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Old 7th December 2017, 02:45 AM   #41
calebprime
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The same simple structures and thinking, turned upside down, also illuminate polyrhythms. Just as notions of low-interval limits clear up some harmonic ideas, the same kind of notion clears up what are the limits of polyrhythmic intelligilibilty.

Suffice to say that some large part of middle-period Carter is both impossible to play accurately and not intelligible or hearable or even recognizable by savants.

That may not be a fatal criticism of the music, but it does give you some perspective on the spirit in which it was written. Being intelligible didn't matter.

It's the inversion of the low-interval limit. The upper bound on resultant rhythms in combination. If the resultant combination r's are faster than you can tap or sing or faster than 15 a second, they're not intelligible.

The static model of harmony would explain the simple Partch up-down generation system, or basic JI. Simple, but I've spoken with some old Boston microtonalists who didn't understand what Partch was doing! That's astounding ignorance in a specialist.
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Old 8th December 2017, 10:24 AM   #42
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Another way of saying the same thing.

First, an ideal sort of definition of consonance. What is pure consonance? It is anything that makes overtones of a fundamental frequency (whether the fund. is stated or not) that is in the auditory range.

I mean integer multiples. This is an extremely robust effect.


Ok, then, does that explain music as it's practiced? (Sophist's approach, etc.)
No, it couldn't and shouldn't.

You have to add, from your listening, all the variation over time.

While a JI model generating overtones from fundamentals all of which share a common overtone (the 1/1) is in a sense a static model, it too implies motion, because each "undertone" of which 1/1 is an overtone is separate from the others, to some degree or almost completely. That is there is a range from related fundamentals like /9 and /3 to fairly unrelated funds. like /13 vs. /12 or something.

So, while it is a model that is static (doesn't take time into account) it is not a model that means that anything goes, that any note in it is as closely related as any other. No, they are closer or more distant to each other.

In the 13-limit model I favor, there is implied motion -- you'd go from a chord on /13 to a chord on /3, which are thought of as separate regions, at least at first, for clarity, and for sonic clarity.

But in the more sophisticated view of the second half of the course, harmony in motion & practice, you could bring in all the effects of everything else, especially those things having to do with passing-tones, or directional tones, or tones in motion over time, in a rhythmic framework.
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Old 8th December 2017, 11:12 AM   #43
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Originally Posted by calebprime View Post
... What is pure consonance? It is anything that makes overtones of a fundamental frequency (whether the fund. is stated or not) that is in the auditory range.

I mean integer multiples. This is an extremely robust effect.


...
Q. Would something like only the 15th partial sounding with the 14th partial -- just those two notes -- be a consonance? You said anything.

A. Shut up, smartass.


Q. Why?

A. No, in that unusual example, you'd have the impression of dissonance until the rest were filled in. So I have to add other restrictions, which is no fun whatsoever, compared to a sweeping generalization. I going [sic!] to go home and drown my sorrows in hookers and blow. See what you've made your noble professor do?

Q. I'm...I'm sorry.

A Apology accepted. There's a book you can read. The psychology of the sensitive person.

Q. Is it right that you cover the entire work of Santana in the first half of the course? That you can't even mention Shostakovich until the second half?

A. Yes. It's fine. shut up.
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Old 10th December 2017, 05:12 AM   #44
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The difference between 40 hz. and 20 hz., etc

This is why I no longer teach.

Dani, here's a soundfile I just concocted by putting the sound of my son as a toddler babbling through an early version of Alchemy.

https://app.box.com/s/4u6k3hjxqholh37q1c0sr2da8huruabc

There's a lot that can be done with Alch. but right now you're hearing the sound slowed down and resonating through a comb filter.

The comb filter frequency starts at 40 hz. You can hear to what degree everything sounds like harmonics of one note.

Then you can hear the frequency move around as I move the dial -- the moves are obvious and not quite accurate, because it's hard to land on the exact right number.

I go up to 80 hz., back down to 40. I go down to 20, and you still have a strong sense of harmony, but you hear things shake, vibrate, flap, quiver, whatever you wish to call it. We're near the threshhold.

At around 16 hz, which I hit and sit on later, you hear the rhythm, but you still hear some of the Chord of I.

