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 Post subject: [MUSIC] Scales without major chords in them
PostPosted: Thu Jan 30, 2014 3:51 pm 
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I was wondering if there existed scales that did not contain major chords at all, yet contained at least one minor chord. I've found all of them:

C Db D Eb F Gb G (Heptatonic)
C Db D Eb G A (Hexatonic)
C Db Eb F G B (Hexatonic)
C Db Eb Gb G A (Hexatonic)
C Db Eb G A B (Hexatonic)

Naturally, subsets of these scales have the same property.
Below are the 5 scales with their triads.

    C Db D Eb F Gb G:
[*]C sus2 {C D G}
[*]C dim {C Eb Gb}
[*]C min {C Eb G}
[*]C sus4 {C F G}
[*]F sus2 {F G C}
[*]G sus4 {G C D}

    C Db D Eb G A
[*]C sus2 {C D G}
[*]C min {C Eb G}
[*]D sus4 {D G A}
[*]G sus2 {G A D}
[*]G sus4 {G C D}
[*]A dim {A C Eb}
(Add Bb and F to get the G minor blues scale)
(Add B, E and Gb to get the A major blues scale)

    C Db Eb F G B
[*]C min {C Eb G}
[*]C sus4 {C F G}
[*]Eb Aug {Eb G B}
[*](G Aug {G B Eb})
[*](B Aug {B Eb G})
(Add Ab and Bb to get the F minor blues scale)
(Add A to get the G Arabian scale)

    C Db Eb Gb G A
[*]C dim {C Eb Gb}
[*]C min {C Eb G}
[*]Eb dim {[Eb Gb A}
[*]Gb dim {Gb A C}
[*]Gb min {Gb A Db}
[*]A dim {A C Eb}
(Add F, Ab and Bb to get the Eb major blues scale)
(Add B, D and E to get the A major blues scale)
(Add E and Bb to get the Db/E/G/Bb whole half diminished scales)
(Add E and Bb to get the C/Eb/Gb/A half whole diminished scales)

    C Db Eb G A B
[*]C min {C Eb G}
[*]Eb Aug {Eb G B}
[*](G Aug {G B Eb})
[*]A dim {A C Eb}
[*](B Aug {B Eb G})
(Add D, E and Gb to get the A major blues scale)
(Add F to get the G Arabian scale)

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 Post subject: Re: [MUSIC] Scales without major chords in them
PostPosted: Sat Feb 01, 2014 7:53 am 
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I've found the scales without minor chords, but with at least one major chord in them, as well:

C Db D E F Gb G (Heptatonic)
C Db E Gb G Bb (Hexatonic)
C D E Gb G Ab (Hexatonic)
C E F Gb G Bb (Hexatonic)

Below are the 4 scales with their triads.

    C Db D E F Gb G:
[*]C sus2 {C D G}
[*]C Maj {C E G}
[*]C sus4 {C F G}
[*]Db dim {Db E G}

    C Db E Gb G Bb:
[*]C Maj {C E G}
[*]Db dim {Db E G}
[*]E dim {E G Bb}
[*]Gb M aj {Gb Bb Db}
[*]G dim {G Bb Db}
[*]Bb dim {Bb Db E}
(Add Eb and A to get the Db/E/G/Bb whole half diminished scales)
(Add Eb and A to get the C/Eb/Gb/A half whole diminished scales)

    C D E Gb G Ab:
[*]C sus2 {C D G}
[*]C Maj {C E G}
[*]C Aug {C E Ab}
[*](E Aug {E Ab C})
[*](Ab Aug {Ab C E})
(Add F, A and B to get the D major blues scale)
(Add A to get the Ab enigmatic scale)
(Add Bb to get the D Arabian scale)

    C E F Gb G Bb:
[*]C Maj {C E G}
[*]C sus4 {C F G}
[*]E dim {E G Bb}
[*]F sus2 {F G C}
[*]F sus4 {F Bb C}
(Add D, Eb and A to get the C major blues scale)
(Add D to get the Gb enigmatic scale)

