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#1
I have two major concerns about music right now. The first is there is no empirical evidence to support the tuning of A = 440. This isnt really a question, but it bothers me. What could we use instead? What naturally resonating pitch would be a better choice to tune our instruments to?

This brings me to my actual question. Why dont we just use the notes of the harmonic series instead of 12 tone equal temperament? I'm not sure I understand. The harmonic series produces naturally occurring overtones, definite empirical meaning. WHy make up approximations? There are many fretless stringed instruments with the perfect ability to play only the notes that exist in the overtone scale. Why isnt that the standard?

If you start on C, and cut it in half, you get C, cut it in thirds and you get G, but it isnt the G we use. It is an actual G in relation to C. Why cant we just make an instrument with all the possible C's. then all the possible G's but the actual G's proportionate to the C's, then in 1/5ths and mark out where those notes exist and so on and so forth until the notes become so small apart that it isnt practical to make more in between notes.

I'm sure this exists and I am sure there is plenty of information on this that I cant find.
#2
Because not everything revolves around science or the guitar.

And because the harmonic series brings wolf tones into discussion, while equal temperament gives a fair approximation for all keys.

(Clarification edit: line 1 was about A440.)
Glad to cross paths with you on this adventure called life
Quote by Jet Penguin
lots of flirting with the other key without confirming. JUST LIKE THEIR LOVE IN THE MOVIE OH DAMN.
Quote by Hail
you're acting like you have perfect pitch or something
Last edited by NeoMvsEu at Mar 13, 2016,
#3
Mmmm... using the harmonic series, or rather pure intervals rather than equal tempered interval, has been used in many tuning systems and is still very common, and often standard in certain instruments, genres, countries, period-accurate music, etc.

The reason why it's not used? Because an instrument using such a tuning system plays poorly in remote keys and you get commas and wolf intervals and other nasty things.

Like this is all common sense and has been widely studied and explored over hundreds of years. I'm not even sure how you can't find information on just intonation and Pythagorean tuning when it was very easy to find.
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#5
The whole foundation of Western music relies on harmony. Without tuning to equal temperament, you would not be able to play with a wide range of instruments, or modulate freely. It actually took a long time to solve the equation to make equal temperament possible (pretty sure it was done by a Chinese prince). Although A=440hz is arbitrary.
#6
Because certain intervals, such as the major third, require flattening that would compromise other keys. So unless you have on string for each key and are planning to play the entirety of the piece on one string, you're limited to a particular key and relative modes, such as what is done with the bağlama. Otherwise significant retuning would be required and it would be almost impossible to play with other instruments.

Again, this is all stuff that has been figured out long ago.
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#7
What do you mean by certain intervals require flattening? I'm not sure I understand where you derived anything that has to do with intervals from the harmonic series. Pretend I'm not a musician and don't care about anything except constructing an instrument that only produces the sounds created by the harmonic series using a given starting point.
#8
Imagine a string, harmonic series would be dividing these using ratios, whereas in equal temperament they are manually divided into 12 equal portions. The problem with pitch is that as you go higher in octaves, you get more frequencies until a the human ear recognises it as a pitch change. Basically it doubles every octave. If do the maths you'll realise that these numbers don't match those in the harmonic series.
#9
Dude, you seriously need to study some music history. The keys/scales are named the way they are because of history. The notes are named the way they are because of history. The tuning is the way it is because of history. A = 440 Hz has to do with history. Everything in music theory has to do with history.


12 tone equal temperament is required for instruments that have keys and frets. Or it isn't if you only want to play in one key. But if you want to play in multiple keys, some kind of a compromise is required for keyboard/fretted instruments. Why 12 tones? That has to do with history. Some other cultures use more than 12 tones. Though I doubt people before baroque/renaissance thought in 12 tones. But that's just how music evolved. Maybe that created best sounding harmonies, I don't know. I guess a lot of it also has to do with keyboard instruments and how to make them sound good.


But the thing is, before 12 tone equal temperament was invented, people played in tunings that sounded great in certain keys and like crap in other keys. People wanted to be able to play in all 12 keys and that's why they came up with 12 TET. As I said, 12 TET (or any kind of temperament) is really only needed for keyboard/fretted instruments (and some other string instruments like harp). If you sing in a choir, your ear will automatically adjust the notes to the harmonies. A choir doesn't sing in 12 TET. Neither does any orchestra that doesn't involve keyboard/fretted instruments.


TL;DR

12 TET is the result of people wondering for hundreds of years about how to make all keys sound good (on keyboard/fretted instruments). People did experiment with different kind of temperaments in the past. 12 TET was the result of that - that's the best way of making every key sound good. Any non-equal temperament will make certain keys sound better than others. 12 TET is a compromise but certain instruments need compromises.