See if you can get a resonant comb filter and try this for yourself -- listen and decide where "harmony" starts to become "rhythm" -- somewhere gradually between 20 and 10 hz.
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Old 10th December 2017, 09:21 AM   #45
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Originally Posted by calebprime View Post
Without being clear about basic grounding of harmonic concepts, students make absurd mistakes about what they say about harmony, and how they analyze the lit.

For example, the person who thought it was significant that a particular C major triad was in "6 4 position" (second inversion, or G in the lowest position) when the lowest note was a G2 -- that is, not a note in the bass register. No, the chord simply had no functional bass. It wasn't relevant to say it was "in .[].. position."

Without theory and practice actually helping each other, as they rarely do with most musicians, it's easy to take a cynical view of theory as just some idle philosophy. Musicians who take this view never innovate in fundamental musical ways, however innovative they may be in extra-musical ways, or however good they are.
I'm one of those people! For starters, I don't understand the notion that, because G2 is not a note in the bass register, it ceases to function as a bass. And... what is a note in the bass register? Is there a specific frequency where a bass ceases to be a bass? Isn't it context dependent? I can imagine a G2 being played by a bass player to determine the fundamental of a given chord. Is that wrong (objectively)?

I'm not talking about inversions played by a single instrument with a bass playing the root (which guitar players in particular tend to see as inversions).
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Old 10th December 2017, 09:32 AM   #46
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Just so we're clear, I mean G2 top space bass clef, or around 196 hz.

With ca. 19.6 hz as an easy-calc approximate root, this G2/196 hz. could be the 10th, 9th, 8, 7....1 of any fundamental.

So it's not "bass-ic" until it's maybe an octave lower.

Think about the voicing of the richest music you know -- bruckner, brahms, wagner. Still way above the low-interval limits, mostly. But I'm on shaky ground there, as I haven't been studying that lit for a while. (give this historical ass. an 90% true.)

It wouldn't be wrong, it would miss the point that it doesn't matter what the inv. is if it's that high, it has no characteristic "inversion" effect anymore.

If asked on a test, what's the inversion? You are correct sir, it's a 6-4, second inversion, g in the "bass", no question.
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Old 10th December 2017, 09:39 AM   #47
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Characteristic "inversion effect" with real low bass:

--the effect of the overtones of the bass clashing with the other notes.

Without that clash, no real inversion effect.
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Old 10th December 2017, 09:41 AM   #48
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On Neo-Riemannian theory, I just read a brief introduction. It's really focused on voice-leading, regardless of tonality/atonality. That's interesting. Also, I just noticed that, given any series of transformations L (leading tone), R (relative) and P (parallel), its repetition leads to the original chord (or group of pitches, or klang). Still not sure if the order of the factors alters the product. I have to figure that out.

Also, I'm curious about how augmented, diminished, seventh and extended chords fit in this theory.
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Old 10th December 2017, 09:43 AM   #49
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I mean that True Bass™ is absolute, gradual, and a function of something like our neural "clock-rate". This is the rate at which we perceive the world, as opposed to the rate at which hummingbirds perceive it, or sloths.

Whatever G2 is, man it's tenor. Not bass.
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Old 10th December 2017, 10:01 AM   #50
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Originally Posted by calebprime View Post
Just so we're clear, I mean G2 top space bass clef, or around 196 hz.

With ca. 19.6 hz as an easy-calc approximate root, this G2/196 hz. could be the 10th, 9th, 8, 7....1 of any fundamental.

So it's not "bass-ic" until it's maybe an octave lower.

Think about the voicing of the richest music you know -- bruckner, brahms, wagner. Still way above the low-interval limits, mostly. But I'm on shaky ground there, as I haven't been studying that lit for a while. (give this historical ass. an 90% true.)

It wouldn't be wrong, it would miss the point that it doesn't matter what the inv. is if it's that high, it has no characteristic "inversion" effect anymore.

If asked on a test, what's the inversion? You are correct sir, it's a 6-4, second inversion, g in the "bass", no question.
Ok. 196 hz doesn't sound like a bass in any way, shape or form. Agreed. Some of the concepts you regularly use are fairly new to me, and I don't know by memory what a G2 is, for example. I looked that up and I saw it referred to as around 98 hz. That still sounds like a bass to me. But, yeah, 196 hz is way too high to be considered a bass.
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Old 10th December 2017, 10:05 AM   #51
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Yeah, there are at least two standards. I forget which one I mean.

