Question about Intervals

[Ed DeGenaro]

What options are there for naming the interval between C and Eb in any possible context, mode or tonality?
In what context/mode or tonality is “minor 3rd” not the correct answer?

When it's a diminished 4th.
As in say mode 7 of melodic minor
1 ♭2 ♭3 ♭4(3) ♭5 ♭6 ♭7

 

[Ed DeGenaro]

Ed (I hope I can call you "Ed"), when I play 0-3-5, what key am I in ?

What else would you call me.

I'm assuming say open E string, you got a few options but the likelihood of a guitarist calling it E minor (which by definition includes either/and/or ♭6 6 ♭7 7).

 

[Eagle]

When it's a diminished 4th.
As in say mode 7 of melodic minor
1 ♭2 ♭3 ♭4(3) ♭5 ♭6 ♭7

Super locrian, great scale

 

[Ed DeGenaro]

True. Simply because there are 7 modes but only 2 types of thirds. So a "dorian" third is no difference from a phrygian or aeolian, but aren´t we nitpicking now? I listed the types of intervals before where only the fourth is ambiguous and needs a context to be defined. That is basic interval theory. If we move beyond that we will soon get into triads and eventually tetrads, and from this point we do consider a triad a triad and not two thirds, one above the other, even if a triad can be considered as such.

There are 4 types of third. You're leaving out diminished and augmented

 

[AFKAEjay(retired)]

When it's a diminished 4th.
As in say mode 7 of melodic minor
1 ♭2 ♭3 ♭4(3) ♭5 ♭6 ♭7

That would be C and E, but point made. One could possibly come up with scenarios for #11/b5 also.

 

[Ed DeGenaro]

The clue is in the title “made easy”
All diatonic harmony is using intervals expressed by their own context .
What is the point of removing the context and then applying major scale concepts on something that is already telling you exactly what the two notes are on your instrument and by definition the distance between.
Harmonising a triad doesn’t keep stopping and comparing it to the major scale when you have learned even basic music theory . 135 246 357 etc not 135 135 135 . That is almost as useless as modal harmony on a bass line.

Scale construction as well as chord construction are based on the major scale.
Intervals are governed by distance with the caveat being that if they're used in a 7 tone pool if notes I.e. scale or mode the 7 note names can only be used once.

As in the major 7 in F♯ is E♯ not F. Although most guitarists would call it F.

 

[Ed DeGenaro]

That would be C and E, but point made. One could possibly come up with scenarios for #11/b5 also.

Or ♯5/♭13 for which I go with the Ike ♭ resolves down, ♯ resolves up.

Let's say this

3 x 3 4 4 4

To this...

X 3 2 2 3 3

I should call the first chord G7♭13♭9
But I daily use I'd call it G7♭9♯5

To make matters worse the first label screams mide V harmonic minor G phryg. Dom. the second mode 7 melodic minor (G altered).

 

[AFKAEjay(retired)]

Or ♯5/♭13 for which I go with the Ike ♭ resolves down, ♯ resolves up.

Let's say this

3 x 3 4 4 4

To this...

X 3 2 2 3 3

I should call the first chord G7♭13♭9
But I daily use I'd call it G7♭9♯5

To make matters worse the first label screams mide V harmonic minor G phryg. Dom. the second mode 7 melodic minor (G altered).

My mental frame is Abm6/G for that one
Tbh…I think I’m pretty purist up to a degree…but.modes of melodic are mentally limited to 2 (1st,7th), modes of harmonic non existent in my mind. All attached to those omissions get a “quick fix”…I’m good as long as I can reproduce stuff. Maybe someday I’ll get into it. Its my version of “why do I need Dorian if I know major”, applied to har/mel minor.

 

[Gothi]

There are 4 types of third. You're leaving out diminished and augmented

I am just sticking to Fux' overview as posted before, and he finds no need to mention these types as individual intervals. Se my quote from Gradus. But melodic and harmonic minor were not in play yet, so it makes sense the terms were not used then.

 

[Ed DeGenaro]

My mental frame is Abm6/G for that one
Tbh…I think I’m pretty purist up to a degree…but.modes of melodic are mentally limited to 2 (1st,7th), modes of harmonic non existent in my mind. All attached to those omissions get a “quick fix”…I’m good as long as I can reproduce stuff. Maybe someday I’ll get into it. Its my version of “why do I need Dorian if I know major”, applied to har/mel minor.

The 6 and m6 approach thank you Barry Harris. Everything modal made more sense after that
But in that respect melodic minor for me is that m6 as a multiple choice
A♭-6 A♭ Mel min

A♭-6/G or G7♭9♯5 A♭ Mel min mode 7 or G altered

A♭-6/D♭ D♭9 A♭ Mel min mode 4 or D♭ lydian dominant

A♭-6/F Fø A♭ Mel min mode or F locrian ♮2/F aeolian ♭5

A♭-6/C♭(B) C♭(B)6♭5 A♭ Mel min mode3 or C♭(B) lydian ♯5

Funny enough I learned all that when taking lessons from Don Mock a good 3 decades ago, but it was like iwas parroting it.
Understanding it came much later after lessons with Barry Harris.

 

[Ed DeGenaro]

I am just sticking to Fux' overview as posted before, and he finds no need to mention these types as individual intervals. Se my quote from Gradus. But melodic and harmonic minor were not in play yet, so it makes sense the terms were not used then.

Debussy says hold my beer...

 

[Sascha Franck]

One could possibly come up with scenarios for #11/b5 also.

