A few more words

Hi, again,

Just to add that if somebody would like to redesign the 12TET scale but he doesn´t know how to work with fractional powers of 2 and besides he is a skilled man on progressions, the right solution is to avail the information contained in the Progression of Musical Cells.

Perhaps I am going to be a blind man because I don´t see the points of Mike.

Thanks

Mario Pizarro

piagui@...

Lima, January 08, 2010--- 10:00 p.m.

__________ Información de ESET NOD32 Antivirus, versión de la base de firmas de virus 4755 (20100108) __________

ESET NOD32 Antivirus ha comprobado este mensaje.

http://www.eset.com

The points are that when you ask us here to judge "how good" your scale is,
the usual approach to take is that we see how accurately it represents
common intervals that we'd like to use, such as 3/2 and 5/4, and weigh that
against how consistent it is, what intervals are tempered out, and so on.

This scale is about as accurate with those as is 12-tet. At the most there
is a 2 cent deviation or so. It is about as good as representing those as
12-tet is.

If you would like to see examples of tunings that differs significantly from
12-tet in its representing of those intervals, search the archives for some
of the well-temperaments that have been used here, or perhaps string up 12
notes of 1/4 comma meantone. Both of those have a more accurate 5/4 and a
less accurate 3/2. Or perhaps you could play around with George Secor's 17
note well temperament, which I believe has a less accurate 5/4 but a more
accurate 7/6 and 9/7.

All of these tunings differ drastically from 12-tet, both audibly and in
theory. Yours is, in comparison, very close to 12-tet. That is the most
honest assessment that I think anyone here can give you about it.

-Mike

On Fri, Jan 8, 2010 at 9:59 PM, Mario Pizarro <piagui@...> wrote:

>
>
> Hi, again,
>
> Just to add that if somebody would like to redesign the 12TET scale but he
> doesn´t know how to work with fractional powers of 2 and besides he is a
> skilled man on progressions, the right solution is to avail the information
> contained in the Progression of Musical Cells.
>
> Perhaps I am going to be a blind man because I don´t see the points of
> Mike.
>
> Thanks
>
> Mario Pizarro
>
> piagui@...
>
> Lima, January 08, 2010--- 10:00 p.m.
>
>
> __________ Información de ESET NOD32 Antivirus, versión de la base de
> firmas de virus 4755 (20100108) __________
>
> ESET NOD32 Antivirus ha comprobado este mensaje.
>
> http://www.eset.com
>
>

Mike B> "The points are that when you ask us here to judge "how good" your scale
is, the usual approach to take is that we see how accurately it
represents common intervals that we'd like to use, such as 3/2 and 5/4,
and weigh that against how consistent it is, what intervals are
tempered out, and so on."

On that note....

I'd appreciate an analysis of the following scale...particularly any mathematical phenomena (IE consistency, common intervals, possible chords, etc.) and/or possible uses plus any other opinions.

The scale is
10/9
5/4
11/8
3/2
5/3
11/6
2/1

Note that I have no clue if this scale has already been created...I simply came up with it trying to accomplish the following (in a 7-tone scale)

A) Imitate 7TET in keeping the minimum ratio between any two root notes maximized (that minimum ratio here is 12/11, 7TET only beats it by a little with a slightly larger 11/10 minimal ratio between any two notes). This would, in theory, minimize harmonic entropy if the instrument was a pure sine wave.

B) Imitate JI in trying to keep low-numbered ratios and maximize periodicity...unlike 7TET.

Thanks, Michael

________________________________
From: Mike Battaglia <battaglia01@...>
To: tuning@yahoogroups.com
Sent: Fri, January 8, 2010 9:19:56 PM
Subject: Re: [tuning] A few more words

The points are that when you ask us here to judge "how good" your scale is, the usual approach to take is that we see how accurately it represents common intervals that we'd like to use, such as 3/2 and 5/4, and weigh that against how consistent it is, what intervals are tempered out, and so on.

This scale is about as accurate with those as is 12-tet. At the most there is a 2 cent deviation or so. It is about as good as representing those as 12-tet is.

