# Need help understanding the neapolitan chord



## Gargamel

After trying to learn lots of harmony, the neapolitan chord is still confusing to me and I don't know how is one supposed to think about it? They way I see it it's not an altered chord, since you can't alter the fundamental itself. And it's not a scale degree. Is it a mixed chord or a superposition of two chords? The beginning of Mozart's Fantasia No. 4 in C Minor makes alot of sense for me, but need help explaining it.


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## Roger Knox

Gargamel said:


> After trying to learn lots of harmony, the neapolitan chord is still confusing to me and I don't know how is one supposed to think about it? They way I see it it's not an altered chord, since you can't alter the fundamental itself. And it's not a scale degree. Is it a mixed chord or a superposition of two chords? The beginning of Mozart's Fantasia No. 4 in C Minor makes alot of sense for me, but need help explaining it.


The neapolitan chord is a major triad which, whether appearing in major or minor keys, has its root on the flattened 2nd scale degree. The "alteration" is the using of that altered scale degree as root. It has the same function as the II chord.

I don't think of it as a "chromatic" chord though, because I believe its origin to be historical, coming from the fact that in the Phrygian scale (the white notes on the piano beginning on E), the second scale degree is only a minor second higher than the tonic note (e.g. F above E). Mode V of the Christian church modes has the same structure as this Phrygian scale. Whether or not this historical account is true, certainly from the Renaissance this distinctive inflection which puts a major triad on the second scale degree is common. Most often the chord is used in first inversion.


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## Vasks

I think of it as a special IV chord because the 4th scale degree is in the bass and is doubled.


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## Woodduck

The use of the flatted second scale degree, with the major triad built on it, is common in the popular songs of the region of Naples, Italy (hence the name "Neapolitan"), whether the basic scale used is major or minor (these songs are frequently in major/minor, often having a verse in the minor and shifting to major for a refrain). If memory serves, the chord is generally used in cadences and usually resolves to the tonic. The flatted second scale degree is also heard in the flamenco music of Spain.

In common practice it's generally heard in first inversion and its function is nearest to that of ii, for which it may substitute.


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## hammeredklavier




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## Gargamel

Roger Knox said:


> The neapolitan chord is a major triad which, whether appearing in major or minor keys, has its root on the flattened 2nd scale degree. The "alteration" is the using of that altered scale degree as root. It has the same function as the II chord.


Your explanation feels right, but abtuse. Every video in youtube talks about what it's used for, but doesn't explain how it "is made".

I feel the neapolitan chord simply an issue of diminished chord on I. So to harmonically understand the neapolitan chord, one only needs to look at the diminished I chord, correct?


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## mikeh375

Gargamel said:


> Your explanation feels right, but abtuse. Every video in youtube talks about what it's used for, but doesn't explain how it "is made".
> 
> I feel the neapolitan chord simply an issue of diminished chord on I. So to harmonically understand the neapolitan chord, one only needs to look at the diminished I chord, correct?


 Not correct. As the guys above have all said, it is simply a major chord whose root is the flattened supertonic of the key you are in and that's how you 'make' 'em.


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## Gargamel

mikeh375 said:


> Not correct. As has been mentioned, it is simply a major chord whose root is the flattened supertonic of the key you are in.


In C major, playing a diminished C triad acts as a VII would, and hence the neapolitan degree acts as a I would.


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## mikeh375

...well yes, you can use the c dim triad to modulate to dflat as it can act as an incomplete dominant to the flattened supertonic, but that's a different thing altogether. The Neopolitan chord in its traditional use resolves into the home key. It does not become a prime functional chord that negates the home key as your example would tend to do. Its use is mostly cadential in common practice harmony.


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## Gargamel

I must have gotten this idea from Mozart's Fantasia No. 4 in C Minor which I mentioned earlier. Right from the start, the piece goes into diminished C, and from there to neapolitan, without key change.


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## hammeredklavier

Gargamel said:


> I must have gotten this idea from Mozart's Fantasia No. 4 in C Minor which I mentioned earlier. Right from the start, the piece goes into diminished C, and from there to neapolitan, without key change.


You mean bar 7 of this (A♭ , D♭ , F):


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## millionrainbows

You have to understand the Neapolitan chord in terms of root movement. Key of C, bII is Db major, going to V (G), to I (C). The Db to G is a tritone relation, related to diminished sevenths. The Db could also have been in a ii -V. So you need to understand this tritone relation, and how these possibilities are generated out of a diminished seventh chord with different roots under it, making it a dominant b9.


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## millionrainbows

mikeh375 said:


> Not correct. As the guys above have all said, it is simply a major chord whose root is the flattened supertonic of the key you are in and that's how you 'make' 'em.


That's misleading. A neopolitan chord is not JUST a major chord on bII.

Gargamel feels that some principle is not being explained sufficiently when he says
_



Every video in youtube talks about what it's used for, but doesn't explain how it "is made".

Click to expand...

_


> _I feel the neapolitan chord simply an issue of diminished chord on I. So to harmonically understand the neapolitan chord, one only needs to look at the diminished I chord, correct?_


_
_
He is seeing some sort of diminished seventh connection, which nobody has explained yet.


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## EdwardBast

I think Vasks is right that it's a special chord, the clue being that the more traditional designation is N6, meaning that it's normal for the 3rd of the chord to be in the bass and doubled. And there's a good reason why the third is doubled: It's because the other tones have strong tendencies downward. To double either of them would necessitate one voice going against its natural tendency, resulting in awkward voice-leading. It's also special in that it nearly always occurs in a specific context, preceding the dominant (or the I6/4-dominant pair), which is what one would expect of an altered IV chord (Vasks) or an altered ii (Mike).

My explanation for the N6 chord's fame and special status is that it's a particularly sweet and exotic pre-dominant, a sound cherished for its special flavor

The chord has nothing whatever to do with diminished chords.


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## mikeh375

millionrainbows said:


> That's misleading. *A neopolitan chord is not JUST a major chord on bII.*
> 
> Gargamel feels that some principle is not being explained sufficiently when he says
> _
> _
> He is seeing some sort of diminished seventh connection, which nobody has explained yet.


Yes it is just that. There is diminished confusion here.
What the OP is seeing are the first three notes of the Fantasia that are an incomplete dim7th triad. The F sharp is merely an accented chromatic ornamental note leading to G which completes the outline of C minor. The second bar uses diminished and aug 6th harmony leading to the dominant. There are many modulations to different and sometimes remote keys in the opening 20 odd bars, befitting a Fantasia. At no point is the N6 in C invoked here and the D flat music in b5,6+7 is the result of modulation, or rather a straight shift from a momentary F major. It in turn moves to other areas via another diminished7th and is not approached as a typical N6 would be and does not resolve as one would neither.

It might be too much of a stretch at this time to start talking about diminished triads, their alternative roots, enharmonic spelling and enharmonic modulation (even though the Mozart does modulate enharmonically in places, notably bar 15-16), don't ya think, unless Gargamel is familiar with such procedures.
Care to tell me what else a Neopolitan 6th is?


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## Woodduck

millionrainbows said:


> You have to understand the Neapolitan chord in terms of root movement. Key of C, bII is Db major, going to V (G), to I (C). The Db to G is a tritone relation, *related to* diminished sevenths. The Db could also have been in a ii -V. So you need to understand this *tritone relation*, and how *these possibilities* are *generated out of a diminished seventh chord* with different roots under it, making *it* a dominant b9.


This looks like a theoretical flight of fancy that explains nothing, and makes something simple seem complex.

"Related to"? "Tritone relation"? "These possibilities"? "Generated out of"? Making _what_ a dominant b9?

What does it mean to say that the Neapolitan is "generated" out of a diminished seventh? How is a diminished seventh relevant at all? The Neapolitan is just a different form of a ii chord, imparting a different "color" to the music. So what if it's spelled like a Db major triad (in C major), and so what if the root of Db makes a tritone with G? That tritone isn't the "source" of the Neapolitan; a Neapolitan with root Db functions quite differently in a musical context from a diminished 7th containing a G and a Db; it certainly isn't "generated" out of it. If the Neapolitan was ever "generated" out of anything, it was the ordinary ii chord and the common musical function that chord performs.

What am I missing here? How is focusing on the tritone, and imagining diminished sevenths, more than a mental game? What does it tell us about the music in which the Neapolitan is used? (These are rhetorical questions. I believe the answers are "nothing," "it isn't," and "nothing.")


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## hammeredklavier

mikeh375 said:


> Not correct. As the guys above have all said, it is simply a major chord whose root is the flattened supertonic of the key you are in and that's how you 'make' 'em.


So what would be the exact line that divides "N" and "♭II"? Is "N" a special kind of "♭II"? The wikipedia talks like the notations "N" and "♭II" can be used interchangeably.

https://en.wikipedia.org/wiki/Neapolitan_chord
"Although it is sometimes indicated by an "N" rather than a "♭II", some analysts prefer the latter because it indicates the relation of this chord to the supertonic.
The Neapolitan most commonly occurs in first inversion so that it is notated either as ♭II6 or N6 and normally referred to as a Neapolitan sixth chord."



Woodduck said:


> If memory serves, the chord is generally used in cadences and usually resolves to the tonic.





mikeh375 said:


> The Neopolitan chord in its traditional use resolves into the home key. It does not become a prime functional chord that negates the home key as your example would tend to do. Its use is mostly cadential in common practice harmony.


So "Neapolitan chords are *mostly* or *generally* used as a predominant function in cadences" - But does this mean "there are *rare* cases of Neapolitan chords *not* used in cadences"? If so, are there any examples?

I think the OP is saying the [ A♭ , D♭ , F ] in bar 7 of Mozart K.475 counts as "N6/4". Would this be actually ♭II6/4?
Btw, Richard Atkinson discusses what he considers as "N6/4" in Mozart K.515:


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## hammeredklavier

Woodduck said:


> imparting a different "color" to the music.


This is actually what I like about MR. He creatively imparts a different "color" to these lifeless discussions.



millionrainbows said:


> nobody has explained yet.


This is the way I like it. The real mystery will stay "unresolved" until MR resolves it with denouement.


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## Woodduck

hammeredklavier said:


> This is actually what I like about MR. He creatively imparts a different "color" to these lifeless discussions.
> 
> This is the way I like it. The real mystery will stay "unresolved" until MR resolves it with denouement.


Don't be cute. There is no "mystery" about this. It was all perfectly clear in the first few posts. If the dicussion is now "lifeless" it's because it was subsequently smothered under irrelevant theoretical baggage concerning "diminished sevenths" or whatever.


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## Woodduck

hammeredklavier said:


> So what would be the exact line that divides "N" and "♭II"? Is "N" a special kind of "♭II"? The wikipedia talks like the notations "N" and "♭II" can be used interchangeably.
> 
> https://en.wikipedia.org/wiki/Neapolitan_chord
> "Although it is sometimes indicated by an "N" rather than a "♭II", some analysts prefer the latter because it indicates the relation of this chord to the supertonic.
> The Neapolitan most commonly occurs in first inversion so that it is notated either as ♭II6 or N6 and normally referred to as a Neapolitan sixth chord."
> 
> So "Neapolitan chords are *mostly* or *generally* used as a predominant function in cadences" - But does this mean "there are *rare* cases of Neapolitan chords *not* used in cadences"? If so, are there any examples?
> 
> I think the OP is saying the [ A♭ , D♭ , F ] in bar 7 of Mozart K.475 counts as "N6/4". Would this be actually ♭II6/4?
> Btw, Richard Atkinson discusses what he considers as "N6/4" in Mozart K.515:


When I said "the chord is generally used in cadences and usually resolves to the tonic," I was talking about Neapolitan folk music. I based that statement on what I remember to be the sound of that music, though I have no examples to cite. I _then_ went on to say, "In common practice..." (careful reading is S-O-O-O-O important!). In common practice the Neapolitan tends to be followed by a dominant, just like an ordinary ii. Because it's followed by a dominant it tends to be found at cadences, but it doesn't have to be.


