Analyzing dyadic theories in triads

MikeB>"I'd like to add that I'd be more open to all of the output from these alternative theories, John's and Michael's and everyone else's, if people would start talking more about triads than dyads."

    Firstly, I don't think there IS an efficient way rate my scales so far as triads as NONE of the generators are constant and everything is irregularly tempered. Any ideas how to do this?

   However, at least SCALA has a "chord presence" function.  Igs suggested 27 odd limit as a good boundary for chords to be "reasonable", so I used that.  I also used an error boundary of 8 cents (so the chords good be as close or closer in accuracy to JI than 12TET).

 The chords Scala gave for the 27 odd-limit within 8-cents search includes 430!!! chords (of course, this includes dyads, tetrad, etc.).

  But here are some of those chords that are triads fitting within the 2/1 octave:
3:4:5
4:5:6
5:6:8
5:6:9
6:8:9
6:7:9
6:8:9
6:9:10
6:8:11
6:10:15
8:9:12
8:11:12
9:11:12
9:11:15
10:12:15
10:11:15
11:12:14
12:14:18
12:15:16
12:18:20
13:14:21
14:15:20
14:15:21
14:20:21
14:21:25
15:16:18
15:18:20
15:20:22
16:17:20
18:22:27
19:23:27

    Far as triads, my scale includes the usual 4:5:6

--- On Sat, 3/19/11, Mike Battaglia <battaglia01@...> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Re: A dyadic analysis of EDOs 4 to 24
To: tuning@yahoogroups.com
Date: Saturday, March 19, 2011, 8:42 PM

On Sat, Mar 19, 2011 at 11:31 PM, cityoftheasleep

<igliashon@...> wrote:

>

> Hi John,

>

> I did this same task a while ago, except that I included intervals in the 2nd octave as well, and used slightly more tolerance in what I consider "good", such that I would add the following intervals to your list:

> 3/1, 5/2, 7/2, 7/3, 9/4, 10/3, 11/3, 11/4, 11/5, 11/9, 12/5, 13/4, 13/5, 13/6, and 15/4 (I may have forgotten a few). This definitely alters the gamut. Also, I allowed a broader tolerance of up to 8 or 9 cents (nothing too rigorously-defined, as different ratios seem to vary in their sensitivity to mistuning). If you like I can post what I came up with, but it will also be available in my upcoming e-book.

How upcoming is it?

I'd like to add that I'd be more open to all of the output from these

alternative theories, John's and Michael's and everyone else's, if

people would start talking more about triads than dyads. Or preferably

triads with the root being doubled down an octave, which I guess are

tetrads. I just don't care about dyadic music, and you can take a lot

of "good" dyads and smush them into a chord that sounds terrible.

-Mike

MikeB>"I'd like to add that I'd be more open to all of the output from these alternative theories, John's and Michael's and everyone else's, if people would start talking more about triads than dyads."

    Firstly, I don't think there IS an efficient way rate my scales so far as triads as NONE of the generators are constant and everything is irregularly tempered. Any ideas how to do this?

   However, at least SCALA has a "chord presence" function.  Igs suggested 27 odd limit as a good boundary for chords to be "reasonable", so I used that.  I also used an error boundary of 8 cents (so the chords good be as close or closer in accuracy to JI than 12TET).

 The chords Scala gave for the 27 odd-limit within 8-cents search includes 430!!! chords (of course, this includes dyads, tetrad, etc.).

  But here are some of those chords that are triads fitting within the 2/1 octave:
3:4:5
4:5:6
5:6:8
5:6:9
6:8:9
6:7:9
6:8:9
6:9:10
6:8:11
6:10:15
8:9:12
8:11:12
9:11:12
9:11:15
10:12:15
10:11:15
11:12:14
12:14:18
12:15:16
12:18:20
13:14:21
14:15:20
14:15:21
14:20:21
14:21:25
15:16:18
15:18:20
15:20:22
16:17:20
18:22:27
19:23:27

    Far as triads, my scale includes the usual 4:5:6

--- On Sat, 3/19/11, Mike Battaglia <battaglia01@...> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Re: A dyadic analysis of EDOs 4 to 24
To: tuning@yahoogroups.com
Date: Saturday, March 19, 2011, 8:42 PM

On Sat, Mar 19, 2011 at 11:31 PM, cityoftheasleep

<igliashon@...> wrote:

>

> Hi John,

>

> I did this same task a while ago, except that I included intervals in the 2nd octave as well, and used slightly more tolerance in what I consider "good", such that I would add the following intervals to your list:

> 3/1, 5/2, 7/2, 7/3, 9/4, 10/3, 11/3, 11/4, 11/5, 11/9, 12/5, 13/4, 13/5, 13/6, and 15/4 (I may have forgotten a few). This definitely alters the gamut. Also, I allowed a broader tolerance of up to 8 or 9 cents (nothing too rigorously-defined, as different ratios seem to vary in their sensitivity to mistuning). If you like I can post what I came up with, but it will also be available in my upcoming e-book.

How upcoming is it?

I'd like to add that I'd be more open to all of the output from these

alternative theories, John's and Michael's and everyone else's, if

people would start talking more about triads than dyads. Or preferably

triads with the root being doubled down an octave, which I guess are

tetrads. I just don't care about dyadic music, and you can take a lot

of "good" dyads and smush them into a chord that sounds terrible.

-Mike