#1
Hi,

I'm pretty new to music theory but I've just been learning about equal temperament and just intonation. Also learnt about Bach, Liszt and the creation of augmented and diminished chords.

What I was wondering basically is are there chords in 12 TET that haven't yet been discovered/ given a name, in the same way that augmented and diminished chords have been?

If not is it possible to find new chords and harmonics in 31 TET or up?
#3
Well, you could try using all three note combinations of the 12 notes. You may find out that most of the most pleasing sound ones are major, minor, diminished and augmented chords. And the others are extended chords with omitted notes.

But the thing is, if you for example started using 1/4 steps, we would just hear them as out of tune notes. You couldn't really build any good sounding chords using 1/4 steps.

We are able to name all chords. It's not rocket science.

You just name a chord by looking at the intervals in the chord. For example if we have notes Ab, C, Eb and G, you would just look at the intervals between the notes. What we have is root, major third, perfect fifth and major seventh. So we know it's an Ab major 7th chord (major triad + major 7th and Ab as the root note).
Quote by AlanHB
Just remember that there are no boring scales, just boring players.

Gear

Bach Stradivarius 37G
Charvel So Cal
Fender Dimension Bass
Hartke HyDrive 210c
Ibanez BL70
Laney VC30
Tokai TB48
Yamaha FG720S-12
Yamaha P115
Last edited by MaggaraMarine at Dec 15, 2013,
#4
So quarter notes can't make nice sounding chords?

Is that because we're used to 12-TET or is that just how it is?
#5
Quote by EddYerb
So quarter notes can't make nice sounding chords?

Is that because we're used to 12-TET or is that just how it is?


You probably could, but we wouldn't hear them as nice sounding because we are used to our way of splitting up music into 12 notes.

I had this experience when i was in central asia, in a part of China. There they had (i believe) 18 notes in their music, cause they split the notes up differently than we do. They said they couldn't stand listening to western music cause it sounded so out of tune, so i believe it's all dependent on what kind of music we are brought up with.

Guthrie Govan demonstrated this very well in a video lesson i saw. He showed using the guitar the "natural" A (the harmonic) and then the fretted A. They are not even on our instruments, neither are they on Piano or bass or violin. Western instruments are made with the small imperfection that we are not 100% in tune all over the instrument.
Fusion and jazz musician, a fan of most music.

Quote by Guthrie Govan
“If you steal from one person it's theft, and if you steal from lots of people it's research”


Quote by Chick Corea
"Only play what you hear. If you don't hear anything, don't play anything."
#6
TS: Yeah, that's one reason. But I think the biggest reason is in physics. If you play a single note, it's not just one frequency - it includes lots of frequencies. Actually if you play a single note, it has the notes of a major chord in it (and more - it actually has all notes of the "overtone scale" in it). But the loudest frequency in the note is of course the root and the next loudest frequency is the fifth. But yeah, that's why major chord sounds good and why some note combinations sound really dissonant.

Oh, and if you know how to play natural harmonics, you can find out which frequencies a single note includes. All natural harmonics you can play on the open E string are actually in the E note. How loud different overtones are makes guitar sound like guitar and piano sound like piano and all different instruments sound different.

Actually 12 TET doesn't make perfect sounding chords either. It's just a compromise. Some intervals in a scale are out of tune (for example major third should be lower than it is). But to make a perfect sounding scale, all the other scales would sound off. So your instrument would only work in one key and you would need different instruments for different keys. Songs that modulate would be pain in the ass. That's why 12 TET was invented. It's a compromise and chords don't sound as good as they could, but at least the instrument works in any key, and the chords still sound good enough. If you had a fretless instrument, you could fine tune every note you play and it would actually sound better than standard guitar. Basically anything that has keys or frets is a 12 TET instrument. But there are lots of non-12 TET instruments like strings/all fretless instruments and wind instruments.
Quote by AlanHB
Just remember that there are no boring scales, just boring players.

