TromboneChat

I like to stretch my pedant muscles once in a while. This time:

The musical harmonic series is, in mathematical terms, depending on how you look at it, actually an arithmetic progression or a harmonic sequence.

For quick reference:

https://en.wikipedia.org/wiki/Harmonic_series_(music)
https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)
https://en.wikipedia.org/wiki/Harmonic_progression_(mathematics)
https://en.wikipedia.org/wiki/Arithmetic_progression

Why do we use the term "harmonic series"?

Well the term "harmonic" refers to music. That mathematical concept is derived from the musical/acoustic principle of harmonics.

On the first link you give:

"The musical pitch of a note is usually perceived as the lowest partial present (the fundamental frequency), which may be the one created by vibration over the full length of the string or air column, or a higher harmonic chosen by the player. The musical timbre of a steady tone from such an instrument is strongly affected by the relative strength of each harmonic."

So it's either the lowest pitch in that harmonic series, or a higher one chosen by the player. Sounds an awful lot like the overtone series.

Quote from: harrison.t.reed on Yesterday at 07:24 AMOn the first link you give:

"The musical pitch of a note is usually perceived as the lowest partial present (the fundamental frequency), which may be the one created by vibration over the full length of the string or air column, or a higher harmonic chosen by the player. The musical timbre of a steady tone from such an instrument is strongly affected by the relative strength of each harmonic."

So it's either the lowest pitch in that harmonic series, or a higher one chosen by the player. Sounds an awful lot like the overtone series.

Sure.

There's another term that uses "series" which in math terms is an infinite sum, not an infinite set.

Quote from: Le.Tromboniste on Yesterday at 06:44 AMWell the term "harmonic" refers to music. That mathematical concept is derived from the musical/acoustic principle of harmonics.

Do you know if "harmonic" was coined by someone, or just kind of evolved linguistically from an earlier language?

Quote from: Andrew Meronek on Yesterday at 08:10 AMDo you know if "harmonic" was coined by someone, or just kind of evolved linguistically from an earlier language?

Harmony, from Greek harmonía.

I mean, many of the basic understanding of acoustics and music came to us from (or through) the Ancient Greeks. That includes the basics of the harmonic series.

We can't be sure that he was the first to experiment with that and figure that out (he probably wasn't) but Pythagoras is generally credited with formulating the basic theory of how harmonics work (which was of course extensively improved and expanded in the centuries since).

Quote from: Andrew Meronek on Yesterday at 08:09 AMSure.

There's another term that uses "series" which in math terms is an infinite sum, not an infinite set.

From my (limited) understanding of advanced maths a series can be any infinite sum OR sequence. The harmonic series is a sequence, not a set (the order of the terms matter), and it is infinite, therefore it is a series.

Quote from: Andrew Meronek on Yesterday at 08:09 AMSure.

There's another term that uses "series" which in math terms is an infinite sum, not an infinite set.

Right, but you asked why we call things what we call them. It's not much of a stretch to see that the paragraph I quoted from the article you sourced is probably why we call it what we do. We are talking about music, and while music teachers (emphasis on teachers) love to say music is math, nearly every musician I know really isn't good at math at all. Music and math might be related, but math and musicians are usually not.

Solved.

If you want to do a topic on "we actually should be calling the overtone series XYZ because of math", don't phrase it as a question you already know the answer to, you smarty pants you.

Quote from: harrison.t.reed on Yesterday at 09:36 AMRight, but you asked why we call things what we call them. It's not much of a stretch to see that tha the paragraph I quoted from the article you sourced is probably why we call it what we do. We are talking about music, and while music teachers (emphasis on teachers) love to say music is math, nearly every musician I know really isn't good at math at all. Music and math might be related, but math and musicians are usually not.

Solved.

If you want to do a topic on "we actually should be calling the overtone series XYZ because of math", don't phrase it as a question you already know the answer to, you smarty pants you.

Yes exactly. Plus the harmonic series in mathematics comes is called "harmonic" because of music, not the other way around!

Quote from: harrison.t.reed on Yesterday at 09:36 AM...We are talking about music, and while music teachers (emphasis on teachers) love to say music is math, nearly every musician I know really isn't good at math at all. Music and math might be related, but math and musicians are usually not...

I recall how in the 80s it was very common to claim "a study shows" that musicians were naturally good with computers.   

Quote from: harrison.t.reed on Yesterday at 09:36 AMMusic and math might be related, but math and musicians are usually not.

Oh, I'm not too sure about that. Many of my musician friends are pretty good programmers and engineers.

Quote from: Le.Tromboniste on Yesterday at 08:20 AMHarmony, from Greek harmonía.

I mean, many of the basic understanding of acoustics and music came to us from (or through) the Ancient Greeks. That includes the basics of the harmonic series.

We can't be sure that he was the first to experiment with that and figure that out (he probably wasn't) but Pythagoras is generally credited with formulating the basic theory of how harmonics work (which was of course extensively improved and expanded in the centuries since).