Glad we agree about that G2.

I feel I may rest now. My work is done.

You have learned much, Dani.
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Old 10th December 2017, 10:12 AM   #52
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Just so we're clear about neo-R theory and me:

--It might well be that a composer or an improviser has benefited from it, but I don't know that. It seems to be "by and for" theorists.

--I don't know it.

--You are smart. You might be able to absorb it into your bag of tricks. Take it into account.

--I would learn it enough to converse with you, but only for that reason.

--It is definitely something you should know if you want to fit into contemp. academic music theory world.

Go for it!
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Old 10th December 2017, 10:35 AM   #53
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Funny anecdote:

Rehearsing with a blues-soul-worldmusic-pseudojazz-whatever quartet, we were playing an instrumental gospelly-soul piece, and there's this part where we play a typical A7alt resolving to Dm. I asked the guitar player, a friend of mine and a fine blues player, both melodically and rhythmically:

Me: What are you playing on the A7 chord?
Guitar player: I'm not playing an A7.
Me: (looking at the bass player) Well, whatever you're playing, it's some type of A7 chord.
Guitar player: I'm playing a Bbm.

He clearly understands that he is not painting the harmonic canvas alone, and understands the function of that Bbm over A (an implicit A7alt, even if there's no 7th), but there's something about non academic guitar players (I don't know, magazines, tutorials, inertia?) that tends to make them think in these terms, whereas no matter how clueless we are, piano players have at least two octaves to figure out what bass sounds like.
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Old 10th December 2017, 10:44 AM   #54
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(mentally puts little finger on C (on D string), then Db,F,Bb all on 6th fret for Bb minor 9 with no bass)

Yeah, A7 #9

(Which is a mis-nomer, because it's really Amin7b5 b4, but that would confuse everybody.)


love it.
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Old 10th December 2017, 11:18 AM   #55
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Thanks, Calebprime. There's tons of information already in this thread about... many things.

I feel like atonality is the end of a journey I'm just starting, which starts with tonality. I've never really been into classical music, but I'm starting to feel like I need to do a historical discovery on my own, as I did with 20th century popular music (and still do) earlier.

While one part of me is playing funky grooves, another part is absorbing lots of fascinating information, and much of that is thanks to you. That could be useful in the future in terms of understanding music with a greater perspective. I feel like I've been on shaky grounds all this time, and I'm experiencing the excitement of discovery. Things like why did medieval musicians used only fifths to harmonize a melody and why the next audacity consisted of adding the third now have a deeper meaning.

JI is interesting, but it will take some time. Same with microtonal stuff. There's so much to learn with 12 equally tempered tones only, starting from Bach.

Serialism? Very interesting. Right now all I can do is cerealism. I don't know if I'll end up there. Depends on how much I am absorbed by other things (including jazz).

Music is soul food. Music theory is intellectual food for soul food. This is a feedback loop that never ends.
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Old Yesterday, 09:19 AM   #56
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Just had another good musical chat with my old friend who teaches jazz piano at Berklee.

He'd been impressed with Cecil Taylor's energy when he heard him in the Village in the late 70's.

I keep saying: Well, let's hear it. What's some good Cecil Taylor?

He said he'd listened to the Ives first piano sonata, then Dark To Themselves, a CT album.

Said he heard stuff going on, not just incoherent skittering.

Later today, if work goes well, maybe I'll give ol' CT another try.

(I've given him about 50 tries, and so far nothing registers on caleb's ears at all, aside from the vague and tentative first 2 minutes of each of his improvs.)

hm. Dark to Themselves
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Old Yesterday, 09:25 AM   #57
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Originally Posted by calebprime View Post
(mentally puts little finger on C (on D string), then Db,F,Bb all on 6th fret for Bb minor 9 with no bass)

Yeah, A7 #9

(Which is a mis-nomer, because it's really Amin7b5 b4, but that would confuse everybody.)


love it.
Count me in! Flatted fourth?
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Old Yesterday, 09:30 AM   #58
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Zee conziztent zpelling of zee A "altered" zcale:

A,Bb,C,Db,Eb,F,G

or ascending Bb melodic minor

A to Db is a weird interval, the diminished fourth, or "flat 4".

But earnest and even slightly scary young Berklee students will shout at you that there can be no "flat four" as an interval, because it's a major third, and the chord comes historically from a "dominant function". The miracles continue!

