Music And Mathemathics

[sigurdV]

I can’t figure out how you’re generating these sequences, Turtle.

 

I get the sequences including most of yours by counting from 0 by (1 to B) modulo b – that is, with generator function

[math]a_{n+1} = ((a_n - 1 + i) \text{mod} m) + 1[/math]

Here are values for m = 1 to 16:

 1

 

What’s you algorithm?

 

Oh my!

Am I in deep ****?

Shall I explain or should I wait in the Queue? (A hint in the search for the uninteresting?

by sigurdV imagined continuous function Q)

Theese able guys REALLY scare me!

Returning from my latest gig in the lair of the wolves, i found my mind refreshinly clear

So what shall I do with it?

 

PS I like your new dress Turtle :thumbs_up

[sigurdV]

Why not explain some easy matters in order to exclude future confusions?(Notice I resisted "confunctions"!)

 

I dont know... Dr Fraud perhaps knows... how much time remains

until my "brain" again is invaded by "ghosts".

 

Meanwhile: I play guitar, since i dont play piano (sigh), so an ordinary book on Harmony Theory is a real disappointment to me! I do some composing and some ...ahem... original thinking

so i decided i needed help from qualified Mathematicians (and SHAZAM! there was Matematicians!!) Perhaps i can get some help after all in my writing a book...

SaY: "Harmony Theory" for Philosophers, Mathematicians and Musicians.

 

Your friendly sigurdV

 

PS BTW The function "Q" is named so because its the first element in "question"

[Turtle]

I find interesting that, periodically, f(n)=n-1, for example, for the following values of n:

2 3 5 11 13 19 29 37 53 59 61 67 83 101 107 131 139 149 163 173 179 181 197 211
227 269 293 317 347 349 373 379 389 419 421 443 461 467 491 509 523 541 547 557
563 587 613 619 653 659 661 677 701 709 757 773 787 797 821 827 829 853 859 877
883 907 941 947 1019

For these 1st 69 cases of f(n)=n-1, n is always prime, but follows no pattern of skipping primes that I can intuit:

1:2 I’m pretty badly off the topic of the mathematics of sound and music, but can’t resist a discrete math indulgence. ;)

 

i did a short poking of the missing primes. (couldn't resist. ;)) while many of the skipped are mersenne primes, some mersenne primes aren't skipped such as 61. (f(61)=60=61-1)

 

[u]f(n) for n=prime & f(n)≠(n-1)[/u]

 

f(7)=3=1/2(7-1) mersenne

f(17)=8=1/2(17-1)

f(23)=11=1/2(23-1)

f(31)=5=1/6(31-1) mersenne

f(41)=20=1/2(41-1)

f(43)=14=1/3(43-1)

f(47)=23=1/2(47-1)

f(71)=35=1/2(71-1)

F(73)=9=1/8(73-1)

f(79)=39=1/2(79-1)

f(89)=11=1/8(89-1) mersenne

...

 

 

 

Oh my!

Am I in deep ****?

Shall I explain or should I wait in the Queue? (A hint in the search for the uninteresting?

by sigurdV imagined continuous function Q)

Theese able guys REALLY scare me!

Returning from my latest gig in the lair of the wolves, i found my mind refreshinly clear

So what shall I do with it?

 

PS I like your new dress Turtle :thumbs_up

 

you might explain if any of our calculations have shown any of what you wanted/expected/imagined to see?

 

that old thing? an homage to maurits.

[CraigD]

Nearly everything I know about acoustical physics and songwriting

The concept im honestly studying in here is: TONALITY

…

Tuning down fourth string to c means fret 0 gives c

fret twelve gives pressed note c overtone c

fret seven gives g g

fret five f c

fret four e e

fret three d# g

fret two d d

fret one c# ?

 

Damn! I cant produce or hear the overtone at fret one:(

The strongest overtones on a string are multiples of its primary tone – that is, they’re 1 or more whole octaves above it, always the same lettered note of the scale, not a different one.

 

You sound like you have a guitar in hand, Sigurd, so let’s try some tricks I imagine you do all the time on it, thinking now about the physics of it. (Everybody else with a stringed thing within reach, play along!) :)

 

Only one string (deaden the other 5) and no fretting (pressing a string down ‘til it rests not on the nut and saddle (most folk call the saddle the bridge, but let’s be technically/hypographically correct here), but on the fret and saddle) needed – all fretting does is shortening the vibrating length of the string.

 

Pick the string in its middle (near the 12th thread). This makes as pure a primary tone as you can make. It also sounds synthetic and crappy – this kind of picking is good for touch and effect, but not the normal pleasant guitar sound.

Lightly touch where you just picked, and the string stops nearly dead.

 

Pick the string at about 1/4th its length (in the usual place, above the sound hole). This makes the primary tone and a strong 1 octive higher (2 times the frequency) overtone, the usual nice guitar sound. Pick again lightly touch above the 12th fret, and the primary tone is deadened, leaving the 1 octave up overtone, as if you’d fretted at the 12th fret.

Pick lightly toughing about the 5th fret (1/4th the length of the string). (Notice you likely moved where you were picking about halfway toward the saddle to make the tone its loudest). This deadens the primary and 1 octave up overtone, leaving the 2 octave up (4 times the frequency) overtone.

Most folk call this sort of primary tone deadening “harmonics” or something like that, and the tones produced the “second harmonic, fourth harmonic”, etc There’s another nice one, the third harmonic, over the 7th fret, that produces a tone 3 times the frequency.

