Composition and Theory


#61

@Brogner

OK…I’m horribly stuck on pages 5 through 9.
I simply cannot make complete tangible sense of what he’s outlining.

I completely understand the ratio fractions from the Pythagorean formation that he’s using, but I cannot make any sense of the relationship that he’s trying to show me in this segment. I tried moving past it in hopes that it would eventually make sense given further details, but that didn’t happen. Instead, it just left me feeling like I wasn’t getting things fully given that I didn’t properly digest this segment, so I went back and re-read it three days in a row repeatedly and I still have no fucking clue what the hell he’s trying to communicate.

The series of digits being infinite, we have to limit it arbitrarily. The limiting number we call index. For our purpose the index 16 is sufficient. Proceeding, then, to divide the string successively by the numbers 2 to 16, we obtain the following series:
1/1 ( C), 1/2 (C2), 1/3 (G2), 1/4 (C2), 1/5 (E2), 1/6 (G2), 1/7 (Bb2), 1/8 (C3), 1/9 (D3), 1/10 (E3), 1/11 (F#3), 1/12 (G3), 1/13 (Ab3), 1/14 (Bb3), 1/15 (B3), 1/16 (C4)

This part I’m fine with.

We write a series on graph paper, in one line from the left to right, using one square (inch or centimeter) for each tone, and next proceed to multiply the string by the same series of digits.

No clue what he means by this. I understand the words, but the meaning is about as evasive as if you just told me that “we are energy, so harmony is found in resonant oneness”.

Now of course we cannot actually multiply the string, but we can imitate the results by using a little trick. That trick is made available through the special quality of one of the intervals we have found, namely, the octave. The octave of a tone, although being a different tone, is a sort of identity, so much so that indeed we call it by the same name. Hence tone relations may be transposed by octaves. Consequently we may begin our multiplication with 1/16 instead of 1/1, simply indicating the octave signatures of the notes we would obtain if we started with 1/1. The experimental series will thus run: 1/16, 2/16…16/16; the intended series: 1/1, 2/1…16/1.

I have, again, no clue what he’s driving at here. I don’t see how the octave is helping here. We’re just running the series forward and backwards numerically.

Given that I understand his nomenclature to mean that 1/1 ( C) is where we start and that 1/2 (C1) is an octave from 1/1, then 1/16 (C4) would be multiple octaves up, not one.

This is a problem I have with him, in general. He’s not clear on his terms, definitions, nor nomenclature. He just whips out the series (for example) without bothering to explain what the hell his shorthand means, and then builds off of that series as if the meaning of the shorthand was understood, without taking any steps to assure that the reader is following along properly with his train of thought and the way he thinks in his personal world.

Anyway…we move on with him running the opposing series, which he arbitrarily calls the “intended series”, again with no explanation as to what the hell that means. Because to me, if you arbitrarily call one series the “experimental” and the other the “intended”, then I’m going to understand you to mean that the first exists purely for the purposes of getting the second, and that the first is not of interest, nor will be used. However, that’s not what he’s doing. So I have no clue what the hell he’s meaning here.

I’m assuming that the “intended” is basically the “negative” series and the experimental is the “positive series”, but he doesn’t use these words because these are clarifications made after him by others.
Anyway…

The result is the following series:
1/1 ( C), 2/1 (C1), 3/1 (F3), 4/1 (C2), 5/1 (Ab3), 6/1 (F3), 7/1 (D3), 8/1 (C3), 9/1 (Bb4), 10/1 (Ab4), 11/1 (Gb4), 12/1 (F4), 13/1 (E4), 14/1 (D4), 15/1 (Db4), 16/1(C4)

Now, this is where I seriously begin to doubt my understanding, because we’re going backwards from the first series (“experimental”), but we’re still increasing what I understood to be the octave nomenclature identifier (the number after the lettering).

The reason I have a major confusion over this is if I follow this logic using wavelength (which is equivalent to a string length for these purposes), then if I run the “experimental” series, we’re fine.

