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

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selig
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20 Aug 2018

Interesting subject, though I believe the title of the thread isn't clear - the natural harmonic "system" (series) is universal and based on math. The Western SCALE system is related to the harmonic series, as is every scale in use, right? This comes from instruments that use the harmonic series to form their notes, such as the bugle which is based on animal horns. Before that, bone flutes (some believed to be as old as 40-60,000 years old) were used, and those unearthed are found to use the pentatonic scale.
https://www.ancient-origins.net/artifac ... tes-020826

More interesting to me is the nearly universal use of the pentatonic scale around the world. It seems to be the most "natural" scale to us humans.
Most intriguing still is this Bobby McFarrin Ted Talk about the pentatonic scale, which is what first opened my eyes to the "magic" of this simple scale.
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Marco Raaphorst
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20 Aug 2018

selig wrote:
20 Aug 2018
Interesting subject, though I believe the title of the thread isn't clear - the natural harmonic "system" (series) is universal and based on math. The Western SCALE system is related to the harmonic series, as is every scale in use, right? This comes from instruments that use the harmonic series to form their notes, such as the bugle which is based on animal horns. Before that, bone flutes (some believed to be as old as 40-60,000 years old) were used, and those unearthed are found to use the pentatonic scale.
https://www.ancient-origins.net/artifac ... tes-020826

More interesting to me is the nearly universal use of the pentatonic scale around the world. It seems to be the most "natural" scale to us humans.
Most intriguing still is this Bobby McFarrin Ted Talk about the pentatonic scale, which is what first opened my eyes to the "magic" of this simple scale.
Pentatonic and 7 note scale are 100% related imo. Pentatonic is just leaving out 2 half steps which makes it a more simple scale. You can also make the scale more simple: 3 steps. Tonica, 3rd and 5th :)

In a way the 12 tone scale can be used in all situations. Every note can work over all chords. Intervals are just intervals, they are fixed. We can indentify them and there are no bad intervals.

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selig
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20 Aug 2018

Marco Raaphorst wrote:
20 Aug 2018
selig wrote:
20 Aug 2018
Interesting subject, though I believe the title of the thread isn't clear - the natural harmonic "system" (series) is universal and based on math. The Western SCALE system is related to the harmonic series, as is every scale in use, right? This comes from instruments that use the harmonic series to form their notes, such as the bugle which is based on animal horns. Before that, bone flutes (some believed to be as old as 40-60,000 years old) were used, and those unearthed are found to use the pentatonic scale.
https://www.ancient-origins.net/artifac ... tes-020826

More interesting to me is the nearly universal use of the pentatonic scale around the world. It seems to be the most "natural" scale to us humans.
Most intriguing still is this Bobby McFarrin Ted Talk about the pentatonic scale, which is what first opened my eyes to the "magic" of this simple scale.
Pentatonic and 7 note scale are 100% related imo. Pentatonic is just leaving out 2 half steps which makes it a more simple scale. You can also make the scale more simple: 3 steps. Tonica, 3rd and 5th :)

In a way the 12 tone scale can be used in all situations. Every note can work over all chords. Intervals are just intervals, they are fixed. We can indentify them and there are no bad intervals.
Not sure the pentatonic is based on the 12 tone scale, since it came into use tens of thousands of years earlier as far as I can tell. If you stack fifths, likely the first interval identified after the octave, the first five stacks produce the pentatonic scale as we know it. Tuning wise, there are MANY different pentatonic scales, so it's a stretch to describe them as 100% related IMO, or to suggest that a pentatonic scale was originally a 7 note scale with two steps left off (since it predates the 7 note scale by many tens of thousands of years according to what I've read). Or maybe I'm mis-reading what you wrote?

I guess you're talking strictly about Western scales, and I'm talking about scales around the world and their ancient history.

https://en.wikipedia.org/wiki/Pentatonic_scale
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Marco Raaphorst
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20 Aug 2018

selig wrote:
20 Aug 2018
Marco Raaphorst wrote:
20 Aug 2018


Pentatonic and 7 note scale are 100% related imo. Pentatonic is just leaving out 2 half steps which makes it a more simple scale. You can also make the scale more simple: 3 steps. Tonica, 3rd and 5th :)

In a way the 12 tone scale can be used in all situations. Every note can work over all chords. Intervals are just intervals, they are fixed. We can indentify them and there are no bad intervals.
Not sure the pentatonic is based on the 12 tone scale, since it came into use tens of thousands of years earlier as far as I can tell. If you stack fifths, likely the first interval identified after the octave, the first five stacks produce the pentatonic scale as we know it. Tuning wise, there are MANY different pentatonic scales, so it's a stretch to describe them as 100% related IMO, or to suggest that a pentatonic scale was originally a 7 note scale with two steps left off (since it predates the 7 note scale by many tens of thousands of years according to what I've read). Or maybe I'm mis-reading what you wrote?