Well, of course today when we have digital instruments, you can change your tuning system at the touch of a button.


What do you mean by certain intervals require flattening?

She means that when compared to 12 TET, the natural major third is flat.


If you don't like 12 TET, start singing in a choir.
Quote by AlanHB
Just remember that there are no boring scales, just boring players.

Gear

Bach Stradivarius 37G
Charvel So Cal
Fender Dimension Bass
Hartke HyDrive 210c
Ibanez BL70
Laney VC30
Tokai TB48
Yamaha FG720S-12
Yamaha P115
Last edited by MaggaraMarine at Mar 13, 2016,
#10
Intervals in the harmonic series tend to be off from equal tempered intervsls. The harmonic series goes:

2:1 - octave
3:1 - octave and a fifth
4:1 - two octaves
5:1 - two octaves and a 3rd
6:1 - two octaves and a 5th
7:1 - two octaves and a b7th
8:1 - three octaves
9:1 - three octaves and a 2nd
10:1 - three octaves and a 3rth
11:1 - three octaves and a flat tritone
12:1 - three octaves and a 5th
13:1 - three octaves and a b6th
14:1 - three octaves and a b7th
15:1 - three octaves and a 7th
16:1 - four octaves

Etc.

Now if we drop those octaves, we get get all just intervals:

9:8 - 2nd
4:3 - 3rd
3:2 - 5th
8:7 - b7th
16:15 - 7th

And so on. Those are perfect intervals, which are used in just intonation. Now, a quick comparison to a 12 TET ratio chart shows you that all the ratios are slightly off from these other than the octave. The 5th is slightly (about 1.96 cents) sharp. The rest of the intervals are sharp or flat as well, with all but the b2nd, 2nd, and b3rd being greater than 5 cents sharp or flat, with some overtones being over 30 cents off.

Some intervals, like the 7th, b5th, and b7th are so far offer that two different ratios are "close enough" to fit the bill within the first 5 octaves. The just b7th could be 8:7 (32:28 for comparison) or 32:29. Those respectively are approximately -31 and +30 cents off from a 12 TET b7th.

The bağlama does exactly what you are describing, using the first 32 harmonics worth of just intervals, thus giving two frets each for the b5th, b6th, b7th, 7th, and 8th, neither of which matches the 12 TET interval with the exception of the 2:1 8th fret, thus making the instrument incompatible with 12 TET instruments as is.

Also I know I definitely goofed some of those ratios by switching the numbers but I can't be bothered to fix them. Just look up a just interval chart if you want the actual ratios of all the notes plus how much they differ from equal tempered intervals.
There's no such thing; there never was. Where I am going you cannot follow me now.
Last edited by theogonia777 at Mar 13, 2016,
#11
Quote by jrcsgtpeppers
What do you mean by certain intervals require flattening? I'm not sure I understand where you derived anything that has to do with intervals from the harmonic series. Pretend I'm not a musician and don't care about anything except constructing an instrument that only produces the sounds created by the harmonic series using a given starting point.
That's perfectly possible, but you won't get anything like the scales that western instruments use.
Every note will certainly be in tune with the reference pitch you begin from. And no doubt you could make some very interesting music with it.

In case it helps, here's a chart of the harmonic series of the guitar A string (the first 19 harmonics anyway):
HARMONIC - FREQUENCY - NEAREST NOTE - cents away from ET   
 1st         110 Hz          A                             
 2nd         220 Hz          A                             
 3rd         330 Hz          E  (329.6)   2 cents sharp    
 4th         440 Hz          A                             
 5th         550 Hz          C# (554.0)  14 cents flat     
 6th         660 Hz          E  (659.2)   2 cents sharp    
 7th         770 Hz          G  (784.0)  32 cents flat     
 8th         880 Hz          A  (880)                      
 9th         990 Hz          B  (987.8)   4 cents sharp    
10th        1100 Hz          C# (1108)   14 cents flat   
11th        1210 Hz          D# (1244.5) 49 cents flat   
12th        1320 Hz          E  (1318.5)  2 cents sharp  
13th        1430 Hz          F  (1396.9) 40 cents sharp
14th        1540 Hz          G  (1568.0) 32 cents flat
15th        1650 Hz          G# (1661.2) 12 cents flat
16th        1760 Hz          A  (1760)
17th        1870 Hz          Bb (1864.7)  5 cents sharp
18th        1980 Hz          B  (1975.5)  4 cents sharp
19th        2090 Hz          C  (2093.0)  3 cents flat
The "cents away from ET" column shows how out of tune each harmonic is with the nearest note in Equal Temperament (the system we tune our instruments to). (The frequencies in brackets are the equal tempered pitches. 1 cent = 1/100 of a half-step, btw.)