If you would like to see examples of tunings that differs significantly from 12-tet in its representing of those intervals, search the archives for some of the well-temperaments that have been used here, or perhaps string up 12 notes of 1/4 comma meantone. Both of those have a more accurate 5/4 and a less accurate 3/2. Or perhaps you could play around with George Secor's 17 note well temperament, which I believe has a less accurate 5/4 but a more accurate 7/6 and 9/7.

All of these tunings differ drastically from 12-tet, both audibly and in theory. Yours is, in comparison, very close to 12-tet. That is the most honest assessment that I think anyone here can give you about it.

-Mike

On Fri, Jan 8, 2010 at 9:59 PM, Mario Pizarro <piagui@ec-red. com> wrote:

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> >
>
>>
>
>>
>
>>
>
>Hi, again,
>
>Just to add that if somebody would like to redesign
>the 12TET scale but he doesn´t know how to work with fractional powers of 2 and
>besides he is a skilled man on progressions, the right solution is to avail the
>information contained in the Progression of Musical Cells.
>
>Perhaps I am going to be a blind man because I
>don´t see the points of Mike.
>
>Thanks
>
>Mario Pizarro
>
>piagui@ec-red. com
>
>Lima, January 08, 2010--- 10:00
>p.m.
>
>>__________ Información de ESET NOD32 Antivirus, versión de la base de firmas de virus 4755 (20100108) __________
>
>>ESET NOD32 Antivirus ha comprobado este mensaje.
>
>http://www.eset. com
>

Hi Michael !

This scale is one of the 36 permutations of Ptolemy's Diatonon Homalon,
described in John Chalmers' "Divisions of the Tetrachord". It has well-balanced 12/11 positions,
and on that point can be considered as among the most circular of Homalon's heptatonic permutations.
These are 24, of several combinatory types between Bayati, Rast, or Mohajira and this one is of a Bayati type.

That's a lovely scale, Greek by definition but it reminds me of some African or Burmese harp scales.
But I would not say it is a "7-edo imitation", not even a quasi 7-edo,
simply because has two 12/11, and those can always be heard as semitones.
That's the big difference with 11/10, that is heard mainly as a whole tone.

Look at it that way :

54 : 60 : 66 : 72 : 80 : 90 : 99 : that's a neutral-diatonic major scale, with Bayati mode from 66.

I found that between this type of scale, that has two 12/11, and 7 quasi-edos there are at least 3 more steps :

1. absence of 9/8 interval : this would be easily done here by changing the 9/8 into a "10/9" :
54 : 60 : 66 : 72 : 80 : 89 : 99 (it even improves the Bayati mode)

2. reduction to only one 12/11 - by changing 99 to 98 :
54 : 60 : 66 : 72 : 80 : 89 : 98 (hear the difference : it looses much of its arabian mood)

3. not a single 12/11 : by changing here 72 to 145 :
108 : 120 : 132 : 145 : 160 : 178 : 196

10/9
11/9
145/108
40/27
89/54
49/27
2/1

or 72 to 291 :
216 : 240 : 236 : 291 : 320 : 356 : 392

Those have 5 "11/10" and 2 "10/9" (well-balanced L s s s L s s), and no "12/11".
That's one 7 quasi-edo scale structure among several others.

- - - - - - -
Jacques

(Posted by Michael Jan 8 2010 / Digest 6411 :)

> I'd appreciate an analysis of the following scale...particularly > any mathematical phenomena (IE consistency, common intervals, > possible chords, etc.) and/or possible uses plus any other opinions.
>
> The scale is
> 10/9
> 5/4
> 11/8
> 3/2
> 5/3
> 11/6
> 2/1
>
> Note that I have no clue if this scale has already been created...I > simply came up with it trying to accomplish the following (in a 7-> tone scale)
>
> A) Imitate 7TET in keeping the minimum ratio between any two root > notes maximized (that minimum ratio here is 12/11, 7TET only beats > it by a little with a slightly larger 11/10 minimal ratio between > any two notes). This would, in theory, minimize harmonic entropy if > the instrument was a pure sine wave.
>
> B) Imitate JI in trying to keep low-numbered ratios and maximize > periodicity...unlike 7TET.
>
> Thanks, Michael

Jacques,

Interesting, I've messed with scales and ended up simply running into Ptolemy's scales before. Where's a good place to find a collection of these?...the few I've seen are simply delightful and very accessible scales.

