tetrachords

[Tricky-Loops]

nothing to helps me.. but thank you all a lot.. i was just dreaming.. so i must change songs other way.. pff....

There's no way out any more - now you will be fed with advanced music theory...

[jancivil]

7-note scales in actual practice, there are really 8 notes, in a way.

These are seven note scales. Full_Stop.

[jancivil]

nothing to helps me.. but thank you all a lot.. i was just dreaming.. so i must change songs other way.. pff....

There's no way out any more - now you will be fed with advanced music theory...

The dude said in response to being shown how useful 'tetrachords' are, 'oh so there's no point'. Completely ready to dismiss some kind of basic factual information as pointless.

So refuse to be fed, like you're going to replace the food with your empty air. The stupidity of this is ASTONISHING. Why are you here? To be snarky about people trying to provide the information? Jesus.

[jancivil]

Didn't understand your point about 2-2-1 being 5 instead of 4. Yes, it's 5 half steps, but it adds up to a 4th.

I'm an idiot. The whole thing became a blur. I think I saw a C scale actually go to D and this seemed to fit. I apologize.

I would also like to know the source for the assertion that it is generally presented as disjunct.

I learned to construct it as conjunct. You're right, if I wanted to edit a wiki article I would need to source it. It's an assumption I arrived at after a few decades.

I have no problem calling (2-1-2) a minor tetrachord, I wrote both minor/dorian in my previous post because some people call it a dorian tetrachord. It's just a name; it really is just "2-2-1". There are other "minor" tetrachords, like phrygian, and Hungarian minor, so the point of calling it dorian would be simply to give it its own name.

It's not a useful name, is it? Why do we need the names which only have meaning in terms of the second tetrachord to denote the first tetrachord?? "Dorian" has no meaning for the first tetrachord. I really like less shit to have to explain to someone new.

Anyway, it's not supposed to be the same as a dorian scale, just as a so-called lydian tetrachord isn't the same thing as a lydian scale.

But Lydian's distinguishing characteristic DOES lie in the first tetrachord.

Conjunct scale construction is fine as far as pure construction is concerned, but when we play and hear 7-note scales in actual practice, there are really 8 notes...

so in a discussion of 'construction' using tetrachords when did we exceed construction and for what actual use?

Furthermore, using the disjunct method allows us to see how all the major scales are "linked" together. If we view it as two major tetrachords, we can say that the upper tetrachord of C can also serve as the lower tetrachod of G, and the upper tetrachord of G is the same notes as the lower tetrachord of D, and so on, around the circle of 5ths/4ths, and we can do the same thing in the other direction.

This is a lot of work to read, I tuned out.


With the conjunction, we have two independent tetrachords without the redundant first note. Lydian/Minor: C D E F#/F# G# A B.

[stringtapper]

So in terms of advancing the idea, we avoid the possible confusion of constructions which exceed the octave.

Tetrachords are generally given as conjunct.

I'd like to see a source for that. In my experience disjunct tetrachords are more often used to explain the construction of scales in modern contexts. Get into Greek music theory and you see both conjunct and disjunct presented as different explanations of scale construction.

Using disjunct tetrachords to explain modes can be just as simple:


Ionian: C-D-E-F / G-A-B-C
Two major tetrachords a perfect fifth apart.

[and more with C as the first and last note of two tetrachords]...

None of the disjunct constructions above exceed the octave.

You have the first note of the lower tetrachord in the upper tetrachord. Therefore your upper tetrachord contains three notes. If you can't see the sense of it I can't help you any more than that.

Again: you want two tetrachords, you have two four notes sets conjunctively. This is the least confusing option.
See my example 'Lydian/Minor': C D E F#/F# G# A B. They're both actually tetrachords! This is clearer, I think. If you like 3 notes as your tetrachord, good for you. I would find that confusing per se.

Sorry but your logic is flawed here. You're saying that because in the disjunct tetrachords the first scale degree is used as both the first degree of the lower tetrachord and the fourth degree of the upper tetrachord that the upper tetrachord somehow only has three notes. Then by your own logic, since in the conjunct configuration the fourth scale degree is used as both the fourth degree of the lower tetrachord and the first degree of the upper tetrachord then one of those tetrachords must also only have three notes! See how the logic is inconsistent and just doesn't work?

