Divine math

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Divine math

Postby Athena on August 31st, 2015, 2:08 pm 

I want to post a few U tube explanations of our brains, math, art and mucic that explain why math has been considered to be divine. Here is the first, it is about Fibonacci numbers.

The Miracle of 528 Hz Solfeggio and Fibonacci numbers
BruineDwerg2012

https://www.youtube.com/watch?v=9oSePXRbW9o

This is about phi and music.

What Phi (the golden ratio) Sounds Like
Michael Blake

https://www.youtube.com/watch?v=W_Ob-X6DMI4
Last edited by Athena on August 31st, 2015, 2:16 pm, edited 2 times in total.
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Re: Divine math

Postby mtbturtle on August 31st, 2015, 2:10 pm 

please include the title and the author of the youtubes along with a brief description preferrably. thank you

I don't wach youtubes that don't come with identifying info.
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Re: Divine math

Postby Athena on August 31st, 2015, 2:18 pm 

mtbturtle » August 31st, 2015, 12:10 pm wrote:please include the title and the author of the youtubes along with a brief description preferrably. thank you

I don't wach youtubes that don't come with identifying info.


I hope the edits meet your standards.
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Re: Divine math

Postby Watson on August 31st, 2015, 2:44 pm 

I like the instruction type video you posted, and beside on the playlist are option to pick which frequency you what to hear. It it is just a drowning noise at 528 HZ, but it seems soothing.

My dryer is the same way. I wonder what HZ it tumbles at?

Thanks, I think I'll explore the other related videos.
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Re: Divine math

Postby Braininvat on August 31st, 2015, 3:33 pm 

528 Hz repairs your DNA? Oh please.
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Re: Divine math

Postby CanadysPeak on August 31st, 2015, 4:04 pm 

Braininvat » Mon Aug 31, 2015 3:33 pm wrote:528 Hz repairs your DNA? Oh please.


It takes 16.35 Hz for mine; my DNA plays bass.
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Re: Divine math

Postby CanadysPeak on August 31st, 2015, 4:34 pm 

This is a subject where Marshall might shed some light. There is a similarity between Fibonacci numbers and musical tuning. This I know, but I lack the well-tempered clavicle to feel it in my bones, so Marshall, please jump in if you will.
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Re: Divine math

Postby someguy1 on August 31st, 2015, 5:18 pm 

There's a difference between numbers and numerology.
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Re: Divine math

Postby Braininvat on August 31st, 2015, 5:50 pm 

528 is a C (5), in a "love tuning" or some European concert tunings where the concert A is 444 instead of 440. (also have musical training)

In the US and many other places, it's a really flat C- sharp. Equal tempering (what JS Bach called well tempering) is not desirable unless an orchestra plays only a 1-4-5 with one selected root.

With a piano, you have to well-temper because the strings can't be altered during play (whereas members of an orchestra can adjust). So you have no choice.

It is true that early fibonacci numbers, put in ratios, relate to basic key relationships in western music. A note, up to its octave, has 8 notes and 13 steps. A 5th is a dominant interval of a scale. And so on.

All the frequencies in the first video are, AFAICT, "love tuning" keys in a six tone structure used in medieval times.
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Re: Divine math

Postby Braininvat on August 31st, 2015, 6:20 pm 

http://www.waronwethepeople.com/432-hz- ... ed-528-hz/

If you really want to drink the koolaid, check out the clash between the 432 hertzers and the solfeggiant 528 hertzers. There will be blood.

And dogs in the neighborhood will be whimpering under the bed.
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Re: Divine math

Postby Athena on September 1st, 2015, 10:35 am 

Braininvat » August 31st, 2015, 1:33 pm wrote:528 Hz repairs your DNA? Oh please.


I didn't know the Hz thing was pseudoscience until reading your post. Actually I wasn't paying attention to that detail, because it was the explanation of math that delighted me. I looked for more information and see in another forum, because this subject involves pseudoscience, it was suggested the thread be closed. I can appreciate that. Science forums do not want to be associated with pseudoscience, and it is good to shoot down things said that lack solid scientific proof.

