Is kind of more than that Ŧยχøя, at least the way I see it.
For instance, we can add any existing interval against the diminished triad, ultimately ending up with a chromatic movement which encompasses all of them.
In this case the b6 is being added, which results in a cycle of M3 or b6s once these are the actual resulting intervals amongst the stacked notes from C7 - Ab7 - E7.
Comparetively when the 8va is subdivided in 6ths/b3s, the whole-diminished ( C°6 - A°6 - Gb°6 - Eb°6 ) is achieved, in other words, a cycle in b3s or M6s.

PS.: You all already know it. I'm just trying to match the pieces of the puzzle together.

 

Last edited by a moderator: Jun 23, 2021

It's certainly another valid and Interesting way of seeing it...

I would point out that,
If you Only played the Chords, that diminished triad will not occur,
it's only when you add the notes of both chords that it appears..

So unless you added those extra notes in the chord/melody, (like I did in the example)
the diminished triad/harmony will be only implicit in a "retrograde" or reflective way,
kinda like "what you don't draw" in a portrait...


However most importantly,
the WH Diminished scale doesn't contain a b7, nor a 3rd and 5th..
And the HW Diminished doesn't contain a b6 (Ab from C), but includes a b2..

So with a C7 + Ab7 it only adheres Partially to the Diminished harmony.

 

Last edited: Jun 23, 2021

I wasn't clear enough, sorry.

I meant this: E°b6 (C7) - C°b6 (Ab7) - Ab°b6 (E7), a cycle of 3 diminished triads with an added b6 - equidistant tetrachords (b6/M3 apart)

Compared to this: A°6 - Gb°6 - Eb°6 - C°6, a cycle of 4 diminished triads with an added M6 - equidistant tetrachords (M6/b3 apart)

But we can cycle diminished triads in every existing intervallic distance (half-step, whole-step, b3/6, M3/b6, 4/5, tritone apart, etc..)

The HW is the WH starting from its 2nd tone, so we can use it as a dominant scale (most common approach).

" So with a C7 + Ab7 it only adheres Partially to the Diminished harmony ". Sure, Dom7s have just 1 tritone.

 

Internet is full of Lalah Hathaway I can't find anything about Layla

 

I don't know what do you mean, or probably incorrect

Audio frequencies are just like rhythms, if you hit something at 440 times per second it will sound in perfect harmony with a A 440
440 hz it means 440 oscillations or vibrations or turns of a wheel per second.

The logic or math to calculate the frequencies known as octaves is just by dividing or multiplying by 2
So to get the next octave we multiply by 2 and we get A 880 then by 2 again and and we get A 1760
The same dividing by 2
440 / 2 = A 220
220 / 2 = A 110
So that is an octave interval

To calculate the other sounds we use similar kind of basic operations, so to get the perfect fifth (or pythagorean fifth) we multiply by 1.5
440 * 1.5 = E 660
Then to get the octave of 660 we multiply by 2
660 * 2 = E 1320

And there is a very logic maths to calculate all the other intervals, but we don't use Pythagorean tunning instead we use a tempered tunning of 12 equally separated intervals or TET 12
So this is what I meant with intervals in a broad way

The frecuencyes of the tempered scale that Midi and any instrument should use for compatibility (not by harmony) is this one


Wikipedia Pythagorean interval
Sevish Scale Workshop

 

To make more sense to you, you could always play with sevenths, ninths and then sixths, augmented or diminished, doesn't matter if are out of scale, the same with mayor and minor third, then you could always remove the unison or the fifth from the chords, this it's used a lot in bossa nova, latin jazz or jazz in general.

The problem of trying to fit to other scales that are not the mayor scale (with the minor and the other 5 modes) is that you will miss the fifth and instead reach many times the tritone that always sound dissonant

Then when playing arpeggios you could add these out of scale notes exactly before falling into the unison mayor or the other mayor chords.

If it's sound good to you then you could make more sense of what is going on check if it fits in some of the scales and then use that scale for the solos.

Another thing related to the solos and that was also commented in this thread is that solos or in improvisation you could play base on the scales or chords that are currently played or in the chords or scales that will be played or were played there is a term for this but i don't remember it right now.

An example of playing in the scale is Pat Metheny an example of playing in the next or before scale is John Scofield generally talking about their styles.