I guess you're talking strictly about Western scales, and I'm talking about scales around the world and their ancient history.

https://en.wikipedia.org/wiki/Pentatonic_scale
The main thing I was trying to write is explain that a tone with harmonics has the same intervals we use in western scales. This is simply a matter of multiplying, taking a tone and multiplying it with 2,3,4,5 etc. Same as with odd and even harmonics.

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Ahornberg
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20 Aug 2018

Today's western harmonic system by dividing an octave into 12 equal steps has a long history. The equal division of the octave showed up in the late 19th century to fit the needs for playing atonal music. At this time it was heavily criticized for reducing 12 different flavours of major and minor scales down to 1 flavour.

Now the situation is, that neither Reason, nor any other DAW provide an easy access to tunings beyond this 12 tone equal system. And so it is hard to explore the endless spaces hidden between the virtual keys on our piano rolls. I cannot set a note halfway or a third between an E and an F (Bitwig is an exception here). I cannot load a tuning table into an RE or into a VST (u-he synths and a handfull of others are an exception here). Dealing with MIDI pitch-bend messages is a mess an counter intuitive for composing something different from the 12 tone equal system.

I created my own tuning after years of research and trial-and-error. I figured out how to set up Thor and Parsec so that I can use my tuning (but I prefer u-he VSTs because they provide a much easier and much more flexible way to get ready for playing). Even a Korg Kronos is easier to set up for custom tunings than any DAW I ever used (the only DAW I know that can "load" a global tuning table is LSDJ that runs on old GameBoy devices).

OT but it has to be said:

So by using computers to compose and/or play music, we are strongly forced to stick to the 12 tone equal system. For all of you who love the 12 tone equal system, that's fine. For the minority who wants more, it's a pain. Even MIDI is not ready for that: imagine, I want to use a 53 note tuning (53 notes per octave), so with MIDI and it's limitation to 128 possible pitches, I can't even span 3 octaves.

I want to encourage everyone to take a listen beyond the western tuning but in the digital world we lack easy-to-use tools to explore the unknown land. There are so many cultures and musical traditions on this planet and they all can't use Reason or any other major DAW to compose their music as we do easily with all that abundance of soft synths and sampled instruments. This makes me sad. :cry:

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selig
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20 Aug 2018

Marco Raaphorst wrote:
20 Aug 2018

The main thing I was trying to write is explain that a tone with harmonics has the same intervals we use in western scales. This is simply a matter of multiplying, taking a tone and multiplying it with 2,3,4,5 etc. Same as with odd and even harmonics.
I guess you could say that all scales are "inspired" by the natural harmonic series, but few (if any?) actually use the exact intervals (certainly not the equal tempered scale).
So it's not exclusive to the western scales, I guess that's all I'm trying to say here.

Another extremely interesting thread non the less - thanks Marco!
:)
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normen
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20 Aug 2018

Ahornberg wrote:
20 Aug 2018
Now the situation is, that neither Reason, nor any other DAW provide an easy access to tunings beyond this 12 tone equal system.
Huh? Logic allows you to tune the whole DAW to any of a HUGE list of classical and modern tunings.

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Ahornberg
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21 Aug 2018

normen wrote:
20 Aug 2018
Ahornberg wrote:
20 Aug 2018
Now the situation is, that neither Reason, nor any other DAW provide an easy access to tunings beyond this 12 tone equal system.
Huh? Logic allows you to tune the whole DAW to any of a HUGE list of classical and modern tunings.
I never used Logic because I'm on Windows. And Logic doesn't go beyond 12 notes per octave, see http://sevish.com/2015/make-microtonal- ... -mac-os-x/ so it wouldn't help me for playing my tuning with 16.5 steps per octave.