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## mikeh375

hammeredklavier said:


> So what would be the exact line that divides "N" and "♭II"? Is "N" a special kind of "♭II"? The wikipedia talks like the notations "N" and "♭II" can be used interchangeably.
> 
> https://en.wikipedia.org/wiki/Neapolitan_chord
> "Although it is sometimes indicated by an "N" rather than a "♭II", some analysts prefer the latter because it indicates the relation of this chord to the supertonic.
> The Neapolitan most commonly occurs in first inversion so that it is notated either as ♭II6 or N6 and normally referred to as a Neapolitan sixth chord."
> 
> So "Neapolitan chords are *mostly* or *generally* used as a predominant function in cadences" - But does this mean "there are *rare* cases of Neapolitan chords *not* used in cadences"? If so, are there any examples?
> 
> I think the OP is saying the [ A♭ , D♭ , F ] in bar 7 of Mozart K.475 counts as "N6/4". Would this be actually ♭II6/4?
> Btw, Richard Atkinson discusses what he considers as "N6/4" in Mozart K.515:


As I mentioned above the Dflat tonality in b5 cf is a key shift and nothing to do with the N6 as understood in its cadential form. It's a transition to another key area - the flattened supertonic. The traditional common practice N6 would not have it's own dominant in play as the Mozart does in b6-7, as that tends to negate the home key and it is that relation to the home key that imparts the N6's special colour.

The key/tonality of N6 can of course be used anywhere and is not restricted to cadential moments, an example of which is the case in point. It is the context and resolution that determines its function and name in CP.


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## Gargamel

millionrainbows said:


> That's misleading. A neopolitan chord is not JUST a major chord on bII.
> 
> Gargamel feels that some principle is not being explained sufficiently when he says
> _
> _
> He is seeing some sort of diminished seventh connection, which nobody has explained yet.


I didn't say diminished seventh. Just diminished triad. (VII means seventh degree, not seventh chord)


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## Phil loves classical

millionrainbows said:


> You have to understand the Neapolitan chord in terms of root movement. Key of C, bII is Db major, going to V (G), to I (C). The Db to G is a tritone relation, related to diminished sevenths. The Db could also have been in a ii -V. So you need to understand this tritone relation, and how these possibilities are generated out of a diminished seventh chord with different roots under it, making it a dominant b9.


This reminds me of Boolean Algebra:

(not A + B) (A+B) = B


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## millionrainbows

Is this famous Rachmaninoff piece an example of a Neapolitan chord in a minor key?


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## mikeh375

millionrainbows said:


> Is this famous Rachmaninoff piece an example of a Neapolitan chord in a minor key?


Yes, Neopolitan _harmony_ or chord. The difference between it and a CP N6 is the b sharp which is in effect a c natural, turning the chord into a dom7th. CP N6's do not normally have that degree in them at cadences for exam purposes. The chord is in 2nd inversion too which is not common for a traditional CP N6. 
So, answer, yes Neopolitan harmony tinged with a bit of no if we are talking strict N6 I'd say. Good example of Neoploitan harmonies useage in normal play and not at cadential points.


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## millionrainbows

mikeh375 said:


> Yes, Neopolitan _harmony_ or chord. The difference between it and a CP N6 is the b sharp which is in effect a c natural, turning the chord into a dom7th. CP N6's do not normally have that degree in them at cadences for exam purposes. The chord is in 2nd inversion too which is not common for a traditional CP N6.
> So, answer, yes Neopolitan harmony tinged with a bit of no if we are talking strict N6 I'd say. Good example of Neoploitan harmonies useage in normal play and not at cadential points.


I'd say that your reply is every bit as 'complicated' as my reply, which robs Woodduck's accusation of its veracity.

I'd be interested to hear Woodduck's thoughts on the Rachmaninoff example.

BTW, I never knew until recently what a Neapolitan chord was, or how it sounded, until I listened to the Beethoven example on WIK (Beethoven's _Appassionata_ Sonata, Op. 57). Then, it became obvious.


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## mikeh375

millionrainbows said:


> I'd say that your reply is every bit as 'complicated' as my reply, which robs Woodduck's accusation of its veracity.
> 
> I'd be interested to hear Woodduck's thoughts on the Rachmaninoff example.
> 
> BTW, I never knew until recently what a Neapolitan chord was, or how it sounded, until I listened to the Beethoven example on WIK. Then, it became obvious.


my reply is correct though and no mention of dim7ths...how about that. The bsharp complicates the matter, it's your example not mine. Did you even know there was a b sharp in that chord?
The OP was resolved a while back as far as I'm concerned.


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## millionrainbows

mikeh375 said:


> my reply is correct though and no mention of dim7ths...how about that. The bsharp complicates the matter, it's your example not mine. Did you even know there was a b sharp in that chord?
> *The OP was resolved a while back as far as I'm concerned.*


Then I can expect you to have little comment on what is to follow?


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## mikeh375

...that depends on what comes next, I mean bless you, but you might need correcting again...:lol:. 
So, did you hear that b sharp then?


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## millionrainbows

mikeh375 said:


> ...that depends on what comes next, I mean bless you, but you might need correcting again...:lol:.
> So, did you hear that b sharp then?


Yes, I very much hear the neapolitan as being a dominant chord, if that's what you mean. That just reinforces what I said about the Neapolitan being a tritone substitution.


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## mikeh375

millionrainbows said:


> Yes, I very much hear the neapolitan as being a dominant chord, if that's what you mean. That just reinforces what I said about the Neapolitan being a tritone substitution.


...it's too complicated. Keep it simple - N6th is a major chord on the flattened supertonic, that's it.(or perhaps think of it like Vasks does).
What I mean about the b sharp is explained above as clearly as it can be. The CP N6 is not a dominant _7th_.


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## millionrainbows

Woodduck said:


> "Related to"? "Tritone relation"? "These possibilities"? "Generated out of"? Making _what_ a dominant b9?


These are creative terms, based on an understanding of "where things come from." If you consider your music theory to be "all givens" without any thought for speculation on 'underlying principles,' then these terms and this kind of thinking would be totally foreign to you.


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## millionrainbows

mikeh375 said:


> ...it's too complicated. Keep it simple - a major chord on the flattened supertonic, that's it.


Even that doesn't make sense. How can a bII be a "substitute" for a II? How do you explain that?


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## mikeh375

millionrainbows said:


> Even that doesn't make sense. How can a bII be a "substitute" for a II? How do you explain that?


that's easy....your head has got in the way along with editing my post to create what looks like a strawman. I didn't say it was a substitute even though it is, especially at cadential points. 
I can explain it away because maybe the composer was feeling exotic at the time.....

Seriously though, like all technique, it's an option and that's the way to think of it instead of getting lost just left of pseud's corner.


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## millionrainbows

;1897068 said:


> that's easy....your head has got in the way. *I didn't say it was a substitute.* But actually it is at cadential points. I explain it away because the composer was feeling exotic.


That's not an answer. Explain how a bII be a "substitute" for a II, unless you think you are exempt because 'you didn't say it was a substitute.'
*
WIK: 
Harmonic function
In tonal harmony, the function of the Neapolitan chord is to prepare the dominant, substituting for the IV or ii (particularly ii[SUP]6[/SUP]) chord.
*
Now I see true colors emerging. Music theorists here simply accept things as 'givens' without understanding any sort of underlying principles.

Understanding principles like this will be the way music theory is taught in the future, in the new paradigm. (see Schenker thread)


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## mikeh375

You can see nothing at all about 'true colours emerging', best not to make assumptions I'd say.
One reason the N6 is a substitute (option) for II in the minor key is to avoid the tritone in the supertonic triad. It is an easy option to use as the triad on VI in a minor key can function as the dominant for the N6 and it can be tonicised in this manner too.


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## hammeredklavier

millionrainbows said:


> How can a bII be a "substitute" for a II?









millionrainbows said:


> Now I see true colors emerging.


What colors are they? The colors of a million rainbows?


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## mikeh375

hammeredklavier said:


> What colors are they? The colors of a million rainbows?


...ha...beat you to it HK...


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## EdwardBast

millionrainbows said:


> Yes, I very much hear the neapolitan as being a dominant chord, if that's what you mean. That just reinforces what I said about the Neapolitan being a tritone substitution.


The N is not a dominant chord. From the perspective of classical theory, the so-called tritone substitutions for dominants in jazz are the result of not making a distinction between augmented 6ths and m7ths. For example, a German +6 chord in classical theory is seen in jazz as a tritone substitution for V/V. There is no new principle here, just a different taxonomy. As ever, the jazz taxonomy is practical, a way to get the right notes under the fingers without worrying about the fine points of voice-leading.



millionrainbows said:


> Even that doesn't make sense. How can a bII be a "substitute" for a II? How do you explain that?


How can you not get this? They both function as pre-dominants. The term substitute in your Wiki quote has the same sense and meaning as it does in the term substitute teacher. The one who shows up every day is the teacher, the one who shows up only occasionally is the substitute. Same thing here. The ii chord is the every day pre-dominant, the N6 is less common and serves the same function, so it's the substitute. There is no "principle" required to explain this. It's just straightforward English usage.


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## millionrainbows

mikeh375 said:


> You can see nothing at all about 'true colours emerging', best not to make assumptions I'd say.


That's entirely up to you, in the way that you choose to answer questions; with reasoning or with pat answers.


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## mikeh375

millionrainbows said:


> That's entirely up to you, in the way that you choose to answer questions; with reasoning or with pat answers.


I answer from professional and practical experience, a different perspective from yours. The 'pat' aswers happen to be the correct ones.


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## millionrainbows

EdwardBast said:


> The N is not a dominant chord. *From the perspective of classical theory, the so-called tritone substitutions for dominants in jazz are the result of not making a distinction between augmented 6ths and m7ths.*


Aha! So again it's a case of notation vs. actual sound. I will follow my ear on this, not my pen.


> *For example, a German +6 chord in classical theory is seen in jazz as a tritone substitution for V/V.*





> There is no new principle here, just a different taxonomy. As ever, the jazz taxonomy is practical, a way to get the right notes under the fingers without worrying about the fine points of voice-leading.


I must commend EdwardBast for acknowledging this. Still, there is inherent confusion and apparent paradox in what you say: is the +6 chord a dominant chord or not?



> How can you not get this? They both function as *pre-dominants.*


"Pre-dominant" is a cop-out term. It's ambiguous, because it doesn't identify the chord itself, but only that it functions as a "pre-dominant," whatever that turns out to be.



> The term substitute in your Wiki quote has the same sense and meaning as it does in the term substitute teacher. The one who shows up every day is the teacher, the one who shows up only occasionally is the substitute. Same thing here.


I disagree. "Substitute" here is referring to a tri-tone substitution, which refers to *dominant* substitutes.



> The ii chord is the every day *pre-dominant*, the N6 is less common and *serves the same function,* so it's the substitute.


I disagree. "Pre-dominant" is a general term, and does not assign a specific function to a chord except in a general way. This "pre-dominant" could be a minor chord (ii) or a bII chord. It's a general term.



> There is no "principle" required to explain this. It's just straightforward English usage.


The principle is that of tritone substitution. I do get it, and got it all along. How can you not acknowledge the information exposed here?


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## EdwardBast

millionrainbows said:


> Aha! So again it's a case of notation vs. actual sound. I will follow my ear on this, not my pen.[/B]


No, it's being able to hear a +6 expanding outward versus a minor 7th contracting. The notation is irrelevant. One can misspell the +6 chord as a minor 7th and it still sounds like it's expanding.



millionrainbows said:


> I must commend EdwardBast for acknowledging this. Still, there is inherent confusion and apparent paradox in what you say: is the +6 chord a dominant chord or not?


The inherent confusion is yours. If it were a dominant chord we would call it a dominant chord, not a +6.



millionrainbows said:


> "Pre-dominant" is a cop-out term. It's ambiguous, because it doesn't identify the chord itself, but only that it functions as a "pre-dominant," whatever that turns out to be.


We've already identified the chord. Or did you forget the thread title and subject?  It's name is N6, its function is pre-dominant.



millionrainbows said:


> I disagree. "Substitute" here is referring to a tri-tone substitution, which refers to *dominant* substitutes.


Don't be ridiculous. It has nothing to do with tritone substitution.



millionrainbows said:


> I disagree. "Pre-dominant" is a general term, and does not assign a specific function to a chord except in a general way. This "pre-dominant" could be a minor chord (ii) or a bII chord. It's a general term.


Duh. It's a general term for pre-dominants. Glad you picked that up 



millionrainbows said:


> The principle is that of tritone substitution. I do get it, and got it all along. How can you not acknowledge the information exposed here?


You have no idea what you're talking about. Haven't for the whole thread. And yet you are once again the most prolific contributor.


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## Woodduck

millionrainbows said:


> "Pre-dominant" is a cop-out term. It's ambiguous, because *it doesn't identify the chord itself, but only that it functions *as a "pre-dominant," whatever that turns out to be.