Of course, if you regard the harmonic series as "natural" and "perfect", then it's the equal temperament system that is "out of tune" .
But (as explained above) that "tempering" (tweaking) of the tuning is essential for our key system to work, so that every half-step is the same size. That way all our chords work the same way, and we can change key without having to retune our instruments all the time.

Obviously, if you don't care about keys and chords (or even scales), and want to make a totally different kind of music, then the harmonic series could be a great reference point.
I'm not going to suggest you "learn some history" . That only matters if it's western music you want to understand! I'll suggest instead you check out Indonesian gamelan (and its unusual tuning system), and the experiments of 20thC western musicians such as Harry Partch and Cornelius Cardew. Lots of fun to be had there!

Here's another site worth studying, on the relation between math and western tuning systems (NB western only):
http://www.yumpu.com/en/document/view/6224469/the-development-of-musical-tuning-systems-midicode
Last edited by jongtr at Mar 13, 2016,
#12
(OP) your posts seem all to have this fascination with "the extreams" of harmonic theory and application. And again you are using the Lydian dominant (13#11) as a spring board..as the fourth mode of the melodic minor is also called the overtone scale

the study and exploration of the overtone series may be of interest to anyone who wants to know the mechanics of sound and the history of this study..it is very "dry" and math intensive and will only give you insight into far reaching aspects of sound and its overtones..

regarding guitar..in standard A-440 tuning..the study of the scale itself is limited by the instruments own limitations..you would have to change tunings many times and even then you would still not encompass the entire study of the overtone scale and its implications..think Pi 3.14159..but it goes WAY beyond that..as does many examples..into micro/macro measurements of sub-atomic particles..or the size of a galaxy or the distance of space between planets ..

if you want a more practical application that you can hear and explore..as I suggested to your last post..read the history of George Russell and his Lydian Chromatic Concept..and how some top named jazz players explored his theory...or go beyond "western" harmony--the study of Eastern Indian music-the sitar in particular-uses and explores micro-tonal sound and its harmonic expansion and limitations (if any) and relies heavily on "overtones" and their use and perception by the listener..this is regarded as a "meditation on divinity" to many sects in India..there are hundreds of "ragas" dedicated to the hindu gods..that have very specific tones that are supposed to affect the hearing and nervous system and produce a meditative state to the listener..and the musician..
play well

wolf
#13
Quote by jongtr

I'm not going to suggest you "learn some history" . That only matters if it's western music you want to understand!

Yeah, that's true. I just got the impression that TS was talking about western music, because he said "Why dont we just use the notes of the harmonic series instead of 12 tone equal temperament?"
Quote by AlanHB
Just remember that there are no boring scales, just boring players.

Gear

Bach Stradivarius 37G
Charvel So Cal
Fender Dimension Bass
Hartke HyDrive 210c
Ibanez BL70
Laney VC30
Tokai TB48
Yamaha FG720S-12
Yamaha P115
#14
I love when I ask questions and people respond by telling me to study music theory (:

I don't understand the problem. I am aware the notes produced in the harmonic series are different than 12 tone. Stop telling me that. That doesn't answer my question at all. My question is why can't I play an instrument that only plays these harmonic overtones? I don't care about not having friends because my instrument is tuned differently. I don't care about not being able to play purple haze in tune with Hendrix. All I care about is finding all the naturally existing notes from a given starting frequency. Those notes mean more to me than a made up diatonic scale. To me the 12 tones are out of tune. I don't want to spend my entire life resonating with an out of tune instrument. I want to resonate with God. I want to play the scales he created.

Maybe the best question is what is the Pythagorean comma? He tried tuning all his notes to a 5th but then found that it didn't align with the octave. That makes absolutely no sense to me. Does that mean if I take a starting note, subdivide it into the overtones, take any overtone and double it, it wouldn't be a perfect octave anymore? I don't get it.
Last edited by jrcsgtpeppers at Mar 13, 2016,
#15
Quote by jrcsgtpeppers
I love when I ask questions and people respond by telling me to study music theory (:
Not me.
Quote by jrcsgtpeppers

I don't understand the problem. I am aware the notes produced in the harmonic series are different than 12 tone. Stop telling me that. That doesn't answer my question at all. My question is why can't I play an instrument that only plays these harmonic overtones?
Well, personally I don't know any instrument that's designed to do that. Except a single guitar string (playing harmonics).
Oh yes, and a bugle, which forms its notes from the harmonic series. In fact, any wind instrument with no holes or valves. (Blow harder, get higher harmonics.)
Quote by jrcsgtpeppers

I don't care about not having friends because my instrument is tuned differently. I don't care about not being able to play purple haze in tune with Hendrix. All I care about is finding all the naturally existing notes from a given starting frequency. Those notes mean more to me than a made up diatonic scale. To me the 12 tones are out of tune. I don't want to spend my entire life resonating with an out of tune instrument. I want to resonate with God. I want to play the scales he created.
Sorry, but now that is funny.
Quote by jrcsgtpeppers

Maybe the best question is what is the Pythagorean comma? He tried tuning all his notes to a 5th but then found that it didn't align with the octave. That makes absolutely no sense to me. Does that mean if I take a starting note, subdivide it into the overtones, take any overtone and double it, it wouldn't be a perfect octave anymore? I don't get it.
You don't get it because you haven't studied it properly. Or maybe the math is too complicated. (It's not simple.)

