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Music Math

10/12/2010 8:50 PM

Since acustic music is "pure math", beings who encounter this wave seem to understand it. Is it because of 1/2.....1/4......1/8.......1/16 etc.?

And isn't music the constant search for perfection?.

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#1

Re: Music Math

10/12/2010 9:30 PM

Of course, those frequency ratios are descending octaves, and perceived as harmonious. In the ascending direction an octave is 2:1, a fifth is 3:2, a fourth is 4:3; and other ratios of fairly small numbers. The Pythagoreans worked out quite a bit of this.

These simple ratios are not in equal temperament, however. As you work back and forth around the circle of fifths, the non-octave intervals of any key can be arrived at by more than one path, for which the successive ratios are not quite equal. This can be compromised by equalizing each semitone to have 12√2 times the frequency of the next lower one.

This off-hand summary does not do justice to the topic, which would make for fascinating historical reading.

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#4
In reply to #1

Re: Music Math

10/12/2010 11:52 PM

A good movie for you...The Red Violin

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#17
In reply to #1

Re: Music Math

10/14/2010 4:15 PM

I remember a fun lab assignment in HS physics class that involved paper folding to determine the location of "frets" of a pythagorean scale, noting the error at the octave. Each group or student was given a different length scale (i.e. guitar vs. violin/mandolin vs. viola etc).

Anyway, here are a couple of music quotes to share, unrelated to the OP per se:

-----------------
To Whom Who Keeps a Record
Music Always Brings Goodness To Us All
P.S. Unless One Has Some Other Motive for Its Use
-Ornette Coleman
-----------------
If more of us valued food and cheer and song above hoarded gold, it would be a merrier world.
J.R.R. Tolkien

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#29
In reply to #1

Re: Music Math

02/10/2012 7:48 PM

I think that this "simplicity" makes "math music" adaptable to the very youngest minds, and should be introduced "in Earnest", to our preschools and kinder gardens. The children will automatically understand it.

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#2

Re: Music Math

10/12/2010 10:43 PM

Interesting

Let me put some abstract thoughts to this and try and get away from the maths involved. They have their place, no doubt but there are other things to consider.

Take it to the level of chemistry for a moment. If you have a liquid (single instrument, source of sound) and dilute it with water by half you have a dilution of the original. Very predictable, just like octaves.

If you have a liquid of different substances (an orchestra) and you dilute, the out come is immensely complex. Now, if you ad a catalyst (frequency?), a sound could be generated that does not come from the maths world. By transplanting emotions it becomes an imponderable maths problem.

Chemistry, at that level of investigation, is the more appropriate science. It makes us the catalyst but who is counting? Abstract enough?

Because maths can exactly create music and follow up by generating a physical sensation which triggers lizard brain reactions in us, it can be used as the measurement of music but not its ruler. There is more to it than that.

I used to work with a young female singer and she kept playing a trick on me. In one passage of the song she hit a note which canceled out (I mean physically) my voice. I had to change what I was singing so it would not happen. She won, if you know what I mean.

I would have liked to have seen the maths to it. Would have looked boring, I suppose.

beings who encounter this wave seem to understand it.

Yeah, they understand it without counting. Its a universal language and computing it is boring. Being able to do the maths is interesting and the craft of the sound engineer. 'What you put in is what you get out' still rules.

Here is "Blue Note" for you:

Gotta go, my pig brain is taking over. Lunch time, Ky.

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#3
In reply to #2

Re: Music Math

10/12/2010 11:50 PM

My good friend Jeff proved this to me a long time ago, by playing his guitar to his child in the womb. (whata liquid, huh) He did this for months, on his Martin D-28. And always said basically what you and

Tornado have so well put. The child later in life has blossomed in the arts and science. Jeff thinks all kinder-gardens should have music at their core, and that most or all children can benefit from acoustic music (a fun search for perfection)

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#5

Re: Music Math

10/13/2010 11:20 AM

I just listen to what pleases me.

No math is involved.