We start at 2109.89 cm wavelength for C0 and end on 131.8~ for C4 and arrive at the same notes along the way in the sequence, and in the right octave for the nomenclature supplied.

HOWEVER
If I then apply this same logic to the “intended” series, I get an ENTIRELY different result.
If I start at 2109.89 cm, I will get the exact same series of notes from the “intended” series as I would from the “experimental” series.
If I start at the other end of the spectrum and start at 8.24 cm, then I will also get the same series as the “experimental”.

But Levy writes out the following note sequence instead as his result:

C, C1, F2, C2, Ab3, F3, D3, C3, Bb4, Ab4, Gb4, F4, E4, D4, Db4, C4

Whereas if you follow the fraction sequence, which ultimately just ends up being a multiplication by the first number because 2/1 is … 2, etc…

Then you get:

C, C1, G2, C2, E2, G2, Bb2, C3, D3, E3, F#3, G3, Ab3, Bb3, B3, C4

Take 2109.89 as your starting wavelength, put that into excel and follow the below:

|Fraction||Decimal|Wavelength|
|---|---|---|---|
|01|01|01|2109.89|
|02|01|02|4219.78|
|03|01|03|6329.67|
|04|01|04|8439.56|
|05|01|05|10549.45|
|06|01|06|12659.34|
|07|01|07|14769.23|
|08|01|08|16879.12|
|09|01|09|18989.01|
|10|01|10|21098.9|
|11|01|11|23208.79|
|12|01|12|25318.68|
|13|01|13|27428.57|
|14|01|14|29538.46|
|15|01|15|31648.35|
|16|01|16|33758.24|

What you’ll get is this:
image

If you take that and convert those ridiculous wavelengths back out, then you’ll get the same run as the “experimental” and not the “intended” series.
(note: I’ve renumbered the octaves to follow Levy’s seemingly “relative” approach to applying octave nomenclature…see comments below about this.)

So I’m entirely lost as to how the “intended” series is supposed to be used.
That’s not even counting that the number sequence for octaves is even more confusing because we’re still going UP in octave count in the “intended” series, but applying the fractions to length you would be going DOWN in octave…not up.

I can only assume he means these octave numbers, then, to mean “away from”, not directionally relevant - though that’s not stated so I have no real knowledge of his intended meaning here.

You can even make this easier by using Hz and reversing the operation.
Instead of multiplying the original starting value (2109.89) by the next fraction (2/1) to get the next (4219.78) wavelength, you can divide the original starting value in hertz (16.35) by the next fraction (2/1) to get the next Hz frequency (8.175).
This gives you the same result as the waveform, but in hertz, which is easier to check since most resources don’t go about listing notes in wavelengths, and most often the ones that do require you to also set a parameter for the air density in question (FYI, when attempting to run vanilla, use Air as the medium at around 20 degrees Celsius - that’ll give you “lab” conditions…more or less).

So this whole section immediately starts to make less and less sense to me the more I try to make sense of it.

That’s to say nothing of the diagram on page 8, which…honestly. I haven’t the FAINTEST idea what the hell he’s attempting to show in meaning with that diagram.

So, yeah…any help you can offer me in understanding what the hell this section is actually attempting to convey, or where I’ve gone horribly wrong would be MUCH appreciated!

Cheers,
Jayson


#62

So.

This is how I take it…

This is a guy sitting next a single string tone producing object. Open it is tuned to C1. He moved his little slide up and down to adjust the pitch of his sting. He begins moving his slide in the ratios mentioned above… And he obtains the overtone series.

That part is easy and makes senses.

Then when he gets to the ratio size of 1/16 (C4) he I assume stopped because I don’t think you could accurately go any higher (I really don’t know) and turns around.

So what he is saying is… that because C1 and C4 are the same tone just (his little trick) octaves apart. He starts on C4 and flips the ratios. (He would get the same test result starting on C1) however C1 is the lowest possible tone his string can make while in open position.