Did you read the site I linked to? That really does answer most of your questions if you take the time to read through. By all means ask if there's specific points there you don't get.
#16
Oh yeah? You know how much I study and what I study? You don't think I've studied everything I can think of related to my questions? Let's hear it internet geniuses. Why don't you explain it. Or you can just keep telling me things I already know. That pisses me off. Thank for tellin me fucking horns can make the first few harmonics. I had no fucking idea.
#17
Quote by jrcsgtpeppers
My question is why can't I play an instrument that only plays these harmonic overtones? I don't care about not having friends because my instrument is tuned differently. I don't care about not being able to play purple haze in tune with Hendrix. All I care about is finding all the naturally existing notes from a given starting frequency. Those notes mean more to me than a made up diatonic scale. To me the 12 tones are out of tune.


Bağlama. Bağlama. Bağfuckinglama. How many times do I have to say it?

Maybe the best question is what is the Pythagorean comma? He tried tuning all his notes to a 5th but then found that it didn't align with the octave. That makes absolutely no sense to me.


If you read the Wikipedia article on it then it would make sense in a minute.

You don't think I've studied everything I can think of related to my questions?


Honestly, I don't think you have unless you haven't thought of anything.
There's no such thing; there never was. Where I am going you cannot follow me now.
Last edited by theogonia777 at Mar 13, 2016,
#18
Pythagorean tuning is based on a perfect fifth of ratio 3:2. Perfect octaves are 2:1. Stacking fifths on top of each other gives the function F(3/2)^x, where F = frequency and X=a whole number.

If we want an octave, that will be an even multiple of the original frequency, specifically F(2)^x, X an integer. I will exclude 0, because that would map back to the original frequency, thus making a unison.

Set the two equal to each other:
F(3/2)^n = F(2)^x
3^n/2^n=2^x (frequency is invariable, distributed power)
3^n=2^(x+n) (exponent properties)

Given that x cannot be 0, this equation can never be true. I'll spare you the proof. QED.
Glad to cross paths with you on this adventure called life
Quote by Jet Penguin
lots of flirting with the other key without confirming. JUST LIKE THEIR LOVE IN THE MOVIE OH DAMN.
Quote by Hail
you're acting like you have perfect pitch or something
#19
Yeah dude I watched like a dozen videos of bağlama music. Very impressive. But I don't think it meets my qualifications. Does it? How many harmonics does it have? The first how many?

I've the wiki article. I know the stories I know the rhymes. There's something I'm just not getting. I even watched proofs on the harmonic series. Plenty of Pythagorus videos. Plenty of everything. Yet I still have questions. Crazy isn't it?

What would it look like if you mapped out all the natural harmonics on a stringed instrument? Like take all the frets of the guitar, where would I have to place them to make only the overtones? What problems would I have doing this with multiples strings to play chords?
#20
Quote by NeoMvsEu
Pythagorean tuning is based on a perfect fifth of ratio 3:2. Perfect octaves are 2:1. Stacking fifths on top of each other gives the function F(3/2)^x, where F = frequency and X=a whole number.

If we want an octave, that will be an even multiple of the original frequency, specifically F(2)^x, X an integer. I will exclude 0, because that would map back to the original frequency, thus making a unison.

Set the two equal to each other:
F(3/2)^n = F(2)^x
3^n/2^n=2^x (frequency is invariable, distributed power)
3^n=2^(x+n) (exponent properties)

Given that x cannot be 0, this equation can never be true. I'll spare you the proof. QED.

What purpose does stacking 5ths serve? All we have done thus far is take one string and a piece of wood just like the man himself and mark out the harmonics. Add frets and now we have a one stringed instrument. Where does this "problem" occur?
Last edited by jrcsgtpeppers at Mar 13, 2016,
#21
Quote by jrcsgtpeppers
Yeah dude I watched like a dozen videos of bağlama music. Very impressive. But I don't think it meets my qualifications. Does it? How many harmonics does it have? The first how many?


17 notes representing up to 32:1 (there are numerous overlaps, such as 2:1, 4:1, 8:1, etc).