When you pick a string around the sound hole in normal playing, the primary and all these overtones are all there, giving the sound its TIMBRE, and making the guitar sound like a string instrument rather than an electronic tone generator. When you want to hear the overtones more strongly, you pick closer to the saddle, making a nice, soulful, eerie sound, which bad, hammy guitarists like I tend to overuse mercilessly – think about the 6-string up-strum of the first E minor chord in Floyd’s “Comfortably Numb”, as played by a room full of jamming, hippies, or one on an amplified acoustic guitar at an open mike bar. :)

 

So stringed instruments make complicated, multi-toned sounds, like a big renaissance church choir in a little box. What the listener hears is less in the domain of acoustical physics than perceptual psychology, and not, I think, as neatly diagram-able. The main rule I know, a songwriting and improvisation rule rarely written or spoken aloud, is that the larger the step in consecutive notes, the happier, the shorter, the sadder. Dropping the third note in a cheerful major chord 1 half step (1/12th of an octave, about 0.94387 the frequency) makes it a gloomy minor chord. Changing a progression from 3 note steps to single or half steps changes a song from festive to brooding – think the difference between ’50-‘60s feel-good pop songs like La Bamba/Good ‘Lovin and the bridge in … well, practically anything by Alice in Chains, ca 1990.

[sigurdV]

EDITION WARNING

 

ahh the foe is on the other shoot. :lol: i had to ask too.

 

 

 

at first i thought you had a repeating error in there, but now i see that i find it interesting that for all f(n) when n is odd, f(n)=f(n+1).

 

 

 

nothing jumps right out at me either. will go off and stare some more.

 

as to music, sigurd originally set f(7) as an octave and equated the steps and the number of steps, f(7)=3, to the musical qualities "scale", "chord", and "tonality". then, i think, he was asking if other sequences/length-of-scales have matching or otherwise musically interesting steps and/or numbers of steps. i can't quite tell what the conclusion is/was.

 

I think youre on it Turtle!

 

Penetrating...("foe on the other shoot") :D

 

But I mean not only "Musically" theres more hands here than I can (he he ) handle.

 

Actually its but an approximation : Key = Tonality ... Just the first step towards a seclusional object.

 

Wat(son)ing the sword stuck in stone (WHAT! """"Concepts forming a group"""" (an ordinary one?)) I realized only a Musician AND a Mathematician MIGHT draw the bloody thing out)

 

On conclusions: Just beginning its amistake to believ f12 to be uof much use sinc 12 is even...HEH! How ODD!

[Turtle]

EDITION WARNING

 

:lol: it's quite automatic with every new post.

 

 

 

I think youre on it Turtle!

 

Penetrating...("foe on the other shoot") :D

 

But I mean not only "Musically" theres more hands here than I can (he he ) handle.

 

Actually its but an approximation : Key = Tonality ... Just the first step towards a seclusional object.

 

Wat(son)ing the sword stuck in stone I realized only a Musician AND a Mathematician MIGHT draw it out.

 

 

mathematically we see from craig's data set that the only f(n)=3's up to f(1000) are f(7) & f(8). makes one want to ask if any other f(n)=3 [pairs] exist. is that your bodkin & h-ear-t? my stick a needle in my i?

[sigurdV]

I wrote a blues...

 

The chords are E major G Major and A major

 

 

E a lot of times, G a few and A a few, and back to E

 

It is in E Major and has no Dominant chord

 

Intro: A wide spaced chord: e g# g e

 

The melody? e d c# b a (blue g#) two times

 

bass ef# g/ G chord

mel ef# g/ g g...

 

Chord A rings out then back to E

mel: silence... b g e (blue g#). ( Coda is E A,chord:e g# d e)

 

 

The text is in swedish.

Goes something like this:

 

1 As if there was a beach

just there for u and me

itll be the harbour

where we may be

 

2 Oh how i wait for u

I just made this necklace

with shells i found here

please come to me

 

3 Oh there i see two stones

they look like u and me

come let us listen

they sing our song

 

sigurdV

[suresh123]

I think Pythagoras is an example who was a mathematician as well as musician too.I think maths essential in daily life and every field involve maths like money counting,share market,daily routine work and music as you are discussing.

exponential growth and decay worksheet

Edited April 18, 2012 by suresh kumawat

[JMJones0424]

When I stumbled on this video, I was immediately reminded of this thread. I hope you find this presentation useful, Sigurd.

 

[sigurdV]

When I stumbled on this video, I was immediately reminded of this thread. I hope you find this presentation useful, Sigurd.

 

Hi! Its a pleasure to hear from you...One of these days ill buy a set of headphones so I can listen and not only look.

Howzit going friend? Your logic insight now enough to understand my solution to the Liar Paradox? Heres the latest formulation:

 

 

Definition:

 

y is a Liar Identity if and only if y is of the form: x = "x is not true",

and if y is true then x is a Liar Sentence defined by y.

 

THESIS:No liar identity is Logically true.

 

Proof (Based on: ( a = b ) implies (Ta<-->Tb) )

 

1. Suppose x="x is not true" (assumption)

 

2. Then x is true if and only if "x is not true" is true (from 1)

 

3. And we get: x is true if and only if x is not true (from 2)

 

4. Sentence 3 contradicts the assumption. (QED)

 

The logical form of the foundation of the Paradox:

 

1. x is not true.

2. x = "x is not true".

 

Some values for x makes the liar Identity Empirically true:

 

1. Sentence 1 is not true. (Liar Sentence)

2. Sentence 1 = " Sentence 1 is not true." (Liar Identity)

 

To get to the paradox one must produce " 3. Sentence 1 is true." from sentences 1 and 2.

But since sentence 2 is BOTH Empirically true and Logically false it can not be a well formed sentence!

Therefore no paradox can be derived from sentence 1,or any other liar sentence.