This is because we're trying to reconcile several things that can't be, like history, logic, consistency, notation, acoustics, ratios.

In all seriousness, because I'm not Keith J., I like to keep my theoretical head screwed on straight -- it helps me. When I understood about "b4", some confusion fell away from my mind.
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Old Yesterday, 10:18 AM   #59
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defined and undefined scale-notes, or "scale space"

The higher the note, the more ambiguous, but that's not important right now.

The more notes, the less undefined space. (Jazz players have conventions so that they can play together, stay out of each other's way. Such as, the bass player is probably going to land on the root on beat 1, and all you should add as a guitarist at first is 3rd and 7th.)

Let an acceptable, euphonious family of chord-scales with 12 tones, the conventional scales, be defined as: all the possible ways 12et pitches may be combined within one octave without producing an 012, or B,C,C# cell (transposable, obviously).

Then any given combination of pitches can be analyzed according to how many scales as defined above may be its superset -- how many combinations of notes without an 012.

A very simple, robust definition that defines the whole conventional family of scales, very neatly.


So, Dani, etc.

What is the total "scale space" as defined above of:

Bb,D,F,Ab?

Bb,D,Ab (just these three)

Bb,C#,D,A?

Bb,C#,D,Ab?

Bb, B, C#, D?

(I do have a point, here.) Paul2* already knows the answer, but he never participates.




* pope avatar, nice guy
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Old Yesterday, 10:49 AM   #60
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btw, whatever its rhetorical failings, and my personal failings, that last post was my finest moment ever, for content.

From this moment on, neither of you two are my friends unless you Dani answer, very carefully.


musique qui est tonale par opposition la musique qui n'est pas tonale?

Code:
p/0/9:...............E  Bb F# A  C# Eb C  F  Ab G  D  B                 THIS ONE
p/11/8:..............Bb Eb A  F  Ab C  D  B  E  G  F# C# 
p/11/6:..............F# C# Bb Eb A  F  Ab C  D  B  E  G  
p/0/0:...............A  C# Eb C  F  Ab G  D  B  E  Bb F#
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Old Yesterday, 11:08 AM   #61
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Originally Posted by calebprime View Post
(I've given him about 50 tries, and so far nothing registers on caleb's ears at all, aside from the vague and tentative first 2 minutes of each of his improvs.)

hm. Dark to Themselves
Some of his solo playing might be appropriate for attempt #51. Silent Tongues may hold some appeal. It's even lyrical at times...
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Old Yesterday, 11:14 AM   #62
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Crikey, before that last post I almost posted "Uh oh I didn't know there would be pop quizzes, I'm getting out of here pronto".

And now my friendship w/Caleb hinges on you Dani. I know you can do it!

I'm visually oriented in the extreme, and I don't have an instrument here with me. That's my excuse and I'm sticking with it. I'll come back to this when I have axe in hand, or humanatone in nose as the case may be.
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Old Yesterday, 11:23 AM   #63
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for you varwoche, only if you post a YouTube of you personally performing Serenade to a Cuckoo with nose flute.
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Old Yesterday, 02:52 PM   #64
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Originally Posted by varwoche View Post
Crikey, before that last post I almost posted "Uh oh I didn't know there would be pop quizzes, I'm getting out of here pronto".

And now my friendship w/Caleb hinges on you Dani. I know you can do it!

I'm visually oriented in the extreme, and I don't have an instrument here with me. That's my excuse and I'm sticking with it. I'll come back to this when I have axe in hand, or humanatone in nose as the case may be.
If only I knew what is it that I'm supposed to do...

I'm thick. I need someone to spell it for me. "Scale space"... ehm...

Gee... what was a triad, again?

Let's give it a try anyway, just with the first one, so Calebprime can see how clueless I am and direct me to the correct way of looking at this... "scale space":

Bb,D,F,Ab

Ok. We got a Bb7, with I, III, V and bVII. And, whatever it is, scale space doesn't refer to each of the 12 tones as possible, or else this exercise would make no sense.

Right now, in my mind, scale space is a bit like fallacy space. I tend to think of already defined scales with names like some people think of defined fallacies with names instead of using logic.

So, when I see that type of chord, in practice I tend to think: Mixolydian, diminished and other combinations. The only note that doesn't fit, according to the "no 012" rule, is A (although I'd probably play it, both as a passing tone or a mistake, but not in the sense of note within a scale... except... wait... the so called bebop scale...). Is that the scale space for the first chord?