The "identity" of a chord consists of two things: 1.) the notes it contains, and 2.) its musical (syntactical) function. Nothing else is needed to "explain" it. In the case of the Neapolitan, 1.) it's the triad built on the flatted second scale degree, and 2.) it occurs preceding the dominant chord (it's a "pre-dominant"), where it can "substitute" for (may be used in the same way as) the ordinary ii chord.

Doesn't that "identify the chord itself"? Where do you get all this "generated out of," "diminished seventh," "tritone substitution" stuff? Your first post here reads:



> You have to understand the Neapolitan chord in terms of root movement. Key of C, bII is Db major, going to V (G), to I (C). *The Db to G is a tritone relation, related to diminished sevenths.* The Db could also have been in a ii -V. So *you need to understand this tritone relation, and how these possibilities are generated out of a diminished seventh chord *with different roots under it, making it a dominant b9.


The statements, "The Db to G is a tritone relation, related to diminished sevenths...So you need to understand this tritone relation, and how these possibilities are generated out of a diminished seventh chord," are nothing more than a pointing out of features or resemblances which you mistake for causal relationships. The Neapolitan is not "identified" - explained or understood - by noting that its root makes a tritone with the root of the succeeding dominant chord, though that is obviously the case. But even more to the point, the Neapolitan is not "generated out of" a diminished seventh, not in any sense of the word "generated." Diminished sevenths have nothing to do with it.

Later you say,



> I very much hear *the Neapolitan as being a dominant chord*, if that's what you mean. That just reinforces what I said about *the Neapolitan being a tritone substitution*.


And then,



> *These are creative terms*, based on an understanding of *"where things come from."* If you consider your music theory to be "all givens" without any thought for speculation on *'underlying principles,'* then these terms and this kind of thinking would be totally foreign to you.


You may "hear" (imagine) whatever you like, and engage endlessly in "creative" (meaningful only to you) terms, but the Neapolitan is not a dominant chord, it does not "substitute" for a tritone, it does not "come from" a diminished seventh, and claiming these things doesn't affirm any "underlying principles." Where the Neapolitan "comes from" is a historical question - did some composer way back when decide to start flatting the supertonic in cadences? did this usage derive from the Phrygian mode, or occur independent of it? - and an etymological/geographical question: the name "Neapolitan" comes from Naples and the indigenous music found there, of which the flatted supertonic, used at cadences, is a feature. I am at least certain that the citizens of Naples never derived their cadential formula from a tritone or a diminished seventh.

Kindly spare me all your usual "thnking out of the box" horse manure, accompanied by the usual descriptions of my intellectual limitations as compared with your own imaginative brilliance. Sometimes a cigar is just a cigar. Whatever a cigar's "identity" might be on somebody's drug trip is of no interest or use to anyone else.


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## millionrainbows

Woodduck said:


> You may "hear" (imagine) whatever you like, and engage endlessly in "creative" (meaningful only to you) terms, but the Neapolitan is not a dominant chord, it does not "substitute" for a tritone, it does not "come from" a diminished seventh, and claiming these things doesn't affirm any "underlying principles."


Yes, the neapolitan functions as a dominant, resolving to V. These kinds of roots are "generated" from diminished seventh forms.

[/QUOTE]*Kindly spare me all your usual "thnking out of the box" horse manure,* accompanied by the usual descriptions of my intellectual limitations as compared with your own imaginative brilliance. Sometimes a cigar is just a cigar. Whatever a cigar's "identity" might be on somebody's drug trip is of no interest or use to anyone else.[/QUOTE]


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## millionrainbows

Woodduck said:


> Where the Neapolitan "comes from" is a historical question - did some composer way back when decide to start flatting the supertonic in cadences? did this usage derive from the Phrygian mode, or occur independent of it? - and an etymological/geographical question: the name "Neapolitan" comes from Naples and the indigenous music found there, of which the flatted supertonic, used at cadences, is a feature. I am at least certain that the citizens of Naples never derived their cadential formula from a tritone or a diminished seventh. Kindly spare me all your usual "thnking out of the box" *horse manure...*


I'm not interested in history or tradition, only in musical principles. EdwardBast has already admitted that, in jazz, the Neapolitan is seen as a tritone substitution.

This resistance to new, egalitarian ideas of music is the old paradigm, which will be replaced by a new paradigm (see the Schenker thread). Change your way of thinking, or be left behind.

A lot of paradigms are being questioned, which the priviedged seem to think are non-existent or marginal. The fact is, they're just invisible to them.

All these priviledged assumptions add up to the state of white music theory today: definitely biased towards the major/minor diatonic system:




EdwardBast said:


> The N is not a dominant chord. From the perspective of classical theory, *the so-called tritone substitutions for dominants in jazz are the result of not making a distinction between augmented 6ths and m7ths. *_(diatonic bias-ed.)_
> 
> For example, a German +6 chord in classical theory is seen in jazz as a tritone substitution for V/V. There is no new principle here, just a different taxonomy. As ever, the jazz taxonomy is practical, a way to get the right notes under the fingers without worrying about the fine points of voice-leading.


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## Phil loves classical

The Neapolitan vs. tritone substitution refer to the different functions even if they incorporate similar notes. An analogy is different functions for the G chord in G major (I) and C major (V) respectively, which incorporate the same notes.


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## millionrainbows

Phil loves classical said:


> The Neapolitan vs. tritone substitution refer to the different functions even if they incorporate similar notes. An analogy is different functions for the G chord in G major (I) and C major (V) respectively, which incorporate the same notes.


Analogies don't work for me. What functions in what keys are you specifically referring to?

Beethoven's use of it in the Apassionata sonata seems to be to be the most clear use.

The deviation from the diatonic scale (ii-V-I) to a chromatic alteration (bii-V-I) is why it is 'special case.'

It seems obvious to me that (key of C) the diminished seventh chord F-Ab-B-D can 'generate' dominant chords by simply placing different roots under it: E, Db, Bb, or G. The connection is G dominant 7. 
Since it's used as a "pre-dominant" of V, the most obvious choice is Db, since it provides a nice leap of roots (Db-G-C).

Actually, this is a sort of "backwards" way of creating a tritone substitution; G7, the goal and diatonic within the key, is first seen as being derived from a diminished seventh "parent" chord, which then can give us E, Db, or Bb as our "pre-dominant" choices. So really, there are other possibilities, not just the bII degree.


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## BabyGiraffe

Million, you are again create more complex theory than what is going on in reality. There were various "Neapolitan/Phrygian" family motivic patterns employed back in the day (that got overused in opera, I guess). It's not hard to see how this became a kind of standard musical gesture. Btw, there was no tritone substitutions in non-12 equal music back in the day (this requires real tritones - like √ 2 tritone, not just enharmonic respelling). 
About the importance of notation and spelling -> we also have talked about this many times - each equal temperament has infinite (but only few of them are simple) number of enharmonic equivalences. If you have consistent notation, you can translate the music to any more accurate tuning that supports the same temperament.
(Translating most of Beethoven's works to 12 equal is actually downgrading them, but that's another story.)


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## millionrainbows

BabyGiraffe said:


> Million, you are again create more complex theory than what is going on in reality. There were various "Neapolitan/Phrygian" family motivic patterns employed back in the day (that got overused in opera, I guess). It's not hard to see how this became a kind of standard musical gesture. Btw, there was no tritone substitutions in non-12 equal music back in the day (this requires real tritones - like √ 2 tritone, not just enharmonic respelling).
> About the importance of notation and spelling -> we also have talked about this many times - each equal temperament has infinite (but only few of them are simple) number of enharmonic equivalences. If you have consistent notation, you can translate the music to any more accurate tuning that supports the same temperament.
> (Translating most of Beethoven's works to 12 equal is actually downgrading them, but that's another story.)


Secondary dominants are simple. V-I is simple.

What's complicated is saying "build a major chord on the bII degree as a substitute for ii-V," and not explaining it. It just is.

I disagree that "there were no tritone substitutions in non-12 equal music back in the day (this requires real tritones)", because of F of the C major scale, and the viiº degree. Tritones are inherent in the C major scale, regardless.


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## mikeh375

I feel for Gargamel and hope he has moved on and is writing some music. He has all he needs to incorporate an N6 into his work if he wishes.


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## BabyGiraffe

millionrainbows said:


> Secondary dominants are simple. V-I is simple.
> 
> What's complicated is saying "build a major chord on the bII degree as a substitute for ii-V," and not explaining it. It just is.
> 
> I disagree that "there were no tritone substitutions in non-12 equal music back in the day (this requires real tritones)", because of F of the C major scale, and the viiº degree. Tritones are inherent in the C major scale, regardless.


Any secondary dominant signifies meantone temperament! There are no real tritone substitution in meantone aside from 12 equal! It's enharmonic modulation that is awkward in meantone and it signifies diaschismic temperament. And there is no tritone in diatonic scale - it's augmented fourth and diminished fifth.
(There are no tritones in Pythagorean tuning, too.)
You need just two commas to define any equal temperament in 5-limit tuning.

Here is a list of some 12 equal commas, each one gives you to loop with 12 keys using various progressions:

1: 32805/32768 1.953721 schisma
2: 67108864/66430125 17.598848 Misty comma, diaschisma - schisma
3: 2048/2025 19.552569 diaschisma
4: 81/80 21.506290 syntonic comma, Didymus comma
5: 531441/524288 23.460010 Pythagorean comma, ditonic comma
6: 128/125 41.058858 minor diesis, diesis
7: 43046721/41943040 44.966300
8: 262144/253125 60.611427 Passion comma (this one is names like that, because of some chord progressions in Appassionata)
9: 648/625 62.565148 major diesis
10: 536870912/512578125 80.163996
11: 6561/6250 84.071438

You don't need any theoretical justification to do any kind of harmonic or melodic gesture (like playing a certain chord on any of the 12 keys)...

(Actually, the only loops that exist between JI tuned chords in 5-limit are found in this subset: using C as tonic: C-Eb-E-F-G-Ab-A (basically, major/minor chord in all inversions). Anything else needs tempering (if don't want false relations when transposing or even in the basic scale, depends on what intervals you want to play).

So, each equal temperament has unique topology compared to just tuning.


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## Phil loves classical

millionrainbows said:


> Analogies don't work for me. What functions in what keys are you specifically referring to?
> 
> Beethoven's use of it in the Apassionata sonata seems to be to be the most clear use.
> 
> The deviation from the diatonic scale (ii-V-I) to a chromatic alteration (bii-V-I) is why it is 'special case.'
> 
> It seems obvious to me that (key of C) the diminished seventh chord F-Ab-B-D can 'generate' dominant chords by simply placing different roots under it: E, Db, Bb, or G. The connection is G dominant 7.
> Since it's used as a "pre-dominant" of V, the most obvious choice is Db, since it provides a nice leap of roots (Db-G-C).
> 
> Actually, this is a sort of "backwards" way of creating a tritone substitution; G7, the goal and diatonic within the key, is first seen as being derived from a diminished seventh "parent" chord, which then can give us E, Db, or Bb as our "pre-dominant" choices. So really, there are other possibilities, not just the bII degree.


Put as simply as possible the Neapolitan substitutes for the IV chord, while the tritone substitution substitutes for the V7 chord. Different functions.


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## Woodduck

Phil loves classical said:


> Put as simply as possible the Neapolitan substitutes for the IV chord, while the tritone substitution substitutes for the V7 chord. Different functions.


I think the Neapolitan is closer in function to the ii than to the IV. It is after all a flatted ii. Try fitting it into various progressions and see if you agree.


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## Gargamel

Woodduck said:


> I think the Neapolitan is closer in function to the ii than to the IV. It is after all a flatted ii. Try fitting it into various progressions and see if you agree.


Like IIIb is close in function to iii? (Although, IIIb and iii replace each others. I'm not sure if iib replaces ii, or if they can co-exist in the same harmony.)


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## mikeh375

Gargamel said:


> Like IIIb is close in function to iii? (Although, IIIb and iii replace each others.* I'm not sure if iib replaces ii, or if they can co-exist in the same harmony.*)


....well to my ears, it sounds pretty good having the two together as a single chord, although I'd fail an academic CP exam if I piled them on top of one another... But no, II and an N6 can't combine to form a chord in its own right in CP usage, although I can imagine a double retardation, c# to d and g# to a almost getting there (in C of course). As always, context has a bearing on how technique is used.

Outside of CP, use your ears and do what appeals to your sensibilities for your own composing. Technique opens your ears and gives you options which you can then use as a base to explore more. Don't get too bogged down, understand the essential principle, try it out a few times, assimilate it and move on.


