribes, 
but mainly because I am also aware that most modern textbooks on music theory DOES NOT show the resulting waves forms of any of the transposition chords that you mentioned and that they consecrate as valid --by royal decree-- in their superior expositions 
(let’s be more clear: In most Music Theory textbooks they do not show anything but just their dictatorial musical decrees and personal opinions), 
and as a consequence, 
their readers can not realize the truth: 
that the resulting waves of those transpositions are totally different from each other, and that there is not any particular relation between their amplitude peaks and their distribution, which is the source of what our ears and brains process. 

Of course, such fairly clear difference between those wave forms, just shout us out loud that the ancient myth that a note is equal to its double is totally false, just a myth.

Thus, no one has any right to state that just by dividing the Octave then you can obtain all the harmonies of the whole real of sounds, and consequently no one has any right to state that the Triplice is contained within any division of the Octave. 

I repeat: ANY NOTE IS NOT EQUAL TO ITS DOUBLE so the TRIPLICE is not contained or embraced by any division of the octave. And I am forced to repeat that up to the point of getting bored, because such primitive myth has been implanted in the brains of so many people, since so long time, to the extreme that it was finally converted into a kind of religious cult or sect.

On the other hand,
The new TRIPLICE is a new open concept, kind of an OPEN SOURCE CODE based on a Consonance Index that can be adjusted according to any new discovery that could be achieved in the Temporal Resolution or the Temporal Modulation Function fields. 
It is not the typical linear rigid rule that controls all those primitive scales, on the contrary it can be extended in other directions, even including the consonance of more than two sounds by means of the extended wave equation that consider the sum of more than two sine functions. More important, it considers the relevance of the ratio 3/1 before 2/1.

Actually, the values shown in the TRIPLICE were chosen according to a very specific consonance index, however there are more options to choose, and even that index can be made more or less restrictive. 

Thus, this is a new concept that does not prostrate before all those decrees from the European royal courts, that used music to dominate the rabble, plebs, and the inferior races of blacks and Indians, by imposing their “superiority” with a bunch of sophisticated falsities, wordy statements always using --to the point of exhaustion— the improper flashy-fancy words: “PERFECT FIFTH”, PERFECT FOURTH”, PERFECT, PERFECT, PERFECT,…, MAYOR, MINOR, COMMA, etc. ”, an endless list that have nothing to do with the main fundament of any scale which is consonance.

Another kind guy in this thread said: “If it is not broken, does not fix it”. 
Well, if someone consider that it was just a glimpse of PERFECTION to construct a scale by dividing the octave in twelve equal parts by means of a geometric ratio, and consequently substituting the rational value 3/2 of the ancient “sacred” PREFECT FIFTH and other notes, by using instead irrational approximations, 
just because King Frederick "the Great of Prussia" stated by royal decree that the noble Bach was right and consequently named him as the music principal assistant of the royal court, even against the opinion of many other musicians. 

If you think that that is PERFECTION, then I definitely think we have entered into the TWINLIGHT ZONE. (All pmusicians calling the note G as the PERFECT FIFTH, as faithfull servants of the King !, The Twinlight zone, indeed)


At this point, it really surprise me to see descendants of the people (black and Indians) that those kings and nobles used to call inferior races, nowadays holding in their hands instruments graduated with such bunch of ridicule and absurd ROYAL rules, and worst, they even singing "protest" and "antiracial" songs obeying the orders of the noble masters of their descendants, that imposed those scales.

That is just striking, mainly because they could easily construct their own true music scales (like the TRIPLICE) instead of continuing to revere, prostrate, praise and admire those that were the symbol of their domination, as well as so many crimes and abuses.

I hope no one will be offended by these true scientific statements. I understand that music scales became kind of religious cult, brain wash. Also hope no one gets surprised by my saying on: “royal decrees”, kings and nobles, because that is the true story, moreover, music scales were not only manipulated and used by kings to dominate what they considered inferior people, 
but also the Popes played the main role on all this, they contributed to throw a veil of mystery and religiosity to all those ancient musical scales and whoever dared to blaspheme against them would be burned by the Holy Inquisition.

