Science Forums

# Music And Mathemathics

## Recommended Posts

:lol:

I thought so, but notice there are functions that gives SOME of the values: f16 for instance!

Perhaps all values are given by a composed function: C= f+g+...? (cearching for C)(Originally i named the searched for function Q)

Can C be made continious as well? Can we then see what f1 and f0 should be?

I cant help observing that some turtles work with lightning speed:)

i have just started working with the programming language python, but i'm not up to snuff to program this. maybe one of our programmers will take an interest. ;)

perhaps there is some composed function, but this irregularity looks all too familiar. makes it all the more interesting to me i must say.

as to 0 & 1 they have no meaning in this context as i said. at best you might say 1 has 0 steps, but as far as music goes, what good is 1 note? i'm off to root up some grub; will check in later. thnx for the exercise. :thumbs_up

• Replies 60
• Created

#### Posted Images

Theres been real progress today, perhaps some summing up?

(1) I start by forming (the set?) 1234567.

That actually is done by selecting 1 and the successor funktion S and...

(Peanos work wasnt much appriciated in the beginning...thanx Peano :)

To begin is to select something. There must be two things the selector and the selected:

Perhaps no beginning can consist of only one thing (but didnt this entry begin with the one thing "T"? Yes but together with "T" was #19). Perhaps big bang cant have been only a single point? Perhaps thats the reason we cant understand absolutes? Any absolute bottom must be binary? For any x to exist there must be a not-x not identical with x?

Im not prepared to make a complete list of absolutes to select particular absolutes from,I will only raise the question if there is a musical absolute, and point out that a mathematical absolute is the set of all sets.

Why am I thinking this possible nonsense?

Hmmm... because thats what this thread is for! Tthoughts on Mathematics and Music are welcome in here :)

(Tthoughts ha ha, theres some funny errors I do I havent the heart to edit them out they might have been consciously put there by my subconscious)

2 Having our beginning set we can (following Cantor) form the set containing all ordered sets with seven elements and select from it: we have two selections

cdefgab and roebvir

There is a basic operation that turns the scale cdefgab into the chord ceghdfa... A scale is used to play melodies on one at a time and a chord is all notes played at once...

if by scale is meant natural numbers and if chord is amount then the musical meaning so far is...eh ...somewhat equivalent with the mathematical meaning (puh) what the case is with colours i will leave as an exercise...

3 applying the basic operation again we come to tonality:

and here the semantic wiew gets hard...It will take time to explain why the third member defines tonality... Also: "tonality" maybe is an even larger concept it aint certain that all tonalities can be derived this way (puh2)

Simply put: the tonality consist of all the chords suited to accompany the melody gotten from the scale.

So this was what i came up with when i wondered what tonality is... I admit that the question doesn occure to ppl often and

the answere is not eagerly awaited for :)

##### Share on other sites

...

Why am I thinking this possible nonsense?

Hmmm... because thats what this thread is for! Thoughts on Mathematics and Music are welcome in here :)

:lol: we think because we can. i think the set of no notes is silence. i think the set of all notes is noise. likewise, i think the set of 1 note is noise. one can make all manner of noisiness of unity. you can pluck it prime, you can pucker it polygonal, you can pipe it perfect, but ya can't make it music. gödel gave us this little tune. (my paraphrase.) any internally consistent mathematical system is incomplete and any complete mathematical system is internally inconsistent. pythagoras' music of the spheres is a bubble pipe dream din. if you haven't already, i recommend you read gödel, escher, bach; an eternal golden braid and then follow that up with a dose of i am a strange loop. they got a good beat & they beat hemlock. :cup:

##### Share on other sites

Hi!

The first one I have and its good, the follow up i havent been able to lay my eyes on.

Did you read my fairytale? Trying to elucidate the concept of "nothing"

What should be analysed now is how meaning arises, the seven note scale has a meaning distinkt from the meaning of the ordered set of the first seven natural numbers, and the meaning of the translation to colours made by saxon.

