Talk:First Five Octaves of the Harmonic Series/WikispacesArchive

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The major third

From my point of view, the introduction of the third (5) is as important as the introduction of the dominant 7th (7) in the third octave. From the mathematical background, none of the prime multiples should be ignored. Thus major third has to be added to the diagram. --- peu Apr 8, 2010

- xenwolf April 08, 2010, 12:10:43 AM UTC-0700


I agree that th introduction of th fifth harmonic is as important as th introduction of th seventh harmonic. Each row of th diagram shows a new octave from th fundamental. Th one labeled "perfect fifth" offers th chord 2:3:4, where th perfect fifth is th new sonority. Th one labeled "dominant 7th" offer th chord 4:5:6:7, & both 5 & 7 are new sonorities. What's missing, perhaps, is th word "chord," as what I'm trying to indicate is that 4:5:6:7 is a "dominant seventh chord" (& by definition, a dominant seventh chord contains 1/1, 5/4, 3/2, & 7/4). I don't intend for th word "dominant 7th" to ignore th presence of th fifth harmonic. Does that makes sense?

- Andrew_Heathwaite April 08, 2010, 06:18:17 AM UTC-0700


I think it would be better to have ther terminus "Dominant seventh chord" in the

diagram because 4:5:6:7 is a clearly chord.

If 1 or 2:3 or 8:9:10:11:12:13:14:15 ... are

treated as chords is discussed controversially.

What do you think?

--- peu Apr 8, 2010

- xenwolf April 08, 2010, 06:29:55 AM UTC-0700


In describing the harmonic series, there is always the choice between inventing a completely new nomenclature without any baggage, and trying to relate structure at least approximately to what we are familiar with. So, calling the 3rd octave "dominant seventh chord" makes it immediately understandable to musicians. We are used to a 7 note diatonic collection and a 12 note chromatic one, so the 8-note 4th octave and the 15-note 5th octave have some simliarities to those which can make it easier to conceptualize them.

- danterosati April 08, 2010, 08:20:12 AM UTC-0700


(@danterosati: I feel a little misunderstood)

and what about this:

  • octave (="harmonic identical"?)
  • perfect fifth (="harmonic cut"???)
  • harmonic chordic
  • harmonic diatonic
  • harmonic chromatic

--- peu Apr 8, 2010

- xenwolf April 08, 2010, 02:05:06 PM UTC-0700


"chord" can mean either the triad as it has developed in western music or the abstract idea of simultaneities, in which case the number of notes in the "chord" (dyad, triad, tetrad, etc) has no limits. calling the 3rd octave "chordic" still is only a mnemonic to relate to what everyone is familiar with. Otherwise, there is nothing about 4:5:6:7 that is necessarily more "chordal" than 8:9:10:11:12:13:14:15, or any other combination of notes.

i'm just riffing here:

the first octave gives us the idea of "tonic", the second, the 5th/dominant relationship that is the foundation of functional harmony, the third octave, the idea of the chord, the fourth octave gives the diatonic scale, and the fifth octave the chromatic scale. The analogies are not exact but interestingly close. Of course, all of this is trying to "explain" the origin of traditional western music in the harmonic series, which, while interesting, is not the only possible approach. If the intent is the harmonic series as compositional material for harmonic series music, then it is not necessarily necessary to relate anything to previous structures, and indeed this may limit possibilites.

- danterosati April 08, 2010, 05:24:04 PM UTC-0700


As for me, I think of th "Diatonic Harmonic Series Scale" & th "Chromatic Harmonic Series Scale" as unprecedented in Western music -- until Partch came along & introduced th 11-limit & others followed with 13, etc (but of course high-prime JI is still extremely uncommon in practice). I think th words "diatonic" & "chromatic" in this context can point at th number of tones in each set & serve as a useful analogy, but I tend to think that traditional diatonic & chromatic music is sufficiently dealt with in th 5-limit & in later music with 12-tone equal temperament.

I am interested in th harmonic series sets in question with an understanding that they are *new* in this culture.

- Andrew_Heathwaite April 08, 2010, 08:26:52 PM UTC-0700


@both: interesting to read your points.

<small>Although I'm still not lucky with the 7th in the table. ;-)</small>

Now another question: where can I find some explanation of the graphics beneath the table? Are these a kind of multi-dimensional coordinate systems?

Thanks in advance,

--- peu Apr 9, 2010

- xenwolf April 09, 2010, 12:42:23 AM UTC-0700


Yes, I intend to revise th graphic when I get some time. Thanks for pointing out th confusion!

Th graphics beneath th table are harmonic lattice diagrams. Th wiki doesn't seem to have any explanation of them, but I found some info here: http://tonalsoft.com/monzo/lattices/lattices.htm

In a sentence, each prime harmonic is given a dimension, & each non-prime odd appears as a combination of primes (eg. 15 as one move to th left (3) & one move up (5)).

- Andrew_Heathwaite April 09, 2010, 06:23:40 AM UTC-0700


Thank you for the link :-) - maybe mentioning the terminus Harmonic Lattice Diagram in the pfd/image could be helpful for the reader they can google after it... --- peu Apr 9, 2010

- xenwolf April 09, 2010, 02:48:51 PM UTC-0700