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## millionrainbows

Woodduck said:


> I think the Neapolitan is closer in function to the ii than to the IV. It is after all a flatted ii. Try fitting it into various progressions and see if you agree.


Key of C:

The ii is seen as fifth, when it goes to V. It's better to talk about root movements.

So a bII needs also to have that "fifth" root movement quality to be similar, not just be in proximity.

Since we can "backwards trace" the given G7 back to a 'parent' diminished seventh of F-Ab-B-D (and simply lowering any note to "generate" our dominant 7 chord, in this case Ab-G),

...then Db-F-Ab-B (Db7) can be "generated" from the same dim 7 in the same way (lowering a tone, D to Db), which "creates" a dominant tri-tone substitute for the G (equal to a V7-i) which "creates" the resolution.

Why do I follow this logic? Because my ear hears it that way. My "logic" came after I heard it. This is the harmonic logic of the ear.

Your "logic" is based on nothing except a new arbitrary root station, because it is called "flatted."

Your way of thinking of a bII as simply "appearing" as an arbitrary root station choice is like working with dead, mummified tones.

My music is "alive" and it moves. Tones are "generated," resolutions are "created," roots "move" in logical ways. My logic is based on harmony, not arbitrary names. Also, my explanations are much lengthier and fuller than your flip dismissals and insulting "horse manure" as you have called it:



Woodduck said:


> Kindly spare me all your usual "thnking out of the box" *horse manure,* accompanied by the usual descriptions of my intellectual limitations as compared with your own imaginative brilliance.


EdwardBast has already confirmed that a German +6 chord is equal to a tritone substitute:



EdwardBast said:


> From the perspective of classical theory, the so-called tritone substitutions for dominants in jazz are the result of not making a distinction between augmented 6ths and m7ths. For example, a German +6 chord in classical theory is seen in jazz as a tritone substitution for V/V. There is no new principle here, just a different taxonomy. As ever, the jazz taxonomy is practical, a way to get the right notes under the fingers without worrying about the fine points of voice-leading.


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## BabyGiraffe

millionrainbows said:


> Why do I follow this logic? Because my ear hears it that way. My "logic" came after I heard it. This is the harmonic logic of the ear.
> 
> EdwardBast has already confirmed that a German +6 chord is equal to a tritone substitute


 1: 125/72 955.031140 cents classic augmented sixth
2: 7/4 968.825906 cents harmonic seventh
3: 225/128 976.537429 cents augmented sixth
4: 59049/32768 1019.550009 cents Pythagorean augmented sixth

1: 16/9 996.089998 cents Pythagorean minor seventh
2: 9/5 1017.596288 cents just minor seventh

Put all these into calculator and compare the results to the comma list that I gave previously.
Not only was theory not created in 12 equal, it goes way beyond it.


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## millionrainbows

BabyGiraffe said:


> 1: 125/72 = *955.031140 cents* / classic augmented sixth
> 2: 7/4 = *968.825906 cents* / harmonic seventh
> 3: 225/128 = *976.537429 cents* / augmented sixth
> 4: 59049/32768 = *1019.550009 cents* / Pythagorean augmented sixth
> 
> 1: 16/9 = *996.089998 cents* / Pythagorean minor seventh
> 2: 9/5 = *1017.596288 cents* / just minor seventh
> 
> Put all these into calculator and compare the results to the comma list that I gave previously.
> Not only was theory not created in 12 equal, it goes way beyond it.


I'm glad you know what you're talking about. Is there something about diminished chords in this? Please expound at length.


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## millionrainbows

BabyGiraffe said:


> Any secondary dominant signifies meantone temperament! There are no real tritone substitution in meantone aside from 12 equal!


Literally, you're right; but if we consider ball-park fifths, it works.


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## EdwardBast

millionrainbows said:


> Analogies don't work for me. What functions in what keys are you specifically referring to?
> 
> Beethoven's use of it in the Apassionata sonata seems to be to be the most clear use.
> 
> The deviation from the diatonic scale (ii-V-I) to a chromatic alteration (bii-V-I) is why it is 'special case.'


The Gb major chord in the first theme of the Appassionata doesn't have a Neapolitan function. It's just a lurch to Gb major confirmed by its by own dominant and vii°7/V (enharmonically spelled). It's a different animal.


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## BabyGiraffe

millionrainbows said:


> I'm glad you know what you're talking about. Is there something about diminished chords in this? Please expound at length.


Diminished chords of 12 equal require 648/625 to be tempered, so augmented fourth and diminished fifths are equivalents, but these aug/dim intervals are not the same as these found in diatonic scale, because they are also altered by syntonic comma. We get diminished temperament. Only 12 equal is ideal for 5-limit diminished temperament with any reasonable amount of notes per octave.
648/625 is 128/125 (minor diesis) x 81/80 (syntonic comma).

We can actually generate all the enharmonic equivalences by using just two basic intervals -> major third and perfect fifth and heavily subdividing and multiplying the pythagorean and minor diesis comma that we get when we multiply them enough times -> 4 times for major third/minor sixth, 12 - for the fifth/fourth.

If you want to consider 12 equal as "septimal" tuning, you need another one-> 131072/117649 = 187.044561 cents.

Diminished chords of meantone are three minor thirds and one augmented second, this means that 126/125 is tempered (81/80 = 225/224 x 126/125).

In non-meantone/non-126/125 tempered, we get by stacking minor thirds - 1262.565148 cents = major diesis +1 octave. This major diesis is equated to a step in 19 equal, so 25/24:648/625 gives "kleisma" comma.

We can easily extend 12 equal in 5-limit to meantone (19 equal, 31 etc) or diaschismic (34, 46 etc), or schismic (41, 53 etc). All these three are temperaments even if the last one sounds like pythagorean tuning and we need hundreds of notes for it to diverge from pythagorean just intonation in a meaningful way.

Here are some "tritones" (augmented fourths)
1: 25/18 568.717426 classic augmented fourth
2: 1024/729 588.269995 Pythagorean diminished fifth
3: 45/32 590.223716 diatonic tritone

Differences found between them.
32805/32768 1.954 cents schisma
2048/2025 19.553 cents diaschisma 
81/80 21.506 cents syntonic comma, Didymus comma

All these three temperament sound better (for harmony) than regular 12 equal and you can translate 12 equal music that is written using the right accidentals, if you want.

We can extend 12 equal to higher-limits like 7-limit or 11-limit etc.
For example: 
81/80 = 225/224 x 126/125, so septimal meantone = 31 equal is good -> augmented fourth is becoming equivalent to 7/5 tritone, diminished fourth becomes septimal "major" third of 9/7.
128/125 = 64/63 x 126/125 = 27 equal, so septimal augmented, it's good scale, but for 7-limit, 12 equal is better in 5-limit
2048/2025 = 64/63:225/224 = 22 equal (basically 34-12 = 22; 34 is good for 5-limit, this one for 7)

The optimal (in terms of consonances) generator for 5-limit is actually not a perfect fifth/fourth.Perfect fifths/fourths means that we are lifting pythagorean (3-limit) to 5-limit. (So, ignoring octaves (number 2), we use irrational numbers that are between numbers that can be written in the form A^3 and Z^3 x Y^5. In terms of purity meantone<diaschismic<schismic<whatever comes next after we divide the octave in more than 600 parts.)

It is actually a minor third (major third is lifting 2.5 subgroup to 5-limit, so numbers that are in the form A^5 vs numbers that are Z^3 x Y^5). Kleismic is good for minor thirds (so we use irrationals that are between different numbers in the form of A^3 x Y^5) and this is form of microtemperament.

Or 3 x 5 = 15, so 15/8 (16/15), but this will gives "cluster" scales, if we want any sort of purity.
Here is one such scale, generated by diatonic semitones/major sevenths:


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## millionrainbows

EdwardBast said:


> The *Gb major chord in the first theme of the Appassionata* doesn't have a Neapolitan function. It's just a lurch to Gb major confirmed by its by own dominant and vii°7/V (enharmonically spelled). It's a different animal.


You're thinking about something else. The WIK example I cited (with sound) is F minor, not Gb major.


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## EdwardBast

millionrainbows said:


> Key of C:
> 
> EdwardBast has already confirmed that a German +6 chord is equal to a tritone substitute:


No, I observed that jazz theory generally doesn't distinguish between the two but that classical theory regards them as quite different because the active intervals resolve differently. This thread isn't about jazz theory.


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## millionrainbows

EdwardBast said:


> No, I observed that jazz theory generally doesn't distinguish between the two but that classical theory regards them as quite different because the active intervals resolve differently. This thread isn't about jazz theory.


I'm very disappointed in that answer, Edward. You should be setting an example of the 'new paradigm' of music theory which is inclusive. 
Instead, you're being divisive.

What's wrong, you don't like jazz music? Why not? Is it for the same reasons as Adorno?


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## Wes Lachot

I'm often not sure where to draw the line between classical and jazz piano music. Sometimes when I'm listening to Brahms, I'll forget what it is and think for a few seconds that it's Bill Evans. And I know Bill Evans' music through and through, used to listen to him play live in Boston, have done many transcriptions, etc. Is it possible to develop a music theory system that does justice to both, and allows future musicians to more clearly understand the connections between them, on paper as easily as through the airwaves? Who knows. Maybe certain information just has to go straight from the pianist's inner ear to the listener's inner ear in order to be appreciated. Music theory is on some level, after all, an art form about an art form, and maybe there will always be something lost in the translation. Or maybe the problem just hasn't been solved yet.


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## millionrainbows

Wes Lachot said:


> I'm often not sure where to draw the line between classical and jazz piano music. Sometimes when I'm listening to Brahms, I'll forget what it is and think for a few seconds that it's Bill Evans. And I know Bill Evans' music through and through, used to listen to him play live in Boston, have done many transcriptions, etc. Is it possible to develop a music theory system that does justice to both, and allows future musicians to more clearly understand the connections between them, on paper as easily as through the airwaves? Who knows. Maybe certain information just has to go straight from the pianist's inner ear to the listener's inner ear in order to be appreciated. Music theory is on some level, after all, an art form about an art form, and maybe there will always be something lost in the translation. Or maybe the problem just hasn't been solved yet.


In saying this, you represent the "new paradigm" of music theory of the future, which is inclusive of jazz ideas, and is not academically rigid. Congratulations. :lol:


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## Torkelburger

MR, do you know the reason why the tritone dominant can substitute for the dominant in jazz?


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## Wes Lachot

I think that this argument could evolve into more of a discussion if certain stipulations were laid down as to the overall system one is talking about. Reading over the thread, I don't see where the table was properly set for what could actually be a pretty substantial back and forth, because I can see two sides to this coin fairly clearly, having been raised somewhat equally on classical and jazz harmony. 

First I'd like to stipulate enharmonic equivalency for the purposes of this discussion, and 12-tone ET system (my rules for this post). 

Next I'd like to stipulate that we are in the present tense--you can walk over to the piano and play the Moonlight or Brahms or Evans right now, and we aren't looking at history, we're listen to sounds, right now, at the piano. Okay, thanks.

There is a valid system behind what MR is saying, and it is the system I teach and developed over several decades. I believe it was first discovered by Erno Lendvai, who proported to find what he called the Axis system buried within Bartok and Kodaly's music. I'm not sure why it never took off--possibly because Lendvai developed a sort of "golden ratio fetish", and most of his book is (IMHO) wasted on some sacred geometry stuff that is, while interesting, more the stuff of stoned hippies listening to Debussy and seeing rainbows oozing from the speakers.

Getting back to the cool part of Lendvai's theory: Like Reimann, he assigns T, D, and S designations to the various diatonic chord degrees, but they are not all the same as Riemann's, and he assigns a T, S, or D designation to all 12 chromatic tones of the scale. He does away with mediant, submediant, supertonic, leading tone designations. Scale degrees I, bIII, bV, and VI are Tonic. Degrees IV, bVI, VII, and II are Subdominant. Degrees V, bVII, bII, and III are Dominant.

So to my point about setting the table, I think it's fair to say that within Lendvai's system MR has a point. I don't think he's made the point, but I think he has one, and is just not illuminating it very well. I have been guilty of the exact same thing many times--thinking that what I have written illustrates my point perfectly, only to read it over the next morning and go "what?".