Gear

Bach Stradivarius 37G
Charvel So Cal
Fender Dimension Bass
Hartke HyDrive 210c
Ibanez BL70
Laney VC30
Tokai TB48
Yamaha FG720S-12
Yamaha P115
#8
I would highly recommend the album "12 Microtonal Etudes for Electronic Music Media" by Easley Blackwood. He goes through 13-24 EDO and composes music to take advantage of the unique characteristics of each temperament. The album is available on Spotify, but I'd also recommend finding the accompanying booklet that explains the decisions he made in the composition process. If you're wondering what's beyond 12 tone harmony, it's a great place to start.
Last edited by TheHydra at Dec 15, 2013,
#9
^I've been searching for decent microtonal music as well as it's pretty interesting. Would love to hear some well/modern produced music (type rock or metal for example) played in quarter/microtone as most I've come across is older piano compositions, or these eccentrics who play random stuff on their customized instrument. I'll check out this guy
#10
Quote by fanapathy
^I've been searching for decent microtonal music as well as it's pretty interesting. Would love to hear some well/modern produced music (type rock or metal for example) played in quarter/microtone as most I've come across is older piano compositions, or these eccentrics who play random stuff on their customized instrument. I'll check out this guy

Check out "City of the Asleep". He makes microtonal progressive metal-ish music in a variety of tunings. And don't knock the eccentrics; they were my first intro to the weird world of xenharmonic music.

Wait, nevermind? Apparently he's disavowed microtonal composition and removed most of his microtonal stuff. What an asshole.
Last edited by TheHydra at Dec 15, 2013,
#11
Have We Discovered All the Chords?
Probably not. but if you're intent on playing them with a guitar, you may have to wait until Homo Sapiens evolves into a form with more fingers.

In any case, your question is a bit incompletely formed. What I think you mean is,"have we discovered all the chords using the current set of established frequencies and intervals", (notes). The answer to that is most likely yes.

However, not even all contemporary cultures use the same set of notes and scales. Indian music employs movable scales.

The overarching question is, would you like the sound of chords made with a different set of tonalities and interval. And that answer is likely, "no, you wouldn't'. Simply because the current set of harmonized scales, is pretty much organic to our culture.

Keep in mind that using an set of 8 tones, (diatonic scale), or even the Chromatic scale, (12 tones covering the same"octave"), only offers so many absolute mathematical possibilities. When you subtract the ones that, "sound like shit to us", I'm pretty sure you'd be left with the chords we're currently using.
Last edited by Captaincranky at Dec 15, 2013,
#12
Cheers guys..

Yeah like I said in the post I'm interested in whether there are undiscovered chords in microtonal music. I don't really understand it to be honest but if there are 7 extra notes you would have there would be some new combinations.

http://www.youtube.com/watch?v=23ImVLezV4c

Sounds like there are some new chords in that?
#13
Quote by EddYerb
Cheers guys..

Yeah like I said in the post I'm interested in whether there are undiscovered chords in microtonal music. I don't really understand it to be honest but if there are 7 extra notes you would have there would be some new combinations.


Sounds like there are some new chords in that?
Given the fact you multiply all factors by each other to come up with a product equaling all the possibilities, how could there not be? The more tones there are at the base, the higher the quantity of the product. The question is how many are useable, and why would anyone consider them, "undiscovered" when you can predict their existence very quickly, using simple math.

The only trick here is, you have to use trial and error to determine which ones are worthwhile, in the sense that are you the only person that would be interested in suffering through listening to them.

And the trial and error part of the, "trip through the harmonic wilderness", isn't anything a thread at UG is going to, "map out for you".

To repeat, proving that combinations of anything could exist, isn't difficult at all, you multiply all the items together, be it tones or thumbtacks and get your answer. Any other extension of this is asking somebody else to multiply and test it out for you.

People keep repeating that music is based in math, and as a matter of fact, it absolutely is.

Music that is generally pleasing to most people, comes out of established combination of measured intervals. In a majority of cases, these are intervals that create even harmonics, and yes, those harmonics are predictable using math.

The more or less, only thing that a human being adds to finally develop music, is pitch selection and timing. The underlying mathematical matrix is already in place.

So, the further music separates itself from mainstream I, IV, V formula, the smaller the audience is likely to be. Which kinda does leaves the distinct possibly that you could wind up playing what you might consider the coolest self discovered chord ever, to yourself.

And yes, I know I'm a d***, I have to deal with me too.
Last edited by Captaincranky at Dec 16, 2013,
#14
I don't see a point in starting to use more than 12 notes. Because most music doesn't even use all 12 notes. Actually most rock guitar solos only use the pentatonic scale - 5 notes. We just find certain note combinations more pleasing to our ears (that's why most pop songs use the infamous "four chord progression"). Also, music isn't all about note choice. It's also about rhythm, the instruments you use and the sounds you use. I mean, listen to 60s music and compare it to 2000s music. I'm pretty sure there are similar kind of melodies and note choices but they still sound completely different.