Here is another speculation that is not proven science coming from H. E. Huntley's book "The Divine Proportion" a study of in mathematical beauty". He speculates the reason some rectangles are more pleasing to us than others, is the same reason some music is pleasing. It is all about the mathematical makeup of our sensors. The arrangement of hairs in our inner ear and nerve impulses of vision that send messages to our brain, and our brains subconsciously react to the ratio. Ratios closest to phi are the most attractive to us. This again is not proven science, but is speculation waiting to be proven or disproven.

For sure when people say things that are only speculative, it is proper to reply with something that is insulting, so people know we know what we are talking about, and the person who is only speculating does not. It is also funny and pleasing to our friends.
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Re: Divine math

Postby Braininvat on September 1st, 2015, 11:54 am 

I think you had a legitimate question, Athena, which I took to be: is there any scientific basis for any of what these videos say. And, since it concerned the possible influence of tones on the human nervous system and behavior, it could certainly be asked here. So, no worries. It's always good to put stuff out there and get it debunked. And anyone should feel welcome to offer further observations about the acoustic aspects of music, math, and effects on the human mind and body.

For example, the tritone used to be considered evil and demonic. It fell between a perfect 4th and a perfect 5th, and so was seen as wrong, a corruption that lay between two "good" intervals. (if you have a keyboard, play a C and an F sharp - that's a tritone) People were frightened by it. Now you hear it to indicate being lost or uncertain or uneasy - George Harrison famously uses a tritone in "Blue Jay Way." In a more upbeat way, it's used in West Side Story, in "A Girl Named Maria" because there, it resolves up to a fifth and so we feel good about it and don't feel uneasy. I'm sure Marshall can say something about these kinds of perceptions of chords and intervals and so on, as CanadysPeak suggested earlier.

Another tidbit - a whole tone scale has no fundamental. That means it has no particular key, because all the tones are a full step apart. Our ears need to hear a half-step here and there for us to know that we are in a particular key in a Western scale mode. So composers (like me, but I'm just an amateur) will sometimes make use of the whole tone scale to indicate being lost and disoriented. Because we don't know what the root is, what key we are in, we feel lost. It can be very effective.
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Re: Divine math

Postby Marshall on September 1st, 2015, 1:26 pm 

CanadysPeak and BiV, thanks for alerting me to this interesting discussion. I regret not knowing much relevant lore.
BiV you are way ahead of me in understanding the musical scale, and things like the "tritone"---maybe I can learn some basics and Athena might get something from hearing a review.

If you touch a guitar or violin string at the halfway. then the two halves vibrate TWICE fast and you get the same note an octave higher. So if the open string is "do" the new note is also "do" but higher.

What happens if you put your finger at a third of the length so only a third of the string vibrates and you get THRICE the frequency? I think the note you get is "SOL" but up an octave.

To get the sol that you sing when you sing a scale you would want to let 2/3 of the string vibrate so that the frequency is 3/2 as fast as with the open string pitch of do.

Is this right?

Code: Select all
note   fraction to let vibrate     speed of vibration
do         all=1                           1
mi         4/5                             5/4
sol        2/3                             3/2
do        1/2                             2


What fractions of the string give you other notes, like RE and FA?
At least approximately.

Apparently around the time of Bach they replaced these simple frequency ratios with powers of the Twelfth Root of Two, or so I dimly recall. but still you get approximately the same numbers on the main ones.

The main takeaway point is: the smaller the part of the string you allow to vibrate, the faster it vibrates and the higher the pitch.


