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The Fine Art of Combining Harmonics

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Re: The Fine Art of Combining Harmonics

#31

Post by seph-reed »

This is really cool, but -- as someone who's been researching just tuning for a while -- I think a lot of very important aspects of human psychology have been overlooked here.

Frankly, familiarity is a vastly more important aspect of music than any micro-tonal artist would like to admit. And while the overtone series is (in many many ways) the root of all music, not every overtone is equal.

For instance: 9/8 (a major second) is just (3 * 3)/(2 * 2 *2) and is generally more consonant (like dull, boring, unmoving: an octave or perfect fifth) than anything with a 5 prime number in it (eg 5/4 a major 3rd). AFAICT, the order of simplicity (dullness -> dissonance) on intervals is 2/1, 4/1, 3/2, 4/3, 3/1, 9/8, 16/9, 5/4, 8/5, 6/5... it's not exactly clear what the math is here.

Also, it's always really, really telling to me when someone shares a music theory without sharing a recording of that theory in action. The site I'm working on lets people use their keyboard to play with every scale, so you can verify that it's not just number play.

Re: The Fine Art of Combining Harmonics

#32

Post by jcpst »

eezurr wrote: post #29
mrob wrote: post #5

>There is of course a questionable degree of dissonance that can be tolerated, but the most obvious fact is that the brain can well be conditioned to accept and even enjoy these dissonances, as long as they are part of the only music it has ever experienced. I disagree. I have listened to a fair amount of music in just intonation, and I am capable of hearing the tuning flaws of 12 equal temperament, but I am still ca…

+1 for Harry Parch. Here's a good introduction for new people [1]. I'd add in Lou Harrison [2] and Tristan Murail [3] Lou Harrison was heavily influenced by Gamelan music, and Tristan Murail is one of the founders of spectralism, which uses spectrograms of individual instruments to build distinct harmonies by having orchestral instruments play the harmonic series as shown on the spectrogram. They stretch this idea ev…

And Gerard Grisey.

Re: The Fine Art of Combining Harmonics

#33

Post by cousin_it »

klysm wrote: post #20

This is incredibly dismissive of any harmony that is based on equal temperament, or anything that isn’t the harmonic series. I don’t think that’s justified - a lot of jazz harmony only sounds good in equal temperament. For instance, minor 6 chords are going to sound terrible.

Huh? To me Dm6 in the just intonation A minor scale sounds fine.

Re: The Fine Art of Combining Harmonics

#34

Post by chipuni »

Please, try playing your harmonic ideas with real sounds.

Here's some things to try:

- How bad or good do two synthesized violins sound together at 800 and 900 hertz? Think about them as overtones: Does adding a tone at 100 hertz resolve the sound? Think of them as undertones: Does adding a new tone at 7200 hertz resolve that sound?

- Does the instrument change the harmony? What happens to harmony when the instrument is a clarinet? What happens to harmony when the instrument is a sine wave? What happens to harmony when the instrument is a tuned tympani?

- Try to play together the overtone series, for example, 1000 hz, 2000 hz, 3000 hz, ... How does that sound?

- Try to play together the undertone series, for example, 2520 hz, 1260 hz, 840 hz, 630 hz, 504 hz, ... How does that sound?

Re: The Fine Art of Combining Harmonics

#35

Post by xavriley »

Harmonic intervals are interesting but they are also misunderstood. Humans are able to distinguish out of tune notes down to a value of about 1%. To get more accurate tuning we tend to listen for beating (a kind of amplitude modulation) instead. This means we can tolerate tuning systems other than just intonation. Another thing to consider - the missing fundamental phenomenon suggests that the ear/brain is actually doing something like autocorrelation. This makes more sense than the idea that we have a template for the harmonic series wired in our brains. Finally auto correlation works for chords too, not just intervals. Every chord has a fundamental period of repetition - shorter periods are widely ranked as more consonant. There are lots of grand music theories that fixate on the harmonic series. The maths is fun, but it can get in the way of more effective alternatives for organising sounds.