Those old and unjustified airs of superiority inherited from those bizarre characters that tuled the European Royalty, as well as from all those fanatical religious manipulators, remain in our societies and social forums nowadays.

Finally in reference to the statement: “mammalian auditory system is inherently biased towards octave-equivalence”. 

That is not true, at all. 
Actually, nobody has a clear idea of what is really going on in the auditory system, __there are only theories and assumptions__, most of them biased assumptions like the one you mention, and the criteria adopted by some pros have been always contradicted by other experts, so please, do not issue sentences that have not been scientifically established. 


2500 years of royal and religious decrees in music, myths, creeds, abuses, manipulations and primitive beliefs, together with Bach's substitutions of what you all continue by calling "PERFECT" notes, is more than enough, indeed. 


Another guy said in some post something like this: 

“I do not have the time to watch it, mainly because it was like walking on grease”

Please, believe me, I totally agree with him, for that reason I later posted the chronology of topics! 
In the video and the book I find myself forced to waste most of the time explaining all the endless list of false statements, errors disguised with flashy names like: The Pythagorean and Ptolemaic Comma (which sounds much more important than the true name: CRUDE PRIMITIVE ERROR), as well as all the European arbitrary and abusive royal decrees, absurd creeds, and primitive beliefs that plagued the music scales till now.

However, to my surprise  most people consider all that stuff so boring only when the veil of those errors and myths is unveiled before their faces, and when some guy reacts against such bunch of creeds, however, when reading Music Theory books they seem to find so amusing and sublime to imprint in their minds all that trash as the most elevated achievement of the european superior race, just as many people did in sumerian times with their gods and their primitive religious cults or sects. 

The truth is that music has been tied to a bunch of crude primitive beliefs that unjustifiably restricts its true scope in terms of the variety of harmonies that can be achieved in the whole realm of sounds. 

The harmonies have been restricted by the whims and airs of superiority of an arrogant class, an abusive and racist coterie that for the first time in history have to face the resistance that never encountered before, thanks to the technological power that is available to a greater number of people today. 

This is the time to free the music from all those unjustified chains, once and for all.


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## aritmo

I know this is not easy to realize the truth, mainly when considering the whole history of music, the pope, the kings, the emperors, the monks and the holly inquisiton, as well as the diverse interests involved. However, that's it.
When you create a scale within the 1-2 interval, then you only have notes within that very specific interval, not more, not less than that. 

If you multiply your scale by 2, then you have another different group of notes (interval 2-4), which has a very specific relation with the notes from the interval 1-2, not more, nor less but just a very specific relation: The relativity in music.

Thus, if one plays a chord of 'n' notes in the former, and then multiply all those 'n' notes by 2, the new chord will sound similar to the former, and this can be scientifically proved by looking at the resulting waves of the chords, which shows similar peak amplitudes and distribution, just scaled.
That's all

Now, if within the interval 1-2 you find that the chord 4, 5, 6 is consonant, then
just because you multiplied one of those notes by 2, you have neither no scientific, musical, ethic, nor any moral reasons at all, to argue that from the point of view of Consonance the chord 8, 5, 6 is related, or similar, or valid when compared to the chord 4, 5, 6. 

If one insists that they are similar, or valid, or related, then one must prove that by showing up the resulting waves forms of each chord, just a I did in the video shown in this thread, like walking on grease  (a pretty simple task not found in almost all music theory textbook). As already said, the peak amplitudes and distribution between such transpositions have no relation at all.

As a consequence, you cannot argue neither that you can find all the harmonies, just by multiplying by 2 any notes from your scale within 1-2, nor that any division of the Octave brings all the possible scales that can be constructed in the whole domain of sounds. It is simply nonsense to read or hear such bizarre thing, however, we read this nonsense everywhere in the literature. 