(But its perhaps only a tangent to the job you and I did today :))

There! now i can temporarily leave #19

Now perhaps the question of finding the function temporarily called C.

Some of its values are the values gotten by y=xx

Damn... i cant write maths... Also our job wasnt really finished, i wanted the values up to 16 printed so I could study them again ...as far as i recall the semantic approach was a disappointment. Oh, i mean seeing the functionvalue and the steppingstones together. As i recall the twelvtone scale destroyed tonality and most chords disappeared. To see is to be sure, but it seems music comes from f7 not f12 as scoenberg works didnt prove. :)

I suddenly realise its significant that 7 is an odd number no even number should make the chord contain all notes of the scale to make f12 work perhaps some magic number should be added.

btw are there more interesting threads you started?(brb)

##### Share on other sites

Hi!

The first one I have and its good, the follow up i havent been able to lay my eyes on.

What should be analysed now is how meaning arises, the seven note scale has a meaning distinkt from the meaning of the ordered set of the first seven natural numbers, and the meaning of the translation to colours made by saxon.

(But its perhaps only a tangent to the job you and I did today :))

fairy tale? :shrug: i think i've read most of what you have writ, so yeah...i read it. :) by-and-large i have laid off numeric fiction, butt i dabbled it sum for the fun of exercsing artistic license. (have you seen the cost to renew one of those these days!!??? good grief!! :lol:) maybe you'll get a kick out of this completely arbitrary poppytrancecock. eyes and ears now! :Glasses: :phones:

ps distinct ;)

1=black=action

2=red=reaction

3=orange=emergence

4=yellow=cycle

5=green=growth

6=blue=interaction

7=indigo=balance

8=violet=choice

9=white=completion

(not on this graph, butt 10=charcoal=bullshit )

##### Share on other sites

fairy tale? :shrug: i think i've read most of what you have writ, so yeah...i read it. :) by-and-large i have laid off numeric fiction, butt i dabbled it sum for the fun of exercsing artistic license. (have you seen the cost to renew one of those these days!!??? good grief!! :lol:) maybe you'll get a kick out of this completely arbitrary poppytrancecock. eyes and ears now! :Glasses: :phones:

ps distinct ;)

1=black=action

2=red=reaction

3=orange=emergence

4=yellow=cycle

5=green=growth

6=blue=interaction

7=indigo=balance

8=violet=choice

9=white=completion

(not on this graph, butt 10=charcoal=bullshit )

Ah!

The music side on this question is hard to work through (who cares abut the circle of fifths)... i think i shall not try to go step by step ... ill do some composing instead:

Composition 1 BEADGCFA#D#G#C#F# (How to Feel Tonality)

Twelve chords one bar each say 6/8

at the end repeat from the beginning...Several times (Some musicians will really hate to play this piece because some chords rarely show up in normal business so eventual shortcomings will show) Listen to it and try to sing something along...

Notice something odd? Yeah you must, so to say, make a new start after ...say... three chords:)

We follow our innate sense of tonality which restricts the chords we expect to hear!

A question is: Can we write a melody that fits? Thats to say :is there a tonality here?

Since you havent experienced the effects of the chords ill wait with the melody... Instead ill cut the circle in half:

Use 8/8 but C and the last B is halved so the last sixth bar contain two chords...

There! As you sing along you notice the difference! now you can easily sing notes notes that fit the whole piece :)

Here is a melody: (better keep it simple huh?) (B)abbbabbb(E)g#bbbc#bbb(A)baaabbaa(D)bbaabbaa(G)gggabbbb©ccdc(B)bbbb

##### Share on other sites

you're welcome. as i say, i have next to zero musical training/ability so i'll have to leave all that business to others better versed. :note:

##### Share on other sites

I venture to guess that I have no more musical aptitude and education than Turtle, however, just to make sure we aren't being too eurocentric...