Same with organ pipes. Admittedly this is so basic as to be something of a bore, something of a drag on Athena's thread. Let me know if I should refrain from intruding it.
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Re: Divine math

Postby neuro on September 1st, 2015, 1:27 pm 

just a "divertissement"...

here are the number of cycles after which a note (initially in phase with a C) comes back closest to be in phase with it:
C+ -- 84 -- .0051
D -- 49 -- .0006
E- -- 37 -- .0007
E -- 50 -- .0039
F -- 3 -- .0045
F+ -- 70 -- .0051
G -- 2 -- .0034
G+ -- 63 -- .0063
A -- 22 -- .0006
B- -- 55 -- .0011
B -- 98 -- .0006

(the third column is the corresponding phase discrepancy, in fraction of a cycle)

No wonder F and G sound good with a C! Just two or three cycles to come back in phase.

But only playing a C together with a C+ (or a B), i.e a half-tone, would be worse than playing a tritone!
Are you surprised it sounds demonic?

We are always looking forward to coming back home!

=========
edited twice to reformat the table
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Re: Divine math

Postby Marshall on September 1st, 2015, 1:37 pm 

That's the right kind of information! Thanks, I may need to correct my rudimentary table

BTW one way to format a table is to use the symbols {code} and {/code} but with square brackets instead of curly.
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Re: Divine math

Postby vivian maxine on September 1st, 2015, 1:49 pm 

Never scoff. We don't know what science will show us tomorrow. What was pseudoscience "yesterday" is science today (Sun rotates around Earth; Tomatoes are a proven poisonous fruit. Earth is flat.)

Correct me if I am wrong but haven't musicians been shown to have mathematical talents and vice versa? The two are related in some way. I don't know how but they are.

Different Hz for different people? Why do I like classical music while another likes rock and roll or other? We are built differently. Who knows about those hairs in the ears?
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Re: Divine math

Postby Marshall on September 1st, 2015, 1:56 pm 

I googled and got something related to your post, Neuro:
http://ptolemy.eecs.berkeley.edu/eecs20 ... scale.html
Code: Select all
do A        440
   B flat   466
re B        494
   C        523
mi C sharp   554
fa D        587
   D sharp   622
so E        659
   F        698
la F sharp   740
   G        784
ti A flat   831
do A        880
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Re: Divine math

Postby Marshall on September 1st, 2015, 2:13 pm 

the ratio between do and mi is 554/440 which is about 5/4

the ratio between do and so is 659/440 which is about 3/2

So maybe that preliminary table is OK

==quote==
The frequencies 440Hz and 880Hz both correspond to the musical note A, but one octave apart. The next higher A in the musical scale would have the frequency 1760Hz, twice 880Hz. In the western musical scale, there are 12 notes in every octave. These notes are evenly distributed (geometrically), so the next note above A, which is B flat, has frequency 440 × β where β is the twelfth root of two, or approximately 1.0595. The next note above B flat, which is B, has frequency 440 × β2.
...
...
The psychoacoustic properties of the musical scale are fascinating. The musical scale is based on our perception of frequency, and harmonic relationships between frequencies. The choice of 12 evenly spaced notes is based on the so-called circle of fifths.
...
...
...
For somewhat more arcane reasons, the interval between A and E, which is a frequency rise of 3/2, is called a fifth. The note 3/2 above E has frequency 988, which is an octave above B-494. Another 3/2 above that is approximately F sharp (740 Hz). Continuing in this fashion, multiplying frequencies by 3/2, and then possibly dividing by two, you can approximately trace the twelve notes of the scale. This progression is called the circle of fifths. The notion of key in music and a scale are based on this circle of fifths.

Where does the C sharp come from in the major triad? Notice that

440 × 5 ≈ 554 × 4.
Among all the harmonic relationships in the scale, A, C sharp, and E have among the simplest. This possibly accounts for the predominance of the major triad in western music.
==endquote==

"Circle of fifths" is a really simple idea. A fifth is just another name for the note "sol" because
do, re, mi, fa, sol
it s the fifth note of the scale!
And sol is always 3/2 the frequency of the key note do.