In the same way, I have no reason to say that multiplying by 3 the notes in the Triplice Scale I will find all the harmonies of the realm of sounds. However, here resides the main difference between the new concept and the ancient Octave myth, because the new methodology based just on a Consonance Index, can be extended from the interval 1-3 to the interval 3-infinite, or any other chosen interval, what only really matters here is the stablished consonance Index. 
The fact that I decided to choose the option to repeat the interval 1-3 is just a matter of choice because of the relevance of the properties of the resulting wave of the chord 3:1 when compared to 2:1, and it has nothing to do with arguing that a any note must be equal to its triple, as has been done with the ancient primitive myth on any note being equal to its double.

A NOTE IS NOT EQUAL TO ITS DOUBLE


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## mikeh375

...but where's the music in order that we can listen and evaluate?


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## vincula

mikeh375 said:


> ...but where's the music in order that we can listen and evaluate?


My sentiments exactly. You can preach microtonality and then compose some music, so that we can hear it. You may or may not like what Jacob Collier does -to name one with a wider audience and appeal- but he certainly implements it. If you believe that you've discovered the truth or however you may label it, it's all just dandy. Just give us some music.

Regards,

Vincula


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## Domingo Gomez

The Missed Link and the Dark Side of Music. New Musical Scale


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## Monsalvat

I'm trying to understand how those of us used to the diatonic2/chromatic divisions of the octave are in the "twinlight _[sic]_ zone." I haven't watched either video; I'm skeptical enough that an "open source code based on a consonance index" is the next big thing in music theory. Music scales aren't brainwashing; I'm also intrigued to see racial theories invoked as a justification for this scale. "Any note is not equal to its double": what do you even mean by its "double"? Do you mean the note an octave higher than a given note? If so, then under most tuning systems, their waveforms are identical save for the frequency of the "double" being twice that of the fundamental. But it's hard to argue when the term "double" doesn't seem to be properly defined anywhere here. I agree with Post 9 completely.

The octave is a natural point from which to start dividing pitch. Even people with perfect pitch have been observed to struggle to correctly identify which octave a particular pitch resides in. This suggests to me that there is something fundamental about the way we perceive pitch, and how we react to the 2/1 (octave) frequency ratio. We can construct perfect fifths, etc. (truly perfect in the sense of Pythagoras, 3/2) and eventually build a Pythagorean scale built exclusively from rational numbers. But this is problematic when transposing (or even just modulating). So, for convenience, we approximate every semitone with the ratio 2[sup]1/12[/sup], the twelfth root of 2, so that the octave is truly perfect and everything else is "close" but imperfect. I can see why someone might object to this last step but it seems to me that the rest of it is straightforward. Of course, 2[sup]1/12[/sup] is irrational, unlike the Pythagorean intervals. But the octave's 2/1 ratio is preserved. 

It seems as if the thesis presented in this thread was that the 3/1 ratio was somehow more foundational than the 2/1 ratio. As an organist, who frequently uses these intervals in registrations, I can confirm that if I have correctly understood this to be the thesis, then this is nonsense. The 3/1 ratio changes the timbre (the "nazard": makes the note sound a bit more nasal) because it is essentially an odd overtone of the fundamental. C and G' (3/1) is very different from C and C' (2/1). It seems to me that it is perfectly reasonable to choose the octave as a starting place, and it seems like a more arbitrary choice to start from the 3/1 C/G' ratio. 

Again I don't see the need to invoke any racial theories; it detracts from what might otherwise have been a serious discussion about the merits or demerits of the proposed scale in this thread. The appeals to brainwashing and "myths" likewise make this whole thread sound like a big conspiracy theory: _they don't want you to know the truth about the octave_ or something similarly bizarre. I also second the notion that "if it ain't broke, don't fix it" and also second the idea that we would need some music written for this system to make a final judgement; in the absence of this music, it's ludicrous to suggest that we should abandon the diatonic and chromatic divisions of the octave and start anew. What an utterly bizarre thread. Fascinating to read but strange to contemplate.