Quote by jrcsgtpeppers
What purpose does stacking 5ths serve?


The Pythagorean tunIng is formed by stacking fifths.
There's no such thing; there never was. Where I am going you cannot follow me now.
#24
The Pythagorean tuning uses one note as a basis for the other notes. It is built by stacking fifths on top of each other.

The comma is the difference between a proper octave and the "octave" created by stacking 13 fifths. If you know the circle of fifths, you should know that it takes thirteen permutations to get back to the beginning:

1-2-3-4-5-6-7 -8 -9 - 10 -11-12-13
C-G-D-A-E-B-F#-C#-G#-D#/Eb-Bb-F -C

A 3:2 perfect fifth is 2 cents sharp of tempered. 12 of these results in the difference between beginning and ending C being 24 cents apart (the ending C is 24 cents sharper), which is quite significant (50 cents = a quarter tone, not a rapper. 100 cents = a semitone, not a dollar.).

Thus, people temper the final interval in order to make a perfect octave between the reference tone and ending tone. However, the 24-cent diminution, which is the aforementioned comma, creates a wolf tone - a tone considered unusable when other notes are played together.

Harmonics are not the same as Pythagorean, per se. Pythagoras used one harmonic, the 3:2 created by dropping the 3:1 down an octave.

Also, this is relevant:
Quote by NeoMvsEu at #33861910
Please read better.
Glad to cross paths with you on this adventure called life
Quote by Jet Penguin
lots of flirting with the other key without confirming. JUST LIKE THEIR LOVE IN THE MOVIE OH DAMN.
Quote by Hail
you're acting like you have perfect pitch or something
#25
My question is why don't we play instruments that produce only the notes contained in the harmonic series. What does that question have anything to do with anything any of you have said?

I can take a string and a piece of wood, connect both sides of the string, pluck it and get a note. I can then mark out the halfway point, the 3rdway point, the 4thway point, the 5thway point and so on and so forth.

What is the problem with this? Is this illegal or something? What gives? Why would anyone want to play these out of tune notes for the sake of having exactly 12 subdivisions? The number 12 isnt special to me. Why would I want anything to do with the number 12? Why would I want to stack intervals? What purpose does stacking intervals serve me?
#26
I take a string, anchor it to some wood. Mathematically approximate the location of all of the harmonics to a certain extant, I assume there are an almost infinite amount of harmonics, sound is quantized thus arbitrarily small intervals cant exist.

Now I have lets say the first 20 harmonics located on my wooden stringed instrument. Those harmonics only exist if the whole string is allowed to vibrate. Adding frets would prevent the other half of the string from vibrating and oscilating thus I would have to mark out frets that match the first 20 harmonic pitches. I would start with the first harmonic, mark those locatins out, add frets, move on the the second, mark those out, add frets, do this until the frets are too close together for my fingers to play.

Where does the problem occur? What step did I do wrong? I should have a one stringed instrument that sounds perfectly in tune with itself. I should be able to play cool tapping licks and have a lot of fun with these naturally occurring non 12 equal tempered notes.
#27
This is an important clarification, so I'm going to make it with obnoxiously normal formatting:


There is exactly nothing wrong with the approach you suggest.


What will be the case, however, is that you won't be able to easily take your instrument out to the local bar, club, garage, basement, or open-air hippy amphitheater and play along with other people in harmony (or at least, not completely). Actually, you still might even be able to play in tune if you stay with certain notes and don't deploy every single harmonic you've fretted out for yourself. Whether or not that will put you closer to god or the universe or the Great 432-Cycle Hum In The Sky is secondary, but if playing with or to other people isn't your goal, then there is not any issue.


Again, there's nothing 'illegal' or 'wrong' about using non-standard notes; only remember that they are non-standard. 12-tone equal temperament starting on A=440hz happens to be the most normative source of musical material in the West nowadays, so if you'll be doing something different, please keep the fact of your departure in mind and don't be upset if you're challenged for it.
You might could use some double modals.
Last edited by AETHERA at Mar 13, 2016,
#28
I was mostly just interested in instruments that accomplish what I have in mind. I enjoyed theognia777 and her vast knowledge of non western instruments, I was actually quite impressed by some of those musicians, but I didnt get a lot of information about the instruments themselves. I would like to know more about this and look at examples before I go and take all the frets off my Jackson and wreck my guitar.

