#1
A new thought occurred to me.

Chords, as you all know are built upon stacked thirds. Traditionally using thirds found in a diatonic scale, to create these chords. As there are seven notes in diatonic thirds, we can only make 7th, 9th, 11th, and 13th chords, as the 15th is the same as the root.

However, whilst using the octatonic diminished scales, an 8th scale degree is available, which allows for the theoretical °15th chord. As the scale is 1, b2, b3, b4, b5, bb6, bb7, bb8, we can use this b8 as a our 15th degree. The chord would have the notes: 1, b3, b5, bb7, b9, b11, bb13, bb15. In the key of C this gives us C, Eb, Gb, Bbb, Db, Fb, Abb, Cbb. There are 8 different pitches present in this chord, thus it cannot be represented another way (without using slash chords or polychords). I know this does not follow the diminished pattern of minor thirds, as there is a major third between the bb7 and the b9, but, as this fits the scale better, I think it is appropriate to name it a °15

Would this be correct theory, or is it getting a little late?
#2
I really wouldn't look at this way, but there are "ways" to do things exactly like this. It's not really invalid, it's just awkward.
Quote by les_kris
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#3
Quote by Corwinoid
I really wouldn't look at this way, but there are "ways" to do things exactly like this. It's not really invalid, it's just awkward.


But it would actually be correct to use a natural root with a diminished 15th (or in this case diminished twice) in a chord?
#4
Correct in what sense? This really doesn't have a direct yes or no answer. How about this, you're free to write anything you want, as long as I'm free to come back 200 years later and explain it differently?

Really, how you want to think about it during the creative process is up to you, this isn't something that's approached very easily... how you convey what you want and how you're using it will largely determine how people try to analyze it. So, again, it's really difficult to just say this is right or this is wrong; you're into an area that classical theory doesn't really explain very well.

Depending on how you're using it, you can view this as a cluster, or secundal harmony, or as a peculiar set, or some other number of ways I don't even know. I wouldn't, personally, try to use any type of harmonic inference (such as the 1 b3 etc) for this -- but that's just me, and I can't honestly sit here and tell you that my word on this is absolute, or even right.
Quote by les_kris
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#5
Why not extend the idea even further? Lets use the whole chromatic scale to make a chord!

You'd have 1 bb3 bbb5 bbbbb7 bbbbbb9 bbbbbbb11 bbbb13 bbbbb15 bbbbbbb17 bbbbbbbb19 b21 bb23 (yes, I did work it out, I'm bored). Edit: Oops I've lost track somehwere, I've only got 10 notes instead of 12. Edit: Fixed

But enough cheap sarcasm.

Point is, you're giving the intervals names that don't really make sense in any practical way. I'd be much more inclined to call the intervals in the HW scale 1 b2 #2 3 #4 5 6 b7. The names of these intervals have a practical meaning to me.
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Quote by MudMartin
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Last edited by Ænimus Prime at Apr 19, 2008,
#6
Quote by Ænimus Prime
Why not extend the idea even further? Lets use the whole chromatic scale to make a chord!

You'd have 1 bb3 bbb5 bbbbb7 bbbbbb9 bbbbbbb11 bbbb13 bbbbb15 bbbbbbb17 bbbbbbbb19 b21 bb23 (yes, I did work it out, I'm bored). Edit: Oops I've lost track somehwere, I've only got 10 notes instead of 12. Edit: Fixed

But enough cheap sarcasm.

Point is, you're giving the intervals names that don't really make sense in any practical way. I'd be much more inclined to call the intervals in the HW scale 1 b2 #2 3 #4 5 6 b7. The names of these intervals have a practical meaning to me.


1 b2 b3 b4 b5 bb6 bb7 bb8 for HW and 1 2 b3 4 b5 b6 bb7 b8 for WH make the most sense to me. Spelling it this way I actually have pitches which make sense, as there are only note per scale degree.

To me it would make even more sense to give them names not based on diatonic nomenclature. Thus we could use a "perfect ninth" as the "octave" (well 2:1 frequency ratio, as the "oct" would have to be changed to "non" making it a "nonave). Then the WH could be spelt 1 2 3 4 5 6 7 8 and the HW could be spelt 1 b2 3 b4 5 b6 7 b8. If only octatonic scales were used, this would be the most logical thing to do, however it would cause confusion with the scale degrees of the diatonic scales, and with diatonic chordology.
#7
i actually have a living example of how something like that might be applicable...

generally, we don't call a 10th a 10th because it's the same as the third... but i have a song (you can hear it as the first song played at http://www.myspace.com/adamsmithsinvisiblehand) that uses a chord vamp which contains two distinct-sounding minor thirds... the approximate tab for the first bit of the chorus is:



e|--7-7-7-7-x--10-10-x-9-9-----|
b|--7-7-7-7-x--7--7--x-7-7--3~-|
g|--7-7-7-7-x--7--7--x-7-7--4~-|
d|--9-9-9-9-x--9--9--x-9-9--5~-|
a|-----------------------------|
E|-----------------------------|



so the middle chord has two minor thirds, and in the context of the song, the notes on the high e string are what drive the chorus melody, so they sound distinct over the rest of the B minor chord that is being played at the same time, which happens to include a minor third. So what do i call my high minor third? a 10th? Or am i supposed to rename the chord to avoid the confusion of naming two minor thirds?
#8
Quote by frigginjerk
i actually have a living example of how something like that might be applicable...

generally, we don't call a 10th a 10th because it's the same as the third... but i have a song (you can hear it as the first song played at http://www.myspace.com/adamsmithsinvisiblehand) that uses a chord vamp which contains two distinct-sounding minor thirds... the approximate tab for the first bit of the chorus is:



e|--7-7-7-7-x--10-10-x-9-9-----|
b|--7-7-7-7-x--7--7--x-7-7--3~-|
g|--7-7-7-7-x--7--7--x-7-7--4~-|
d|--9-9-9-9-x--9--9--x-9-9--5~-|
a|-----------------------------|
E|-----------------------------|



so the middle chord has two minor thirds, and in the context of the song, the notes on the high e string are what drive the chorus melody, so they sound distinct over the rest of the B minor chord that is being played at the same time, which happens to include a minor third. So what do i call my high minor third? a 10th? Or am i supposed to rename the chord to avoid the confusion of naming two minor thirds?
You can have octaves of the same note in a chord without calling it something different. Chord names arent that precise.
#9
^

yeah, it's just that in this case there's a grey area, since the extra minor third is a seperate line within the guitar part... i'm not really hung up on it, but i thought it was a similar situation to what the thread starter described.
#10
^Not really.

To me it would make even more sense to give them names not based on diatonic nomenclature.
Exactly, octatonic scales are the square peg to the diatonic system's round hole. In the first post you nearly fit it in, but cheated a little by making up an interval, namely the double-diminished octave.

So yeah as Cor said, it doesn't matter what you call it in the creative process, I would analyse your double-diminished octave as a minor seventh.
My name is Andy
Quote by MudMartin
Only looking at music as math and theory, is like only looking at the love of your life as flesh and bone.

Swinging to the rhythm of the New World Order,
Counting bodies like sheep to the rhythm of the war drums