The fact is there have been conjunct and disjunct tetrachordal combinations used to form larger scales since the Greeks. Both ways are legitimate depending on the context and the type of scale being formed.

You're basically saying that the disjunct conception does not produce "actual tetrachords." It's demonstrably false.

C-D-E-F# is a tetrachord. G-A-B-C is a tetrachord. Fact. No way around that. Put the two together and you have a Lydian scale on C, octave to octave.

Again, people have been looking at tetrachords like this since the Greeks. They've also been looking at them in conjunct terms.

Both are valid. If one works for better for you, fine.

[jancivil]

ok, fine. They're both actually tetrachords within the confines of the octave. That's why I edited it to say 'contained'.

[stringtapper]

With the conjunction, we have two independent tetrachords without the redundant first note. Lydian/Minor: C D E F#/F# G# A B.

But you still have redundancy. You're repeating the fourth scale degree. In fact there's no way around repetition using either method.

So why is one type of redundancy troubling to you but the other isn't??

[jancivil]

You're saying that because in the disjunct tetrachords the first scale degree is used as both the first degree of the lower tetrachord and the fourth degree of the upper tetrachord that the upper tetrachord somehow only has three notes. Then by your own logic, since in the conjunct configuration the fourth scale degree is used as both the fourth degree of the lower tetrachord and the first degree of the upper tetrachord then one of those tetrachords must also only have three notes! See how the logic is inconsistent and just doesn't work?

True.

So why is one type of redundancy troubling to you but the other isn't??

I want the tetrachords to happen within the octave. In a seven-tone scale. I think the conception is clearer rather than this 8-note row appearing.

[sammy24]

Why do we need the names which only have meaning in terms of the second tetrachord to denote the first tetrachord??

But Lydian's distinguishing characteristic DOES lie in the first tetrachord.

That's true. But I would still make the point that since these tetrachords can be used as either upper or lower, 50% of the time you're going to run into a situation where the tetrachord name doesn't fit so great.

For instance: (using the conjunct method, for your sake) So a major scale has a lower major tetrachord, and an upper lydian. But these four notes (F, G, A, and B, in the key of C) in this context don't project a lydian modality. We are using a name which has meaning in terms of the 1st tetrachord to denote the 2nd tetrachord.

Similarly, a 2-1-2 tetrachord would be the upper tetrachord for a phrygian scale (using conjunct). So calling the 2-1-2 tetrachord "minor" in this context doesn't really fit, because as you said before, the name minor only has meaning in terms of the 1st tetrachord, and here it is the 2nd tetrachord.

One other point I realized - according to the conjunct method, the 2-1-2 tetrachord makes up BOTH tetrachords of a natural minor scale, and only occurs in a Dorian scale as the 1st tetrachord. So it does make sense to refer to 2-1-2 as minor. But with the disjunct method, just the opposite occurs: both tetrachords of a dorian scale are 2-1-2. But a natural minor scale only has 2-1-2 as its lower.
So with this method, it does makes sense to call 2-1-2 dorian, because it IS associated with the 2nd tetrachord of a dorian scale which contains the characteristic nat 6 scale degree. So I guess it's really just depends on the way you look at it.[/quote]

[jancivil]

/So, I'm wrong to place what works best for me as if primary or something. Looking around it looks like 3, with often a whole tone disjunction and then another 3 is a more typical construction. I always thought it odd though./

I'm just saying, Sam, less lingo is better. Dorian lower tetrachord, Aeolian lower tetrachord and some others you brought in, we don't need all of this naming. Naming is a middleman in the exchange and this one doesn't enhance it, it doesn't show anything more. That rubbed me the wrong way.

- upper lydian (F, G, A, and B, in the key of C) in this context don't project a lydian modality

There is a certain logic to this, but we require 'in this context' for it to work. You mean the ear is definitely taking C as fundamental. If you play the B over a strong F in the bass, or we have dwelled on F in the harmony, the B has a Lydian feeling to it. Objectively is that necessarily a true statement? But if that works for you, who am I to say.

"call 2-1-2 dorian" this is exactly what I dislike about this whole exercise. I can't use that. Dorian is knowable in that the 6th is higher than the 6th in minor aka aeolian, or what-have-you. For a western musician it makes sense/is typically learnt as minor with a raised 6th, and we're done. You're arguing for it as a name for something else - are you going to use it for Aeolian or the other things now? - and I can't agree.

