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Double flatted notes

Discussion in 'Music Theory [DB]' started by IamGroot, Aug 7, 2018.


  1. IamGroot

    IamGroot

    Jan 18, 2018
    Some of the modes of Harmonic scales have double flatted notes if the note is to reflect the correct degree of the scale:

    3 mode of Harmonic Major scale 1 b2 b3 bb4 5 b6 b7
    7 mode of Harmonic Major scale 1 b2 b3 4 b5 b6 bb7
    3 mode of Double Harmonic Major (Ultraphrygian) 1 b2 b3 b4 5 b6 bb7
    7 mode of Double Harmonic Major (Locrian bb3 bb7) 1 b2 bb3 4 b5 b6 bb7
    7 mode of Harmonic Minor 1 b2 b3 b4 b5 b6 bb7.

    The double flat notation above is an artifact of some music analysis software I am developing.

    But as far as notation, I assume you show double flats only when the key signature requires it.

    Any thoughts?
     
  2. turf3

    turf3

    Sep 26, 2011
    I would say the exact correct answer would be "show double flats when the key signature and the harmony require it". For example I think of a C dim7 as C-Eb-Gb-A but I believe it might be more correct as C-Eb-Gb-Bbb. (Theory experts feel free to correct my assumptions.)

    I would not get overly exercised over this if your objective is just to write things out for musicians to play - although most of us hate things like mixing sharps and flats in a single chord, or refusing to put courtesy accidentals on the ground that they are not strictly required, and other stuff that makes it hard to read at sight.

    If this is for a theory or composition course then you will want it to be strictly correct, of course, and where there is disagreement or ambiguity, to follow the preferred practice of one's professor. And there are many places where academics disagree. Remember that academic disputes are so violent because the stakes are so small.
     
    Last edited: Aug 7, 2018
  3. IamGroot

    IamGroot

    Jan 18, 2018
    Would you kindly explain "when...harmony requires it."
     
  4. IamGroot

    IamGroot

    Jan 18, 2018
    Thanks for your expanded answer.
     
  5. IamGroot

    IamGroot

    Jan 18, 2018
    Thanks for the answer. I will stay away from the music academics, but unfortunately, not the mathematical ones. Musical scales systems are good analogies for larger mathematical systems that are difficult to comprehend. My life will be easier if I can stick with bb3's instead of 2s in the wrong slot..
     
  6. Sneakyfish

    Sneakyfish

    Jan 24, 2014
    London, UK
    AWESOME!!! :)

    In all honestly I don't think it will result in musical analysis that's comprehensible. It sounds like you're making work for yourself and the end-user of your software. Allow me to explain why I think this is...

    In the list of modes, you state: ultralocrian = 1, b2, b3, b4, b5, b6, bb7 (correct)

    The supertonic of ultralocrian is more accurately described as a b2 (or as a #1 ?! XD ). If you did want to describe the II degree of ultralocrian as a kind of 3rd interval (why though?), you would be forced to describe it as a triple flat third (bbb3). It will be more complex in the long run to go about calling 2nd intervals something other than what they are.

    A bb3 in Ultralocrian would result in a major 2nd interval (M2 as opposed to minor 2nd (m2)) and therefore be a non-scale tone (an outside note). Ultralocrian does not have a M2 in it, so if you used it over ultralocrian, it would be some kind of passing tone. If you did include it in the scale spelling, then ultralocrian would begin with three consecutive semitones yielding a chromatic sound. It would also not be ultralocrian anymore, but rather some octatonic scale.

    For clarity, we generally try to avoid naming consecutive degrees of a scale using the same interval type. Unless it's unavoidable.

    A scale might, for instance, be tonally ambiguous and contain both major and minor thirds.

    But, if we do try to keep naming things this way (only using bb's & bbb's instead of the sensible name of the interval), ultralocrian potentially becomes:

    1, bbb3, b3, bbb5, b5, b6, 6
    or
    C, D#bb or Ebbbb, Eb, Gbbb, Gb, Ab, A

    (hehe... wait... *leans in closer* whaaaaatt?!)

    Allow me to repeat: D#bb or Ebbbb

    Yes... E quadruple flat... or a D that's simultaneously sharp and flat...

    Weirdness A, or weirdness B?

    Personally, I would be scared away from music notated this way. Or else rewrite it in a way that is legible.

    The other problem with spelling the scale this way is that it could destroy accepted chord names. It makes using the usual dim7 over ultralocrian a theoretical problem, as ultralocrian apparently no longer contains any kind of 7th! You would have to keep the chord naming system the same, while changing the way you look at scales.

    Suddenly, major 3rd's aren't major 3rd's anymore, because we have to use bb's now. So they're in fact, double flat diminished 5th's or triple flat perfect 5th's. So how would you analyse a simple major chord in the absence of thirds?

    Additionally if you were to use chord extensions, naming them becomes difficult. For example, a b9 chord would now become a bbb10 !
    13 chords would become bbb15's !!!!

    As a bassist, working out chord-scales in a jazz setting would be a nightmare! Not to mention improvising around chords labelled this way.

    It really is making it harder to analyse scales and chords together.