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#6
In reply to #5

Re: Music Math

10/13/2010 11:54 PM

To sum up all:

Music is pleasing and enjoyable sound manifestation controlled by mathematical rules

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#7

Re: Music Math

10/14/2010 12:38 AM

What you have found (given in our high school book of tables- called Clarke's table) is too basic. I am Indian. Western Music where MJ and other rock bands are popular with youngsters - is simply harsh on ear drums.

Listen to Indian classical (especially Hindustani) vocal or instrumental (Sitar, Sarod, sntoor, flute, tabla) etc - all are based on maths. I am not a musician myself, but I understand that within this octave, further subdivisions have been made totalling 22 - in Hindustani music. Now (what you understand as Do, re , me fa, so la, ti) - in Indian - it is Sa, re, ga , ma pa, da ni. Imagine by some repetition you get 22 steps. Then use your permutation and combination in maths and write down each combination. Each of those combinations are given a name called Raga. In India there is company making musical rhythm (7 notes, 22 notes, 16 notes etc etc) - and this works like a clock / base. This is kept next to every Hindustani musician- for co-ordinating the vocalist, tabla, harmonium and other instrument players. That is how Indian classical music sounds melodious - unlike the western jumping MJ accompanied by loud drums on stage.

Did you know that the great Nobel laureate Sir C V Raman (who worked on light) also worked on Tabla (percussion instrument? May be you could go to Google now and see how he sprinkled Talcum powder to find of effect of fundamentals and harmonics emanating from our Tabla.

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#8
In reply to #7

Re: Music Math

10/14/2010 1:18 AM

What you said is very nice. The western currently popular music is very harsh for my ears too. In fact it is harmful for the ears and the mind ultimately. But, I know in western music also, there are many classical soft music very soothing to ears.

I am also not a musician. Still I was fortunate to learn little bit (to my limited capacity) of music from Ustad Saiuddin Dagar.

As I understand, Sa, re ga, ma ,pa, dha (not da as you say), ni or in western system Do, re, me......) are just some steps of frequencies. These are not absolute steps. The frequencies vary seamlessly from lowest to highest frequency... which in Indian music is known as MIND (MI like me of english... so it is not pronounced like word mind of English). Besides, ga of one scale becomes sa of other scale and all scale goes up.

Also, there are very fine steps of each tune.. which are called Shruti. For example there are some 9 Shruti of Ni only. The frequency of each shruti is little different than each other still they are is some specific ratios.

The instrument you are referring, giving clock base is fashion of the day. The real musician doesn't need it. Ustad Dagarji used to tell us that he was made to practice each sequence of tunes (swara) 5000 times each by his guru. How can he go wrong if it is practiced no many times! The time base is given by Tabla.. rhythm. Base of scale is given by Tanpura or Tambora, which is tuned to match with the raga to be sung or played on instrument.

The strings of the instrument (on back side of string instruments) give harmonics to the played tune by main string. In case of singing, the Tanpura gives harmonics for the sung tunes.

The mind can be easily sung (by good singer of course... not by some one like me). In case of string instruments, it is played by pulling the string while striking the string. In flute it is generated by opening the hole slowly.

My words are just incapable of describing all the beauty and the theory of Indian music. With properly sung/ played Indian music, the tears flow automatically through one's eyes.

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#9
In reply to #8

Re: Music Math

10/14/2010 2:06 AM

Yes , of course when some Hindustani musicians sing - you just close your eyes and enjoy- music goes directly to the SOUL (heart). You can feel calmness, serenity, peace. Indian music is to be enjoyed even if you don't understand it. Many have made studies of lowering of heart beat or lowering of blood pressure. You can see brightness in eyes and a calm face in great musicians - as totally different from half clothed dancing across the stage by western DJs (pushed by sponsoring MNCs to India) - I don't know whether it appeals to the software people techies. In fact creative software writing may be better if there is soft Indian Hindustani music in the background sometimes.

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#15
In reply to #8

Re: Music Math

10/14/2010 9:40 AM

I did not talk about western music. I talked about understanding

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#20
In reply to #15

Re: Music Math

10/14/2010 5:46 PM

Hi Craig

When the twain meets nobody will understand because the sound will render every one transfixed and incapable of measuring or understanding. There will be no need for maths because it overwhelms the people "in the know" completely.