How does that seem so far


#63

I will say his over use of the word senarius does agitate me a bit. I even googled it and it left me more confused.


#64

And then he talks about how the typical view of a minor chord is that it is a “disturbed” major chord.

He says that the major third is found in the over tone series… so it makes sense that it is part of the major triad. The major triad is considered consonant.

The minor triad is considered consonant too however. Levy I think is making the argument that because the Minor third is not found in the over tone series, that there is no logical way the minor third can be considered consonant, and instead should be considered dissonant.

But the minor third does feel consonant, but how if it is not found in the over tone series?

Answer… undertone series.

The minor third is a major third from the faith of the chord.

So talking about C

There are 2 notes located a major third away from C

Those two notes are Ab and E

There are only two notes located a perfect 5th away from C

those two notes are F and G

F minor is what we call one chord and C Major is what we call another.


#65

Basically what we call “minor” chords are really major chords built backwards.

That is is reasoning for “minor” chords sounding consent, because again the minor third is not found anywhere in the over tone series and he asks the question, how far can you flatten a third before it becomes destroyed. Why does the minor third work when a sharpened third doesn’t sound consonant

His reasoning is the idea of undertones


#66

OK, that lines up.
Jesus!

Would it kill the guy to explain his nomenclature and terms?
All of this confusion was because he used “C4” twice in two very different meanings. In the “experimental” he meant that C4 was literally C4, while in the “intended” he meant that it was C4 IF we flipped the string backwards entirely and considered higher notes as lower octaves and lower notes as higher octaves…that C0 now becomes C4 and C4 becomes C0.

Or, heaven forbid, he could have just fucking used regular octave notation for the “intended” series so that instead of writing:

C, C1, F2, C2, Ab3, F3, D3, C3, Bb4, Ab4, Gb4, F4, E4, D4, Db4, C4

He could have very well just written:

C4, C3, F2, C2, Ab1, F1, D1, C1, Bb0, Ab0, Gb0, F0, E0, D0, Db0, C0

And saved a shitload of frustrating confusion.

So that clears that issue up.

THANK YOU!!



Now, I still haven’t the faintest idea what the hell he’s trying to show with that damn diagram with seemingly arbitrarily assigned degrees of strings on it.

I get that it’s a grid of both series crossing each other, I get that.
However, he entirely loses me on what the strings running across it are showing us, or how we determine our angle of any given string, or determine what thing we cross along the way should we care about…when along the string’s path across the grid is it meaningful?

He explains it, but again…his command of language is…convoluted at best.

edit: OH FOR FUCKS SAKE! No wonder! He’s fucking Swiss! That explains everything! lol

Cheers,
Jayson


#67

Yeah, he just means “the first 6”…again, going for the absolute most obscure way of conveying that idea possible…even for the 60’s era at the height of his musical prowess.

Senarius does mean a grouping of six in Latin, but damn man. What’s wrong with just saying sextet?
Or even easier…since you wrote it out anyway

The so-called senarius , comprising the first six ratios…

Why not just NOT write senarius and just say, “the first six ratios”?
If you’re going to insist on defining senarius as a variable in your theory, perhaps…I don’t know…define it.

Saying, “The so-called senarius” doesn’t tell most readers that you are now defining senarius as what follows.
It usually tells readers that there already is a thing called senarius and that that thing, separate from this theory because it is “so-called” by people…since “so-called” means that…it means other people call it that conventionally…it doesn’t mean you made up a definition for a variable… - anyway, that that thing, senarius, is some other thing containing six musical items and that you are exposing some property of it containing six ratios . It also assumes that the readers are familiar with this senarius as a common term.

But since none of this is the case, it just leaves the common reader confused.

It would at least gone a long way if he would have just written,

“We will call the first six ratios senarius, meaning a group of six…”

Copy that gold leader! Everyone follows!

