Re: [MMM] JI question: Marcel's JI

Marcel>"53tet tempers the difference between 32/27 and 1215/1024, 128/81 and 405/256, 256/243 and 135/128, etc. This way you lose out important information. (not to mention that you'd have to do JI to get this kind of information at first)"

    Fair enough, you indeed need to re-interpret those ratios as nearby JI ratios to get that information back.  But, my point...is the tempered/"slightly impure" ratios are often close enough to JI ratios you can easily deduce what JI ratios they can best act as.

>"The thing is that not all major thirds are pure as 5/4. In many situations to play a certain major third as 5/4 would be to play it out of tune as the music calls for a 81/64 for instance in that function."

   In what-cases/why would the 81/64 be preferred?  Does it, bu chance, have anything to do with making the tonic and dominant chords (IE those used for relaxing/resolving parts) more pure and certain others less pure to establish a consistent/predictable relationship for where
resolving parts of the scale are?

--- On Sun, 2/27/11, m.develde@... <m.develde@gmail.com> wrote:

From: m.develde@... <m.develde@...>
Subject: Re: [MMM] JI question
To: MakeMicroMusic@yahoogroups.com
Date: Sunday, February 27, 2011, 8:09 AM

Hi Michael,

First of all, if you're stacking 2 5/4 major thirds to get a 25/16 then

you're not doing real Just Intonation anymore, but rather some out of tune

rational intonation which has been wrongly labelled "just intonation" in the

past.

And no, temperaments do not offer insight into the functioning of music.

At best, take 53tet and compare it to my JI in a limited form for common

practice music (just a chain of fifths and a single other chain of fifths

5/4 relative to it).

53tet tempers the difference between 32/27 and 1215/1024, 128/81 and

405/256, 256/243 and 135/128, etc.

This way you lose out important information. (not to mention that you'd have

to do JI to get this kind of information at first)

On top of that, 53tet does not sound as good as JI.

etc etc etc.

Furthermore, you seem to think that my JI has issues with getting ratios

pure?

It does not in any way whatsoever.

The thing is that not all major thirds are pure as 5/4.

In many situations to play a certain major third as 5/4 would be to play it

out of tune as the music calls for a 81/64 for instance in that function.

The tonal side of music comes from the underlying mathematics, not the other

way around.

-Marcel

From: Michael

Sent: Sunday, February 27, 2011 4:59 PM

To: MakeMicroMusic@yahoogroups.com

Subject: Re: [MMM] JI question

Marcel>"Also, my JI gives deep insight into the functioning of music and is

a composition aid if understood well enough. Temperaments offer no such

thing."

Isn't it fair enough to say temperaments can be explained as rounding

between fundamentals of JI IE if you take a tempered 5/4 and another

tempered 5/4 to get the nearby 14/9 instead of the 25/16 you get from 5/4 *

5/4...you are getting "more ratios near perfectly Just...instead of less

ratios that are exactly/perfectly Just?

How do you get around this issue? How do you get as many ratios

"virtually perfect" as possible without tempering? And, if it involves

higher-limit fractions that form together to make lower-limit ones,

shouldn't you be calling it Rational Intonation rather than Just Intonation?

http://tonalsoft.com/enc/r/rational-intonation.aspx

Hi Michael,

Here a very simple example where 81/64 is preferred.
Play this chord: 1/1 3/2 9/4 27/8 4/1 81/16

For another clear musical example see Drei Equale no1 (pdf in my folder "Marcel" on MMM files) and the chord progression between the 2 diminished chords (middle of the song).
(that particular chord progression is a clear comma pump without solution in "classic 5-limit JI")
But if you look closer, there are many more Pythagorean chords throughout the song.

It has to do with pure 3/2 fifths.
The tuning structure music uses then indeed generates relaxing points and points with tension.
The dominant in true major is 3/2 15/8 9/4, which is "relaxing", but adding a 7th by 8/3 makes it tension. (there's more going on but won't get into that now)
In true minor (rarer than you'd think in common practice it looks like to me now) the dominant major (of harmonic minor mode) is for instance:
15/16 45/32 15/8 64/27 -> 5/8 3/2 15/8 5/2
and then to the relative major 1/1 3/2 2/1 5/2 for instance.
But see the 15/16 32/27 45/32 dominant above, seen from 15/16 it is: 1/1 512/405 3/2, much tension.
There are 3 different major triads in my JI, 1/1 5/4 3/2 (root from the base chain of fifths), 1/1 81/64 3/2 (root from both chains of fifths possible) and 1/1 512/405 3/2 (root from the 5/4 chain of fifths)
Similarly there are 3 different minor triads in my JI: 1/1 6/5 3/2 (root from the 5/4 chain of fifths), 1/1 32/27 3/2 (root from both chains of fifths possible) and 1/1 1215/1024 3/2 (root from base chain of fifths).
This is for almost all common practice music. Once we add the 7th harmonic chain of fifths many more possibilities arise but I won't get into that now (I'll demonstrate it soon though)

-Marcel

From: Michael
Sent: Sunday, February 27, 2011 5:16 PM
To: MakeMicroMusic@yahoogroups.com
Subject: Re: [MMM] JI question: Marcel's JI

>"The thing is that not all major thirds are pure as 5/4. In many situations >to play a certain major third as 5/4 would be to play it out of tune as the >music calls for a 81/64 for instance in that function."

In what-cases/why would the 81/64 be preferred? Does it, bu chance, have anything to do with making the tonic and dominant chords (IE those used for relaxing/resolving parts) more pure and certain others less pure to establish a consistent/predictable relationship for where
resolving parts of the scale are?