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Old Yesterday, 03:10 PM   #65
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You do not relish Tranya as I.

However, your basic intuition is sound.

Yeah, that's right only the a is bad, but, as you say, music.

But I'm talking about a static sort of exercise.

You make a list of all the possible ok scales.

eta: or, come to think of it, you use caleb's computer program that crashed your computer.

It turns out to be not that many, and they make interesting patterns,
and in the process, you find some fresh sounds.

So there, Mr. not-quite-living-up-to-my-narcissistic-expectations!

Dani is too cool for school, for exhaustive work like this -- sort of like filling out taxes, or simple math, or shopping list, intellectually, except: the sweet, sweet, unbearably magnificent harmonies that await the canine that pursues them, lean and smiling!
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Old Yesterday, 03:12 PM   #66
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Names of common scales I can think of for Bb, D, F, Ab. On Bb:

Mixolydian
Diminished halftone-wholetone
Lydian b7
Mixolydian b9b13
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Old Yesterday, 03:17 PM   #67
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what's mixolydian b9 b13

lessee

c,db,e,f,g,ab,bb

ok, got it.

F harmonic minor.

but I did wrong key, no matter.

Heh. I'll have to check to see if you got them all. This is simple right/wrong.

Those are all the basic types, I think, but there may be some transp./ maybe harm major also?

I'm about to eat and my sugar is dangerously low. If you kill your professor, no more Tranya.

anyway. that was the least interesting of the bunch!
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Old Yesterday, 03:18 PM   #68
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Between the Mixolydian and the Mixolydian b9b13, there are two more combinations (b9 only, b13 only).
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Old Yesterday, 03:24 PM   #69
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Yeah, so additional nice colors of scales you didn't mention.

eta: you beat me to it.
mixo b6
altered

and there are probably 3 to 6 more, this is sort of the point.

that is, if we make an exhaustive search, it will still be a small
number, and there may be a few that we didn't think of right away.
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Old Yesterday, 03:27 PM   #70
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Originally Posted by calebprime View Post
Those are all the basic types, I think, but there may be some transp./ maybe harm major also?
That would be mixolydian b9 then. And from the melodic minor we can get a mixolydian b13.
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Old Yesterday, 03:30 PM   #71
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you don't have to do them all, but take 1 or 2 of the less conventional.

So you have to actually think about it.
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Old Yesterday, 03:31 PM   #72
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Stop call it mixolydian not-mixolydian, it's barbaric, dammit!

They'd laugh you right out of ii V school!

mixolydian b9? mixo b13?

you need more consistent parlay
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Old Yesterday, 03:34 PM   #73
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Originally Posted by calebprime View Post
Yeah, so additional nice colors of scales you didn't mention.

eta: you beat me to it.
mixo b6
altered

and there are probably 3 to 6 more, this is sort of the point.

that is, if we make an exhaustive search, it will still be a small
number, and there may be a few that we didn't think of right away.
Altered (if we're talking about the same scale) doesn't fit. The problem is with the fifth. It has two neighbors a half tone apart.
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Old Yesterday, 03:51 PM   #74
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Originally Posted by calebprime View Post
What is the total "scale space" as defined above of:

Bb,D,F,Ab?

Bb,D,Ab (just these three)

Bb,C#,D,A?

Bb,C#,D,Ab?

Bb, B, C#, D?
Ok. Let's try with the whole bunch:

Bb,D,F,Ab: all, except A.

Bb,D,Ab: all, except A.

Bb,C#,D,A: all, except B, C, Eb, Ab.

Bb,C#,D,Ab: all, except C, Eb, A.

Bb, B, C#, D: all, except C, Eb, A.
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Old Yesterday, 04:08 PM   #75
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I'll need some type of clue for the which series is tonal and which isn't exercise, because I don't have the slightest idea. For some reason I can't quote the post. It's #60.

ETA: Wait. The first one is a tonal row, and the other ones arent? Why?

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Old Today, 03:54 AM   #76
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Dani, I was looking for the actual scales, beyond only pitches that are excluded. Figuring out which single pitches are excluded is first step. Then figure out which combinations of pitches are excluded. Then which scales are possible. (Conventional, according to this arbitrary (but good!) definition.