Some of the stuff that I am pointing out here it's also commented in this video, as you like Tom Jobin this will make a lot of sense (it's more historical but the analysis is quite good from music theory perspective)

The Girl From Ipanema is a far weirder song than you thought

 

This is more or less what I was trying to convey. I know, it's useless, but...

 

So here lies the "conundrum"...

440 * 1.5 = E 660 / 2 = 330 , thus an odd harmonic from A 110

 

Sure. The chorus from Garota de Ipanema is an ascending chromatic modulation. Similarly the tune Inútil Paisagem, refered a few pages ago, uses the same stylistic approach, but descending.

Thanks

 

Didn't you know "Chr. Mod." is a Sinful TABOO word in this thread?
If the Expert Academicists hear ya, oh my..

 

Tell me about it Ŧยχøя...

Here is the thing, let's find out a way to justify it as being some sort of subdominant substitution so that we could be on pro-righteous path...

 

No no no.. It's the Mother of the Relative Supramediant of the Parallel siamese cousin of the SubTonic Prime..
Check you facts bro!

 

Last edited: Jun 24, 2021

Thanks for the enlightenment ! Hail my Savvy Guru !

 

What about start approaching chords from now on? Upper-extensions, quartal, quintal, modal, etc... bringing harmonization to the table, thus actually start putting to use the aforementioned (heinious) 6 scales?

 

Hence, may no other arrogant-pedantic-venomous-deaf-prick (myself, the muffin-man), to dare bringing about his questioning, but THE GUITAR to become our teacher as of now then?

 

So...
What do you guys think about this "Garota the Ipanema" little thing the video is talking about?

I find it Interesting that there's full sections in a given tonality,
which Never get to play the Tonic root Chord of that tonality..

And from the top of my head,
I cannot think of another Example that does this in any style other than Bossanova.

Any Examples that you know of?

And how would you Describe/explain the whole thing?
How can a tonality be established if the Tonic is Never ever played?

Where/how is that tonality Implied?

Why consider those chords be inside the tonality of a nonexistent Tonic,
instead of considering it in relation to what is/has actually been played?

I considered it a strange/complex track,
but I just played it without really thinking about the implications..


And that's pretty much it,
another track that I thought could be interesting to bring would be: Chega de Saudade,
which has a great (almost too good) Melody and very Nice/smooth modulations..

And I don't recall the exact number right now,
but must certainly be one of the Record holders in raw Number of chords..

 

On another topic...
I always loved/found interesting the Intro chords of Vivo Sonhando..

There's I guess many versions and ways to voice it or label it,
but I would play it this way:

Gmaj7 - G6 - Cm9/G - Cm7/G

In Guitar it's played like:
-x- -x- -x- -x-
-3- -3- -3- -4-
-4- -4- -3- -3-
-4- -2- -1- -5-
-x- -x- -x- -x-
-3- -3- -3- -3-

And the notes included would be...

Gmaj7: 1-3-5-7
G6: 1-3-5-6
Cm9/G: 1-b3-5-b6 (could be also called Gmb6, but you loose part of the effect of that voicing)
Cm7/G: 1-b3-b6

Gmaj7: G F# B D (in this order)
G6: G E B D
Cm9/G: G Eb Bb D
Cm7/G: G G^ Bb Eb

Alternatively, the Cm9/G chord can also be labelled EbMaj7/G,
which is interesting...

But this type of versions seem to go for a final Eb6/G,
which doesn't sound as nice/interesting. (to me)

And that's pretty much it..


I always found this to be Hauntingly beautiful,
if you listen Closely is a very Interesting effect..

And it always reminded me of Debussy,
or something more aching to an Orchestral type harmony/voice modulation..


In this sense, a modulation is surely happening in the Third chord,
where the initial Major/Lydian scale would become a regular Aeolian or probably Harmonic Minor scale,
another option could be Aeolian b5/Locrian nat2 scale if you wanted to preserve the #4/b5 note.

Or even a "Aeolian b5 nat7" or "Locrian nat2 nat7" scale, which is the third mode of Hungarian Major scale,
if you wanted to preserve both the b5 and the nat7, while adhering to the Minor tonality of that moment.