And the minor third could as well be an augmented/sharp (naming pretty much depending on your preferences) 2nd.
But all that is irrelevant as long as all you try is to describe the distance between one tone from another in an equal tempered environment without any musical context - the only weird thing being that we took the names of the intervals from what actually is a very contextual thing, namely a heptatonic scale. That's where all the confusion comes from.
Had music theory's historic development "decided" to simply stick with plain distances and used semi/halftones (or maybe semi/halftones and wholetones) for any labelings, there'd be zero issues. What we're arguing about being called, say, an augmented 4th, diminished 5th or tritone would simply be 6 HTs or 3 WTs. Case closed.

But as is (and I don't see a way out of that dilemma as soon as you need to verbalize things, it's just too late in musical history to revolutionize that stuff) we just try to stick with using a kind of "most commonly used" approach. As a result, an interval of 3 semitones is usually called a minor third, even if it could as well be a sharp 2nd depending on context.

And as if that wasn't confusing enough already, there's still no generalized naming for some interval, even in case the function is clear. Do we say j7, maj7, 7+, #7, △7 in a chord symbol? Do we even leave the 7 out? I've seen all of it. And do we write Cm. C-, Cmin or c? And what if we wanted to describe the presence of a minor third in whatever chord or scale analysis? Do we say 3m, m3, 3-, b3, 3min or what? Again, I've seen it all.

In the end, even if all of this is still raising issues, I hardly ever had much of a problem when actually explaining things to someone. In case of a doubt, there's always either notation (which, while not perfect, is at least much more exact than verbalization) or the location of whatever notes on the fretboard (or any other instruments means to play a note).

 

[Gothi]

Debussy says hold my beer...

Debussy was born 1862. Gradus came out 1725. That does leave some room for romantism to expand and alter Fux’ approach. Would take a time machine for Fux to hold his beer.

 

[AFKAEjay(retired)]

The 6 and m6 approach thank you Barry Harris. Everything modal made more sense after that
But in that respect melodic minor for me is that m6 as a multiple choice
A♭-6 A♭ Mel min

A♭-6/G or G7♭9♯5 A♭ Mel min mode 7 or G altered

A♭-6/D♭ D♭9 A♭ Mel min mode 4 or D♭ lydian dominant

A♭-6/F Fø A♭ Mel min mode or F locrian ♮2/F aeolian ♭5

A♭-6/C♭(B) C♭(B)6♭5 A♭ Mel min mode3 or C♭(B) lydian ♯5

Funny enough I learned all that when taking lessons from Don Mock a good 3 decades ago, but it was like iwas parroting it.
Understanding it came much later after lessons with Barry Harris.

Yup, I do the same.
For me it started with applying the framework of the “I’ll have a banana lick” on everything I could, in combination with a touch of “convert to minor”

Made a “I’ll have a banana lick “ demo 6 years ago:

 

[Aelred]

I am just sticking to Fux' overview as posted before, and he finds no need to mention these types as individual intervals. Se my quote from Gradus. But melodic and harmonic minor were not in play yet, so it makes sense the terms were not used then.

Well, I got Aristotle's demonstration mixed up with Pythagoras, who was meant to have done it in antiquity and no one ever checked again until Vincenzo Galilei. I've been re-reading the Metaphysics and the "invention" of Potential and Kinetic Energy and attributed incorrectly.

Pythagoras also thouoght music could be medicinal - and also preferred stringed instruments over, say, the flute. This was all quite well known and taught to me in school, not University. Well, I found Vincenzo Galilei many years after the Honors in Puire Mathematics in the early 80's.

No one picked up the Vincenzo Galilei changing history, science, music, culture and the course of Western Civilization because he couldn't tune his lute satisfactorily due to theory ruling over practice? Rock'n'Roll or what? The original tone-chaser!

Terms such as "modes" come directly from mathematics. Just an historical fact. Funny how they are all using Ancient Greek names...

From https://medium.com/@sumit.tripathi/musical-modes-and-mathematics-ebcc5df417f3:

I'll get back to fumbling G major and minor, string by string, so the practice dominates the theory and becomes muscle memory.

All of you are far better and more knowledgable musicians than I will ever be, or even strive to be. Just having some fun with a guitars, pedals and amps at my leisure.

Thanks for the entertainment!

 

[Sascha Franck]

Funny how they are all using Ancient Greek names...

How is that funny? It's where they originally come from (at least sort of).

 

[Aelred]

How is that funny? It's where they originally come from (at least sort of).

I guess it's a popular form of expression in England and Australia. Irony is involved somewhere.

That was exactly the point - it comes from Ancient Greece - as did Pythagoras, Aristotle and Western notions of rationality.

And music.

 

[Ed DeGenaro]

I guess it's a popular form of expression in England and Australia. Irony is involved somewhere.

That was exactly the point - it comes from Ancient Greece - as did Pythagoras, Aristotle and Western notions of rationality.

And music.

That's assuming his doctrines started there rather than taken from India by way of Egypt.

 

[Sascha Franck]

That's assuming his doctrines started there rather than taken from India by way of Egypt.

Which isn't too unlikely, from all I know.

 

[Aelred]

That's assuming his doctrines started there rather than taken from India by way of Egypt.

Historically, it was Pythagoras' experiment that was considered the authority - although Pythagoras was said to have gleaned his knoweldge from Egypt.

We don't have those Egyptian sources, nor were they used by Renaissance folk when they rediscovered Socrates, Plato and Aristotle and kicked off the explosion of Western Civ we still live in - although we seem to hate it now and seek to discredit whenever possible.

Now how about Vincenzo being the first Rock'n"Roll dude who changed history, music, culture and science by doing repeatable experiments (!! A Big Deal !!) rather than relying on theory?

His damn lute didn't sound right, and his sources were Pythagoras for theory and Arsitotle's logic and demonstration.