[jancivil]

the other thing, for me is I think of 4 as the middle of the thing. Lydian chromatic concept type of thing. you see me placing it with a +4.

modal playing; let's say we'll use two chords; & get a double vantage point.
Let's take a mixolydian mode, say on D and the bass is defining things D, C. Back and forth, D, C.
So we get a lydian second perspective when we're sitting on C. {C D E F# G A B [C]} and then back to D bass {... G A B C [D]}, this _4_ is what I took as the crux point of the thing.

[sammy24]

listen, no prob, if 'dorian' bothers you so much, then 'minor' it is. That's fine.

I've found that music terminology is so often not universal. I mean, look at chord symbol systems; I read once that a colleague of a particular author once documented over 100 ways he had come across for indicating a major 7th chord!

So I'm pretty flexible when it comes to terminology. When I discuss music in a public setting, like this one, I try to cover more bases, because there may be people out there who are comfortable with a different term for the same thing.

[Aroused by JarJar]

Tetrachords have been around for 2,500+ years. Conjunct tetrachords were the ancient starting point, and they're still around in some Middle Eastern maqams.

The medieval church modes are a kind of reboot- they got it all wrong as far as ancient Greek music, but so what, they still made great scales and music. The Church modes are concieved of in disjunct tetrachords.

If you're creating your own, new, music, you can think about it any way you'd like. Tetrachords can also be disjunct at the "tritone" rather than at the fifth, or even overlap. Maqams also use scales of overlapping trichords and tetrachords. It all makes sense when you modulate in the ancient or Middle Eastern sense.

It's easiest to give an example.

Let's say we have C,Db,Eb,F,Gb,Ab,Bb. That would be two conjunct diatonic tetrachords for the ancient Greeks. That might sound crazy if you know Western modal theory, but if you think about the word "diatonic", two tones, it makes sense. The space between C and F is divided into two whole tones and a semitone left over. It's 1-2-2. Same thing for C,D,E,F, except that's 2-2-1. And there's 2-1-2, C,D,Eb,F. These are all diatonic tetrachords- in conjunct form they share a tone (F in the example).

Originally the octave wasn't as important as it became later (it's still not as central in the East as it is in the West). So C,Db,Eb,F,Gb,Ab,Bb could very well be the whole scale. Like Middle Eastern music, an ancient scale might have an ambitus of more or less than an octave. But go ahead and make it C,Db,Eb,F,Gb,Ab,Bb,C.

To hear an ancient way of modulation, and to see how tetrachords work, jam on this scale for a whole, until it settles in your ear. Then "sharp the Gb to G" and keep going. Now the scale is C,Db,Eb,F,G natural, Ab, Bb,C. It's the same two diatonic tetrachords, except that now they are disjunct (one whole tone apart). 1-2-2, whole tone, 1-2-2 (we all will recognize this as "phrygian" from the Church modes). In tetrachordal thinking, you're not really sharping the Gb to G, you're playing the tetrachord at the disjunct rather than the conjunct. This might seem a trivial distinction, but it is not, as you'll see when go further afield and especially when you're playing microtonal scales like the ancients did and they still do in the East.

For a stronger effect, try C,C#,D,F,F#,G,Bb, and don't go to the octave. This is two conjunct chromatic tetrachords (made of permutations of 1-1-3 steps). Then modulate to C,C#,D,F,G,G#,A,C, two disjunct chromatic tetrachords.

Even in 12-tET the possibilities are endless. You can modulate by permution of the tetrachord:
C,D,E,F,G,A,B,C to C,D,E,F,G,Ab,Bb,C (the upper tetrachord permutes to 1-2-2 from 2-2-1).

from there you could go to C,D,E,F,Gb,Ab,Bb, diatonic tetrachord conjunct with chromatic tetrachord, and drop a Bb below the C to get Bb,C,D,E,F,Gb,Ab,Bb (the conjuct tetrachords on top of a whole tone) and so on.

Then of course there are all the modes of these scales resulting from different combinations of tetrachords.

The most revered tetrachord of ancient times had already died out more than two thousand years ago, because only masters could perform it and it is very somber and dark. C,C+,C#,F, two "quartertones" and a wide "major third". 1/2-1/2-4. You can play it on a fretless, maybe a fretted guitar if you're a fierce bender.