It's kind of the same as coming up with more letters because the alphabets are limiting because there's this and this many combinations (OK, there are more alphabets than there are notes but you get the idea). Certain combinations of letters are more common in our words. And still we have so many words. And with them we can express ourselves really well. And I think same goes with music. We come up with new kind of sounding stuff all the time.
Quote by AlanHB
Just remember that there are no boring scales, just boring players.

Gear

Bach Stradivarius 37G
Charvel So Cal
Fender Dimension Bass
Hartke HyDrive 210c
Ibanez BL70
Laney VC30
Tokai TB48
Yamaha FG720S-12
Yamaha P115
Last edited by MaggaraMarine at Dec 16, 2013,
#15
Quote by MaggaraMarine
I don't see a point in starting to use more than 12 notes. Because most music doesn't even use all 12 notes. Actually most rock guitar solos only use the pentatonic scale - 5 notes. We just find certain note combinations more pleasing to our ears (that's why most pop songs use the infamous "four chord progression"). Also, music isn't all about note choice. It's also about rhythm, the instruments you use and the sounds you use. I mean, listen to 60s music and compare it to 2000s music. I'm pretty sure there are similar kind of melodies and note choices but they still sound completely different.
.
Music is math, and it is also physics. The pitches we have chosen have only two primary functions, this first being simple standardization. This allows people with different languages to communicate in the same musical vernacular, which is kind of miraculous, if you pause to think about it. The second is vibrational energy, and the properties of resonance it imparts in different ways to different materials. The factors of the number two keep showing up in the physical world, and how we measure it. In music the factor of two, (halving or doubling of frequency), presents us with the basic octave. For intervals comprised of multiple pitches, to be successful, they need reinforce, not inhibit one another. De-tune your guitar, you'll find it kills the sustain. But when the frequencies are where they're supposed to be sustain increases.

Two primary factors are commonly used in measuring the quality of sound delivered by audio amplifiers, "harmonic distortion", and "inter modulation distortion" have profound inplication in the creation of sound, particularly from polyphonic instruments. Harmonic distortion, is generally pleasant, as the harmonic content is primarily even order. In other words, every tuned instrument has a primary, user selected pitch, but is producing other octaves and intervals alongside of that pitch. That's what gives every physical material its unique sound.

"Inter modulation distortion", is what happens when an amplifier is presented with two notes, which interact in such a way, that a summed note is created, not consonant with the pitches input. These are odd order harmonics, and are unpleasant to most people. It's why you can't play the 3rd when using high gain, the already present multiple harmonics combine with the odd order 3rd and create intervening notes out of context with the tuned structure of the scale.

Summing can easily be explained thus, you play a root, and a minor 3rd, the amplifier sums the two pitches. What comes out the other end of the amp, is a root, a minor 3rd, plus an extraneous 3rd tone, halfway between the two. Put in a C and an Eb, and you can very easily get a "C +2/3 (66 cents sharp), which corresponds to an Eb @ 66 cents flat.

Now, we've eliminated intervals that are perceived as dissonant from our musical scales. Embracing "micro-tonality", can only re-interject the dissonances that we've been distilling out for many centuries.

I think the topic of this thread was unfortunately conceived as stated. The question, "do you think there are undiscovered chords" wanders too far afield of any of the existing, tenets of established harmonic relationships or realities to be a valid inquiry....and is unnecessarily vague and naive as well.

(Sorry, but that's what I've taken away from it).
Last edited by Captaincranky at Dec 16, 2013,
#16
Some pretty interesting stuff in this thread:

[q]De-tune your guitar, you'll find it kills the sustain.[/q]

(Whats fascinating about this is that i dont have perfect pitch or anything, so its odd that someone knew that when tuned an even harmonic, its more pleasing(?), because for me it really makes no difference as long as the harmonies aren't unpleasant with the rest of the guitar. The guitar being a bit louder is cool though, and not something I had ever considered really)

All natural harmonics you can play on the open E string are actually in the E note. ( actually knew this, but never really related it to the string itself, which is cool )


I want to buy an electric at some point, so i can see what all this "distortion" hype is about, i like my acoustic just fine :P