I have a question about the harmonic series. This series goes on forever, how many intervals does it take before the notes (other than the starting note)to naturally form octaves of themselves? and how many different notes does it actually produce? Does it produce an infinite amount of different notes? Or at some point, does it no longer produce new notes, but only octaves of the previous notes?
#29
Have you even thought of the dwindling harmonic ENERGY it takes to make higher harmonics? On my bass I can make just less than 5 octaves of harmonics

String G
G-D-G-B-D-F-G-A-B-C#-D-F-G .... F
Glad to cross paths with you on this adventure called life
Quote by Jet Penguin
lots of flirting with the other key without confirming. JUST LIKE THEIR LOVE IN THE MOVIE OH DAMN.
Quote by Hail
you're acting like you have perfect pitch or something
#30
Quote by jrcsgtpeppers
I have a question about the harmonic series. This series goes on forever, how many intervals does it take before the notes (other than the starting note)to naturally form octaves of themselves? and how many different notes does it actually produce? Does it produce an infinite amount of different notes? Or at some point, does it no longer produce new notes, but only octaves of the previous notes?



Well you start with your base frequency and and double it to get the octave, multiply the fundamental by 3 to get the perfect 5th, multiply by 4 to get another octave of the fundamental, multiply by 5 to get the major 3rd, multiply by 6 to get another perfect 5th, etc. Basically anytime it hits a multiple of a previous frequency that's an octave, anytime it hits a number that's not a multiple of anything you haven't hit yet it's adding in another note in between.

If you'll look at the chart under "harmonics and tuning" on wikipedia look at the harmonic numbers in order (1, 2, 3, 4 etc) and notice how it jumps around. First it just doubles, then at 3 it goes for the halfway point, then goes to the top and hits the octave again, fills in the major third, hits the 5th again, fills in the ~b7, then it starts at the top again hitting every note that's been hit, plus the ones in between. The further you go the more in between notes you get, but you also continue to hit multiples of every note you've already got. It repeats itself but adds more as well.

After a point the spacing gets so close together that it's hard to distinguish between them, much less play it.


I know it's been covered, but I'm typing now and feel like reiterating - if you try to stick with a pure harmonic series you're throwing away the ability to change keys and have them all sound the "same". Not that there's anything inherently wrong with that, but it's a trade off.

If you take the harmonic series of 110, "A" and compare it to the harmonic series of 330 "E", the 3rd note in the A series, which is the most closely related without being a multiple (and thus the same) you'll see that the a lot of the same frequencies are used at first. Say the original, A, root is "1" so that the root of E, 330, is "5" in the E series (referring to the notes as intervals of A) you'll see 5, 5, 2, 5, 7, 2, 4, 5, and then you hit a note that's in between 110x13 and 110x14. I don't have enough understanding of the math to know if it does hit it eventually further down the "A chain", but regardless, it will clash against the b6 and b7 of the original key and they're much stronger than anything further down the line. Sorry if the way I wrote that is confusing. Basically the "E, B, G, and D" from the A series match up with the E series, and then it starts getting screwy and those are only a 5th away. From what I understand from reading (haven't done the math) the further away you try to modulate (like a major 3rd or a minor 2nd) the more screwed up it gets.

Of course this all goes away if you're not using frets or keys or anything set - then you can adjust by ear. If you want keys or frets it either limits your ability to change keys and have your ratios right (you have to play in one key all the time for it to sound "perfect"), or else you go with an equal temperament scheme so that everything's out a little bit by the same amount. Honestly it sounds fine to me and that's what it's all about right?


edit: sorry for all the repetition. I was doing some of the math as I was writing that to make sure I got it right and I think the recursiveness seeped into my thought process


double edit - just had a thought. if you follow the logic that it keeps adding in the in between notes all the way down basically any note will show up in the series somewhere down the line and at least be a low octave of something[/] way down the line.
Last edited by The4thHorsemen at Mar 14, 2016,
#31
My question is why don't we play instruments that produce only the notes contained in the harmonic series.


If you want an instrument that is capable of playing all those harmonics you are after, trumpet or any brass instrument is your answer. Actually, the whole brass playing technique is based on the harmonic series.

The trumpet's three valves are there to allow you to play chromatic notes. But pushing down a valve actually just lengthens the tube and lowers the pitch. It allows you to play different harmonic scales.



Of course you can play notes above those but it requires some advanced technique. Actually, I think horn would be a better instrument for achieving more harmonics easier. Or why not trombone? It has a slide so you can play any note you want.
Quote by AlanHB
Just remember that there are no boring scales, just boring players.

Gear

Bach Stradivarius 37G
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Last edited by MaggaraMarine at Mar 14, 2016,
#32
Quote by jrcsgtpeppers
Oh yeah? You know how much I study and what I study? You don't think I've studied everything I can think of related to my questions? Let's hear it internet geniuses. Why don't you explain it. Or you can just keep telling me things I already know. That pisses me off. Thank for tellin me fucking horns can make the first few harmonics. I had no fucking idea.
Jeez, what did you do, get up on the wrong side of your bridge?
#33
Quote by jrcsgtpeppers
I have a question about the harmonic series. This series goes on forever, how many intervals does it take before the notes (other than the starting note)to naturally form octaves of themselves? and how many different notes does it actually produce? Does it produce an infinite amount of different notes? Or at some point, does it no longer produce new notes, but only octaves of the previous notes?