Ah, thanks for reminding me of that. I wasn't aware that the term "harmony" comes from Greek, though. 

Quote from: Le.Tromboniste on Yesterday at 08:25 AMFrom my (limited) understanding of advanced maths a series can be any infinite sum OR sequence. The harmonic series is a sequence, not a set (the order of the terms matter), and it is infinite, therefore it is a series.

Do you have an example of a formal math harmonic series that is not a sum? The Wiki doesn't bring one up:

https://en.wikipedia.org/wiki/Series_(mathematics)

Along the lines of being a pedant, I think that it's worth making a bit of extra effort to try to align terms used in different fields. There are so many fields of study in the world now, and having each speak their own dialect really makes it difficult for people to cross genres, so to speak. Usage of "series" in music versus in math is one example. Another comes up where I work:

I was once upon a time a Computer Science major. In computer programming, we have these things called variables. Now in a prominent industry software programming environment that uses ladder logic based on a visual design for electrical prints (RSLogix, for anyone curious) they call variables tags. I know there is a good historical reason for this: these tags in the software once were associated with actual tags that would get put on wires and cables. But now, these tags generally are not except in special cases but are still called tags in this environment instead of variables, even though in the rest of the computer programming world, "variables" is the term of choice. Things like this are just one of many, many little things that makes for extra work when translating ideas between fields.

Quote from: Andrew Meronek on Yesterday at 11:16 AM

 Now in a prominent industry software programming environment that uses ladder logic based on a visual design for electrical prints (RSLogix, for anyone curious) they call variables tags.
Yes, I've used that software, especially a program using the first couple letters of the alphabet.

it defies everything taught in computer programming classes:  top down, modular design, single entry single exit, single reference, a bunch more I've long since forgotten.  Every single line in a program can call any other line or be called by any other line.  And NOBODY bothers to document.  I came to hate it. 

I first saw it in 1990 with my first manufacturing plant job, in rural Alabama where few if any of the mechanics finished high school.  Most had never seen a computer.  They actually did understand ladder logic to an extent, but not enough to use the program.  It came with an interface board that needed DIP switches set, and interrupt requests configured.  Needless to say all that landed on my desk. 

Quote from: Andrew Meronek on Yesterday at 11:16 AMAlong the lines of being a pedant, I think that it's worth making a bit of extra effort to try to align terms used in different fields. There are so many fields of study in the world now, and having each speak their own dialect really makes it difficult for people to cross genres, so to speak. Usage of "series" in music versus in math is one example.

Well they do call it a harmonic series in math, no? How is it not aligned? 

What would you like to call it?


Should we change the World Series to the World Championship? Come to thing of it, it only involves the american pro leagues, so World is also wrong, should we call it the American National Championship?

Quote from: Le.Tromboniste on Yesterday at 01:48 PMWell they do call it a harmonic series in math, no? How is it not aligned? 

In math, the harmonic series is an infinite sum, not the same as how musicians use the term.

Quote from: Andrew Meronek on Yesterday at 08:38 PMIn math, the harmonic series is an infinite sum, not the same as how musicians use the term.

Yes but they're not talking about maths.

Are you saying nobody should be using the word series in any context because it has a different meaning in maths as the general meaning people understand it to have?

I really don't see where you're going with this argument. It's a bit obtuse and sterile

Quote from: Le.Tromboniste on Today at 03:42 AMYes but they're not talking about maths.

Are you saying nobody should be using the word series in any context because it has a different meaning in maths as the general meaning people understand it to have?

I really don't see where you're going with this argument. It's a bit obtuse and sterile

No. I'm suggesting to use the words in the same way that mathematicians use the words. Or, lacking that, to at least learn how the terms differ.

Quote from: Le.Tromboniste on Today at 03:42 AMAre you saying nobody should be using the word series in any context because it has a different meaning in maths as the general meaning people understand it to have?
Quote from: Andrew Meronek on Today at 05:36 AMNo. I'm suggesting to use the words in the same way that mathematicians use the words.
Quote from: harrison.t.reed on Today at 08:15 AM

Yup, got nothing more to say

"Series" has a lot of uses outside of even music or math that are not exactly like how it is used in music or math so maybe it is asking more than we need for even the music and math "series' to align exactly.

a television series
a series of steps
The World Series
the HAL Series 9000
a twelve-tone series ("serial" music)
wiring in series

You'll never be able to conform all those.

Quote from: robcat2075 on Jan 20, 2018, 09:31AMYou'll never be able to conform all those.

I never said I want to. 

Quote from: Le.Tromboniste on Jan 20, 2018, 09:16AMYup, got nothing more to say

OK . . .

If you're not interested in looking at a different angle to try to come to a deeper understanding of some of music theory, why take part in this thread?

Quote from: Andrew Meronek on Jan 21, 2018, 06:20AMOK . . .

If you're not interested in looking at a different angle to try to come to a deeper understanding of some of music theory, why take part in this thread?