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 Post subject: Re: [MUSIC] Scales without major chords in them
PostPosted: Sat Feb 01, 2014 9:59 am 
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I've found all the scales that do not contain diminished chords as well:

C D Eb E F G (Hexatonic)
C D Eb E G Ab (Hexatonic)
C D Eb E G B (Hexatonic)
C Eb E F G Ab (Hexatonic)
C Eb E F G B (Hexatonic)
C Eb E G Ab B (Hexatonic)

Below are the 6 scales with their triads:

    C D Eb E F G
[*]C sus2 {C D G}
[*]C min {C Eb G}
[*]C Maj {C E G}
[*]C sus4 {C F G}
[*]F sus2 {F G C}
(Add A and B to get the A minor blues scale)
(Add Gb, A and Bb to get the C major blues scale)
(Add Bb, Db and Ab to get the Bb major blues scale)

    C D Eb E G Ab
[*]C sus2 {C D G}
[*]C min {C Eb G}
[*]C Maj {C E G}
[*]C Aug {C E Ab}
[*](E Aug {E Ab C})
[*]Ab Maj {Ab C Eb}
[*](Ab Aug {Ab C E})
(Add Bb, Db and F to get the Bb major blues scale)
(Omit E to get G Japanese/C Hirajoshi scales)

    C D Eb E G B
[*]C sus2 {C D G}
[*]C min {C Eb G}
[*]C Maj {C E G}
[*]Eb Aug {Eb G B}
[*]E min {E G B}
[*]G Maj {G B D}
[*](G Aug {G B Eb})
[*]G sus4 {G C D}
[*](B Aug {B Eb G})
(Add A and F to get the A minor blues scale)
(Add A, Db and Gb to get the A major blues scale)

    C Eb E F G Ab
[*]C min {C Eb G}
[*]C Maj {C E G}
[*]C Aug {C E Ab}
[*]C sus4 {C F G}
[*](E Aug {E Ab C})
[*]F sus2 {F G C}
[*]F min {F Ab C}
[*]Ab Maj {Ab C Eb}
[*](Ab Aug {Ab C E})
(Add Bb, Db and D to get the Bb major blues scale)

    C Eb E F G B
[*]C min {C Eb G}
[*]C Maj {C E G}
[*]C sus4 {C F G}
[*]Eb Aug {Eb G B}
[*]E min {E G B}
[*]F sus2 {F G C}
[*](G Aug {G B Eb})
[*](B Aug {B Eb G})
(Add A and D to get the A minor blues scale)
(Add Bb to get the B Persian scale)

    C Eb E G Ab B
[*]C min {C Eb G}
[*]C Maj {C E G}
[*]C Aug {C E Ab}
[*]Eb Aug {Eb G B}
[*]E min {E G B}
[*]E Maj {E Ab B}
[*](E Aug {E Ab C})
[*](G Aug {G B Eb})
[*]Ab min {Ab B Eb}
[*]Ab Maj {Ab C Eb}
[*](Ab Aug {Ab C E})
[*](B Aug {B Eb G})

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- Eric


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 Post subject: Re: [MUSIC] Scales without major chords in them
PostPosted: Mon Feb 10, 2014 5:21 am 
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Location: Sao Paulo, Brazil
Very nice study, do you play guitar?


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 Post subject: Re: [MUSIC] Scales without major chords in them
PostPosted: Mon Feb 10, 2014 7:56 am 
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Is it coincidence that, excluding the major and minor Heptatonic scales listed, that all of these scales are hexatonic, or is there some underlying reason found in the mathematics of music? If the latter, do you think you could explain the reason in a way comprehendible to someone without sight and with no knowledge of music theory?

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 Post subject: Re: [MUSIC] Scales without major chords in them
PostPosted: Mon Feb 10, 2014 2:14 pm 
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Jeffery Mewtamer wrote:
Is it coincidence that, excluding the major and minor Heptatonic scales listed, that all of these scales are hexatonic, or is there some underlying reason found in the mathematics of music? If the latter, do you think you could explain the reason in a way comprehendible to someone without sight and with no knowledge of music theory?


