Yahoo Tuning Groups Ultimate Backup tuning So Three, Part 2

My four choices for settings on my group are as follows:
Members (upload/modify/download files)
Limited (members can download files; moderators can upload/modify/download files)
Moderators only (upload/modify/download files)
Off (no one can access the Files feature)
The broadest one is “members” which is the setting I chose. I can’t post a link to my files on this group.
Carl Luma said: “You can … open the archives of your list to nonmembers and post a link here, and ask for comments.” “There is a setting in your group's management area that allows you to set whether message archives are available to members only, or to anyone. Currently, only members
of your group can see the messages there.
No I can’t. If it truly is beneath you to join my group, or join my group and immediately quit as has been done on this list, just send me an email and I will send you some material.
In this group you can go here:
/tuning/topicId_78854.html#78854
and review my position that sine waves and points of resolution are pretty much worthless in evaluating a chords degree of consonance.
Small integers are also pretty much useless.
WHY?
Let’s take one of my more consonant chords which has a coefficient of consonance of 0.60952389. It has 1 4 3 4 steps, or (16/15)(5/4)(6/5)(5/4). The integers add up to 60.
(16/15)(5/4)(6/5)(5/4) (16/15)(5/4)(6/5)(5/4).
Now let’s multiply adjacent intervals together over two octaves and see what happens.
(4/3)(3/2)(3/2)(4/3)(4/3)(3/2)(3/2)
Now let’s multiply each of three adjacent intervals together over the same two octaves and see what happens.
(8/5)(15/8)(8/5)(5/3)(8/5)(15/8)
Of course, when you multiply each of four adjacent intervals together over two octaves, you get;
(2/1) (2/1) (2/1) (2/1) (2/1)
No let’s take another one of my chords that has a coefficient of consonance of 0.674157303.
4 3 2 3 (5/4)(6/5)(10/9)(6/5)
The integers add up to 50. This chord is less consonant even though the integers are smaller.
(5/4)(6/5)(10/9)(6/5) (5/4)(6/5)(10/9)(6/5)
Now let’s multiply adjacent intervals together over two octaves and see what happens.
(3/2)(4/3)(4/3)(3/2)(3/2)(4/3)(4/3)
Now let’s multiply each of three adjacent intervals together over the same two octaves and see what happens.
(5/3)(8/5)(5/3)(9/5)(5/3)(8/5)
Of course, when you multiply each of four adjacent intervals together over two octaves, you get;
(2/1) (2/1) (2/1) (2/1) (2/1)
To summarize, for the chord 1 4 3 4 you get a coefficient of consonance of 0.60952389, which is more consonant than the chord 4 3 2 3 which has a coefficient of consonance of 0.674157303. Add up the digits of the fractions that make up 1 4 3 4 and you get 60. For the chord 4 3 2 3 you get 50. Add up the integers of the fractions for all intervals over two octaves, excluding all 2/1 and you get 254 for the more consonant chord 1 4 3 4, and you get 207 for the less consonant chord 4 3 2 3.
Let’s try this again using only the chord in question.
(5/4)(6/5)(10/9)(6/5)
(3/2)(4/3)(4/3)
(5/3)(8/5)
2/1
The integers add up to 93 for the chord 4 3 2 3.
(16/15)(5/4)(6/5)(5/4)
(4/3)(3/2)(3/2)
(8/5)(15/8)
2/1
The integers add up to 116 for the chord 1 4 3 4.
The integers are clearly larger in the more consonant chord and smaller in the less consonant chord. So how often does this happen? More often than not!
So I have concluded that sine waves and the point of resolution cannot be used to measure consonance, and the size of the integers cannot be used to measure consonance. So the question begs, how do you measure consonance? The coefficient of consonance!
Oh, did I forget to point out that you can’t hear the dissonance in the 16/15 interval because it is in consonance with a tone an octave higher. The seven step intervals in 1 4 3 4 are more consonant than the five step intervals in 4 3 2 3. Go ahead and try it by ear if you don’t believe me.
News you can use.
C (9/8) D (10/9) E (6/5) G (5/4) B (16/15) C
C (5/4) E (6/5) G (10/9) A (9/8) B (16/15) C
C (5/4) E (16/15) F (9/8) G (10/9) A (6/5) C
C (10/9) D (9/8) E (16/15) F (5/4) A (6/5) C
Note that the placement of the D is different in the first set of notes than the last set of notes, and that there is a C and an E is in every set of notes. So you cannot use the first set of notes at the same time as the last set of notes. You can only use three systems at a time. But you can jump off one set of notes onto another at C and E. Of course, you can jump from one system’s F G A or B to another system’s F G A or B if both systems have the desired jump off point.
If you follow this procedure, it will be impossible to play a dissonant interval. Note that you can also delete a note at any time by multiplying together adjacent intervals.

So Three, Part 2

🔗Joseph Bernard <bjosephmex@...>

🔗Carl Lumma <carl@...>