"Deeper understanding? I just want to know which stinkin copper-zinc alloy this trumpet mouthpiece I bought goes to!"

Quote from: Andrew Meronek on Jan 21, 2018, 06:20AMOK . . .

If you're not interested in looking at a different angle to try to come to a deeper understanding of some of music theory, why take part in this thread?

Well you're right on one thing, I'm going to leave this thread because I have no interest in it. But you're wrong on the rest. You assume without knowing me I don't have an understanding of it (which I do, to the extant that I studied music and not physics or engineering. I did take acoustics classes and read on the subject and have worked a lot with the concept of harmonics when learning about intonation and different tuning systems. But I of course know much less about acoustics than a trained sound engineer or acoustician) and that I have no interest in learning about it (which I very much do).

But the thing is, you haven't really approached any aspect of music theory in any kind of depth thus far in the discussion, you have merely made a barely substantiated case about how we call it, and that's it. Want to talk about the harmonic series in depth? Go, I'll have things to say and things to learn.

But merely discussing how bad the name it has had for decades is based on the fact that it doesn't line up with another field's terminology is a sterile and pretty useless discussion. A) nobody cares how it's called if they understand what it is and how it works, B) we're not going to change the name that every musician and every acoustician and every book uses at the end of this discussion. It'll still be called the harmonic series at the end of the day.

Quote from: Le.Tromboniste on Jan 21, 2018, 12:19PMBut merely discussing how bad the name it has had for decades is based on the fact that it doesn't line up with another field's terminology is a sterile and pretty useless discussion. A) nobody cares how it's called if they understand what it is and how it works, B) we're not going to change the name that every musician and every acoustician and every book uses at the end of this discussion. It'll still be called the harmonic series at the end of the day.

It's not a *bad* name, just trying to be part of a discussion about improving it. Innovation comes very often from cross-disciplinary insights.

Quote from: Andrew Meronek on Jan 21, 2018, 06:18AM
QuoteYou'll never be able to conform all those.I never said I want to. 

But it seems you are wanting to relate "harmonic" series and mathematical series.

My assertion is that they are not highly related.  They happen to have "series" in both their names, but there isn't some hidden greater meaning in that.

The Mathematical series intends to show a sum of harmonics.  According to Wikipedia:

QuoteIts name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string
The whole article is here: https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)

We know that there are vibrating modes of a string or column of air.  In fact, the sound we produce is a mixture of harmonics; the relative amplitudes of them dictating the tonal quality.  My sound is not a pure wave and I suspect nobody else's is either.

Quote from: BGuttman on Jan 21, 2018, 04:22PM  My sound is not a pure wave and I suspect nobody else's is either.

That is correct. In fact nothing naturally produces a pure wave, the only way to do it is electronically and although it's "pure", it sounds to us very foreign and not natural at all.

Quote from: robcat2075 on Jan 21, 2018, 02:08PMI never said I want to. 


But it seems you are wanting to relate "harmonic" series and mathematical series.

My assertion is that they are not highly related.  They happen to have "series" in both their names, but there isn't some hidden greater meaning in that.

No, I was trying to assert, however badly, that they are noy highly related and that there are other concepts in math that relate to a musical harmonic series better. There are actually a couple of different concepts in use in math, with different terminology, that are used more precisely:

The harmonic sequence is the set of fractions of it's unit length a string vibrates when driven: 1/1, 1/2, 1/3, 1/4, . . .

An algebraic progression, in our case derived by adding one to each successive term, is the substance of the extended ratio of frequencies that sound a driven string: 1,2,3,4, . . . is the progression; 1:2:3:4: . . . is the extended ratio.

I've seen people use "musical harmonic series" for both. They are certainly closely related, but not the same thing. I've also seen people refer to a specific octave of the musical harmonic series: 8/8, 9/8, 10/8, 11/8, 12/8, 13/8, 14/8, 15/8 which is a different way of expressing a part of that extended ratio.

Quote from: robcat2075 on Jan 21, 2018, 02:08PMI never said I want to. 


But it seems you are wanting to relate "harmonic" series and mathematical series.

My assertion is that they are not highly related.  They happen to have "series" in both their names, but there isn't some hidden greater meaning in that.

No, I was trying to assert, however badly, that they are noy highly related and that there are other concepts in math that relate to a musical harmonic series better. There are actually a couple of different concepts in use in math, with different terminology, that are used more precisely:

The harmonic sequence is the set of fractions of it's unit length a string vibrates when driven: 1/1, 1/2, 1/3, 1/4, . . .

An algebraic progression, in our case derived by adding one to each successive term, is the substance of the extended ratio of frequencies that sound a driven string: 1,2,3,4, . . . is the progression; 1:2:3:4: . . . is the extended ratio.

I've seen people use "musical harmonic series" for both. They are certainly closely related, but not the same thing. I've also seen people refer to a specific octave of the musical harmonic series: 8/8, 9/8, 10/8, 11/8, 12/8, 13/8, 14/8, 15/8 which is a different way of expressing a part of that extended ratio.