Re: The Fine Art of Combining Harmonics

#36

Post by necrotic_comp »

seph-reed wrote: post #31

This is really cool, but -- as someone who's been researching just tuning for a while -- I think a lot of very important aspects of human psychology have been overlooked here. Frankly, familiarity is a vastly more important aspect of music than any micro-tonal artist would like to admit. And while the overtone series is (in many many ways) the root of all music, not every overtone is equal. For instance: 9/8 (a major…

yep - I came in here to talk about "familiarity" as the bedrock of how we listen to tunes. In my estimation, music is a constant juggling act between familiarity and novelty, and bending too much on one side or the other trends towards boredom.

I would argue that some of the pure intonation music (i.e. Michael Harrison's Revelations) or alternate tuning (i.e. Lamonte Young's Well Tuned Piano) is striking initially because of how alien it sounds, but to my ear a lot of it doesn't feel like it does too much more than that both as a function of the tuning and the difficulty in building a moving composition in something so foreign.

The standard tunings in Western Music are well-worn, but they can give a rich vocabulary for dissonance and consonance and have the psychological familiarity to build up emotional abstractions that some of the more adventurous scales do not.

Re: The Fine Art of Combining Harmonics

#37

Post by crawfordcomeaux »

chestervonwinch wrote: post #11
crawfordcomeaux wrote: post #7

Earlier quoted context omitted.

I accidentally abandoned many of my preferences (likes/dislikes) and automated judgments. I took this newfound perspective into music, embodying the idea of "there are no wrong notes." I find deep joy in sitting at a 120+ year old pump organ, holding a mishmash of dissonant notes, including some out of tune ones, and wiggling one of the keys to learn to spot it in the mashup. It gives me a chance to witness the inter…

> I accidentally abandoned... It sounds like you made a conscious and intentional decision. How does one drop their preconceived judgements by accident?

I was aiming to abandon judgments of things and had no idea it meant how my body reacts to things would change, that I'd effectively disable disgust in myself, that country music would become rockin (and that I'd enjoy all other forms of music, food, smells, drinks, and people...children went from obnoxious to adorable in weeks).

The intention was to try something very broad that would likely cover moral judgments. I did make a conscious decision, but the side effects were for sure happy accidents.

Re: The Fine Art of Combining Harmonics

#38

Post by mreid »

iainctduncan wrote: post #25
TheOtherHobbes wrote: post #9

Earlier quoted context omitted.

Sethares and Tymoczko are the go-tos on this. But there's a lot more to creating interesting musical structures than creating chords out of mathematical structures that are based on the harmonic series. The more time I spend trying to understand music, the less I understand it. That's what makes it so endlessly fascinating.

I've read quite a bit on this, but not Sethares, do you have a recommendation for starting on his work? thanks!

I'm not the parent, but I think they are referring to William Sethares' book "Tuning, Timbre, Spectrum, Scale": https://www.springer.com/gp/book/9781852337971

It's a fascinating take on how those concepts relate to each other. You can find some of the papers that were synthesized into that book on his web page: https://sethares.engr.wisc.edu/pubs.html

Re: The Fine Art of Combining Harmonics

#39

Post by seph-reed »

necrotic_comp wrote: post #36
seph-reed wrote: post #31

This is really cool, but -- as someone who's been researching just tuning for a while -- I think a lot of very important aspects of human psychology have been overlooked here. Frankly, familiarity is a vastly more important aspect of music than any micro-tonal artist would like to admit. And while the overtone series is (in many many ways) the root of all music, not every overtone is equal. For instance: 9/8 (a major…

yep - I came in here to talk about "familiarity" as the bedrock of how we listen to tunes. In my estimation, music is a constant juggling act between familiarity and novelty, and bending too much on one side or the other trends towards boredom. I would argue that some of the pure intonation music (i.e. Michael Harrison's Revelations) or alternate tuning (i.e. Lamonte Young's Well Tuned Piano) is striking initially be…

My theory is that music is something of a "matching puzzle."

- using only these tones

- and only the intervals between them

- I will construct an elaborate yet consistent path

- which will stray into a place that's hard to resolve from

- then impress you with how I "solve" it

--------

So when playing with just intoned, I've applied this theory and it works. I've shown it to friends and they like it... they can't even tell it's just intuned.

My favorite so far is using 7/6 and 9/7 as my major and minor thirds. If you multiply them together you get 3/2. Just like you do with 6/5 and 5/4. Pretty cool eh?

As long as the first note and the last are familiar, people seem to be okay with it.

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