So within the Axis system it is not only reasonable but absolutely correct to state that the N6 chord, being a bII, does indeed have a Dominant function, because that is merely stating the obvious--it's true by definition within the system. And it makes sense to jazz musicians who recognize the 4 ways that Dominant chords tend to resolve as being more equal. (Those 4 root motions being down P5 (authentic), down m2 (tritone sub), up M2 ("back door"), and down M3 (as illustrated by Schumann's Kinderscenen #1, bar 12, The Beatles "I Want To Hold You Hand", etc.).

So you're thinking "but it doesn't resolve to I, it resolves to V", and that is sometimes true, but N6 also quite often resolves to I6/4, in which case it makes perfect sense as a D to T progression (that then usually goes V : I, the more usual D to T progression.) What about the case where N6 resolves to V? We see it as a D to D tonality shift, but not a Functional shift.

There is a lot more to say about this system, but I will save it for another time.


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## EdwardBast

Wes Lachot said:


> So you're thinking "but it doesn't resolve to I, it resolves to V", and that is sometimes true, but N6 also quite often resolves to I6/4, in which case it makes perfect sense as a D to T progression (that then usually goes V : I, the more usual D to T progression.) What about the case where N6 resolves to V? We see it as a D to D tonality shift, but not a Functional shift.


Wrong on two counts. The I6/4 chord in these situations is not (or only rarely) tonic in function. It is generally a dominant with ongoing unresolved non-harmonic tones. You're confusing taxonomy with function. Where N6 resolves to V it is subdominant. The clue that it's a functional shift is the word resolve.


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## Wes Lachot

Edward,

The I6/4 chord may be said to "function" as a Tonic in many textbooks--we all know that, presumably. What I am stating is that in the Axis system we don't jump through hoops to explain why a I chord "functions" like a V chord. Rather, the sounds are judged at face value. A I chord functions as a I regardless of inversion. What if I said a I chord "functions" as a III because it's in 1st inversion? This is the sort of thing that the Axis system seeks to clarify. I'm not saying that it should be your or anybody's cup of tea, just explaining the system for those who may not be familiar with it.


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## millionrainbows

I would expect Edward's answer to be something along the lines of "But we're not discussing axis theory."


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## Wes Lachot

millionrainbows said:


> I would expect Edward's answer to be something along the lines of "But we're not discussing axis theory."


My reason for bringing the axis system into this particular conversation was merely to try to rescue the thread from what seemed to me to be a less than meaningful discussion. I thought injecting some fresh ideas into the conversation would be a good thing, and as MR noted above, it is a "new paradigm". This does happen to be a theory which unifies classical and jazz functional harmonic thinking, for those who are looking for such a theory going forward. It doesn't negate other theories--they are after all only theories--but it is a very helpful theory in and of itself.

I am interested in hearing what Edward has to say, since he seems to have offered some very thoughtful perspectives in a number of threads. He may not have been aware that there is a system out there that does attempt to unify classical and jazz theory, when he made his statement above that they were two different things (paraphrasing). Or maybe he was aware--only he can tell us that.

For those interested in a further discussion of Neapolitan 6 chords, I started a new thread titled "Beethoven's Razumovski 3 Aug6 to N6 Magic Trick". It's cool how he used these chords as a sort of Swiss army knife to make his way through modulations to and from distant key areas.


----------



## millionrainbows

Wes Lachot said:


> My reason for bringing the axis system into this particular conversation was merely to try to rescue the thread from what seemed to me to be a less than meaningful discussion. I thought injecting some fresh ideas into the conversation would be a good thing, and as MR noted above, it is a "new paradigm". This does happen to be a theory which unifies classical and jazz functional harmonic thinking, for those who are looking for such a theory going forward. It doesn't negate other theories--they are after all only theories--but it is a very helpful theory in and of itself.


I always go by what my ear tells me, and I now realize this makes me a "harmonic" thinker.

Others here seem content to stick strictly to axiomatic CP theory, and prefer not to even question this. A Neapolitan chord has a root on bII, end of story...no "why" or how it may have been derived.

Woodduck was complaining about my idea of how such a chord could be "generated" or created from a diminished context. When basic terms and ideas of mine are questioned in such an inflexible way, I am not inspired to go into depth.



> I am interested in hearing what Edward has to say, since he seems to have offered some very thoughtful perspectives in a number of threads. He may not have been aware that there is a system out there that does attempt to unify classical and jazz theory, when he made his statement above that they were two different things (paraphrasing). Or maybe he was aware--only he can tell us that.


Good luck with that.



> For those interested in a further discussion of Neapolitan 6 chords, I started a new thread titled "Beethoven's Razumovski 3 Aug6 to N6 Magic Trick". It's cool how he used these chords as a sort of Swiss army knife to make his way through modulations to and from distant key areas.


Yes, this "Swiss army knife" has been in use for a while, even sooner than some would have us believe.


----------



## Woodduck

millionrainbows said:


> I always go by what my ear tells me, and I now realize this makes me a "harmonic" thinker.
> 
> Others here seem content to stick strictly to axiomatic CP theory, and prefer not to even question this. A Neapolitan chord has a root on bII, end of story...no "why" or how it may have been derived.
> 
> Woodduck was complaining about my idea of how such a chord could be "generated" or created from a diminished context. When basic terms and ideas of mine are questioned in such an inflexible way, I am not inspired to go into depth.
> 
> Good luck with that.
> 
> Yes, this "Swiss army knife" has been in use for a while, even sooner than some would have us believe.


I think we are all (or at least those of us who haven't given up and gone off to watch a soap opera or something) waiting to see the process by which the Neapolitan is "derived" or "generated" from a diminished chord. What does this generation or derivation look like in practice? Were there intermediate forms used during the transition from diminished chord to Neapolitan? I'm confused, in part, because it's clear to me that a diminished chord containing the flatted second scale degree can't have a function similar to that of a Neapolitan.

I understand harmonic relationships by ear, not by theory, of which I am not a thorough student. Can you help my ear in understanding how a Neapolitan can derive from a diminished chord?


----------



## millionrainbows

Woodduck said:


> I think we are all (or at least those of us who haven't given up and gone off to watch a soap opera or something) waiting to see the process by which the Neapolitan is "derived" or "generated" from a diminished chord. *What does this generation or derivation look like in practice? Were there intermediate forms used during the transition from diminished chord to Neapolitan?* I'm confused, in part, because *it's clear to me that a diminished chord containing the flatted second scale degree can't have a function similar to that of a Neapolitan. *
> 
> I understand harmonic relationships by ear, not by theory, of which I am not a thorough student. Can you help my ear in understanding how a Neapolitan can derive from a diminished chord?


It just sounds like a b9 dominant to me. As soon as I heard the Beethoven example on WIK, I knew.

1.) Every dim 7 can become a *dom 7 *by simply lowering any tone to become a root. Since there are 4 notes in a dim7, there are 4 different possible dominants to be derived. Thus, dim 7 C-Eb-Gb-A can become B7 by lowering C to B, Eb-D gives D7, Gb-G yields A7, and A-Ab becomes Gb7.

2.) Also, you can keep the dim 7 intact and place 4 _other_ roots below it, which you get from the parent diminished scale (C-D-Eb-F-Gb-Ab-A-Bb), to produce *dom b9 chords.* For dim 7 C-Eb-Gb-A, these other roots are D, F, Ab, and Bb. Beethoven does this very clearly in the String Quartet in F, Op. 135, last movement.

Schoenberg talks about this in his Harmonielehre, and with Piston in his Harmony text mentions substituting a G root to resolve B dim (viiº), which is the same as no. 2 above.

Keep in mind that dim 7s are symmetrical and repeating, and each inversion contains the same 4 notes: C-Eb-Gb-A/Eb-Gb-A-C/Gb-A-C-Eb/A-C-Eb-Gb, then back to C. The "lowering" note method (no. 1) also produces inversions of the dom7s, as well as no. 2. 
_________________________________________________________________________

In the case of a Neapolitan on bII (key of C), it is a substitute or 'related transitional dominant' for G (V), just as it says it is. Taking the "parent" dim 7 chord Ab-B-D-F, and placing G under it as the root, G is a G 7(b9) dominant (G-Ab-B-D-F), and is related to Db7(b9) (Db-D-F-Ab-B) via the "parent" diminished seventh chord, using the principle of no. 2 (above).

*One must assume that G and Db are in this relationship to begin with; *it's a principle which must be assumed before hand. Is this the problem? This idea is an assumed underlying principle based on harmony. It should be seen as a unifying principle which underlies all dominant relationships, and tonality itself.

Since bII (Db) is not diatonic, this explanation covers that very well, as well as explaining the G and Db connection, and their both being dominants.

Since diminished seventh forms are symmetrical, they reflect this symmetry in the relationships they uncover. They are thus part of tonality itself. This is easier to see as a chromatic principle, not diatonic. It's also the reason Pat Martino applies it to the guitar, which is a chromatic instrument by nature, not diatonic as the keyboard is.


----------



## Woodduck

millionrainbows said:


> It just sounds like a b9 dominant to me. As soon as I heard the Beethoven example on WIK, I knew.
> 
> 1.) Every dim 7 can become a *dom 7 *by simply lowering any tone to become a root. Since there are 4 notes in a dim7, there are 4 different possible dominants to be derived. Thus, dim 7 C-Eb-Gb-A can become B7 by lowering C to B, Eb-D gives D7, Gb-G yields A7, and A-Ab becomes Gb7.
> 
> 2.) Also, you can keep the dim 7 intact and place 4 _other_ roots below it, which you get from the parent diminished scale (C-D-Eb-F-Gb-Ab-A-Bb), to produce *dom b9 chords.* For dim 7 C-Eb-Gb-A, these other roots are D, F, Ab, and Bb. Beethoven does this very clearly in the String Quartet in F, Op. 135, last movement.


I get all of that. Changing roots under a dim7 is a handy way of modulating. Quite evocative. Wagner does it often.



> Schoenberg talks about this in his Harmonielehre, and with Piston in his Harmony text mentions substituting a G root to resolve B dim (viiº), which is the same as no. 2 above.
> 
> Keep in mind that dim 7s are symmetrical and repeating, and each inversion contains the same 4 notes: C-Eb-Gb-A/Eb-Gb-A-C/Gb-A-C-Eb/A-C-Eb-Gb, then back to C. The "lowering" note method (no. 1) also produces inversions of the dom7s, as well as no. 2.
> _________________________________________________________________________
> 
> In the case of a Neapolitan on bII (key of C), it is a substitute or 'related transitional dominant' for G (V), just as it says it is.


Given that the Neapolitan is usually followed by the dominant chord, it isn't typically a substitute for V. In functional terms it _may_ substitute for V - I think Mahler likes to use it that way - but more commonly it substitutes for ii or IV and is followed by V. And what do you mean "just as it says it is"? You're the only one I hear saying it.



> Taking the "parent" dim 7 chord Ab-B-D-F, and placing G under it as the root, G is a G 7(b9) dominant (G-Ab-B-D-F), and is related to Db7(b9) (Db-D-F-Ab-B) via the "parent" diminished seventh chord, using the principle of no. 2 (above).


Ah, I see what you're up to. Cute trick. But I'm troubled by the word "related"...



> *One must assume that G and Db are in this relationship to begin with; *it's a principle which must be assumed before hand. Is this the problem? This idea is an assumed underlying principle based on harmony. It should be seen as a unifying principle which underlies all dominant relationships, and tonality itself.
> 
> Since bII (Db) is not diatonic, this explanation covers that very well, as well as explaining the G and Db connection, and their both being dominants.
> 
> Since diminished seventh forms are symmetrical, they reflect this symmetry in the relationships they uncover. They are thus part of tonality itself. This is easier to see as a chromatic principle, not diatonic. It's also the reason Pat Martino applies it to the guitar, which is a chromatic instrument by nature, not diatonic as the keyboard is.


Ill-defined terms, obscuring the untenability of the premise... This gives me a touch of indigestion. As far as I can see, all you've really done here is use the multi-directional, ambiguous identity of the dim7 as a device for creating the impression of nonexistent relationships. Switching roots under a dim7 doesn't establish any functional relationshp between the roots; the fact that different dominant minor ninths share a dim7 doesn't constitute much of a relationship, doesn't define the Neapolitan as a substitute for V, and doesn't show that it "derives from," or that it's "generated by," the diminished 7th. Finally, the notion that the ambiguity of the dim7 is "a unifying principle which underlies all dominant relationships, and tonality itself" sounds crazy. Dominant relationships and tonality itself can and do exist without diminished sevenths entering the picture. The ambiguous dim7 is not the matrix from which tonality arose.


