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You can look at a root as the 0th overtone, but in minor do you know some "deductive" reason for the -2nd overtone to be a root of the minor chord?

An illustrating explaining what I'm talking about:

enter image description here

Aaron
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dziwak1
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    This may have lost something in the translation but it makes no sense. – Tim Jun 07 '21 at 19:16
  • @Tim it is not my native language, for example: in A minor notes are derived from E but A is still a root – dziwak1 Jun 07 '21 at 19:19
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    The A minor scale is derived from C major, not E major. The roots have nothing to do with harmonics. – Aaron Jun 07 '21 at 19:21
  • ok, but in the C major you dont have A minor per se, one can construct it from I and IV – dziwak1 Jun 07 '21 at 19:30
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    The fundamental is typically counted as the first harmonic. The second harmonic is the first overtone. – phoog Jun 08 '21 at 02:28
  • @phoog ok, i edited – dziwak1 Jun 08 '21 at 07:02
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    Please do not vandalize your posts. By posting on the Stack Exchange network, you've granted a non-revocable right for SE to distribute that content (under the [CC BY-SA 4.0 license](https://creativecommons.org/licenses/by-sa/4.0/)). By SE policy, any vandalism will be reverted. – tripleee Jun 10 '21 at 11:42

2 Answers2

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It sounds like you're homing in on the idea of harmonic dualism, a concept heavily discussed by nineteenth-century German music theorists.

In short, the notion of harmonic dualism states that, if major triads are built upwards from the overtones of a given root/fundamental, the minor triad is built downwards by finding different roots/fundamentals that generate that starting tone.

Thus, starting on C, the opening partials of the C harmonic series create C, E, and G. But moving downwards from that same C, the first fundamentals to create that C end up being F, A♭, and C.

I've briefly discussed dualism further in my answer to Is the IV chord a perfect fifth in disguise?

Harmonic dualism is experiencing something of a comeback these days in its updated guise of negative harmony. If you're interested, check out the tag.

phoog
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Richard
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    Not a fan of this idea. We don't arbitrarily "build" a major chord off a root. We observe which notes ring out in subdivisions of a vibrating surface. This is easily done by (silently) holding down a high E on a piano and tapping a C. The E will ring out sympathetically. If you do the same with A-flat, it will not. That is because harmonics are real physics, not an arbitrary collection of pitches. This is a pretty good case where made-up theory just doesn't get the point. – Bennyboy1973 Jun 07 '21 at 23:10
  • @Bennyboy1973 Perhaps I was unclear, because we're saying the same thing: the major triad is not arbitrary, but it's from the harmonic series. – Richard Jun 07 '21 at 23:23
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    I'll also say that I'm not a fan of harmonic dualism, I'm just sharing the theory :-) – Richard Jun 07 '21 at 23:23
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    Don't worry, it's not an accusation-- you dirty, lowdown harmonic dualist! :D – Bennyboy1973 Jun 08 '21 at 04:21
  • @Bennyboy1973 ok, but this is exactly why i asked, because when reference is C then A-flat is not overtone, but if reference is A-flat then C is somehow 3°. Also if reference is F then C is 5°. It is clear that F is the root but what is the reason? – dziwak1 Jun 08 '21 at 07:23
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The minor scale descending IS very close to a major scale:

major asc. = C (+2) D (+2) E (+1) F (+2) G (+2) A (+2) B (+1) C min desc. = C (-2) B♭(-2) A♭(-1) G (-2) F (-2) E♭ (-1) D (-2) C

So the only difference is the interpolation of the last two steps. If you replace the D in the min descending with D♭, then you have A♭ Major or f minor.

It's actually a pretty interesting observation, but to answer your question in a simpler way-- the 2nd overtone of a series is the dominant, so the 2nd "subtone" would be that inverted: the subdominant.

Bennyboy1973
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  • thx for reply that subdominant would be then Bbminor because we are on negative direction now? – dziwak1 Jun 08 '21 at 10:30
  • No, we're starting in C. The subdominant of C is F. If you mirror a major C scale downward, you end up with f minor-- the minor subdominant of C. – Bennyboy1973 Jun 08 '21 at 10:56
  • What do you mean by "interpolation"? – user1079505 Jun 08 '21 at 15:18
  • @user1079505 inter means between - normal you have interval of a second between 6° and 7° degrees so you expecting to have the same interval between -6° and -7° degrees, but in fackt you have a semitone. interpolation from semitono to second gives you a negative leading note – dziwak1 Jun 08 '21 at 19:33
  • @user1079505 why they closed post if question is strictly formulated - "why fundamental tone is not the root of a minor chord" and nobody answered this ? ? – dziwak1 Jun 08 '21 at 19:37
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    @dziwak1 I just answered your question about why it was closed, and got a formal warning message about it and the message deleted. The reason is that SE ALLOWS anybody with a certain number of posts to close a question-- and a certain section of the community take delight in closing as many questions as they can. That there were ALREADY ANSWERS and an interesting discussion going on means nothing to them. "I don't like this question, so I'll make sure nobody else can enjoy discussing it." – Bennyboy1973 Jun 08 '21 at 21:35
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    @dziwak1 The reason the question is closed is not that it's uninteresting but that it's unclear what do you ask about. It's impossible to answer such question. Richard hinted with several topics which might be related, but it's hard to do more. Do you ask about naming chords in music theory, or history of temperaments, or something completely else? You list several first harmonics, several subharmonics (a bit exotic concept on its own) without explaining what you conclude from them. – user1079505 Jun 08 '21 at 23:06
  • @user1079505 ok, anyway i dont know how to make new line in comment here – dziwak1 Jun 08 '21 at 23:09
  • @Bennyboy1973 i was new here now understood what is going on. To clarify – i dont beliefe that B♭minor is a subdominant in C major, I meant the ♭vii chord, not the ♭7° scale degree. For fundamental note C there are two systems called Cmajor and Fminor. B♭minor as a chord would be 'antidominant' for fundamental note C - just like Gmajor is dominant chord created on 5° (dominant degree) upward - B♭minor would be antidominant chord created on -5° (4°) downward. – dziwak1 Jun 08 '21 at 23:17
  • I think I was a little too dismissive in my first comments. Although harmonically, there's no case for "flipped" notes, in terms of a lot of theory, it actually makes some sense. I'm going to stop commenting and go actually read some of this literature. Can you go edit your original question to ask 1 very specific question, so it can be voted to re-open? I'm getting in trouble raging about closed questions all the time. :D – Bennyboy1973 Jun 08 '21 at 23:38