Instead of dividing the octave into 12 tones, the Arabic system is to divide it into 24 tones.

While we commonly use seven notes from the octave to make a scale, five note scales are very common in other parts of the world, and six note scales exist as well.

EDIT: While looking through the HyperPhysics entries concerning music, I found a humorous nugget under consonance:

When you define "consonance" as "pleasing to the ear", then of course you have to ask "whose ear?". You can get into such intense debate about what is "pleasing" that some have come to define music as "sounds organized by human beings" to accede the endless variety.
Edited by JMJones0424
##### Share on other sites

I venture to guess that I have no more musical aptitude and education than Turtle, however, just to make sure we aren't being too eurocentric...

Instead of dividing the octave into 12 tones, the Arabic system is to divide it into 24 tones.

While we commonly use seven notes from the octave to make a scale, five note scales are very common in other parts of the world, and six note scales exist as well.

EDIT: While looking through the HyperPhysics entries concerning music, I found a humorous nugget under consonance:

As "the host" in here I welcome your interesting entry

First: Only INTEREST in Music and/or Mathematics is needed to qualify for making entries in here,

you dont have to personally being able to sing or add...There is help to be found if your contributions need it :)

Second: My own study in here IS progressing (but slowly), my hypothesis

perhaps is that "tonality" is defined in a certain way from the selection of the scale.

Your contribution needs the hardworking turtle to work f up to f24 ...

Also implies the question how to handle different scales with the same size...

AND introduces the concept of "Consonance"... Well Done! Thanx!

Third: We need able Intellectual Musicians interested in Harmony Theory to appear... All I can do is pray

PS Thanx for updating your posts.

##### Share on other sites

Hi!

...

btw are there more interesting threads you started?(brb)

by-the-by. better to make new posts for afterthoughts than to edit them into older posts. i've learned the edits often go unread. ;)

hello again. yes...>> synergetics: explorations in the geometry of thinking

...Second: My own study in here IS progressing (but slowly), my hypothesis

perhaps is that "tonality" is defined in a certain way from the selection of the scale.

Your contribution needs the hardworking turtle to work f up to f24 ...

...

here's f(24). (please check all my work; i've been known to err.)

f(24)=11

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

1 3 5 7 9 11 13 15 17 19 21 23 2 4 6 8 10 12 14 16 18 20 22 24

1 5 9 13 17 21 2 6 10 14 18 22 3 7 11 15 19 23 4 8 12 16 20 24

1 9 17 2 10 18 3 11 19 4 12 20 5 13 21 6 14 22 7 15 23 8 16 24

1 17 10 3 19 12 5 21 14 7 23 16 9 2 18 11 4 20 13 6 22 15 8 24

1 10 19 5 14 23 9 18 4 13 22 8 17 3 12 21 7 16 2 11 20 6 15 24

1 19 14 9 4 22 17 12 7 2 20 15 10 5 23 18 13 8 3 21 16 11 6 24

1 14 4 17 7 20 10 23 13 3 16 6 19 9 22 12 2 15 5 18 8 21 11 24

1 4 7 10 13 16 19 22 2 5 8 11 14 17 20 23 3 6 9 12 15 18 21 24

1 7 13 19 2 8 14 20 3 9 15 21 4 10 16 22 5 11 17 23 6 12 18 24

1 13 2 14 3 15 4 16 5 17 6 18 7 19 8 20 9 21 10 22 11 23 12 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

##### Share on other sites

Turtle is not infallible??? Gaahhhhhhhhhhhhhhhhh!

To what other use should this entry be put? Hmmmm

Perhaps I should explain why the mystical signs "fx" etc occur?

On the mathematical hand theres yet not much more than a beginning exercise on ordinal numbers: 7 in particular...Right?

On the musical hand we see f7 as the naturally given Major Scale and we aim to see what results can be got by applying methods on it :)

And lets forget about the nth hands temporarily...