----------



## millionrainbows

Woodduck said:


> I get all of that. Changing roots under a dim7 is a handy way of modulating. Quite evocative. Wagner does it often.
> Given that the Neapolitan is usually followed by the dominant chord, it isn't typically a substitute for V. In functional terms it _may_ substitute for V - I think Mahler likes to use it that way - but more commonly it substitutes for ii or IV and is followed by V.


No, no. It's a V of V. 
bII (key of C), is a substitute (for ii or IV) or _'related transitional dominant'_ to G (V), just as it says it is (a substitute for ii or IV.
i.e, the _bII is a secondary dominant (V of V)._ Forgive me if I wasn't clear.



> Ill-defined terms, obscuring the untenability of the premise... This gives me a touch of indigestion. As far as I can see, all you've really done here is use the multi-directional, ambiguous identity of the dim7 as a device for creating the impression of nonexistent relationships.


Gee, thanks a lot, Woodduck.



> Switching roots under a dim7 doesn't establish any functional relationship between the roots; the fact that different dominant minor (flatted) ninths share a dim7 doesn't constitute much of a relationship, doesn't define the Neapolitan as a substitute for V, and doesn't show that it "derives from," or that it's "generated by," the diminished 7th.
> 
> Finally, the notion that the ambiguity of the dim7 is "a unifying principle which underlies all dominant relationships, and tonality itself" sounds crazy. Dominant relationships and tonality itself can and do exist without diminished sevenths entering the picture. The ambiguous dim7 is not the matrix from which tonality arose.


Okay, explain Db as a root.

That's why I am a fool to even try to talk to you. I think I'll let Wes take over from here in dealing with you. But you did ask for my explanation, and like a fool, I gave it to you.

_



I understand harmonic relationships by ear, not by theory, of which I am not a thorough student. Can you help my ear in understanding how a Neapolitan can derive from a diminished chord?

Click to expand...

_What a tease! My mistake. 
_*
My posts, my responses, and my ideas about music theory are not fodder for your invalidation-mill. I have just as much right to participate in this theory forum as you do. *_

As my old mantra goes:

_*I am worthy. I belong. I have something valuable to contribute.
*_


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## Woodduck

millionrainbows said:


> No, no. It's a V of V.
> bII (key of C), is a substitute (for ii or IV) or _'related transitional dominant'_ to G (V), just as it says it is (a substitute for ii or IV.
> i.e, the _bII is a secondary dominant (V of V)._


Why call the Neapolitan a secondary dominant? It CAN be used as a substitute for V/V, but it can be used in other ways too. It can be used in place of ii, II (V/V), IV or V, depending on the musical context.



> Forgive me if I wasn't clear.


By page six we ought to be able to be clear, yes?



> Okay, explain Db as a root.


What shall I explain about it?



> That's why I am a fool to even try to talk to you. I think I'll let Wes take over from here in dealing with you.


OK, put him on the phone.



> My posts, my responses, and my ideas about music theory are not fodder for your invalidation-mill. I have just as much right to participate in this theory forum as you do. [/B][/I]
> 
> As my old mantra goes:
> 
> _*I am worthy. I belong. I have something valuable to contribute.
> *_


Inserting different roots beneath a dominant seventh to produce different dominant minor 9ths is interesting, but I can't see it as an explanation of why we have the Neapolitan or how it functions, much less as a "principle" that tonality is based on. The N6 isn't a dominant 9th, and I see no reason to assume that it "comes from" one, in theory or in practice. Wouldn't it be more useful to our understanding of its origins to look at the earliest uses of it we can find? Doesn't practice precede theory? The flatted supertonic is characteristic of the Phrygian mode, which makes its occurrence pretty ancient, and it crops up through the succeeding centuries. Whatever the reason for its use in a given instance, I feel sure that no one in the year 1400 was thinking or feeling diminished sevenths or dominant ninths.

Googling turned up this essay, which attempts to trace the evolution of the Neapolitan and gives some early examples of the use of the flatted supertonic:

https://urresearch.rochester.edu/institutionalPublicationPublicView.action?institutionalItemId=7769

It appears that Monteverdi may have been one of the first to use the Neapolitan in the form we now consider typical.


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## Guest

I don't know much about the Neapolitan chord, but I sure do love the ice cream!! Does it taste anything like that?


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## Guest

The OP asked a simple question which was answered correctly and succinctly by Edward Bast back on page 1 (#14). The only thing lacking so far is to give a few notated examples showing how the chord is made and treated, plus a few examples from the repertoire.

Here is a PDF I made for my harmony students that offers a very simple summary (it's in French, you can Google translate it).

View attachment N6 presentation document.pdf


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## millionrainbows

Woodduck said:


> Why call the Neapolitan a secondary dominant? It CAN be used as a substitute for V/V, but it can be used in other ways too. It can be used in place of ii, II (V/V), IV or V, depending on the musical context.


Ok, I have no problem with that. My responses are not definitive "all or nothing" statements.



> By page six we ought to be able to be clear, yes?


If you want that kind of clarity in a world of possibilities such as music, then good luck. I'm fresh out of axioms.



> What shall I explain about it?


Nothing, diatonically.



> Inserting different roots beneath a dominant seventh to produce different dominant minor 9ths is interesting, but I can't see it as an explanation of why we have the Neapolitan or how it functions, much less as a "principle" that tonality is based on. The N6 isn't a dominant 9th, and I see no reason to assume that it "comes from" one, in theory or in practice. Wouldn't it be more useful to our understanding of its origins to look at the earliest uses of it we can find? Doesn't practice precede theory? The flatted supertonic is characteristic of the Phrygian mode, which makes its occurrence pretty ancient, and it crops up through the succeeding centuries. Whatever the reason for its use in a given instance, I feel sure that no one in the year 1400 was thinking or feeling diminished sevenths or dominant ninths.


I think they were hearing them, in relation to what made sense to their ears.



> Googling turned up this essay, which attempts to trace the evolution of the Neapolitan and gives some early examples of the use of the flatted supertonic:
> 
> https://urresearch.rochester.edu/institutionalPublicationPublicView.action?institutionalItemId=7769
> 
> It appears that Monteverdi may have been one of the first to use the Neapolitan in the form we now consider typical.


Interesting, but I'm not a music historian, nor do I pretend to be.


----------



## millionrainbows

Woodduck said:


> I get all of that. Changing roots under a dim7 is a handy way of modulating. Quite evocative. Wagner does it often...Given that the Neapolitan is usually followed by the dominant chord, it isn't typically a substitute for V. In functional terms it _may_ substitute for V - I think Mahler likes to use it that way - but more commonly it substitutes for ii or IV and is followed by V. And what do you mean "just as it says it is"? You're the only one I hear saying it.


I meant to say bII is a substitute for ii, going to G. You don't have to bite my head off.



> Ah, I see what you're up to. Cute trick. But I'm troubled by the word "related"...*Ill-defined terms, obscuring the untenability of the premise...* *This gives me a touch of indigestion. *As far as I can see, all you've really done here is use the multi-directional, ambiguous identity of the dim7 as a device for creating the impression of nonexistent relationships. Switching roots under a dim7 doesn't establish any functional relationshp between the roots; the fact that different dominant minor ninths share a dim7 doesn't constitute much of a relationship, doesn't define the Neapolitan as a substitute for V, and doesn't show that it "derives from," or that it's "generated by," the diminished 7th.


Well, I happen to disagree.



> Finally, the notion that the ambiguity of the dim7 is "a unifying principle which underlies all dominant relationships, and tonality itself" *sounds crazy.* Dominant relationships and tonality itself can and do exist without diminished sevenths entering the picture. The ambiguous dim7 is not the matrix from which tonality arose.


Please try to be civil and respectful, Woodduck. BTW, that "matrix" idea is a good metaphor to describe the chromatic nature of the diminished seventh/dominant connection.

In your explanation, the bII just "appeared" as a way of doing things. Sounds like "poof!" It's magic!


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## millionrainbows

Christabel said:


> I don't know much about the Neapolitan chord, but I sure do love the ice cream!! Does it taste anything like that?


Yes, and it looks like a million rainbows.


----------



## Wes Lachot

TalkingHead said:


> The OP asked a simple question which was answered correctly and succinctly by Edward Bast back on page 1 (#14). The only thing lacking so far is to give a few notated examples showing how the chord is made and treated, plus a few examples from the repertoire.
> 
> Here is a PDF I made for my harmony students that offers a very simple summary (it's in French, you can Google translate it).
> 
> View attachment 141708


TalkingHead,

Thanks for making available your PDF of your summary of typical Neapolitan chord usage. In your accompanying post you state that Edward Bast's post #14 answered the OP's "simple question" "correctly and succinctly", and that the only thing lacking was "a few notated examples". I agree, and your PDF summary does include some prime examples of the Neapolitan chord in typical use. I was happy to see that in fact your PDF also included two examples that are not covered by Edward Bast's post #14 (which Bast did not put forward as definitive, incidentally). These would be the examples where the Neapolitan chord resolves directly to a diminished chord. The resolution to a diminished chord from the Neapolitan chord was, in fact, one of Johann Sebastian Bach's typical chord progressions. (I am confining my current discussion to the direct resolution from N6 to target chord.) This resonated with something I was reading in an essay just yesterday:

I recommend that everyone read the 1939 essay by Emmett Lewis to which Woodduck provided a link in post #79, if you have not already done so. Here's the link again for your convenience:

http://hdl.handle.net/1802/8238

In reading the essay, it becomes clear that Bach had quite the affinity for the diminished chord following the Neapolitan chord, and there were at least two different diminished chords he preferred. Here are a few quotes from the Lewis essay, all of which refer to compositions by J.S. Bach:




> p39) In the 371 Chorales, Bach used the Neapolitan sixth chord only once, in "Ach Gott, vom Himmel sieht darein"; Introducing a phrase, followed by a diminished seven chord…





> p40) From the Eb Minor Prelude of The Well Tempered Clavier, Vol. 1, there is another example of the Neapolitan as an altered second class chord...Again the diminished seven chord in arpeggio form follows the Neapolitan.
> 
> p40) (with respect to the Bach Gesellschaft) The Prelude in C# Minor contains a Neapolitan, again followed by a diminished chord...
> 
> p42) Later, in the same work, a Neapolitan over a pedal-point appears in preparation for a cadence, followed by the favored diminished seventh chord...
> 
> pp42-43) A most effective Neapolitan sixth chord appears in No. 33, near the end of the chorus, "Christ is Bound and Led into the City". As this chord is extended over the measure, it is quite intense. The diminished seventh chord follows the Neapolitan before the cadence chords appear.
> 
> p45) (with respect to St. John Passion) In the Largo of the same sonata, there is a very straightforward use of the Neapolitan, preceded by the subdominant and followed by his (Bach's) favorite chord, the diminished seventh...
> 
> p45) A dominant 9th chord precedes the Neapolitan, and a diminished seventh chord follows it in the flute sonata #5.


The only reasonable take-away from Lewis's extensive research in this narrow field of study is that the Neapolitan chord resolving to a diminished chord is one of Bach's favored chord progressions. Lewis even points out one example that fails to go to a diminished chord as if it were an oddity:




> p43) In the Evangelist's recitative, No. 30, somewhat the same arrangement is found, with the exception that the diminished seventh chord is omitted.


So much for the Neapolitan chord having nothing whatsoever to do with diminished chords. I understand that may not be exactly how Bast meant it at the time, but as it stands that statement in such a definitive form in his original post could be confusing to the uninitiated or to Bach lovers, IMHO.

From here I would suggest that readers download the file and decide for themselves what's in it. I thought it held a wealth of information that raised many questions, rather than providing pat answers. I even found the possible origins of one of Beethoven's uses of the Neapolitan chord in the Moonlight, which I will share about in another post. It was a great read and I appreciate Woodduck posting it.


----------



## Guest

Wes Lachot said:


> [...] I was happy to see that in fact your PDF also included two examples that are not covered by Edward Bast's post #14 (which Bast did not put forward as definitive, incidentally). *These would be the examples where the Neapolitan chord resolves directly to a diminished chord.* *The resolution to a diminished chord from the Neapolitan chord* was, in fact, one of Johann Sebastian Bach's typical chord progressions. [...]


Thank you for your reply and link to the Lewis dissertation.

I wouldn't say that the N6 _resolves_ to a diminished chord; rather, the N6 _moves onto_ a diminished chord and then finds its resolution on the V chord that follows. The diminshed chord (vii°/V) that is interposed beween the N6 (_bII6)_ and the dominant (V) is simply *a passing chord*.