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## Domingo Gomez

Monsalvat said:


> I'm trying to understand how those of us used to the diatonic2/chromatic divisions of the octave are in the "twinlight _[sic]_ zone." I haven't watched either video; I'm skeptical enough that an "open source code based on a consonance index" is the next big thing in music theory. Music scales aren't brainwashing; I'm also intrigued to see racial theories invoked as a justification for this scale. "Any note is not equal to its double": what do you even mean by its "double"? Do you mean the note an octave higher than a given note? If so, then under most tuning systems, their waveforms are identical save for the frequency of the "double" being twice that of the fundamental. But it's hard to argue when the term "double" doesn't seem to be properly defined anywhere here. I agree with Post 9 completely.
> 
> The octave is a natural point from which to start dividing pitch. Even people with perfect pitch have been observed to struggle to correctly identify which octave a particular pitch resides in. This suggests to me that there is something fundamental about the way we perceive pitch, and how we react to the 2/1 (octave) frequency ratio. We can construct perfect fifths, etc. (truly perfect in the sense of Pythagoras, 3/2) and eventually build a Pythagorean scale built exclusively from rational numbers. But this is problematic when transposing (or even just modulating). So, for convenience, we approximate every semitone with the ratio 2[sup]1/12[/sup], the twelfth root of 2, so that the octave is truly perfect and everything else is "close" but imperfect. I can see why someone might object to this last step but it seems to me that the rest of it is straightforward. Of course, 2[sup]1/12[/sup] is irrational, unlike the Pythagorean intervals. But the octave's 2/1 ratio is preserved.
> 
> It seems as if the thesis presented in this thread was that the 3/1 ratio was somehow more foundational than the 2/1 ratio. As an organist, who frequently uses these intervals in registrations, I can confirm that if I have correctly understood this to be the thesis, then this is nonsense. The 3/1 ratio changes the timbre (the "nazard": makes the note sound a bit more nasal) because it is essentially an odd overtone of the fundamental. C and G' (3/1) is very different from C and C' (2/1). It seems to me that it is perfectly reasonable to choose the octave as a starting place, and it seems like a more arbitrary choice to start from the 3/1 C/G' ratio.
> 
> Again I don't see the need to invoke any racial theories; it detracts from what might otherwise have been a serious discussion about the merits or demerits of the proposed scale in this thread. The appeals to brainwashing and "myths" likewise make this whole thread sound like a big conspiracy theory: _they don't want you to know the truth about the octave_ or something similarly bizarre. I also second the notion that "if it ain't broke, don't fix it" and also second the idea that we would need some music written for this system to make a final judgment; in the absence of this music, it's ludicrous to suggest that we should abandon the diatonic and chromatic divisions of the octave and start anew. What an utterly bizarre thread. Fascinating to read but strange to contemplate.


All you have said here is exactly the same the professor answered to the student in the video. You express yourself as the owner of the truth, with the same arrogance and prepotency that Bach's protector (The King) dictated his royal musical mandates. From all that you said, without any scientific proof, it is clear that you also think of yourself as the creator of laws and we must prostrate before what you say and mandate, so funny, indeed. Your music theory is not but a bunch of myths, lies, primitive beliefs, and royal mandates, that should be put in a paper bag and thrown at the pigs. In reference to what you contemptuously call "racial theories" those are not "theories" but HISTORY OF MUSIC and black-&-native people who until recently were never allowed even to step into a music hall because they could stain your sacred music scale. 
The contemptuous way you talk just corroborates what has happened with this bunch of primitive beliefs, and myths that have been used to manipulate, control and exploit people. The change is coming on and you will not be able to stop it.


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## mikeh375

again...are there any audio examples of this musical emancipation?
If one is to use scales like the one proposed in this thread then there still has to be organising principles, ie. theory, in order for composers to navigate the new aural fields and create something non random and cohesive. Given your condemnation of how music has evolved over the centuries and in particular, your social railling against theory, what theories/techniques of harmony, counterpoint and general composition do you deem suitable to use in this new sound world that do not invoke a racist sound or insult?


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