I do not think it is a coincidence, this is mathematics for sure, music theory is kind of geometry, and maybe we could get some pentatonic or other scale that have such similar behaviour such as a ## (double sharp scale) but i think they would sound as the others that has the same harmonic fields intervals (frequence intervals).

Also i do not think that you have an easy way to teach music theory, you can image like a rainbow where each music note is a color, each color, from the very first to the last has a large stripe of this rainbow (full tone) but from the 3rd to the 4rd and from the 7th to the 8th notes you have a shorter stripe (half of the others = half tone).

It is like a hearing ilusion (not an optic ilusion) where every half tone (half note) sounds like an accident on the scale, but that ones (3rd to 4rd and 7th to 8th) amazingly sounds natural! (Even having half of the hertz of the others frequence it sounds the same way)

That is why you have that black piano notes on a piano keyboard in a irregular pattern such as (white, white, black, white, black, white, white, etc) and not a regular constant (black and white)

The scale sounds natural, from the 3rd to the 4rd notes and from the 7th to the Octave (where a full cycle will start again but a octave higher or lower) the sound will be so natural for hearing as from the other notes where the interval is larger)

hard to explain this scales without some maths but normally a scale has 7 notes and other scales with less notes are an abreviation of a larger scale... The chords are generated by the interval of tones among each notes, and also half tones known as sustains # or bemols = b.


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 Post subject: Re: [MUSIC] Scales without major chords in them
PostPosted: Tue Feb 11, 2014 12:22 pm 
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szykman wrote:
Very nice study, do you play guitar?

I've played the drums for a couple of years, but had to stop 3 years ago because of ringing in my ears (tinnitus).
I do still write music using FL Studio.

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 Post subject: Re: [MUSIC] Scales without major chords in them
PostPosted: Tue Feb 11, 2014 3:24 pm 
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Since there have been a couple of questions, I will describe my simple deduction method I used to find these scales.

Let's say one wants to find (a) scale(s) not containing any major chords, but at least one minor chord.

We start out with C min. This gives us the first 3 notes in our scale: C, Eb, G.
This also gives us the first notes we cannot use in our scale, because it will form a major chord with others already in the scale. These are: E (gives C E G - C Maj), Bb (gives Eb G Bb - Eb Maj) and Ab (gives Ab C Eb - Ab Maj)

If we use Db, no notes are eliminated. Our scale is now C, Cb, Eb, G.
If we use D, B is omitted because it will form G B D - G Maj. Our scale is now C, Cb, D, Eb, G.
If we use F, A is omitted because it will form F A C - F Maj. Our scale is now C, Cb, D, Eb, F, G.
Gb is the last available note, and when used, it will not create any major chords, so we use it to complete our scale.
The first scale is then C, Cb, D, Eb, F, Gb, G (Heptatonic)

For the next scale, when you get to the choice between F and A, you use A instead of F. This cancels out the remaining note Gb, it would form D Gb A - D Maj. This gives the second scale: C, Cb, D, Eb, G, A (Hexatonic)

Keep going like this to find the rest of the scales with the desired properties.

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 Post subject: Re: [MUSIC] Scales without major chords in them
PostPosted: Wed Feb 12, 2014 11:11 am 
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Joined: Wed Aug 03, 2011 3:44 pm
Location: Sao Paulo, Brazil
Hello

this chords generated by this scales are very usefull on jazz guitar especially as "passing chords" when you apply the jazz harmonic field (using chords with 4 notes like 7ths and 9ths, dim, sus, aug, dom or major etc...) as passing chords...

i like making music on computer, i have a m-audio controller, korg kaoscilator, there are many gadgets and programs that expose all chords and are really many chords to learn ; )

i found this:

http://www.musicawareness.com/intervals.html

is a music theory with mathematic approach that is really well explained and fully explained as well...


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