As to the *origins of the N6* and further examples from the repertoire, please see the two PDFs which I have attached here:

View attachment N6 examples (p1).pdf

View attachment N6 examples (p2).pdf


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## millionrainbows

Pardon me, I must have stumbled into the Music History thread. :lol:


----------



## Wes Lachot

TalkingHead said:


> Thank you for your reply and link to the Lewis dissertation.
> 
> I wouldn't say that the N6 _resolves_ to a diminished chord; rather, the N6 _moves onto_ a diminished chord and then finds its resolution on the V chord that follows. The diminshed chord (vii°/V) that is interposed beween the N6 (_bII6)_ and the dominant (V) is simply *a passing chord*.
> 
> As to the *origins of the N6* and further examples from the repertoire, please see the two PDFs which I have attached here:
> 
> View attachment 141758
> 
> View attachment 141759


Thanks for providing more info on Neapolitan chord uses for the group.

As for my choice of the word "resolves", you can just use the words "proceeds to", because this is not about the semantics of that word, which I tried to make clear in my post by specifying "I am confining my current discussion to the direct resolution from N6 to target chord". The reason for keeping the discussion narrower is that what I see on this forum is a lot of people talking past each other and ending up in flame wars either because there is a imbalance of knowledge, but also, just as crucially, because the terms of debate were never laid down clearly. I am trying to avoid that second pitfall by defining a more narrow, digestible topic for discussion, at least for my posts. I am happy to broaden out the discussion at a later time, after the real points in my post above have been addressed and commented on.

So I am interested to hear what you and others have to say about the actual meat of my post.


----------



## EdwardBast

Wes Lachot said:


> So much for the Neapolitan chord having nothing whatsoever to do with diminished chords. I understand that may not be exactly how Bast meant it at the time, but as it stands that statement in such a definitive form in his original post could be confusing to the uninitiated or to Bach lovers, IMHO.


No, the definitive statement is correct in the context of the OP. Gargamel was suggesting that the N6 chord arises as (or as a goal of?) an altered I chord! (See below) It was the derivation of the chord that was under discussion. It helps to acquaint oneself with the prior discussion before wading in.



Gargamel said:


> Your explanation feels right, but abtuse. Every video in youtube talks about what it's used for, but doesn't explain how it "is made".
> 
> I feel the neapolitan chord simply an issue of diminished chord on I. So to harmonically understand the neapolitan chord, one only needs to look at the diminished I chord, correct?


I concur with Talking Head's observation that diminished chords don't resolve the N6, but have a passing function to the actual resolutions on V. The explanation for Bach's practice is no doubt discomfort with the melodic use of diminished 3rds and direct cross relations.


----------



## millionrainbows

Wes Lachot said:


> Thanks for providing more info on Neapolitan chord uses for the group.,,As for my choice of the word "resolves", you can just use the words "proceeds to", because this is not about the semantics of that word, which I tried to make clear in my post by specifying "I am confining my current discussion to the direct resolution from N6 to target chord".




It doesn't work that way. You made a mistake; the Neapolitan chord doesn't "resolve" to a diminished. 
I didn't get away with my use of "substitute for G" for about the same reason; I meant "substitute for ii." But it's too late now; I posted it.




> The reason for keeping the discussion narrower is that what I see on this forum is a lot of people talking past each other and ending up in flame wars either because there is





> *a imbalance of knowledge**,*but also, just as crucially, because the terms of debate were never laid down clearly. I am trying to avoid that second pitfall by defining a more narrow, digestible topic for discussion, at least for my posts. I am happy to broaden out the discussion at a later time, after the real points in my post above have been addressed and commented on.




You can't presume to "control" a discussion in this manner. Besides, it's not a debate.

Any mistakes you make, such as saying "resolve" will be dealt with strictly and directly, with no concession to "the semantics of the word" or "confining or narrowing your discussion."
If you make a mistake, and use the wrong term such as "resolve," your *"imbalance of knowledge*" will be dealt with.



> So I am interested to hear what you and others have to say about the actual meat of my post.


What? About the N6 "resolving" to a diminished chord?


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## EdwardBast

Wes Lachot said:


> Thanks for providing more info on Neapolitan chord uses for the group.
> 
> As for my choice of the word "resolves", you can just use the words "proceeds to", because this is not about the semantics of that word, which I tried to make clear in my post by specifying "I am confining my current discussion to the direct resolution from N6 to target chord". The reason for keeping the discussion narrower is that what I see on this forum is a lot of people talking past each other and ending up in flame wars either because there is a imbalance of knowledge, but also, just as crucially, because the terms of debate were never laid down clearly. I am trying to avoid that second pitfall by defining a more narrow, digestible topic for discussion, at least for my posts. I am happy to broaden out the discussion at a later time, after the real points in my post above have been addressed and commented on.
> 
> So I am interested to hear what you and others have to say about the actual meat of my post.


I think Talking Head and I understand the "target chord" to be the V, because that is the N6's ultimate goal in all of these examples. The N6 and V are the essential, invariant elements in the progression. From this perspective, the intervening diminished chords Bach uses, the I6/4 chords, and so on, are not targets, they are pathways to the target that generally smooth the voice-leading.

Thanks for the interesting Bach examples! I don't look at the proceedings as a debate, but as a cooperative effort to assemble a more complete picture. I wonder if the OP is still interested?


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## millionrainbows

Wes Lachot said:


> The only reasonable take-away from Lewis's extensive research in this narrow field of study is that *the Neapolitan chord resolving to a diminished chord *is one of Bach's favored chord progressions. Lewis even points out one example that fails to *go to a diminished chord* as if it were an oddity...




It's really too bad you used that word "resolve." 
"Go to" might have worked, or your earlier phrase "the diminished chord *following* the Neapolitan chord..."



> So much for the Neapolitan chord having nothing whatsoever to do with diminished chords. I understand that may not be exactly how Bast meant it at the time, but as it stands that statement in such a definitive form in his original post could be confusing to the uninitiated or to Bach lovers, IMHO.


The statement means what it means. The Neapolitan chord has nothing whatsoever to do with diminished chords. And remember, this is not a debate, because nothing is up for debate. The OP's question is our main concern, not some crazy, chromatic jazz-like questioning of common practice procedures.

Thanks for the Bach examples which show diminished chords in the proximity of the N6 chords, although they have nothing to do with each other.


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## EdwardBast

millionrainbows said:


> The statement means what it means. The Neapolitan chord has nothing whatsoever to do with diminished chords. And remember, this is not a debate, because nothing is up for debate. The OP's question is our main concern, not some crazy, chromatic jazz-like questioning of common practice procedures.




You haven't followed the discussion and don't understand the issues. You haven't understood the discussion from the beginning. The OP was talking about diminished chords _before_ the N6 chord resolving to the N as in a vii°-I progression. He was talking about a diminished chord built on the first scale degree as what establishes a N6 chord. This has nothing to with how a N6 is derived or established. This is the context in which I said it has nothing to do with diminished chords.

The rest of us are talking about diminished chords _after_ the N6 chord and before the V chord. Here too the diminished chord has nothing to do with defining or establishing the N6 chord. Rather, it links the N6 chord and its goal on V, a completely different context which you also have failed to grasp.

I'd also like to point out that, once again, you have been the main contributor to a thread in which few if any of your posts have been on point for any of the issues raised by the OP.


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## millionrainbows

EdwardBast said:


> You haven't followed the discussion and don't understand the issues. You haven't understood the discussion from the beginning. The OP was talking about diminished chords _before_ the N6 chord resolving to the N as in a vii°-I progression.


I was commenting on Wes Lachot's post, so apparently he doesn't either. You don't know what I just said. And you thanked him for the Bach examples, instead of declaring them off-topic.



> He (the OP) was talking about a diminished chord built on the first scale degree as what establishes a N6 chord. This has nothing to with how a N6 is derived or established. This is the context in which I said it has nothing to do with diminished chords.


I know; it has to do with a diminished chord built on the second scale degree (D-F-Ab-B), or viiº B-D-F-Ab if you prefer) not the first scale degree.



> The rest of us are talking about diminished chords _after_ the N6 chord and before the V chord. Here too the diminished chord has nothing to do with defining or establishing the N6 chord. Rather, it links the N6 chord and its goal on V, a completely different context which you also have failed to grasp.


You're not interested at all in how that Db got there? I guess not, as long as it's axiomatic.



> I'd also like to point out that, once again, you have been the main contributor to a thread in which few if any of your posts have been on point for any of the issues raised by the OP.


My "sins" are very few compared to the hubris I've experienced on this thread. You are totally closed-off to a more expansive discussion, as Wes has already pleaded for, and has been duly punished for.


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## EdwardBast

millionrainbows said:


> I know; it has to do with a diminished chord built on the second scale degree (D-F-Ab-B), or viiº B-D-F-Ab if you prefer) not the first scale degree.


Read the OP again. All of your responses and you still don't know what it said?



millionrainbows said:


> You're not interested at all in how that Db got there? I guess not, as long as it's axiomatic.


I'm pretty sure the big word doesn't mean what you think it means.



millionrainbows said:


> My "sins" are very few compared to the hubris I've experienced on this thread. You are totally closed-off to a more expansive discussion, as Wes has already pleaded for, and has been duly punished for.


No, we had a discussion about the diminished chords he mentioned and merely disagreed on how to characterize them. Wes made a number of valuable contributions to this thread and others and they have been highly appreciated.


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## millionrainbows

EdwardBast said:


> Read the OP again. All of your responses and you still don't know what it said?


Hey, man, we can talk about what we think is relevant, and I'm sure I speak for Wes Lachot as well. All these "personal interjections and scoldings"n are what's _really_ off-topic.



> I'm pretty sure the big word doesn't mean what you think it means.


Axiomatic? Very similar to "dogmatic."



> No, we had a discussion about the diminished chords he mentioned and merely disagreed on how to characterize them. Wes made a number of valuable contributions to this thread and others and they have been highly appreciated.


Yes, but he said "resolved" and that's all you concentrated on until just now.


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## millionrainbows

Knorf said:


> In an abstract sense, I have an inordinate fondness for the "French" augmented sixth chord, for so many reasons, including that there are only six distinct transpositions in terms of pitch class.


That sounds awfully diminished-y to me.

"What's a pitch-class?"


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## EdwardBast

millionrainbows said:


> That sounds awfully diminished-y to me.
> 
> "What's a pitch-class?"


Pitch-class is a term, favored by set theorists, referring to all the instances of a particular note in any octave considered collectively (as a class), rather than to any particular pitch as designated by a frequency (or an Acoustic Society of America number designation.) So a particular individual pitch might be described as A 440 or as A4. If one refers to the pitch class A, however, one means any and all As, as in, for example, all eight on a standard piano keyboard or all the musically useful As within the range of human hearing.


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## millionrainbows

EdwardBast said:


> Pitch-class is a term, favored by set theorists, referring to all the instances of a particular note in any octave considered collectively (as a class), rather than to any particular pitch as designated by a frequency (or an Acoustic Society of America number designation.) So a particular individual pitch might be described as A 440 or as A4. If one refers to the pitch class A, however, one means any and all As, as in, for example, all eight on a standard piano keyboard or all the musically useful As within the range of human hearing.


Are there any caveats?


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## EdwardBast

millionrainbows said:


> Are there any caveats?


Not sure what you mean.

The terminology is used a lot when talking about 12-tone music. Saying that the next pitch class is going to be A makes it clear that it could be an A in any octave or in any voice or instrument, since the pitches of a tone row aren't fixed to one register the way the notes of a tonal melody tend to be.


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## millionrainbows

Why would you need to identify a "G" as a "G" in 12-tone or serial music? Do the pitches share an identity? I thought all the pitches were on a number line, like from 0-127, as in MIDI, without regard to their pitch identity as letter-names.
How many pitch classes are there?


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## Gargamel

millionrainbows said:


> Why would you need to identify a "G" as a "G" in 12-tone or serial music? Do the pitches share an identity? I thought all the pitches were on a number line, like from 0-127, as in MIDI, without regard to their pitch identity as letter-names.
> How many pitch classes are there?


Why would you need to identify "G" as a "G" in tonal music instead of, say, interval ratios in respect to the tonic?

"Do the pitches share an identity?" Share an identity with what? A pitch class, where "G" is in, contains all the "Gs" in all registers.