Did you actually read my earlier post? Did you not understand the chart?
I listed the first 19 harmonics of A=110. You can see the other notes produced, and how they're calculated (by simply multiplying the fundamental).

If you want equivalents on the guitar, try this (overtones of A):
1st harmonic = open A string
2nd harmonic = A, 3rd string fret 2 (12th fret 4th string)
3rd harmonic = E, 1st string (all the following are on 1st string)
4th harmonic = A, fret 5
5th harmonic = C#, fret 9 (the fretted note is a little sharper)
6th harmonic = E, 12
7th harmonic = G (1/3 of a half-step flat), fret 15
8th harmonic = A, fret 17
9th harmonic = B, fret 19
10th harmonic = C#, fret 21 (sharp, as previous)
11th harmonic = in between D and D#, frets 22/23
...
etc.
You can see that the notes get closer and closer together, and many end up between the frets - such as the 11th harmonic and the 13th, which is between F and F# (frets 25/26, if you had such frets).

All of those notes are, of course, contained in the A string itself, but increasingly fainter the higher they go. But if you want, you can produce most of them (up to the 9th anyway) by picking them on the A string. The nodes (touch points) occur over the following frets:
2nd harmonic= fret 12 (A)
3rd = 7, 19 (E)
4th = 5, 24 (A)
5th = 4, 9, 16 (C#, 14 cents flat of ET)
6th = 3 (approximately) E
7th = in between 2 and 3, a little nearer 3 (G, 32 cents flat of ET)
8th = in between 2 and 3, a little nearer 2 (A)
9th = 2, B (4 cents sharp of ET).

The higher the harmonic, the closer to the bridge you need to pick, to make sure you're not picking over a node itself. (Remember the harmonic number is the same as the string fraction.) Also you need to be more and more precise with where you touch, because the notes get closer and closer.

The only harmonics that are in tune with ET are all the A's (2nd, 4th, 8th, 16th etc). All the others are out of tune to varying degrees, but the 3rd and 6th (E) are only 2 cents sharp of ET.

You'll also notice that the harmonic pitches get closer and closer together, in a gradual progression. Eventually, when you get to the 17th or 18th harmonic, the notes are a half-step apart. Beyond there, they're less than a half-step apart.

BUT... that's just information about the harmonic series and the guitar! (probably not what you need to know....)
What I forgot to say in my earlier posts - and I really should have thought it! - is that you can easily program a synth to produce these pitches. Rather than struggle with a trombone - or playing harmonics on a guitar string (or ripping the frets off!) - get yourself a programmable synth.
Even the free recording program Audacity allows you to generate your own frequencies (using simple sine, square or sawtooth waves, so you may not like the sounds.)
(Of course you can use a slide on a guitar - and keep your frets - but then you need to be really sure where your harmonic pitches are.)
Last edited by jongtr at Mar 14, 2016,
#34
A music major produced a sound track "feedback/feedfront" with a synth..and several tape loops .. recording the lowest tone possible at the slowest speed possible and fed that into a feedback mode..that of course produced "a scale of overtones" then fed that into another tape loop..etc..and while you could hear the overtones creating higher and higher scales..you could not decipher any particular note or melodic pattern..much like wave after wave..as it went into the higher registers the patterns became tighter and brighter..at a certain point you could no longer hear the beginning of a new pattern ...

an artist I know did the same thing visually..using a copy machine..he had a page with large type that said "the disappearing project"
He then copied that page and from that copy he copied it etc..after 50 or so pages the type broke up into wide spaced dots and you could no longer read the statement and eventually you would need visual enhancements (magnifying glass etc) to see any trace of text left-and ultimately a pure blank page...everything decomposes at a point..nothing is free..cut something in half does not mean you now have "two" of something

I believe John Cage had a similar "project" in his work..what I am curious about is what kind of composition can be created with the middle to extreme ends of this endeavor..interest fades fast with repetition no matter how creative
play well

wolf
Last edited by wolflen at Mar 14, 2016,
#37
Quote by jrcsgtpeppers
My question is why don't we play instruments that produce only the notes contained in the harmonic series. What does that question have anything to do with anything any of you have said?


We do. Any instrument without stops or keys can play a ideal intervals in any key. All the strings (except guitar), voice, trombone, slide guitar,probably some brass instruments if the player is good... The problem is that instruments like normal guitar and keyboards have very ffixed pitches, so they have to compromise on interval "purity" in order to sound decent in every key.