It is like that in any other human activity. Be it a well tuned V8 super car or a well composed curry. One does not have to be a chef, cook or conductor to know if any of the above are well composed. You do not have to know that palm sugar was used as a sweetener. This is all well known.

I was and am the most terrible maths student but just by looking at the numbers and the aesthetics of the structure of a formula helps me get it. This makes it easier for me to understand the verbal explanation of/on the given subject, challenge. For me the general understanding of the structure is important and not the specialized details, on any subject.

In any discipline that has been studied and taught by authorities in their field there will be magic. Not like in a card trick, no, god plays no dice. Some thing that is given gratis once a certain level of studies has been achieved, a bonus. This bonus is what true artists in their field are after. I still try but have not the time to physically train, the meat hit steel stuff, a bit masochistic really.

The unexpected, the improvisation is the driving force. This virtuosity, mastery, again not only in music, is what I think is the main motive. The repeatability of what it feels, sounds, smells, reacts like. Very much the reason for people to take drugs. Like I mentioned in my earlier post chemistry, maths and much more does come into it, not only in music.

Just a quick word on east or west and what music they listen to. Every one deserves what they get. Some modern musicians (sound engineers) are reinventing the wheel and think that the sun shines out of their back sides. Its not the sun guys, have a closer look (listen) its just a micro chip. I hope my "Dude" reads this but it is not likely.

Nothing is more pleasing than to even touch a well (perfectly) tuned instrument. The tuning is of utmost importance. My daughter in law and I had an argument about the badly out of tune piano they have in their house. She said "well its only to be practiced on".

Her ignorance of the fact that my grand daughter might have more sensitive ears than her and dread and dislikes playing was brought forward by me. It physically hurts to listen but not to her. Further explaining it didn't help. They know not what they are doing and grand dad is a bit weird anyway............

Giving the music student a badly tuned instrument is like giving them salty chocolate. They'll never get onto it, if they have any talent at all. Yep, you guessed it, this not only goes for music. A bad saw can stop a talented person from being a carpenter. Only after he knows the value of a sharp tool will he enjoy building his house.

Gods and music don't mix, they are already an emulsion. We can only ever be the catalyst in the equation. Like in a sexual act, the heart beat rules from the start.

Just another ten bar (psi), Ky.

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#28
In reply to #20

Re: Music Math

10/15/2010 2:03 AM

......"oppernockity is tuning .....

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#37
In reply to #20

Re: Music Math

10/22/2018 12:09 AM

The insight in your post is so in tune. A good friend of mine has been tuning pianos for most of his life. He tunes by ear, he is amazing, and his d-28 and his heart rule from the start. He is so involved with small children, and others, with his "music". They have found flutes made from bone with the early humans, so they (i think) as you put it, already an emulsion. T Y

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#10

Re: Music Math

10/14/2010 2:23 AM

Music/math is the only universal language, this forum thread has people from the U.S., India, and Australia, and from posts yet to be, all agreeing on the same thing. . . sometimes math sounds great! War smore! I wrote a song about it, it goes . . . .

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#11
In reply to #10

Re: Music Math

10/14/2010 3:23 AM

Absolutely - maths & music is universal. Externally Hindus and Muslims may be seen at logger heads. but most great musicians in India are Muslims. Many Muslims have sung great songs invoking Indian Gods. In Indian Hindu wedding - mostly we have Shehanai music by great Ustad Bismillah Khan (now no more). But some how we do not find similar sentiments shown by Muslims from other parts of the world to other religions. It is a pity- they are fanatical.

Western classical ( I have heard mostly great orchestra bya big ensemble) - is also nice.

Divekar

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#12
In reply to #11

Re: Music Math

10/14/2010 5:31 AM

Ustad Saiuddin Dagar, I mentioned in my earlier post is also Muslim, but all compositions he sings are Hindu gods prayers. He was almost outcast in local Muslims for many years for the same reason. But thanks to wisdom of Muslims here, just recently he was called to sing at dargah of Muslims.

Hindus accept Muslims as great singers as well as Muslims here sing prayers of Hindu gods, here in India. It is great virtue. But, as I understand, Muslims in Pakistan have changed the traditionally used names of ragas, just because they appear to have Hindu names.

