Our western harmonic system explained in a simple way (I hope)

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Marco Raaphorst
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18 Aug 2018

Our western scale system, based on the major scale (and relative church scales like Dorian etc), seems to be following the mathematics and physics when pitching tones.

Yeah, sorry, my English is not perfect, so I hope I can manage :D

With tone pitching I mean: if you take for example an A note at 440 hertz and double it you get an A at 880. This is what we call the octave. If you multiply the A440 with 3 you get: 1320 hertz, this frequency (a note we call an E) is related to the A440 as a quint/fifth interval. 4 time 440 = 1760 hertz, which means it is two octaves related to the A440. If we multiply 440 with 5, we get: 2200. This tone is a C# and is a major third interval.

So this happens when you start multiplying. You can try this yourself using a couple of strings with the same length and doing this:
- leave one like it us, untouched
- cut one string in half
- cut one string in 3 equal parts
- cut one string in 4 equal parts
- cut one string in 5 equal parts

What you just did is create the same tones as I am describing above. These strings form a major chord including 2 additional octaves. So the tonality is, thanks to the octaves, crystal clear. And it is 100% major sounding. Cool right?

But a more simple trick is using a synth. For example using Europa and select a couple of oscilators/wavetables and check your spectrum analyser:
If you set it to Basic Analog you'll get relative pure Sine Wave tone with no overtones (only at an extremely low level, but this is how sine waves work: no overtones!)
If you set it to Square-Ramp you will see these overtones appear in the spectrum analyser: C3 C5 E5
If you set it to Saw-Triangle you see this: C3 C4 G4 C5 E5 G5
If you set it to Pulse Width you see this: C3 C4 G4 C5 E5 G5

So the first 5 harmonics (the 1st harmonic being the tonica, the base tone) of a NOTE are forming the notes of a major chord in the same way as when we would multiply a pure tone. And notice how the Square-Ramp is missing a couple of overtones, a couple of octaves. But it still creates a major third triad.

Btw if you would look at the 7th harmonic it is a A#5. A flatted 7 (ha!). So the first harmonics are forming a major 7 chords, a blues chord, a dominant 7. Isn't that funky?

So the natural harmonics of most tones are simply a matter of multiplications of the root note.

If you have like 4 synths with a pure sine wave playing C3, C4, G4, C5, E5 & G5, this will sound the same (except for the timbre) as playing ONE note using a saw wave synth for example. This is how it is all so related. 100%

And for those of you who are aware of distortion/saturation, either analog or digital, those tones C3, C4, G4, E5, G5 are 100% the same as odd an even harmonics.

So saturation is following the exact same physics as what happens when we start cutting strings in half, 3 times etc or when we look at the natural harmonics of tones.

These tones are forming the major scale. Multiplications of 2 and 4 will create octaves, and 3 and 5 will create an fifth and a major third. So now you will start to understand why the 1, 3 and 5 are so powerful in Western music. These tones are simply the result of simple basic physics and I am absolutely sure our brains are trained to recognise those very common intervals, simple distances between frequencies. We can all count 'till 7 right? :D

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etyrnal
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18 Aug 2018

Not a fan of major keys

Sent from my XT1575 using Tapatalk


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Marco Raaphorst
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19 Aug 2018

etyrnal wrote:
18 Aug 2018
Not a fan of major keys

Sent from my XT1575 using Tapatalk
minor is just a turnaround of the major key, same notes, only different root

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Ahornberg
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19 Aug 2018

my 2 cents :puf_bigsmile:

Our modern western system divides the octave into 12 equal steps:
  • One octave equals 1200 cents.
  • One semitone equals 100 cents.
  • A major third equals 400 cents.
  • A pure fifth equals 700 cents.
  • A minor seventh equals 1000 cents.
But in the overtone series, these values show up like this:
  • One octave equals 1200 cents.
  • Semitones are all different in size, depending on their position to the root note.
  • A major third equals 386 cents.
  • A pure fifth equals 702 cents.
  • A minor seventh equals 969 cents.
So by dividing the octave into a different number of steps than 12, we could get closer to match the frequencies of the overtone series. E.g. 19 tones per octave (some heavy metal guitarists do so) or 31 tones, maybe 34 tones per octace or 41 or even 53 (the base for arabic scales). I prefer 16.5 tones per octave. Some prefer to divide the interval of a duodecime (an octave plus a perfect fifth, that sums up to 1902 cents) into 13 equal steps. Others divide octaves into unequal steps like Werckmeister or Valotti did centuries ago.

And I haven't even talked about the minor scales ...