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## Bwv 1080

But pitch class only locally refers to a specific note, like G, it changes with transposition and inversion. PCs can be thought of more like chord tones. When tonal music refers to the third of a chord it specifies a specific note only in relation to a particular root and transposition will change the note. If you look at a piece by, say, Elliott Carter and he may be using the pitch class set (which he referred to as chords) 0146. This is like a chord, a minor triad would be written as 037. Each note in the pc set / chord is a pitch class but the actual note depends on the transposition


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## millionrainbows

Bwv 1080 said:


> But pitch class only locally refers to a specific note, like G; it changes with transposition and inversion. PCs can be thought of more like chord tones. When tonal music refers to the third of a chord it specifies a specific note only in relation to a particular root and transposition which will change the note. If you look at a piece by, say, Elliott Carter, he may be using the pitch class set (which he referred to as chords) 0146.
> This is like a chord, a minor triad would be written as 037. Each note in the pc set / chord is a pitch class but the actual note depends on the transposition


Ahh, so instead of referring to "a particular note," pitch class refers to a relationship. So the numbers are quantities, not identities.

"037" means zero, minor third above zero, fifth above zero.

In other words, the relationships of a minor triad, without specific note names.

In this case, the definition in post #98 is somewhat lacking.


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## Gargamel

Bwv 1080 said:


> But pitch class only locally refers to a specific note, like G, it changes with transposition and inversion. PCs can be thought of more like chord tones. When tonal music refers to the third of a chord it specifies a specific note only in relation to a particular root and transposition will change the note. If you look at a piece by, say, Elliott Carter and he may be using the pitch class set (which he referred to as chords) 0146. This is like a chord, a minor triad would be written as 037. Each note in the pc set / chord is a pitch class but the actual note depends on the transposition


Sure you're not confusing pitch class with set class or set class types? Babbitt consistently employs the term "pitch class" to denote global pitch (ie. "G" is always "G"), though at the same time he uses it as a representation of the prime form of the 12-tone row. If transformation (Rx, Ix, RIx) or transposition (Tx) is specified, the pitch classes remap to other pitch classes.

In lieu of representation of the prime form, he may spell rows as pair of integers (E. G. 1.3, 2.1, 3.0, 4.7, 5.e, 6.9, 7.t, 8.2, 9.4, 10.6, 11.5.) I'm no musicologist but I think I read somewhere Elliott Carter sometimes uses nonstandard terminology?


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## millionrainbows

EdwardBast said:


> ...*Saying that the next pitch class is going to be A *makes it clear that it could be an A in any octave or in any voice or instrument, since the pitches of a tone row aren't fixed to one register the way the notes of a tonal melody tend to be.


Pitch classes are referred to as letter names? Something seems to be missing in this definition.

I thought the pitch letter-names were "mapped" to numbers.
WIK: To avoid the problem of enharmonic spellings, *theorists typically represent pitch classes using numbers beginning from zero,* with each successively larger integer representing a pitch class that would be one semitone higher than the preceding one, if they were all realised as actual pitches in the same octave. Because octave-related pitches belong to the same class, when an octave is reached, the numbers begin again at zero. One can map a pitch's fundamental frequency f (measured in hertz) to a real number...
This creates a linear pitch space in which octaves have size 12, semitones (the distance between adjacent keys on the piano keyboard) have size 1, and middle C (C4) is assigned the number 0 (thus, the pitches on piano are −39 to +48).

...So "pitch class" is not really about "all Gs in any octave" (note identity), but is about relationships between notes (interval quantities) expressed as numbers, not letter names.

Too complicated for ya?


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## EdwardBast

millionrainbows said:


> Pitch classes are referred to as letter names? Something seems to be missing in this definition.


That wasn't a definition. Yes, sometimes they are.


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## Gargamel

millionrainbows said:


> ...So "pitch class" is not really about "all Gs in any octave" (note identity), but is about relationships between notes (interval quantities) expressed as numbers, not letter names.


Even so, I don't think Bwv 1080 is correct. Pitch class refers to a value globally: the two notes "G", and "A", can never belong to the same pitch class, no matter how you would transpose the set.


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## Bwv 1080

Gargamel said:


> Sure you're not confusing pitch class with set class or set class types? Babbitt consistently employs the term "pitch class" to denote global pitch (ie. "G" is always "G"), though at the same time he uses it as a representation of the prime form of the 12-tone row. If transformation (Rx, Ix, RIx) or transposition (Tx) is specified, the pitch classes remap to other pitch classes.
> 
> In lieu of representation of the prime form, he may spell rows as pair of integers (E. G. 1.3, 2.1, 3.0, 4.7, 5.e, 6.9, 7.t, 8.2, 9.4, 10.6, 11.5.) I'm no musicologist but I think I read somewhere Elliott Carter sometimes uses nonstandard terminology?


Allen Forte uses the term as I described above.


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## millionrainbows

Gargamel said:


> Even so, I don't think Bwv 1080 is correct. Pitch class refers to a value globally: the two notes "G", and "A", can never belong to the same pitch class, no matter how you would transpose the set.


Yes, but you're "backwards translating" pitch-class into tonal terms. Pitch-class is about relationships and quantities, not identities, so they are expressed as number quantities, not letter-name identities.

All that "pitch-class" numbers means is that each successively larger integer represents a pitch class that would be one semitone higher than the preceding one, if they were all realised as actual pitches in the same octave.

Because octave-related pitches belong to the same class, when an octave is reached, the numbers begin again at zero.


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## EdwardBast

millionrainbows said:


> Too complicated for ya?


No, I've studied atonal theory and analyzed atonal music. I'm just curious why you are tacking all of this off-topic stuff onto a thread about Neapolitan 6 chords? Why don't you start another thread?


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## Gargamel

millionrainbows said:


> Because octave-related pitches belong to the same class, when an octave is reached, the numbers begin again at zero.[/FONT][/COLOR]


Also known as MOD-12.



millionrainbows said:


> Yes, but you're "backwards translating" pitch-class into tonal terms. Pitch-class is about relationships and quantities, not identities, so they are expressed as number quantities, not letter-name identities.
> 
> All that "pitch-class" numbers means is that each successively larger integer represents a pitch class that would be one semitone higher than the preceding one, if they were all realised as actual pitches in the same octave.




I don't see anything in Babbitt's writings which is inconsistent with "pitch class" as a tonal term. I've read quite a bit, and the "dogma" is to use pitch class and row order number interchangeably (as if they were the same thing). The pitch classes are almost always used to represent a 12-tone row in prime form, so that if one wishes to specify a transformation (Rx, Ix, RIx) or transposition (Tx), the pitch class numbers will not remap to other pitch classes, but they will still represent the 12-tone row in prime form. For example, for the T6 transposition of the pitch class set 012, one still writes "012" (E. G. "T6 x 012"), instead of writing "678". I believe this is how way Babbitt and his scholars use the term "pitch class" and hopefully you see that there need to be no inconsistencies here with the tonal application of "pitch class".


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## millionrainbows

Gargamel said:


> For example, for the T6 transposition of the pitch class set 012, one still writes "012" (E. G. "T6 x 012"), instead of writing "678". I believe this is how way Babbitt and his scholars use the term "pitch class" and hopefully you see that there need to be no inconsistencies here with the tonal application of "pitch class".


Of course the transposition is always 012; otherwise, it would involve tonal identities (678). The numbers are quantities, not identities.


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## Gargamel

Leaving 20th century music, does renaissance music have a place in this thread? Can we consider some interaction of medieval modes to shed some light on the neapolitan?


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## Gargamel

One thing I've been thinking about is the character of the Neapolitan seventh chord, and whether this can help understand the Neapolitan chord, if as Bergson says, that to understand is to create. It's a dominant seventh chord (ie. a triad plus a minor seventh). Why not a major seventh chord? Well, this is perhaps evident if we remember that a Neapolitan chord is flattened 2nd degree, and owes its dominant-seventh-chord character to the 2nd degree. Is the fundamental (Db in the C major scale) subsidiary to the other tones, as I might conjecture whether the central idea of the Neapolitan chord is not to spit out a diminished iv chord (F, Ab, B), and as a final touch furnish it with an appropriate fundamental (which in the C major scale would be Db)?


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## EdwardBast

^ ^ ^ Db - B isn't a minor seventh, it's an augmented 6th. Hence, Db, F, Ab, B isn't a dominant 7th chord. Spelled that way the chord would likely be functioning as an augmented 6th chord going to V/IV.

No, "the central idea of the Neapolitan chord is [most assuredly] not to spit out a diminished iv chord."


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## Gargamel

EdwardBast said:


> ^ ^ ^ Db - B isn't a minor seventh, it's an augmented 6th. Hence, Db, F, Ab, B isn't a dominant 7th chord. Spelled that way the chord would likely be functioning as an augmented 6th chord going to V/IV.
> 
> No, "the central idea of the Neapolitan chord is [most assuredly] not to spit out a diminished iv chord."


Why does some sources (Wikipedia, etc.) talk about a Neapolitan seventh chord, if, although enharmonically equivalent seventh chord, it's not a seventh chord?


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## EdwardBast

Gargamel said:


> Why does some sources (Wikipedia, etc.) talk about a Neapolitan seventh chord, if, although enharmonically equivalent seventh chord, it's not a seventh chord?


You should read the Wiki article more carefully. If one builds a 7th chord on bII it is not going to be functioning as a Neapolitan chord. Using the example key of C major, Db, F, Ab, Cb will be the dominant of a triad built on bV. If it's spelled enharmonically as Db, F, Ab, B, it will usually be an augmented 6th chord resolving to V/IV. So, the term "Neapolitan 7th chord" is just a sloppy, misleading way of describing a couple of harmonies that are not really Neapolitans and don't function as Neapolitans. The term should be avoided.


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## Bwv 1080

EdwardBast said:


> You should read the Wiki article more carefully. If one builds a 7th chord on bII it is not going to be functioning as a Neapolitan chord. Using the example key of C major, Db, F, Ab, Cb will be the dominant of a triad built on bV. If it's spelled enharmonically as Db, F, Ab, B, it will usually be an augmented 6th chord resolving to V/IV. So, the term "Neapolitan 7th chord" is just a sloppy, misleading way of describing a couple of harmonies that are not really Neapolitans and don't function as Neapolitans. The term should be avoided.


Yes, more simply, a dominant 7 on bII is a tritone sub for V so it resolves to I (V/IV), same as the A6 chord, which is a tritone sub for the V/V


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## Civilization3

Woodduck said:


> I think the Neapolitan is closer in function to the ii than to the IV. It is after all a flatted ii. Try fitting it into various progressions and see if you agree.


It's a subdominant harmony, that's a distinction without a difference. ii6 is the same as IV functionally. ii5/3 it doesn't as closely resemble. The proximity of bII to ii is not very relevant.


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## Civilization3

So, confounding it with flat five substitute in jazz is no good. Already been stated, but a subdominant function harmony is no substitute for a dominant function or vice versa. Sure, you may do an F Ab Db with a G bass and have a V7b5b9, but this is a different harmony with a different function as per I. That muddies the waters with no insight as to the meaning of the harmony.


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## hammeredklavier

bars 210~214: watch?v=Dzmj8lRLHh0&t=11m30s ("VI - *iv - V* - i6 - VI - iv - V - i"). In bar 211, there is a sustained tone, F, and inner lines, "Db - C - B" and "Eb - D", making the "progression" in bar 211 "sound" like [ Neapolitan chord (F, Ab, Db) -> minor/minor 7th chord (F, Ab, C, Eb) -> V4/2 chord (F, G, B, D) ]. I've been intrigued by it; sounds like an elaborate use of the Neapolitan chord. Btw, I also like the D in bar 213 ("*iv - V* - i")


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## hammeredklavier

millionrainbows said:


> Beethoven's use of it in the Apassionata sonata seems to be to be the most clear use.
> 
> 
> EdwardBast said:
> 
> 
> 
> The Gb major chord in the first theme of the Appassionata doesn't have a Neapolitan function. It's just a lurch to Gb major confirmed by its by own dominant and vii°7/V (enharmonically spelled). It's a different animal.
Click to expand...

MR might have meant the third movement: watch?v=8RlqQTUFxMY&t=17s [0:20] ("i - *N* - V - VI - iio6 - V - i")


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## EdwardBast

hammeredklavier said:


> MR might have meant the third movement:
> 
> 
> 
> [0:20] ("i - *N* - V - VI - iio6 - V - i")


No, he meant the first movement (as does almost everyone referring to the famous move to the Neapolitan in Op. 57). Otherwise he would have said he meant the finale.


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