This would be a bit of work, especially if one hasn't been doing it in a while. It gets better with practice.





Microtonal Scales to the rescue!

I hadn't realized how incredibly good and useful 69Dodge's program is for exactly this, as well as every other musical calculation. And freeware, too. amazing.


Conventional 1-octave scales for given situations:

(note: program gives only names of scale-groups, so everything is called Lydian, for example.)

Code:
Bb, D, F, Ab:

Octatonic-Diminished  Harmonic Minor       Ascending Melodic Minor  
(A# B C# D E F G G#)  (Bb B D Eb F Gb Ab)  (Bb C D Eb F Gb Ab)      
                                           (Bb C D E F G Ab)        

Harmonic Major        Lydian                                        
(A# B C# D F F# G#)   (Bb C D Eb F G Ab)                            
(Bb B D Eb F G Ab)    




Bb, D, Ab:

Octatonic-Diminished  Harmonic Minor       Ascending Melodic Minor  
(A# B C# D E F G G#)  (Bb B D Eb F Gb Ab)  (A# B C# D E F# G#)      
                                           (Bb C D Eb F Gb Ab)      
                                           (Bb C D E F G Ab)        

Harmonic Major        Lydian               Whole-Tone               
(A# B C# D F F# G#)   (Bb C D Eb F G Ab)   (A# C D E F# G#)         
(Bb B D Eb F G Ab)                                                  




Bb, C#, D, A:      

Harmonic Minor     Harmonic Major      Augmented 1-3     
(Bb C# D E F G A)  (Bb C# D E F# G A)  (Bb C# D F Gb A)  




Bb, C#, D, Ab:

Octatonic-Diminished  Ascending Melodic Minor  Harmonic Major       
(A# B C# D E F G G#)  (A# B C# D E F# G#)      (A# B C# D F F# G#)  



Bb, B, C#, D:

Octatonic-Diminished  Harmonic Minor      Ascending Melodic Minor  
(A# B C# D E F G G#)  (A# B C# D E F# G)  (A# B C# D E F# G#)      

Harmonic Major                                                     
(A# B C# D F F# G#)

Incidentally, the competence you'd develop with scales in this kind of work is exactly the same as if you'd taken The Lydian Chromatic Concept at NEC, except stripped of all the good and bad stuff that George Russell brought to it. This approach is strictly logical -- it's trivial for a computer. I spoke with one sax player who had taken a little Lydian Chrom. and boy was she hopelessly confused about helping herself with theory! A little knowledge is temporarily very confusing for some students, I guess. I don't mean to sound snotty, but it was strange to see her tie herself in knots trying to understand what scales to play on chords.
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Old Today, 08:39 AM   #77
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I promise not to post a lot of this stuff, but

here's the 12 x 4 array above, treated like a 4-part chorale, lowest note in "bass" position, etc.

with added analysis showing the conventional scales that fit with these chords.

Code:

Code:
p/0/9:...............E  Bb F# A  C# Eb C  F  Ab G  D  B                  
p/11/8:..............Bb Eb A  F  Ab C  D  B  E  G  F# C# 
p/11/6:..............F# C# Bb Eb A  F  Ab C  D  B  E  G  
p/0/0:...............A  C# Eb C  F  Ab G  D  B  E  Bb F#

                     0  1  2  3  4  5  6  7  8  9  10 11



0 -- a,f#,bb,e
no: ab,b,f 
Octatonic-Diminished   Ascending Melodic Minor  Harmonic Major      
(A Bb C C# D# E F# G)  (A Bb C D E F# G)        (A Bb C# D E F# G)  
 

1 -- c#,c#,eb,bb
no: d,   no a,b   no c,b   no e,f   

number of scales found: 12

Octatonic-Diminished   Harmonic Minor        Ascending Melodic Minor  
(C# D# E F# G A Bb C)  (C# D# E G G# A# B)   (C# D# E F# G# A# C)     
                       (Db Eb F Gb A Bb C)   (Db Eb F G A Bb C)       
                                             (C# D# F G G# A# B)      

Harmonic Major         Lydian                                         
(C# D# E F# G A# B)    (C# D# E F# G# A# B)                           
(Db Eb E G Ab Bb C)    (C# D# F F# G# A# B)                           
                       (Db Eb F Gb Ab Bb C)                           
                       (Db Eb F G Ab Bb C)                            