>"3. not a single 12/11 : by changing here 72 to 145 :
108 : 120 : 132 : 145 : 160 : 178 : 196"

Now this is definitely an improvement to take into consideration!

The closest ratio here is more like 11/10 and less like 10/9 and more quasi-7EDO than my scale which "only" gets to 12/11 and not the larger/more desirable 11/10 as the smallest interval in the scale.
Also that scale fits pretty closely with the x/27th partials of the harmonic series for the most part and every fraction has a common denominator of 3 (IE 108 = 3 * 36 and 54 = 3 * 18).

Another question: did the scale you mention already exist or did you just manage to come up with it? :-)
I'm definitely going to have to try composing with that one....

Thank you very much for your post...this is immensely helpful. :-)

________________________________
From: Jacques Dudon <fotosonix@...>
To: tuning@yahoogroups.com
Sent: Tue, January 12, 2010 10:54:16 AM
Subject: [tuning] Re:I'd appreciate an analysis of the following scale

Hi Michael !

This scale is one of the 36 permutations of Ptolemy's Diatonon Homalon,
described in John Chalmers' "Divisions of the Tetrachord". It has well-balanced 12/11 positions,
and on that point can be considered as among the most circular of Homalon's heptatonic permutations.
These are 24, of several combinatory types between Bayati, Rast, or Mohajira and this one is of a Bayati type.

That's a lovely scale, Greek by definition but it reminds me of some African or Burmese harp scales.
But I would not say it is a "7-edo imitation", not even a quasi 7-edo,
simply because has two 12/11, and those can always be heard as semitones.
That's the big difference with 11/10, that is heard mainly as a whole tone.

Look at it that way :

54 : 60 : 66 : 72 : 80 : 90 : 99 : that's a neutral-diatonic major scale, with Bayati mode from 66.

I found that between this type of scale, that has two 12/11, and 7 quasi-edos there are at least 3 more steps :

1. absence of 9/8 interval : this would be easily done here by changing the 9/8 into a "10/9" :
54 : 60 : 66 : 72 : 80 : 89 : 99 (it even improves the Bayati mode)

2. reduction to only one 12/11 - by changing 99 to 98 :
54 : 60 : 66 : 72 : 80 : 89 : 98 (hear the difference : it looses much of its arabian mood)

3. not a single 12/11 : by changing here 72 to 145 :
108 : 120 : 132 : 145 : 160 : 178 : 196

10/9
11/9
145/108
40/27
89/54
49/27
2/1

or 72 to 291 :
216 : 240 : 236 : 291 : 320 : 356 : 392

Those have 5 "11/10" and 2 "10/9" (well-balanced L s s s L s s), and no "12/11".
That's one 7 quasi-edo scale structure among several others.

- - - - - - -
Jacques

(Posted by Michael Jan 8 2010 / Digest 6411 :)

I'd appreciate an analysis of the following scale...particularl y any mathematical phenomena (IE consistency, common intervals, possible chords, etc.) and/or possible uses plus any other opinions.
>
>
>The scale is
>10/9
>5/4
>11/8
>3/2
>5/3
>11/6
>2/1
>
>
>Note that I have no clue if this scale has already been created...I simply came up with it trying to accomplish the following (in a 7-tone scale)
>
>
>A) Imitate 7TET in keeping the minimum ratio between any two root notes maximized (that minimum ratio here is 12/11, 7TET only beats it by a little with a slightly larger 11/10 minimal ratio between any two notes). This would, in theory, minimize harmonic entropy if the instrument was a pure sine wave.
>
>
>B) Imitate JI in trying to keep low-numbered ratios and maximize periodicity. ..unlike 7TET.
>
>
>Thanks, Michael