So "circle of fifths" means that you keep multiplying the basic keynote "do" frequency by 3/2 and you will get (to close approximation) all the notes of the scale.
Some of them will come out in higher octaves, though. So as you go along multiplying by 3/2 whenever they get an octave too high you divide by two, to bop them back down into the right do-re-mi scale.
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Re: Divine math

Postby Marshall on September 1st, 2015, 2:48 pm 

1 do
3/2 = 27/12 sol, that is seven halftones up from do.
9/4 ---> 9/8 = 22/12 = re, that is two halftones up from do
27/16 = 29/12 = la, that is two halftones up from sol
81/32 ---> 81/64 = 24/12 = mi, that is four halftones (two full tones) up from do
243/128 = 211/12 = ti, that is one halftone down from the do at the top of the scale.
...
...
and so it goes.

"do-to-sol" is an especially nice relationship and in this sequence if you take any note as the new keynote then the next note is the "sol" corresponding that new "do"
in that way most of the notes of the scale are generated naturally, by this nice relationship:

do, sol, re, la, mi, ti, ...
here if you take sol as your new "do", then the next one, re, is the "sol" of that new do.
then if you take THAT as your new "do", then the next one, la, is the "sol" of THAT new do.

You keep going up by a jump or interval which musicians call a "fifth", the "do-sol" interval..
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Re: Divine math

Postby Braininvat on September 1st, 2015, 6:33 pm 

Kudos to Neuro and Marshall for some great music theory demystification. If you listen to jazz, blues or rock, you probably find a scale from ancient Greece enjoyable: it is called Mixolydian mode. In the key of C, you play the regular notes except you flatten B. The Star Trek (original series) theme is a very simple use of the Mixolydian mode. That flat 7th at the start says you have gone far (interstellar space), but you eventually find your key and go home. (NPI)
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Re: Divine math

Postby Watson on September 1st, 2015, 8:26 pm 

I am just watch a show on netflix, The Code, episode 1. If you can get it, this is exactly what it is about starting at about 16 minutes in, for about 10 minutes. Now Marshall's comments make sense to me, at least more so.
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Re: Divine math

Postby neuro on September 2nd, 2015, 7:09 am 

I'd just add a note on the mathematics I proposed above, just to make it more common-sense:
when I point my attention to the number of cycles needed for a tone to come back in phase with a fundamental note, that is because a sound is neat, clear and precise when the vibration repeats identically in time, at high frequency.
The picture below shows sinusoids (which obviously repeat identically at high frequency) on the left; their relative frequencies reflects those of the notes in C major scale.
In the other two panels, the results are shown of playing a fundamental with each of the notes of the major scale. It is easily seen that almost identical waves repeat at high frequency for C+E, C+F, C+G and C+A.
notes.jpg

C+E+G is the typical C-major chord.
A+C+E is the typical A-minor chord.
F+A+C is the typical F-major chord.
So, each of these pairs belong to a typical chord, confirming that it "sounds good".
C+D, which does repeat, but with a long period, would not be perceived as a clear precise and stable sound. Somewhat funny. You would find this combination in a D7 chord, which typically keeps you suspended, waiting for G major (or minor) conclusion.
C+B, on the other hand, i.e. just a semitone, is a particularly complex wave which only "rarely" repeats.
If you consider that the frequency ratio of F+ to C - which is a tritone, mentioned above by BIV - is almost precisely sqrt(2), 1.4142, you realize that the length and complexity of the resulting wave would be similarly discouraging.
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Re: Divine math

Postby vivian maxine on September 2nd, 2015, 7:20 am 

Braininvat » September 1st, 2015, 5:33 pm wrote:Kudos to Neuro and Marshall for some great music theory demystification. If you listen to jazz, blues or rock, you probably find a scale from ancient Greece enjoyable: it is called Mixolydian mode. In the key of C, you play the regular notes except you flatten B. The Star Trek (original series) theme is a very simple use of the Mixolydian mode. That flat 7th at the start says you have gone far (interstellar space), but you eventually find your key and go home. (NPI)



I was thinking the same. Then I was wondering. What happens to these ratios if you use the 12-note scale? It is 12 notes, isn't it - a scale used in certain parts of the world? India? Elsewhere?