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Marco Raaphorst
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21 Aug 2018

selig wrote:
20 Aug 2018
Marco Raaphorst wrote:
20 Aug 2018

The main thing I was trying to write is explain that a tone with harmonics has the same intervals we use in western scales. This is simply a matter of multiplying, taking a tone and multiplying it with 2,3,4,5 etc. Same as with odd and even harmonics.
I guess you could say that all scales are "inspired" by the natural harmonic series, but few (if any?) actually use the exact intervals (certainly not the equal tempered scale).
So it's not exclusive to the western scales, I guess that's all I'm trying to say here.

Another extremely interesting thread non the less - thanks Marco!
:)
I would not say inspired, our western intervals are the same as the harmonics. They use exactly the same calculation rules. The only clever thing which was invented was equal temperament because harmonics are only equally related to one key, tone.

12 tone is perfect imo. But some might say, 24 is better. But you need equal temperament imo. And I love it. I hate a perfect fifth, which sound less funky than an "out of tune" equal temperament fifth.

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normen
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21 Aug 2018

Marco Raaphorst wrote:
21 Aug 2018
I hate a perfect fifth, which sound less funky than an "out of tune" equal temperament fifth.
I find it funny that you go on about the 5th, which is the one that is the least out of tune in pretty much all the tunings.

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Marco Raaphorst
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21 Aug 2018

normen wrote:
21 Aug 2018
Marco Raaphorst wrote:
21 Aug 2018
I hate a perfect fifth, which sound less funky than an "out of tune" equal temperament fifth.
I find it funny that you go on about the 5th, which is the one that is the least out of tune in pretty much all the tunings.
Yes but most inportant one!

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selig
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21 Aug 2018

Marco Raaphorst wrote:
I would not say inspired, our western intervals are the same as the harmonics. They use exactly the same calculation rules. The only clever thing which was invented was equal temperament because harmonics are only equally related to one key, tone.

12 tone is perfect imo. But some might say, 24 is better. But you need equal temperament imo. And I love it. I hate a perfect fifth, which sound less funky than an "out of tune" equal temperament fifth.
Do you love it or do you hate it?!? [emoji6]

What you say is only true for Just Intonation. It is the only scale with intervals “the same as the harmonics”. That is, IF you’re talking about the early harmonics (harmonics are infinite, so at one point they would represent ANY interval you want!). Our modern equal tempered scale makes adjustments to these intervals and thus only the octave falls on the same frequencies as the natural harmonic series’ early harmonics.

Beyond that, it’s really only with electronic music where these tunings are ultra precise.

For example, when a choir sings, or a string orchestra plays (or brass or anything really) they naturally tune to the best “third” or “fifth” to fit the current key. Additionally, there will always be some pitch variation between instruments playing the same note, and there will never be absolute “perfect” intervals except with electronic instruments.

So looking at the history of tuning and scales, it’s likely that it’s only been recently (historically speaking) that the ideal of “precise” intervals has existed in practice, meaning the last few thousand years with the invention of the modern instruments we know today. And one could further argue that it’s only with electronic instruments that you can get so precise and stable with tuning as to precisely illustrate the differences between these scales/tunings.

Historically…
Pythagorean tuning was the first attempt at creating a 7 and 12 tone scale (and also the pentatonic), and was in use from the 6th century BC up through the 15-16th century AD. But it had such dissonant thirds (both minor and major) it caused music to be written far simpler than today’s music. It also had issues to deal with such as the Pythagorean comma and the wolf fifth.

Next up (late 6th century) were the first attempts at a more useful 7 and 12 tone scale (starting with Gioseffo Zarlino) using the perfect fifth and also adding perfect minor and major thirds.

All this eventually leads to the equal tempered scale, and you can read more about the lead up to this scale here (finally my freshman “History of Music” class has some practical application!).

https://en.m.wikipedia.org/wiki/Just_intonation




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selig
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21 Aug 2018

Marco Raaphorst wrote:
normen wrote:
21 Aug 2018
I find it funny that you go on about the 5th, which is the one that is the least out of tune in pretty much all the tunings.
Yes but most inportant one!
After the octave, of course! ;)


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Marco Raaphorst
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21 Aug 2018

selig wrote:
21 Aug 2018
Marco Raaphorst wrote:
Yes but most inportant one!
After the octave, of course! ;)


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Even more important because without it we would never go back to the tonica 😎

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