Hi Michael,

I have analyses of several of Ptolemy's scales
in a webpage dedicated to exactly that, and also
in each of the webpages of the ancient Greek genera:

http://tonalsoft.com/enc/p/ptolemy.aspx
http://tonalsoft.com/enc/d/diatonic-genus.aspx
http://tonalsoft.com/enc/c/chromatic-genus.aspx
http://tonalsoft.com/enc/e/enharmonic-genus.aspx

The pages about the genera also compare Ptolemy's
scales to those of other well-known Greek theorists.

But of course there are many, many more.
Probably the most exhaustive reference to Ptolemy's
scales is _Divisions of the Tetrachord_, by our
very own group member John Chalmers, and now available
as a set of free downloads:

http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/index.html

PS: One other thing i want to point out here is
something i mention on my website:

The Greek words _sytonon_ and _malakon_ are
often rendered in English as respectively "intense"
and "soft". But in the context of tuning theory,
where the Greeks always referred to the
stretched strings of a lyre, they really should
be translated as "tense" and "relaxed".

The _diatonon syntonon_ or "tense diatonic" was
so named by Ptolemy because the note above the
bottom of the tetrachord (_parhypate_) was the
highest _parhypate_ used in any of his diatonics
with the exception of that in the _homalon_ or
"even", which is also often translated poorly as
"smooth". The name of the syntonic-comma comes
from a comparison of this "tense diatonic" with
pythagorean tuning.

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Jacques,
>
> Interesting, I've messed with scales and ended up simply running into Ptolemy's scales before. Where's a good place to find a collection of these?...the few I've seen are simply delightful and very accessible scales.

correction of a typo:

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:

> The Greek words _sytonon_ and _malakon_ are
> often rendered in English as respectively "intense"
> and "soft". But in the context of tuning theory,
> where the Greeks always referred to the
> stretched strings of a lyre, they really should
> be translated as "tense" and "relaxed".

Unfortunately the main word in that whole paragraph
is the one i mistyped: it should be _syntonon_.

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

Yes, I agree, Plolemy's scales are wonderful. You find them, as I said, in John Chalmers's book, and certainly in the Scala archive.
I didn't mean to say it was an improvement, these were just examples of how you can mute from your scale structure
(neutral diatonic) to another (7 quasi-edo), since you were interested in the the 7-edo aspect - and also examples of the perceptive importance of the number, in such scales, of the 12/11-neutral second type of interval, which act as semitones.
It's a scale I just made up, but I have hundreds of those because I worked a lot many years ago, on scales classification, and specially on the different classes of neutral diatonics, that are a huge part of the traditional folk tunings from the wole world.
If you look in the Scala archive at "dudon-thai", you will find some 7 quasi-edo model of a different scale structure, made up of 6 "11/10" type of interval for only one "10/9". Do you hear any difference between those and this two "10/9"
(108 : 120 : 132 : 145 : 160 : 178 : 196) ?
- - - - - - -
Jacques

> Jacques,
> Interesting, I've messed with scales and ended up simply running > into Ptolemy's scales before. Where's a good place to find a > collection of these?...the few I've seen are simply delightful and > very accessible scales.
>
> >"3. not a single 12/11 : by changing here 72 to 145 :
> 108 : 120 : 132 : 145 : 160 : 178 : 196"
>
> Now this is definitely an improvement to take into consideration!
>
> The closest ratio here is more like 11/10 and less like 10/9 and > more quasi-7EDO than my scale which "only" gets to 12/11 and not > the larger/more desirable 11/10 as the smallest interval in the scale.
> Also that scale fits pretty closely with the x/27th partials of the > harmonic series for the most part and every fraction has a common > denominator of 3 (IE 108 = 3 * 36 and 54 = 3 * 18).
>
> Another question: did the scale you mention already exist or did > you just manage to come up with it? :-)
> I'm definitely going to have to try composing with that one....
>
> Thank you very much for your post...this is immensely helpful. :-)