Thank you Neuro and Marshall. I did not know about those ratios. How did music become so well-apportioned?
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Re: Divine math

Postby vivian maxine on September 2nd, 2015, 10:44 am 

"+D, which does repeat, but with a long period, would not be perceived as a clear precise and stable sound. Somewhat funny. You would find this combination in a D7 chord, which typically keeps you suspended, waiting for G major (or minor) conclusion.
C+B, on the other hand, i.e. just a semitone, is a particularly complex wave which only "rarely" repeats." (Neuro)

Neuro, is this then what the professor was doing one day when he played a phrase and stopped just short of finishing it? He walked away, stopped, turned and said "all right; I'll release you from your tension" and played the last cord of the phrase. We could actually feel our tension ease. Is this what you are describing? Since this was basically a foundation course, the professor didn't go into the explanatory detail that you do but it sounds the same.
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Re: Divine math

Postby neuro on September 2nd, 2015, 10:48 am 

I'd say so.

And about your previous post, vivian,

The 12 notes are the same ones that Marshall listed in this post.

It is not something different.

The strict relation of music to maths specifically arises from the fact that different sounds (vibrations at different frequencies) combine into patterns that are also periodic, but more complex. If they happen to show no periodicity, then we perceive them as noise rather than sound. The maths come from the fact that a 200 Hz (cycles per second) wave is in phase with a 100 Hz wave 100 times per second, whereas a 150 Hz wave only is in phase 50 times per second (3 cycles at 150 Hz = 2 cycles at 100 Hz, a 2/3 ratio). So, it actually is all a matter of ratios; and the simpler these ratios are, the "simpler" is the sound, i.e. it is felt as a more harmonic and "clean" sound.

The reason why the notes are 12 is related to the fact that, as I reported above, a 12-log-intervals (equal-ratio intervals) scale between 1 and 2 hosts a number of quite good approximations to simple ratios:
[1.0595 ~ 18/17 !! no good, a single semitone];
1.1225 ~ 10/9;
1.1892 ~ 6/5;
1.2599 ~ 5/4;
1.3348 ~ 4/3;
[1.414 !! no good, tritone!] ;
1.4983 ~ 3/2;
1.5874 ~ 8/5;
1.6818 ~ 5/3;
1.7818 ~9/4;
[1.8877 ~ 17/9 !! no good: one single semitone below the harmonic = 2 x]
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Re: Divine math

Postby vivian maxine on September 2nd, 2015, 11:41 am 

neuro » September 2nd, 2015, 9:48 am wrote:I'd say so.

And about your previous post, vivian,

The 12 notes are the same ones that Marshall listed in this post.

It is not something different.

The strict relation of music to maths specifically arises from the fact that different sounds (vibrations at different frequencies) combine into patterns that are also periodic, but more complex. If they happen to show no periodicity, then we perceive them as noise rather than sound. The maths come from the fact that a 200 Hz (cycles per second) wave is in phase with a 100 Hz wave 100 times per second, whereas a 150 Hz wave only is in phase 50 times per second (3 cycles at 150 Hz = 2 cycles at 100 Hz, a 2/3 ratio). So, it actually is all a matter of ratios; and the simpler these ratios are, the "simpler" is the sound, i.e. it is felt as a more harmonic and "clean" sound.

The reason why the notes are 12 is related to the fact that, as I reported above, a 12-log-intervals (equal-ratio intervals) scale between 1 and 2 hosts a number of quite good approximations to simple ratios:
[1.0595 ~ 18/17 !! no good, a single semitone];
1.1225 ~ 10/9;
1.1892 ~ 6/5;
1.2599 ~ 5/4;
1.3348 ~ 4/3;
[1.414 !! no good, tritone!] ;
1.4983 ~ 3/2;
1.5874 ~ 8/5;
1.6818 ~ 5/3;
1.7818 ~9/4;
[1.8877 ~ 17/9 !! no good: one single semitone below the harmonic = 2 x]



Thank you, Neuro. I did see Marshall's post this morning. (Always late to the table.) This is most interesting. It takes several readings to get onto it but it's clear as a bell once I do.