Although, you can't really have two ideal intervals going at the same time, so you can't even have a "pure" triad, because one of the constituent 3rds will be sharpened or flattened in order to make the 5th pure. Now, if you go play your guitar and bend up to the ideal thirds, you'll hear they produce a godawful 5th.

Basically the point is that the math of the harmonic series does not produce the same numbers by starting at different points in the original harmonic series.

Because variations of the octave, 4th, and 5th are so obvious to the listener, it makes a lot more sense to fudge the intervals that have more aural wiggle room. That means modern tuning is made so that all of the perfect intervals are as close to ideal as possible.

Quote by jrcsgtpeppers
Oh yeah? You know how much I study and what I study? You don't think I've studied everything I can think of related to my questions? Let's hear it internet geniuses. Why don't you explain it. Or you can just keep telling me things I already know. That pisses me off. Thank for tellin me fucking horns can make the first few harmonics. I had no fucking idea.


If you don't know something yourself, you're not in a good position to tell other people they are wrong.

You're getting answers you find frustrating because you're asking questions that bear little relevance to the creating or playing of music. It's like you're going into a car dealership and getting really hung up on whether the tailpipe exhaust is close to its ideal volume relative to engine temperature. Yes, it's part of the car, but it has nothing to do with actually driving or owning it. And even if the poor car salesman could produce the equation that defines tailpipe volume, you wouldn't have any idea how to use it.

It's clear there's a particular answer you're expecting, but you need to accept that such answers don't always exist. You'd learn a lot more if you'd read the factual, historical information people are posting.

You're also being really hard headed about background information. You get told to study music history because your questions are answered quite thoroughly by it. Where do you think any of us learned about these concepts? We studied or took classes about music history, theory, or composition. There's usually no short way to explain these things except by crudely piling these concepts in chronological order.

Your insistence on mathemtizing music is frankly baffling, especially since this conversation makes it apparent that you're not grasping the math end of music theory, either. There's a reason that most composers only get into this kind of mathy music when they're doing niche PhD stuff: it's not interesting to most listeners, and using math in music still requires a very strong understanding of how melodies and harmonies are perceived by listeners. You can have fun with the harmonic series and wolf notes all you like, but if you want to turn interesting sounds into music, you still need practice making music.
Last edited by cdgraves at Mar 14, 2016,
#38
The harmonic series is infinite, this can be proven mathematically. It will theoretically create an infinite number of NEW notes that have not occurred previously in the harmonic series. It will also continue to produce an infinite number of octaves of every single one of those new notes it creates.

1) as pointed out above the dwindling harmonic ENERGY it takes to make higher harmonics.

2) Also human perception is limited. If we programmed a synthesizer to play scale based on a the harmonic series with 8192 distinct notes per octave we couldn't tell the difference between any ten neighbouring notes.

So yeah it's theoretically possible but not practically

In regard to setting up a fretted instrument it is very limiting to do so in just tuning as you can only ever play in one key. But it also begs the question - why use frets? Frets limit you to predefined tones. Fretless stringed instruments are capable of playing any increment of any tone you want depending on where you put your finger.

So if you want to play in the "key of God" then ditch the guitar and pick up a violin...

...or get a fretless guitar
https://www.youtube.com/watch?v=ewCZ-TWdx40
Go nuts Peppers
Si
#39
Quote by jrcsgtpeppers
I have two major concerns about music right now. The first is there is no empirical evidence to support the tuning of A = 440. This isnt really a question, but it bothers me. What could we use instead? What naturally resonating pitch would be a better choice to tune our instruments to?

This brings me to my actual question. Why dont we just use the notes of the harmonic series instead of 12 tone equal temperament? I'm not sure I understand. The harmonic series produces naturally occurring overtones, definite empirical meaning. WHy make up approximations? There are many fretless stringed instruments with the perfect ability to play only the notes that exist in the overtone scale. Why isnt that the standard?

If you start on C, and cut it in half, you get C, cut it in thirds and you get G, but it isnt the G we use. It is an actual G in relation to C. Why cant we just make an instrument with all the possible C's. then all the possible G's but the actual G's proportionate to the C's, then in 1/5ths and mark out where those notes exist and so on and so forth until the notes become so small apart that it isnt practical to make more in between notes.

I'm sure this exists and I am sure there is plenty of information on this that I cant find.



What Hz A is, is arbitrary, and makes no difference. We have to use some standard, and for historical reasons it just ended up being that.

We use equal temperament now, because that way, when we switch key it won't sound different.

If you want to know first hand, just get yourself a piano plugin that lets you tune it that way, and play around with it.
Last edited by fingrpikingood at Mar 14, 2016,
#40
I think the TS should take up the Theremin, and pray for perfect pitch.

Although, why under take this campaign even if you have perfect pitch, unless you have a frequency counter in you head as well....?
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