    I wonder, how is your program arriving at its output? I assume some kind of spectral analysis. And in what form is the output? Do you intend to have entirely mathematical output of floating-points in Hz for the user, or output using standard musical notation? If you intend to use standard notation, shouldn't it be in the form people actually read? I, for one, would have a hard time reading quadruple flat notes and understanding them as scale tones. The end-user of your program, even if it's just you, ought to be able to input correct information into the program. If the program doesn't in this case allow you to properly specify interval types and scale degrees, then IMHO it needs redesigning.
     
  7. IamGroot

    IamGroot

    Jan 18, 2018
    @Sneakyfish

    Thanks for your interest. I misled you when I said "Musical analysis". What I volunteered to do is develop a simple spreadsheet for scale properties as a "straw dog" to developing an algorithm for a similar but much larger system that has nothing to do with music. Scales have some very nice mathematical properties because they are a "circular group" with a small amount of elements (12).

    The bb3 issue was just one to clear away a question for a power point presentation when I am going to have an illustration of a piece of music. I appreciate your input.

    The musical analogy goes like this:
    1) Given a "chord" (say C E G Bb), how do you identify all scales that share those exact notes.
    2) Can you efficiently identify scales that almost fit the criteria (say 3 out of 4 notes) quickly.

    These questions are not a big deal with Western scales as there are relatively few commonly used ones. For a 7 note system, there are (I am guessing) 84 or so 7 note scales, which represents 5 common families with 7 modes plus maybe 7 uncommon families (say one based off the enigmatic scale) There are potentially >`500, but the number gets whittled down due to "rules" such as intervals can only be half, whole or 1.5.

    If you had a "scale" system with 1000 notes instead of 12, the number of potential scales grows factorially to an astronomical number, (n!/(k!(n-k)!). So you look for different ways to answer questions 1` and 2 cuz your going to need a bigger computer.

    This is what retired people do when they get together.
     
    Last edited: Aug 7, 2018
    Sneakyfish likes this.
  8. IamGroot

    IamGroot

    Jan 18, 2018
    I am getting back to working on the program.

    The weirdness if you use rigourous scale degree convention is there just like you said. This is what the modes of a chromatic scale looks like. I use that scale for debugging. Capture.PNG
     
    Sneakyfish likes this.
  9. Sneakyfish

    Sneakyfish

    Jan 24, 2014
    London, UK
    I see. Well, your system definitely works... Scale degrees going across, Modes going down...
    And I see why the chromatic scale would yield bbb's and bbbb's and so forth. A good test.

    Owing to the way the table works, you have to regard all scales/modes as diatonic. So, the seventh note (for example) of your chromatic scale is viewed in relation to a diatonic system. Therefore it has to be described in this table as bbbbb7, odd but interesting!

    You would indeed require an algorithm to determine what notes are produced by 'scale A' (referenced from the table), but wouldn't you also need to give it a key or root note to work from as well? With that information the algorithm could calculate the other notes in the scale. But without it, won't it be restricted to telling you shared intervals only as opposed to their actual note names?

    Given the right algorithm, I don't see any reason why you shouldn't be able to calculate the notes of all scales in all keys and cross-reference them against your search. Sure, y not?

    Your table is certainly efficient in storing the information. I wonder what the larger system you're working on could be? You're looking for commonalities across "scale systems with 1000 notes"... the musical equivalent would be microtonal scales and modes... so something quite nuanced or detailed in some way... I wonder what kind of data you actually intend to be storing/analysing? You seem to be building some kind of memory architecture? One of a fair size if I read you correctly. I can only conclude that you are programming HAL9000 or Skynet, I beg you to stop this madness and come back to us Gr00t!

    lol Retired from doing what?
     
  10. IamGroot

    IamGroot

    Jan 18, 2018
    Very groggy this morning, but here is an attempt at an answer.

    Owing to the way the table works, you have to regard all scales/modes as diatonic. So, the seventh note (for example) of your chromatic scale is viewed in relation to a diatonic system. Therefore it has to be described in this table as bbbbb7, odd but interesting!

    It's Diatonic in this case, because n=7. Have not really thought through for n=8+ . I just want to get it working for n=4 to 7

    You would indeed require an algorithm to determine what notes are produced by 'scale A' (referenced from the table), but wouldn't you also need to give it a key or root note to work from as well? With that information the algorithm could calculate the other notes in the scale. But without it, won't it be restricted to telling you shared intervals only as opposed to their actual note names?

    I am starting off with three representations for a 12 note system :
    1) C, C#, D.........B
    2) 1,2,3,.....12
    3) 1,2,3......C (Alphanumeric single digit) digit

    Scales intervals are (0-12) or (0-C)

    Scales have multiple formats:
    1) Note Count, Family, Mode..... 712 for example is the dorian mode pattern (7 notes, major scale, 2nd mode). Associate it with a D note and you get D Dorian.

    2) Interval: D dorian is 1 2 b3 4 5 6 b7 which becomes 1 3 4 6 8 10 11 which is the alphanumberic string 13468AB .

    3) Interval (HW) Dorian is WHWWWW which is the string 212222. Minor Pentatonic is 1.5 2 2 1.5 which is 3223.

    3) Binary on a group of 12. Dorian is 10110101010101 which is decimal 2901

    Yes, larger systems and there may a sharp between B and C and E and F when we get to the real thing, but right now we want to sell what we are doing based on a familiar concept, musical scales.

    This idea started maybe two years ago as a BS session between talks.. One fellow is now dead, the other (a retired math professor who is very good in applied math as he worked as a consultant) is seriously ill. And I am freshly retired.
     

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