I think us musicians will skip the numbers... translating them to notes or names of notes is necessary.

Well then , ordinary Harmony Theory skips the story of how all notes of the Major Scale can be derived from a single note...eh... tone! (Its a better chance that story be found in...say...a book on guitar repair)

And starts with determining the intervals of the scale... in other words: The elements of f7 can all be found at irregular intervals in f12 and f24.

Isnt it amazing if this "irregularity" really can be traced back to the playing of one note?

Thats to say a single wave in air recieved by the ear!

If so, why cant this irregularity likewise be traced down to a single lightwave?

And is it really true that...say... f24 cannot be derived in the same way? :blink:

PS Ive named the continious (and universal?) function im hunting for :C ...Of course its suppose to be a joke but i sinCerely cant remember where i thought the speed of light enters into music?

PPS Dont worry turtle Ill check your work in minutest detail, I expect to be be finished around the end of eternity.

##### Share on other sites

Turtle is not infallible??? Gaahhhhhhhhhhhhhhhhh!

To what other use should this entry be put? Hmmmm

Perhaps I should explain why the mystical signs "fx" etc occur?

On the mathematical hand theres yet not much more than a beginning exercise on ordinal numbers: 7 in particular...Right?

On the musical hand we see f7 as the naturally given Major Scale and we aim to see what results can be got by applying methods on it :)

And lets forget about the nth hands temporarily...

I think us musicians will skip the numbers... translating them to notes or names of notes is necessary.

Well then , ordinary Harmony Theory skips the story of how all notes of the Major Scale can be derived from a single note...eh... tone! (Its a better chance that story be found in...say...a book on guitar repair)

And starts with determining the intervals of the scale... in other words: The elements of f7 can all be found at irregular intervals in f12 and f24.

Isnt it amazing if this "irregularity" really can be traced back to the playing of one note?

Thats to say a single wave in air recieved by the ear!

If so, why cant this irregularity likewise be traced down to a single lightwave?

And is it really true that...say... f24 cannot be derived in the same way? :blink:

:lol: you wax poetic. anyway, you liked my graph. that was f9 and i didn't 'splain it so's you could play/sing it. a few have tried musicalizing it, or some variations, but you might like a turn. :xparty: so, this is a "power" series graph and it's for f7. (mod 7 mathematized) the ugly details aside for the time beat, you can see what you see of the numbers/colors/notes as you want to see them musically/tonally/noteally. the entire block of colored & numbered cells repeats endlessly (to the right & down in the graph) i do have f12 i think if you want, but i don't think i ever took it to f24. i also have f7 & f12 for a "polygonal" series (very pythagorean!), a multiplicative series, and an additive series. i may have some of these out to f(17). let me know...they go for \$17 each. :lol:

oh... kp(f(7))=6

i hope you like how many ones you get. :D

anyway, mystical katabatak powers f(7). :Whistle: ?

##### Share on other sites

Gods in heavens! What monster have i let loose in here... :doh:

I stand corrected its not only the concept of ordinal numbers on display its also number theory among other things in the form of modulo 7: Ill return to bed , pull the blanket over my head and dream of successors saving me from the impossibly long nightmare awaiting around the corner.

##### Share on other sites

I just opened the thread Mathematics and Music in the music forum!

Hopefully musicians interested in Harmony Theory will arrive, claiming to have no mathemathical ability...

We will help them there wont we?

##### Share on other sites

Well then , ordinary Harmony Theory skips the story of how all notes of the Major Scale can be derived from a single note...eh... tone! (Its a better chance that story be found in...say...a book on guitar repair)

And starts with determining the intervals of the scale... in other words: The elements of f7 can all be found at irregular intervals in f12 and f24.

Isnt it amazing if this "irregularity" really can be traced back to the playing of one note?

Thats to say a single wave in air recieved by the ear!

If so, why cant this irregularity likewise be traced down to a single lightwave?