As you say, many great singers from India are Muslims, and are well accepted by all Hindus in India.

Though I do agree with you that Muslims in India, sing their classical singing, where Hindu gods are prayed, let us not change the direction of this thread to this different aspect. Music should be beyond the religions

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#22
In reply to #11

Re: Music Math

10/14/2010 6:06 PM

We understand a lot of our maths was originally created by Muslim cultures.

I can't tell you what though cause I'm not a maths historian.

Dub

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#13

Re: Music Math

10/14/2010 6:40 AM

Congratulations you have picked one of the most subjective of questions

Physics and perception of sound not equal, for example differences in each individuals ears make this problem as it itself is classed as an acoustical amplifier and mechanical impedance matching device.

Pitch is a subjective term, frequency is the associated physical term, and the two only have a general relationship.

Subjective timbre or quality of sound and the physical spectrum of the sound are related but not equal.

The Haas, or precedence effect describes the ability of the ear to integrate all sound arriving in the ear within the first 50msec, making it sound louder.

Harvey Fletcher tried to synthesize piano sounds. It was emphasised that piano strings are stiff strings and vibrate like a combination of solid rods and stretched strings. This means that the piano overtones are not strictly harmonic. bells produce a wild mixture of overtones, and the fundamental frequency is not even graced with the name among specialist in the field. The overtones of drums are not harmonically related, although they give richness to the sound. Triangles and cymbals give such a mix of overtones that they blend reasonably well with other instruments. Non harmonic overtones produce the difference between organ and piano sounds and give variety to musical sounds in general.

To add you have to consider philosophy's like aesthetics in sound,again based on perception. most people will find that major chords sound pleasing, and minors sad.

However some of us like some dissonance in our music, i like Thelonious Monk most non jazz people hate it, but all the dissonance makes me happy.

Which summarises as some physics and plenty of maths, but so many different perceptions of the outcome.

References F.Alton Everest (Master Handbook of Acoustics fourth edition).

Good Health Dub.

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#18
In reply to #13

Re: Music Math

10/14/2010 4:59 PM

This is why it is so interesting about perception. In the womb, it's an incredible awareness, and mostly overlooked.

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#21
In reply to #18

Re: Music Math

10/14/2010 5:51 PM

Could be natures way of initially programing us for the environment we are to be born, ie would you be different if born into a violent war torn area filled with tension in peoples voices or a calm society where people have the luxury of music and gentle conversation, i think its impossible to determine.

In general people are mainly characterised by there environment as you get a certain percentage of human traits relative to the situation in that environment. I have found despite all peoples differences ie religious, colour, body weight, sexuality, country, village, street etc you will always have a common mix of common people. Ie every society has a serial killer its just in some societies they do not show up, religious fanatics there all the same in all our cultures and they cause all us normal people in all our country's and cultures a head ache, not forgetting your greedy man, hes there too, the list of all the types you can imagine are every where only some places things are the norm others not so. Is music is in the mix though mm? ill get back to you one day.

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#14

Re: Music Math

10/14/2010 8:51 AM

I am an American Indian and I make american Indian Flutes www.Nakatoshaj.net

here is an answers for your question:

Music is and has always been, Mathematics were created by minds seeking to communicate in symbols and these symbols required rules so that they could be developed and expressed. Music is and the Idea of music must be agreed upon.

So when you find agreement enjoy yourself there is more magic in the great mystery without needing to postulate your own existance with mental masterbation.

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#19
In reply to #14

Re: Music Math

10/14/2010 5:07 PM

"Music is and has always been" enough said

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#26
In reply to #14

Re: Music Math

10/14/2010 10:44 PM

I would rather put same thing in different language:

Music was already there, much before mathematics. But, when people started analysing music in terms of mathematics / sound frequency, they surprisingly found that the ration of frequencies between two successive note Re/Sa, Ga/Re is always same.

The mathematical way is just an interpretation of the music.

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#38
In reply to #14

Re: Music Math

10/22/2018 12:16 PM

The earliest humans made flutes and through communication they figured out exactly where to put the holes. There is a flutemaker in mancos colorado who put a c d out of him playing in mesa Verde cliff palace, still my most favorite "music". Spirit/music.....music/spirit.