2 -- eb,bb,a,f#
no: ab,b, no d,e no f,g    no e,f 
Octatonic-Diminished   Harmonic Minor       Harmonic Major      
(D# E F# G A Bb C C#)  (Eb F Gb A Bb C Db)  (Eb F Gb A Bb C D)  
                       (Eb F# G A Bb C D)                       


3 -- c,eb,f,a
Octatonic-Diminished  Harmonic Minor       Ascending Melodic Minor  
(C D Eb F Gb Ab A B)  (C Db Eb F Gb A Bb)  (C Db Eb F G A Bb)       
                                           (C D Eb F G A B)         

Harmonic Major        Lydian                                        
(C Db Eb F Gb Ab A)   (C D Eb F G A Bb)                             
(C D Eb F Gb A Bb)                                                  



4 -- f,a,ab,c#
Harmonic Minor      Ascending Melodic Minor  Harmonic Major       
(F F# G# A B C# D)  (F F# G# A B C# D#)      (F Gb Ab A C Db Eb)  
                                             (F G# A B C# D E)    

Augmented 1-3                                                     
(F G# A C Db E)                                                   


5 -- ab,f,c,eb
Octatonic-Diminished  Harmonic Minor        Ascending Melodic Minor  
(Ab A B C D Eb F Gb)  (Ab B C D Eb F G)     (Ab Bb C D Eb F Gb)      

Harmonic Major        Lydian                                         
(Ab A C Db Eb F Gb)   (Ab Bb C Db Eb F Gb)                           
                      (Ab Bb C Db Eb F G)                            
                      (Ab Bb C D Eb F G)                             

Code:
p/0/9:...............E  Bb F# A  C# Eb C  F  Ab G  D  B                 
p/11/8:..............Bb Eb A  F  Ab C  D  B  E  G  F# C# 
p/11/6:..............F# C# Bb Eb A  F  Ab C  D  B  E  G  
p/0/0:...............A  C# Eb C  F  Ab G  D  B  E  Bb F#

                     0  1  2  3  4  5  6  7  8  9  10 11


6 -- g,ab,d,c
Harmonic Minor      Ascending Melodic Minor  Harmonic Major    
(G Ab B C D Eb F)   (G Ab Bb C D E F)        (G Ab B C D E F)  

Lydian                                                         
(G Ab Bb C D Eb F)  


7 --  d,c,f,b
Octatonic-Diminished  Harmonic Minor     Ascending Melodic Minor  
(D Eb F Gb Ab A B C)  (D Eb F G Ab B C)  (D Eb F G A B C)         
                      (D E F G# A B C)                            

Harmonic Major        Lydian                                      
(D E F G Ab B C)      (D E F G A B C)                             



8 -- B,D,E,Ab
Octatonic-Diminished  Harmonic Minor      Ascending Melodic Minor  
(B C# D E F G G# A#)  (B C D E F G# A)    (B C D E F# G# A)        
                                          (B C# D E F# G# A#)      

Harmonic Major        Lydian                                       
(B C D E F G Ab)      (B C# D E F# G# A)                           
(B C# D E F G# A)            

9 -- E,B,G,G
Octatonic-Diminished  Harmonic Minor       Ascending Melodic Minor  
(E F G G# A# B C# D)  (E F# G A B C D#)    (E F G A B C# D)         
                      (E F# G A# B C# D)   (E F# G A B C# D#)       
                      (E G G# A# B C# D#)                           

Harmonic Major        Lydian               Augmented 1-3            
(E F G Ab B C D)      (E F G A B C D)      (E G Ab B C D#)          
(E F# G A# B C# D#)   (E F# G A B C D)                              
                      (E F# G A B C# D)                             




10 -- Bb,E,F#,D
Harmonic Minor      Ascending Melodic Minor  Harmonic Major      
(A# B C# D E F# G)  (A# B C# D E F# G#)      (Bb C# D E F# G A)  
                    (Bb C D E F# G A)                            

Whole-Tone                                                       
(A# C D E F# G#)                                                 


11 -- F#,G,C#,B                                         
Harmonic Minor      Ascending Melodic Minor  Harmonic Major       
(F# G A# B C# D E)  (F# G A B C# D# E)       (F# G A# B C# D# E)  

Lydian                                                            
(F# G A B C# D E)
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