Also the progression could be described as featuring a chromatic 7>6>b6 voice leading movement,
where notably when the b6 comes, also the nat3 goes b3..


I'm not an expert in Voice Leading and modulations of this type,
but I always wondered how "normal" could this be Perceived,
and how would it be Labelled/Cataloged or Described from the Traditional/Orthodox point of view..

And yeah,
I wonder if this could be a good/direct example of yet another "obscure" concept called "Pitch Axis Modulation"..
(May the Academists Forgive me, Holy Mother of God..
but Yes, I said it.. lol)

So what's your Thoughts??

 

Last edited: Jun 25, 2021

About this question...

See the Video below - interesting for your specific question and for the broader main question of the thread.

From (lecture one of six) Leonard Bernstein Lectures "The Unanswered Question 1973"

The whole lecture series is of course absolutely brilliant.
In this lecture you get a very rapid (almost cartoon like) tour of how diatonicism and chromaticism developed.

Find the section that starts at about 57 mins 10 secs where he discusses Mozart's G minor symphony.
Bernstein uses this section to illustrate what he calls "free chromaticism elegantly contained"
or "the creative ways in which chromatic flexibility can be systematically contained within the framework of tonic dominant relationships"

It's all entirely brilliant but listen especially to the section at 1:06:20 where he demonstrates
Mozart' s final movement - development section, which he describes as
"an atonal sounding passage that uses every one of the 12 chromatic tones EXCEPT the tonic G"

www.youtube.com/watch?v=8fHi36dvTdE

p.s.
Again I find myself praising something for its musical greatness
even when it's music that I don't derive a lot of listening pleasure from.

 

It's surely an interesting lecture, thanks for linking it.

I find interesting that Mozart implies a Eb7 chord after that first Chromatic line + Diatonic fifths movement..

But I don't really see how is this related to Garota de Ipanema's topic of Tonicless/Rootless implication of Tonality..

I mean Chromatic Approximation for modulating to foreign keys, is a Different topic altogheter,
and I think it's a more straightforward/easily graspable empirical concept..
Compared with the Subtlety of implying a Tonality without ever playing the implicit Tonic in a Chord + Root form..

It's like talking about something without ever addressing the actual topic,
or drawing something without drawing the actual Object, just part of its surroundings..


Also, I think "playing rootless" is not that much of a foreign concept,
in the sense of eluding the root in a melody, or improvising with a rootless Scale over a given context.

But it's different when we're talking about Chords/progressions,
or at least eluding the Tonic/Root chord altogheter..


But yeah, that's only the end of it..
I will watch the rest of the Lecture later,
maybe he addresses that topic more directly in the part that's featured on Adam Neely's video..

 

Last edited: Jun 25, 2021

Re: these comments...

True... not exactly the same concept, just related.

But the puzzle over what you call "eluding the Tonic/Root chord" I'm not sure what the puzzle is here.
In many songs that are based in modes other than classic Major(Ionian) or minor(Aeolian)
it is immediately simpler to directly think in the appropriate mode rather than trying to shoehorn it into some classical view of Major(Ionian)+alterations or minor(Aeolian)+alterations.
For example, see the links included at the end of this comment.
https://audiosex.pro/threads/changing-keys-in-hip-hop-pop-music.51666/#post-448094

The first example at https://audiosex.pro/posts/411869/ is a song that I hear as having Eb minor as its tonal home.
But I immediately qualify that by saying it is in Eb Dorian - and not in Eb natural minor(Aeolian)
The four chords used in the song are Eb minor, Gb Major, Ab Major, Bb minor
Those four chords makes perfect sense as ii, IV, V, vi of the Db major diatonic space but the song is in a tonal sense anchored to the ii chord and Db Major is never used (but why would we care about that?)
Someone locked into seeing traditional key signatures might unnecessarily complicate it by saying the song is formally in the Db Major diatonic space then wonder why we never see the I chord Db Major. But why do that? Why not just see it as Eb Dorian from the outset; i.e., describe the diatonic space as Eb Dorian, and regard Eb Dorian as the home key.

Sorry, that's a rushed comment but the link above leads to several comments that discuss this in more detail.
And even more apologies if the (alleged) puzzle over the missing "I" chord is something else entirely that I've failed to notice here.