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#16

Re: Music Math

10/14/2010 11:21 AM

"Is it because of 1/2.....1/4......1/8.......1/16 etc.?"

Fractions? Why is music in fractions when decimals are easier to work with?

It's not like decimal or metric music would sound different, would it?

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#23
In reply to #16

Re: Music Math

10/14/2010 7:19 PM

no, but it is 1/2 way,1/2 way 1/2 way,etc. instead of ,500 way

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#24

Re: Music Math

10/14/2010 7:52 PM

I agree with #23. In theory, at least, the ratios are exact numbers rather than decimal approximations. 4/3 ≈ 1.33, but 4/3 ≠ 1.33.

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#31
In reply to #24

Re: Music Math

02/11/2012 11:50 AM

That is exactly why I think that kids "get it". Practice , practice , and the search for perfection. Autistic kids have an interesting auditory system. Harmonics are key and kids have an innate awareness of old music. The new stuff is not comfortable music. A guitar up against the womb is incredible. Let's get more music into kids.

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#32
In reply to #31

Re: Music Math

02/11/2012 7:36 PM

found this on FB

C, E-flat, and G go into a bar. The bartender says, "Sorry, but we don't serve minors." So E-flat leaves, and C and G have an open fifth between them. After a few drinks, the fifth is diminished, and G is out flat. F comes in and tries to augment the situation, but is not sharp enough. D comes in and heads for the bathroom, saying, "Excuse me; I'll just be a second." Then A comes in, but the bartender is not convinced that this relative of C is not a minor. Then the bartender notices B-flat hiding at the end of the bar and says, "Get out! You're the seventh minor I've found in this bar tonight." E-flat comes back the next night in a three-piece suit with nicely shined shoes. The bartender says, "You're looking sharp tonight. Come on in, this could be a major development." Sure enough, E-flat soon takes off his suit and everything else, and is au natural. Eventually C sobers up and realizes in horror that he's under a rest. C is brought to trial, found guilty of contributing to the diminution of a minor, and is sentenced to 10 years of D.S. without Coda at an upscale correctional facility.

Nice little gem I thought. Enjoy your weekend, Ky.

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#25

Re: Music Math

10/14/2010 8:00 PM

Tube it - if your location allows youtube Mathematical Music

Also listen to all of RUSH .... especially "Moving Pictures" and "2112".

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#30
In reply to #25

Re: Music Math

02/10/2012 8:22 PM

I lost that link and now, thanks to guest, I was reminded.

Thanks again, Ky.

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#27

Re: Music Math

10/15/2010 12:00 AM

I just wanted to share that in Indian music - we have appropriate ragas / music system - to be sung in the morning, afternoon, evening , night as also different ragas for spring, rainy season, winter season etc to suit the atmosphere in the air. Add to that is the ragas involving other moods - feeling of loneliness, loss of beloved etc.

Now digressing a bit - our classical dance forms are also (visual) mathematical - you can say. There is meaning in every movement - unlike the western dance forms. I don't know whether ballet or any dance forms conveys any meaning - or is just supposed to be rhythmic.

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#33

Re: Music Math

05/26/2016 12:12 AM

Craig, I'll begin with answering your second inquiry. What I think "perfection in music" is best interpreted as is growth or a constant state of expansion; It is all relative, nothing is perfect. Therefore sound is vast, it all depends on the abilities of the composer. That isn't my full theory or explanation, but enough to help with part of your question.

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#34
In reply to #33

Re: Music Math

05/26/2016 12:44 AM

As for the first part your correct, the closest any "being"'s who have attained the said perfection, organically are mozart and bach, (A metaphor to explain further) which I would describe these two composers as the only few to achieve making neurons processing information as well as synapses firing, audible. Regardless of they're feats music is in everything and not limited to their sound. Hope this helps as well.

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#35
In reply to #34

Re: Music Math

05/26/2016 12:48 AM

That is perfection.

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#36
In reply to #35

Re: Music Math

05/26/2016 1:21 AM

Despite the date I had to comment, I'll leave the above here for passers by this astray

and tomb of a discussion.

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