Because there are continually anchors for your ears in pure fourths and fifths, microtonal variations of the steps dividing the tetrachords are natural. If you play on an instrument of flexible pitch, you'll find yourself rediscovering all kinds of ancient and Eastern variations.

I could go on, or you could download THE book of tetrachords, which has been offered for free for some years now:

http://eamusic.dartmouth.edu/~larry/pub ... etrachord/

[jancivil]

No one knows what the musical point might have been with the original work resulting in 'tetrachords', if any. It's all speculative. This was technical research into the nature of the thing.

"the most revered"; I never heard that one. EG:

Didymos chromatic tetrachord 16:15, 25:24, 6:5
Eratosthenes chromatic tetrachord 20:19, 19:18, 6:5
Ptolemy soft chromatic 28:27, 15:14, 6:5
Ptolemy intense chromatic 22:21, 12:11, 7:6
Archytas enharmonic 28:27, 36:35, 5:4

Revered as a beautiful idea in ratios qua ratios? The difference betwen 20:19 and 19:18 in a row? It is two versions of , more or less a semitone per 1:1 to our terminology; we're going to pretty much choose one or the other in our scala file in terms of musical use. It's hard to feature someone playing these around the campfire: someone hears the Archytas and goes 'oh yeah, that's the one' and then 'Yes, we concur'.

I've gone fairly deeply into it. Such as Alain Danielou with North Indian intonations. He arrives at '22' with a just system with alternates, designed to give 3:2 fifths relationships as it is important to the way raga is made, using the syntonic comma 81:80 to add ten tones to the usual 12 (Sa and Pa, tonic and P5 as inviolate).

http://en.wikipedia.org/wiki/Just_inton ... ian_scales

There is no 22-tone 'scale'. Further into it, he gives 53 notes as actually useful in practice and provides a rationale. There is no 53-tone scale though. "playing microtones" is a western construction of what happens.
There are expressive reasons for these. In India it's handed down from guru and it's done by ear and by indicating on a sarod where the things are found. Arabic thought is more concerned with the math; the instruments are built to provide it to a person that isn't doing the math though. This is where I got involved with it, trying to sort out fretboards and research into possibilities. My pal Hansford Rowe plays a just-intonation bass which looks complicated.




Anyway, good point about the Maqams, per "conjunct". that's how I think of them anyway.

[Aroused by JarJar]

No one knows what the musical point might have been with the original work resulting in 'tetrachords', if any. It's all speculative. This was technical research into the nature of the thing.

"the most revered"; I never heard that one. EG:

Didymos chromatic tetrachord 16:15, 25:24, 6:5
Eratosthenes chromatic tetrachord 20:19, 19:18, 6:5
Ptolemy soft chromatic 28:27, 15:14, 6:5
Ptolemy intense chromatic 22:21, 12:11, 7:6
Archytas enharmonic 28:27, 36:35, 5:4

Revered as a beautiful idea in ratios qua ratios? The difference betwen 20:19 and 19:18 is not so useful musically. It is two versions of a close interval, more or less a semitone to our terminology. we're going to pretty much choose one or the other in our scala file in terms of musical use. It's hard to feature someone playing these around the campfire: someone hears the Archytas and goes 'oh yeah, that's the one' and then 'Yes, we concur'.

The ratios are specific intonations- flavors. The tetrachords could be flavored in different ways, but they were distinguished by steps, large and small. The specific ratios given by theorists range from numerological fantasy to practical tunings, you can tell which ones were on paper and which ones were real by using them on acoustic instruments.

There is a very big difference between 1-2-2, 1-1-3, and 1/2-1/2-4 divisions of the tetrachord. Regardless of the exact (or inexact) tuning, two semitones and a jump to a pure fourth does not sound like two quatertones and a jump to the fourth. The soft chromatic is in between, but that wouldn't be contrasted with a near-identical intonation of chromatic or enharmonic.

The enharmonic was considered the most noble and difficult tetrachord, and was already rare at the time of the ancient documents we have.

The ancient traditions were continued by Persian, Arabic and Balkan musicians. It's not a matter of Greek music being some great mystery, it's a matter of Western musicologists doing historical revisionism to avoid facing the glaringly obvious and documented "oriental" nature of the music, exactly as their counterparts in the visual arts deliberately scraped the paint off Greek statues for centuries, in order to invent a "European" version of ancient Greece that never was.