Its interesting too that theres probably music oriented people in the neighboorhood of newton and einstien, i mean how did they know... If you were to give a violin to someone who'd never heard music, sorta curious what they would come up with... maybe the octave, but the rest is sorta up for grabs.
#17
Quote by blunderwonder
Some pretty interesting stuff in this thread:

[q]De-tune your guitar, you'll find it kills the sustain.[/q]

(Whats fascinating about this is that i dont have perfect pitch or anything, so its odd that someone knew that when tuned an even harmonic, its more pleasing(?), because for me it really makes no difference as long as the harmonies aren't unpleasant with the rest of the guitar. The guitar being a bit louder is cool though, and not something I had ever considered really)
There are two variables at work, Interval, and absolute pitch.

Absolute pitch is only necessary to insure that the standard guitar tuning is the same the world around. (*) To put it another way, say you're from Timbuktu, and a guy from Iceland comes to jam with you. When he pulls his guitar out of the case, the notes his strings are tuned to, should be identical to yours.

The more important issue is "interval", which is distance shorthand for the frequency differential of two, (or more). pitches.

So, you can make the frequency of the base tone, what ever frequency you choose, but the relative distances, (interval), between the strings, must remain at the same ratio, to retain the same harmonic. relationship.

Let's say we decide that the note, "A" is 100Hz. An octave lower would be half that value, 50Hz, and the octave above would be 200Hz.

Now we change that same "A" note, to 90Hz, it's lower octave would be 45Hz, and the octave above would be 180Hz. But, RELATIVE mathematical distance (the ratio of 1/2X to 1.0 to 2X), is preserved, and the instrument is still, "in tune", with respect to the overall harmonic content it is generating. So, the intervals themselves are what the human mind finds soothing, (very crudely put, "major happy, minor sad"), and you don't need perfect pitch or absolute standard tuning to enjoy those benefits. Just perfect relative pitch, and perfect relative tuning.

Quote by blunderwonder
Its interesting too that theres probably music oriented people in the neighboorhood of newton and einstien, i mean how did they know... If you were to give a violin to someone who'd never heard music, sorta curious what they would come up with... maybe the octave, but the rest is sorta up for grabs.
Actually, the discovery and development of musical intervals, keys and scales has been distilled and defined over the course of many centuries. And FWIW, ancient Gothic cathedrals played a big part in it. Many of our musical principles have evolved alongside of our faith in God. You've surely heard of "Gregorian Chants", which are all modal! Interval began to coalesce there, and evolved into out modern keys. (And least in the western world). The rest of the planet and it's musical conventions are a whole 'nuther can of worms.

(*) Worldwide standards of measure, always recall this mnemonic device, "a pint's a pound, the world around". (A pint of water weights exactly one pound, avoirdupois). Troy weight and knots, I'll leave to the experts to explain...
Last edited by Captaincranky at Dec 16, 2013,
#18
i know the knots one... if youve ever seen master and commander, its from dragging a rope in the water, counting to 10ish? and seeing how many knots passed, that distance of rope probably some calculation using gravity, and a clock, since its easy. IVe never heard of troy weight.

I took physics so I did all that with the tubes and harmonics, and the silly expirment with the strings and whatnot, but when you said the sustain is better on a tuned guitar, i think was surprised that a guitar was made to have certain notes played, like the distance from bridge to nut is such that a an E will play very evenly, i wasnt talking about the intervals between different notes and their harmonics Oo, Im gonna give it a go one day, and see if makes it easier to tune by ear, i can usually hum a G from a song im familiar with, but if it just holds better when its exactly at E, maybe that would be cool. I remember reading somewhere that an oboe is always tuned to Bb or something weird like that.

/e also, I think perhaps E, is E, because it is harmonically pleasing by itself, not considering the other intervals. I just mean, some people with big ears may find 100hz more pleasing than 100.8hz, someone did decide E was E afterall :P
Last edited by blunderwonder at Dec 16, 2013,
#19
There are an infinite number of pitches and intervals, many of them much more in-tune than what is available on 'standard' instruments.
The Harmonic Series is the source of this infinite number of pitches, and there are untold numbers of beautiful chords waiting to be discovered.
There are many composers out there now who are doing this. FreeNote Guitars have extra frets to get Harmonic Series pitches. Bands like the Fretless Brothers are using these new notes and chords to change the language of music.
www.fretlessbrothers.com
www.microtones.com