Harmonic Series?

Seriously, i've never heard of "harmonic series" before! What is a harmonic series? What is it for?

I am so frustrated, its like i was supposed to know what a harmonic series is a long time ago.

Tchaikovsky doesn't mention it in his harmony guide :/

The harmonic series is the series of overtones of a fundamental pitch, so if the fundamental frequency is f then the frequencies in the harmonic series are f, 2f, 3f, 4f, 5f,... and of course double the frequency means one octave higher. Other ratios correspond more or less precisely to diatonic intervals - for instance 3:2 corresponds to a perfect fifth. However, apart from the 2:1 ratio for an octave, the intervals do not correspond exactly to intervals within equal temparement.

The harmonic series is less a "musical" element than it is "scientific". 

It's the physics behind how musical instruments work and is especially important for brass instruments. 

I suppose an understanding of it can help in writing (especially for brass) when knowing how "far" an interval might be, as far as which partial (level?) of the series you're starting on.

The harmonic series is less a "musical" element than it is "scientific". 

 

It's the physics behind how musical instruments work and is especially important for brass instruments. 

 

I suppose an understanding of it can help in writing (especially for brass) when knowing how "far" an interval might be, as far as which partial (level?) of the series you're starting on.

Indeed, sounding harmonics is the physical foundation of brass playing and the harmonic series is the basis for Pythagorean ideas of consonance and harmony, deriving from a study of the lengths of vibrating strings in relation to frequency hence musical pitch. String players, needless to say, can stop strings at a different position to obtain a different pitch, but brass (except the slide trombone) does not have that advantage: special techniques are used to make an instrument sound in tune. It's a moot point how much an understanding of the series aids composition; while awareness of which harmonics will actually be used in a performance might allow some notion of how a group of brass instruments will blend together in harmony, writing should be assumed to conform to the usual chromatic scale - the real problem is thus not how far a given harmonic might differ from a "standard" pitch, because all notes are expected be "in tune", the real problem is the difficulties brass players have in rendering the composer's intentions. Skilled brass players are an extraordinarily valuable asset!

Do kids these days not know about google?

If you could learn everything you wanted from google schools, universities and this forum would be useless. 

You can learn by experimentation too. Find a piano and try this. Press and hold  A(440Hz) above middle C without sounding it. Then strike the A (220Hz) an octave below and let it go. You should hear the A440 ringing. this is because it is the first harmonic of the lower A. Try this again, this time holding down the E above A440. And you will hear this string resonate, the second harmonic of A220, but at a lower volume. You can do this for every harmonic that is based on the fundamental pitch. See the series here. https://en.wikipedia.org/wiki/Harmonic_series_%28music%29. All musical instruments produce these harmonics, but at different volumes. For example, the clarinet produces a sort of hollow sound because of the preponderence of odd harmonics. You can train yourself to hear these harmonics when deciding which instruments and the notes they play will work together in an orchestration.

If you could learn everything you wanted from google schools, universities and this forum would be useless. 

You're saying they aren't?

You can learn by experimentation too. Find a piano and try this. Press and hold  A(440Hz) above middle C without sounding it. Then strike the A (220Hz) an octave below and let it go. You should hear the A440 ringing. this is because it is the first harmonic of the lower A. Try this again, this time holding down the E above A440. And you will hear this string resonate, the second harmonic of A220, but at a lower volume. You can do this for every harmonic that is based on the fundamental pitch. See the series here. https://en.wikipedia.org/wiki/Harmonic_series_%28music%29. All musical instruments produce these harmonics, but at different volumes. For example, the clarinet produces a sort of hollow sound because of the preponderence of odd harmonics. You can train yourself to hear these harmonics when deciding which instruments and the notes they play will work together in an orchestration.

This isn't the best way to familiarize yourself with the harmonic series for several reasons:

a) The harmonic series is comprised of integer ratios which produces frequencies not found in the equal tempered chromatic scale. More important than the order in which the "notes" come in the series are the exact frequencies of said notes as they are essential to understanding the harmonic series and how it serves as the basis for intonation in non-fixed pitch instruments and the voice

b) What you're hearing is just the undampened string vibrating sympathetically with the harmonics of the struck string. All of the "harmonics" on a 12-TET piano except for those with an octave relationship to the fundamental will be faint (with some exceptions) because the mismatched frequencies don't resonate very strongly.

c) Piano strings are somewhat inharmonious and their partial vibrations (especially those of the lower strings) do not conform exactly to the model of the harmonic series.

What I would recommend instead is to pick up overtone singing (which is not as difficult as it seems) or experiment with the harmonic series on a bowed string instrument. Through a process called mode-locking which I must admit I do not fully understand, the periodic vibrations the vocal cords effect on the column or air inside the throat and the bow on a string cause the harmonics to become (in most cases) ideally harmonious. Going about it this way is way more beneficial to your hearing and also gives you hands-on experience with the actual series itself which to me makes me appreciate it in a much more profound way.

By the way, have you guys noticed how the harmonic series is an endlessly repeating fractal pattern? Compare the normal harmonic series to that built on every even harmonic, and that to the series built on every fourth harmonic starting on the fourth harmonic. More concisely, on each new octave at the nth partial (1,2,4,8,16,32 …) , a new sub-series is started, with every nth partial belonging to it. Where it gets interesting is that these sub-series are inharmonious (because every repeating partial except for octaves of the fundamental become more and more compromised the higher up you go).* I have only calculated the series up to the 32nd partial though so I do not know how distorted the series gets at the edge of human hearing.

If anybody is interested, these are the first 32 partials on the fundamental A0 (for no other reason than it is the lowest note on the piano):

The numbers next to each note refer to the harmonic number, octaves are boxed, fifths are circled, and the cent deviations refer to how much the notes on an equal tempered piano need to be adjusted to conform to the harmonic series. An effort was made to make the series fit "in the key of A major" but it is not always intuitive. I did not use any microtonal accidental symbols, so in the highest partials two partials are represented by the same note sign with different frequency deviations.

* I obviously rounded all of the numbers to two decimal places and I don't quite remember the original numbers. For example, the fifth partial and the tenth here show the same deviation in cents but it may well be that they are not identical and that the thirds and sixths deteriorate less. The fifths for example become "very" out of tune immediately after the 3rd partial.

It is possible in the case when  the knowledge of the inside structure of the matter with which is operated almost or quite doesn't influence on the results. The use of the majority of  music instruments is such  one. The new structure  of music note  which I have proposed is definitely  other case.  Its use is realized by the computer program  
 (see http://home.arcor.de/yuri.vilenkin/new-music-atoms.html )
I understand that people  have little time to learn program  instructions and anybody is difficult to make up his mind for that. Therefore I have attached  links to several example mp3 files of created music segments in the category Electronic ( topic-Example mp3 files)  . In any case I would be very grateful for  comments.

Greetings
Yuri Vilenkin

besam-14aug.mp3

donna-14aug.mp3

libiamo-14aug.mp3

santa-14aug.mp3

wagn-14aug.mp3