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normen
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19 Aug 2018

Ahornberg wrote:
19 Aug 2018
my 2 cents :puf_bigsmile:

Our modern western system divides the octave into 12 equal steps:
  • One octave equals 1200 cents.
  • One semitone equals 100 cents.
  • A major third equals 400 cents.
  • A pure fifth equals 700 cents.
  • A minor seventh equals 1000 cents.
But in the overtone series, these values show up like this:
  • One octave equals 1200 cents.
  • Semitones are all different in size, depending on their position to the root note.
  • A major third equals 386 cents.
  • A pure fifth equals 702 cents.
  • A minor seventh equals 969 cents.
So by dividing the octave into a different number of steps than 12, we could get closer to match the frequencies of the overtone series. E.g. 19 tones per octave (some heavy metal guitarists do so) or 31 tones, maybe 34 tones per octace or 41 or even 53 (the base for arabic scales). I prefer 16.5 tones per octave. Some prefer to divide the interval of a duodecime (an octave plus a perfect fifth, that sums up to 1902 cents) into 13 equal steps. Others divide octaves into unequal steps like Werckmeister or Valotti did centuries ago.

And I haven't even talked about the minor scales ...
Yeah, thats the thing - theres Jazz logic and then theres decades and centuries worth of wars over tunings. And then in prehistory theres probably also thousands of years of getting used to all kinds of tunings for the 3rd :) But it's strange right? It's as if the universe is saying "Pure can't be complicated, stop the sophistry!" ;)

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Marco Raaphorst
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19 Aug 2018

Harmonics are perfectly related to one key, with equal temperament we made all semitones equal. Makes sense imo. I must say a perfect fifth doesn’t sound so perfect to me. But I understand why the flat 5 interval (devil’s interval, major 3rd to a flatted 7) sounds better when the interval is wider which is why in blues the minor 3rd is pitched upwards

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normen
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19 Aug 2018

Marco Raaphorst wrote:
19 Aug 2018
I must say a perfect fifth doesn’t sound so perfect to me. But I understand why the flat 5 interval (devil’s interval, major 3rd to a flatted 7) sounds better when the interval is wider which is why in blues the minor 3rd is pitched upwards
Wat? The 5th is pretty much the only thing thats "correct" in the usual western scale and the same as in a pythagorean scale - which I assume you mean when you say "perfect" outside of the term "perfect fifth"? The scale that actually happens when you divide the string. That fifth is the only thing we really have in our current western music.

The 3rd and where its put is something completely different, musically. Thats what I alluded to, that one's been moved around for thousands of years.

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Marco Raaphorst
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20 Aug 2018

normen wrote:
19 Aug 2018
Marco Raaphorst wrote:
19 Aug 2018
I must say a perfect fifth doesn’t sound so perfect to me. But I understand why the flat 5 interval (devil’s interval, major 3rd to a flatted 7) sounds better when the interval is wider which is why in blues the minor 3rd is pitched upwards
Wat? The 5th is pretty much the only thing thats "correct" in the usual western scale and the same as in a pythagorean scale - which I assume you mean when you say "perfect" outside of the term "perfect fifth"? The scale that actually happens when you divide the string. That fifth is the only thing we really have in our current western music.

The 3rd and where its put is something completely different, musically. Thats what I alluded to, that one's been moved around for thousands of years.
I mean the flatted fifth, the devil's interval, the tritone, which is used in dominant 7 chords is like blues etc.

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normen
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20 Aug 2018

Marco Raaphorst wrote:
20 Aug 2018
normen wrote:
19 Aug 2018


Wat? The 5th is pretty much the only thing thats "correct" in the usual western scale and the same as in a pythagorean scale - which I assume you mean when you say "perfect" outside of the term "perfect fifth"? The scale that actually happens when you divide the string. That fifth is the only thing we really have in our current western music.

The 3rd and where its put is something completely different, musically. Thats what I alluded to, that one's been moved around for thousands of years.
I mean the flatted fifth, the devil's interval, the tritone, which is used in dominant 7 chords is like blues etc.
Ah right, well that one doesn‘t sound right no matter where you push it ^^

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Marco Raaphorst
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20 Aug 2018

normen wrote:
20 Aug 2018
Marco Raaphorst wrote:
20 Aug 2018


I mean the flatted fifth, the devil's interval, the tritone, which is used in dominant 7 chords is like blues etc.
Ah right, well that one doesn‘t sound right no matter where you push it ^^
I love dominant 7s. And with the minor third a little up, like in blues, it's fan-tas-tic imo.