If I wrote a science paper the way he writes, I’d be skinned alive!
Even reading Niels Bohr’s papers were easier going than this, and that man is terribly convoluted and stuffed up. Hell, Paul Dirac is practically a walk in the park next to Levy’s articulation, and Dirac is so eccentric that you question his understanding that he exists in this reality at times.

Jesus, TELSA is easier to read than this guy, and Tesla is by far one of the most convoluted people I’ve ever had to dig through because he REALLY and quite earnestly didn’t care if you understood what he was writing or not. If you didn’t; that’s your fault, tough shit. He didn’t want to write that down anyway, you should just piss off and get out of his way because in asking him to write it down, you’re slowing him down.

Cheers,
Jayson


#68

@Brogner

What do you think about breaking off into a new thread just about negative theory?

That way if someone comes along later and would be interested, they don’t have to crawl through a thread of general chatter to find pieces.

Because this is going to be a long conversation, I can tell.

Cheers,
Jayson


#69

I just honestly hope I am right lol, and I am just assuming that to help me connect all of the dots but it makes sense right?

Yeah I think you nailed it here, he doesn’t “bridge gaps” very well leaving people like us going WTF?

Okay you just shed some light on this for me… LIFE SAVER!

YES PLEASE


#70

I need math help

Could some one read these two pages and help me understand how the author gets the ratio 3:2 to describe a string divided 3 equal times.

The thing that gets me is that he describes 1 string divided in to 2 equal parts as 1:2, but when he divided 1 string into 3 equal parts it is 3:2


#71

I’ll read later - just waking up.
For now, this may help.
https://en.m.wikipedia.org/wiki/Pythagorean_tuning

Cheers,
Jayson


#72

A = 440Hz.
Open A string on the guitar has a 1:1 ratio with itself = 440/440
Fret it at the 12th fret and you divide the string in half = 880/440 = 2 = 2:1 ratio
Fret it at the 7th fret and you divide the string in thirds. 7th fret is an E with the frequency of 659.26. 659.26/440 = 1.498 so ~ 3:2 ratio. It’s the perfect fifth of A.


#73

Gotcha. Wish he would have clarified that better. And plus 3 : 2 is the correct ratio of a fifth above, however instruments and the tempered scale are not tuned perfectly. so the 5th is slightly flat.

Thank you


#74

Yes, if you played modern music with Pythagorean theory of divisional frequency ratios, it would sound like shit. Which is why you see Levy constantly doing things like noting that there’s no such note as a given result and then he therefore picks which frequency alignment he thinks best fits (granted, so far every check I’ve done on him when he does this shows that he picks the frequency that has the smallest distance from the actual frequency value obtained by the math - which is reasonable).

Also…it should be noted that his own symphonies which are composed using these methods are quite dissonant. Sometimes to a severe degree which really challenges the ear.

Cheers,
Jayson


#75

So I wrote out 2 chords

One sticking strictly to the overtone series

One sticking strictly to tempered tuning

Can you figure out which is which??

=)

The overtone series one I kinda had to rig and get as close as possible… unfortunately I don’t have a frequency generator


#76

I’m sorry, aside from the initial attack, which is incredibly brief, it’s almost impossible to tell that I’m hearing a chord with the sound that’s being used. After the initial fast decay and short release attack, the sound that follows sounds like a single note to the ear given the sample.

Cheers,
Jayson


#77

Lol, the first one is in tune to the overtone series and the second is in tune to the tempered scale. I can tell the difference. It’s not in the attack it’s in the sustain.

The first one will sound like a single note because it’s close in tune

The second one contains a tritone… surprised you can’t pick it out


#78

Yeah, all I’m hearing is basically a single tonal sound after the first half second.

Cheers,
Jayson


#79

Man I can here it clear as day… even on my iPhone speaker. O well


#80

I can hear the chord on the initial staccato strike. The sustained sound is where it drops.
If that initial strike held it would be easier.

Cheers,
Jayson