And is it really true that...say... f24 cannot be derived in the same way? :blink:

It's imperative that I repeat again my previous caveat. I really don't know what I'm talking about at all. However, this discussion has piqued my interest in the mathematical underpinnings of music, and I might have come across the answer to some of these questions. Most of this (including the images) can be found directly in HyperPhysics

How is a scale constructed from a base tone?

Take any tone of frequency n, small integer ratios of n will sound more consonant. (the reference point is usually 440 Hz, corresponding to A4) To increase pitch, multiply by the ratio, to decrease pitch, divide by the ratio.

2:1 octave

3:2 fifth

4:3 fourth

5:4 major third

6:5 minor third

*Who the hell came up with this nomenclature?

The circle of fifths, a pentatonic scale, is therefore completed-

source

Notice the gaps between D and F and also between A and C. These are filled with the semitones E and B to complete the standard heptatonic scale. Add in semitones between the five whole tones and you end up with the twelve tone chromatic scale. Arabic music further divides this again into quartertones to end up with 24 total tones. Most every scale is composed of 5, 7, or infrequently 6 of these tones.

It should be noted that this ends up with irregular spacing between the tones, measured in cents. Five cents is generally the smallest interval detected by the human ear. There are different temperaments, which are different strategies for "fudging" these variations in order to normalize the scale and make transposing to different keys easier.

source

Why is all of this different for sight?

The easiest answer is that sound and electromagnetic radiation, while both can be measured in frequencies, are not the same. Sound is an oscillating wave of pressure through a medium. Light is a stream of wave-like (and equally particle-like) photons. EM radiation does have harmonics which comes into play. I am most familiar with this in regard to radio waves. Antennas generally need to be constructed so that they are at least 1/4 wavelength, and need integer length ratios (1/4, 1/2, 1, 2, etc.) Otherwise interference arises from out of phase waves. Transmitters usually have to be designed to suppress unintended transmission on harmonic frequencies. This was especially a problem with older analog cellphone towers that broadcast around 800-900MHz being picked up on civilian band 400-450 MHz radios.

Next step, channel my inner Waterhouse and build a pipe organ computer :phones:

##### Share on other sites

Surprise Surprise: Questions in here gets answers! :weather_storm:

So theres something special with f5 , is it the entry point? f12-f7=f5 ! (look at a piano f7 is white f5 is black)

I think it will take me some time to assimilate this (Damn busybodies forcing me to work for an understanding! Bah!)

First result of (argg)work: cdfga, first result of c, is not in itself part of the circle of fifths, if so the notes should be ordered like this: fcgda.

Whenever possible, use small letters for numbers/notes and big for chords. Might as well write out the circle of fifths,

tons of students have stared at it with blank faces wondering what it is all about: F C G D A E B F#C#G#D#A# -_-

Ordinarily the chords is put like a clock with "C" as number twelve and i refuse to consider if there is some deep

alfabetological secret behind that.Instead I beg the wolves in this thread to stop howling and get me a picture.

Now an exercise for those of musical ineptitude: seek out a piano and play the black, and only the black tangents (here i perhaps should warn mathematicians that "tangent" as used here has nothing to do with curves) go ahead and smack them in any order...you can even try more than one at a time... Sounds surprisingly good huh? Now do the same with the whites... Which colour wins? f5 or f7?

##### Share on other sites

Gods in heavens! What monster have i let loose in here... :doh:

I stand corrected its not only the concept of ordinal numbers on display its also number theory among other things in the form of modulo 7: Ill return to bed , pull the blanket over my head and dream of successors saving me from the impossibly long nightmare awaiting around the corner.

let me correct you. :lol: i wasn't asserting modulo 7 -or any other modulo n- is related to harmonics, i was/am asking. can you/do you -et al?- get any sense of your musical intuitiveness tingling when you look at the graph, or is it dissonant for/to you?

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.