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normen
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20 Aug 2018

Marco Raaphorst wrote:
20 Aug 2018
And with the minor third a little up, like in blues, it's fan-tas-tic imo.
How much "little" is is very important there - it can transform the whole scale and music completely :)

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Marco Raaphorst
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20 Aug 2018

normen wrote:
20 Aug 2018
Marco Raaphorst wrote:
20 Aug 2018
And with the minor third a little up, like in blues, it's fan-tas-tic imo.
How much "little" is is very important there - it can transform the whole scale and music completely :)
if you push the minor to a major, it is still good.

I think the tritone is pure magic. it's a perfect in the middle. it is the foundation of pop music. and it leaves room for bending :)

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Ahornberg
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20 Aug 2018

some theory and listening examples https://www.kylegann.com/tuning.html

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Marco Raaphorst
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20 Aug 2018

Ahornberg wrote:
20 Aug 2018
some theory and listening examples https://www.kylegann.com/tuning.html
problem is: it can never be absolute, it needs to be relative. equal temperament is ideal imo. we need to switch keys all the time. I love jazz, Steely Dan, Bach, the great key shifters.

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normen
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20 Aug 2018

Marco Raaphorst wrote:
20 Aug 2018
if you push the minor to a major, it is still good.
Well yeah, many - especially classically trained - musicians only seem to hear "major, minor or blues" these days, kinda sad. It all went away for the sake of key changes.

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Marco Raaphorst
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20 Aug 2018

normen wrote:
20 Aug 2018
Marco Raaphorst wrote:
20 Aug 2018
if you push the minor to a major, it is still good.
Well yeah, many - especially classically trained - musicians only seem to hear "major, minor or blues" these days, kinda sad. It all went away for the sake of key changes.
you can play the blues with key changes. in fact the blues is one big key change in a way. adding major 7s which go outside modality

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Ahornberg
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20 Aug 2018

Marco Raaphorst wrote:
20 Aug 2018
Ahornberg wrote:
20 Aug 2018
some theory and listening examples https://www.kylegann.com/tuning.html
problem is: it can never be absolute, it needs to be relative. equal temperament is ideal imo. we need to switch keys all the time. I love jazz, Steely Dan, Bach, the great key shifters.
It depends on the style/genre of the music you play. For modern music, an equal tuning fits more but baroque music sounds best in non-equal tunings. The following list of emotions related to different musical keys only makes sense for non-equal tunings https://ledgernote.com/blog/lessons/mus ... -emotions/

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Marco Raaphorst
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20 Aug 2018

Ahornberg wrote:
20 Aug 2018
Marco Raaphorst wrote:
20 Aug 2018


problem is: it can never be absolute, it needs to be relative. equal temperament is ideal imo. we need to switch keys all the time. I love jazz, Steely Dan, Bach, the great key shifters.
It depends on the style/genre of the music you play. For modern music, an equal tuning fits more but baroque music sounds best in non-equal tunings. The following list of emotions related to different musical keys only makes sense for non-equal tunings https://ledgernote.com/blog/lessons/mus ... -emotions/
even so most baroque music is played on equal temperament. and I love it. church organs in equal temperament are great imo.

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Ahornberg
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20 Aug 2018

Marco Raaphorst wrote:
20 Aug 2018
Ahornberg wrote:
20 Aug 2018


It depends on the style/genre of the music you play. For modern music, an equal tuning fits more but baroque music sounds best in non-equal tunings. The following list of emotions related to different musical keys only makes sense for non-equal tunings https://ledgernote.com/blog/lessons/mus ... -emotions/
even so most baroque music is played on equal temperament. and I love it. church organs in equal temperament are great imo.
here's a compairson of 4 different tunings

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Ahornberg
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20 Aug 2018

here another compairson


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Marco Raaphorst
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20 Aug 2018

did the blind test. equal I prefer.

I have listened to Bach since birth. my father in an organ player

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Ahornberg
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20 Aug 2018

Marco Raaphorst wrote:
20 Aug 2018
did the blind test. equal I prefer.

I have listened to Bach since birth. my father in an organ player
In the western world, we are all "trained" to equal tuning. Historical performance practice, including the tuning a piece of music is written for, is rather new. And going beyond western tuning is very unusual in the western world. Just take a listen to Easley Blackwood's microtonal etudes:



or have fun wit Gamelan (people in Indonesia consider this as the "right" tuning):



also Aphex Twin experimented wit microtunings:



Although playing microtonal in Reason is tricky (but that's another story).

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Ahornberg
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20 Aug 2018

some key instruments with alternate layout and pitch possibilities:






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Marco Raaphorst
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20 Aug 2018

I am not interested in microtonal, still trying to train my ears on modal stuff. most of it sounds out of tune to me. Aphex stuff in general is superb but his microtonal stuff doesn't touch me.

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