Music, itself, came first, of course - to our consciousness, at least. Then we learn why we call it music as opposed to noise. And that would lead to another whole thread about the question "What is music?". Best not get into that.
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Re: Divine math

Postby neuro on September 3rd, 2015, 5:12 am 

vivian maxine » September 2nd, 2015, 4:41 pm wrote:And that would lead to another whole thread about the question "What is music?". Best not get into that.

I believe this has something to do with what we are discussing in the other thread
mtbturtle » September 2nd, 2015, 7:37 pm wrote:I think for Plato it would be according to The Good.
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Re: Divine math

Postby vivian maxine on September 7th, 2015, 11:38 am 

Just a bit of icing on the cake about scales. I found this this morning when satisfying my curiosity after reading that Isaac Newton, when conducting his experiment separating white light through a prism, wrote of five primary colors: red, yellow, green, blue and violet. He later added orange and indigo because he viewed color as, like music, capable of harmonies, the seven colors matching the seven notes of the Dorian scale. It seems there are seven of these scales (modes) and each suits a particular mood in music. Fascinating.

http://www.wisegeek.org/what-are-the-se ... -music.htm
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Mnemonic for the seven modes I, D, Ph, Ly, M, A, L

Postby Marshall on September 7th, 2015, 12:16 pm 

That's a nice schematic summary of the different Modes, or scales. It could be useful, and help understand what a scale is. It is a ladder or flight of steps going up one octave with a certain combination of WHOLE and HALF steps
vivian maxine » Mon Sep 07, 2015 8:38 am wrote:Just a bit of icing on the cake about scales. I found this this morning when satisfying my curiosity after reading that Isaac Newton, when conducting his experiment separating white light through a prism, wrote of five primary colors: red, yellow, green, blue and violet. He later added orange and indigo because he viewed color as, like music, capable of harmonies, the seven colors matching the seven notes of the Dorian scale. It seems there are seven of these scales (modes) and each suits a particular mood in music. Fascinating.

http://www.wisegeek.org/what-are-the-se ... -music.htm


Thanks Viv, I had never seen before the mnemonic for remembering the Modes.

Ionian, Dorian, PHrygian, LYdian, Mixolydian, Aolian, Locrian

I Do PHollow loneLY Men And Laugh

I'll write down the notes of each scale, for the key of C. That way I can play the different scales on the piano and hear what they sound like. Ionian is just the C-Major scale, and Aolian is just the C-minor scale.

Remember that a Half step means stepping up the frequency by 21/12 = 1.0595
and a Whole step raises the frequency by 21/6 = 1.1225
An OCTAVE is a doubling of frequency and you can get an octave by any sequence of 5 wholes and 2 halves.
5/6 plus 2/12 makes 6/6. So 21/6x 21/6x 21/6x 21/6x 21/6x 21/12x 21/12 = 26/6 = 21=2
What determines the MODE is the ORDER those five wholes and two halves come in.

Ionian Mode (W-W-H-W-W-W-H) [this is our usual major scale, do re mi fa....etc]
C D E F G A B C

Dorian Mode (W-H-W-W-W-H-W)
C D Eb F G A Bb C

Phrygian Mode (H-W-W-W-H-W-W)
C Db Eb F G Ab Bb C

Lydian Mode (W-W-W-H-W-W-H)
C D E Gb G A B C

Mixolydian Mode (W-W-H-W-W-H-W)
C D E F G A Bb C

Aeolian Mode (W-H-W-W-H-W-W) [this is our "minor" scale]
C D Eb F G Ab Bb C

Locrian Mode (H-W-W-H-W-W-W)
C Db Eb F Gb Ab Bb C
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Re: Divine math

Postby vivian maxine on September 7th, 2015, 12:41 pm 

I wanted to listen to that example but found they want my email address first. Said no thanks. It would be interesting to hear each, knowing what mood each sets.
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