Re: [tuning] Strictly Proper/All Prime Scale Correction: Re: Dantonicity

Jacky Ligon wrote,

> There seems to have been some kind of mistake about the ratios used
in the complete scale, so I'll clarify them here

Yes, that's different than what's up at the Tuning Lab -- the two
examples have identical 10-tone subsets of the 12 note set you give
here: 1/1 19/17 13/11 29/23 7/5 3/2 11/7 5/3 23/13 13/7 2/1. What are
the specific scales that you are actually using on the two examples?
Is this 10-tone scale a typo?

> It is probable that since you didn't have all the ratios, it might
be why your results are different from that of Scala.

Yes, but as far as propriety is concerned, you'd only be interested in
the results of the specific scales or subsets that you are using, not
the whole 12 note mapping (as I'm assuming your not considering the
whole to be a "scale").

> I would like to kindly request that you show me how to do the above
analysis. I can see that you have modally transposed the original
scale to each successive row. Explain the "overlaps". And most
importantly - how do I interpret the data? What am I looking for?

I'll give it a go... try looking at each column as a distinct interval
class; here you'd have 2nds, 3rds, 4ths, 5ths, 6ths, 7ths, 8ths, 9ths,
and 10ths:

193 289 401 583 702 782 884 988 1072
97 209 390 509 590 692 795 879 1007
112 293 413 493 595 699 782 911 1103
181 301 381 483 586 670 799 991 1088
119 200 302 405 489 617 810 907 1019
81 182 286 370 498 691 787 899 1081
102 205 289 418 610 707 819 1000 1119
103 187 316 508 605 717 898 1018 1098
84 212 405 501 614 795 914 995 1097
128 321 418 530 711 830 911 1013 1116
193 289 401 583 702 782 884 988 1072

If I were poking around on my own and came upon this 10-tone (Tuning
Lab) scale of 1/1 19/17 13/11 29/23 7/5 3/2 11/7 5/3 23/13 13/7 2/1, I
would probably look at it as a 1, 2, 3, 4, #5, #6, #7, 8, 9, 10, 11...
and certainly in a general sense as having a two step size
cardinality, and therefore a 8L 2s LssLssssss step structure (where L
and s simply mean large and small in a generalizes whole and half
sense). Looking at it this way, you can see that you have a plethora
of ambiguities: See how only the major 10th and the minor 2nd are
truly distinct... how a 2=b3, 3=b4, 4=b5, etc.,... the ambiguity
spread across the #5, 6, and b7... the #5 and #6 noticeably larger
than the b6 and b7?

For much more on "propriety" and "efficiency," try checking the
archives. And definitely keep asking questions! I think this helps
everyone, certainly me anyway.

> Thanks for analyzing this today, it helped me to realize that the
full scale may not be posted correctly.

Remember it's relevant in this case to distinguish between larger
sets, or total complexes of intervals, and actual "scales."

As far as the Scala questions go, I'm afraid you'll have to wait for
someone else to jump in, as I've never used it and am not familiar
enough with it... I'm sure someone else will jump in and clear it up
for you though.

ds

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:
> Jacky Ligon wrote,
>
> > There seems to have been some kind of mistake about the ratios
used
> in the complete scale, so I'll clarify them here
>
> Yes, that's different than what's up at the Tuning Lab -- the two
> examples have identical 10-tone subsets of the 12 note set you give
> here: 1/1 19/17 13/11 29/23 7/5 3/2 11/7 5/3 23/13 13/7 2/1. What
are
> the specific scales that you are actually using on the two examples?
> Is this 10-tone scale a typo?

Dan,

Forgive me for not making this more apparent. I have no clue how the
values for the 12 Pitch Chromatic scale became corrupted. And you are
right, I should have been more specific about the details, because as
I describe my musical examples being in a major and minor diatonic
scales - I can see that it would have been far better to show the
ratios for the modes used. So again here's the chromatic scale values:

0: C 1/1 0.000 unison, perfect prime
1: C# 31/29 115.458
2: D 19/17 192.558
3: D# 13/11 289.210
4: E 29/23 401.303
5: F 17/13 464.428
6: F# 7/5 582.512 septimal tritone
7: G 3/2 701.955 perfect fifth
8: G# 11/7 782.492 undecimal augmented fifth
9: A 5/3 884.359 major sixth
10: A# 23/13 987.747
11: B 13/7 1071.702 16/3-tone
12: C 2/1 1200.000 octave

And here are the 2 modes used in my musical examples:

Major Scale: 1/1, 19/17, 29/23, 17/13, 3/2, 5/3, 13/7, 2/1
Minor Scale: 1/1, 19/17, 13/11, 17/13, 3/2, 11/7, 23/13, 2/1

>
> Yes, but as far as propriety is concerned, you'd only be interested
in
> the results of the specific scales or subsets that you are using,
not
> the whole 12 note mapping (as I'm assuming your not considering the
> whole to be a "scale").
>

A chromatic scale of which the 2 above modes are subsets. Many times
I'll create a chromatic scale with 12 or more pitches to the octave,
and derive modal patterns from the overall scale tuning - and I seem
to often prefer many varieties of 8 tone scales. The goal of this
experiment, I guess was to hear how the major and minor diatonic
modes derived from this chromatic scale would sound in a musical
context.

>
> Remember it's relevant in this case to distinguish between larger
> sets, or total complexes of intervals, and actual "scales."

Yes, a point well taken, and a serious omission on my part.

Thanks,

Jacky Ligon

Jacky Ligon wrote,

> I describe my musical examples being in a major and minor diatonic
scales

OK, neat, I think I got it all now. Does Joseph Pehrson know about the
mislabeled Tuning Lab examples yet -- Joe?

Here's a couple of quick analytical type ruminations for whatever
they're worth... I think that the 1/1 19/17 29/23 17/13 3/2 5/3 13/7
2/1 all prime major scale, with its near 4:5:6:7 V, could be said to
most resemble (at it's simplest interpretation) some variation of a:

5/3-------5/4------15/8
\ / \ /|\
\ / \ / | \
\ / \ /21/16\
\ / \ / ,' `. \
1/1-------3/2'-----`9/8

The 1/1 19/17 13/11 17/13 3/2 11/7 23/13 2/1 all prime minor -- ?
Though once again, with it's nearly septimal minor sevenths, probably
something on the order of this 7-limit scale:

14/9------7/6-------7/4------21/16
`. ,' `. ,' `.
`1/1'-----`3/2'-----`9/8

However, I personally really like an odd sort of 'three plane'
interpretation that substitutes an 11/7 for the 14/9 (1/1 9/8 33/28
21/16 3/2 11/7 7/4 2/1) better than the 7-limit interpretation of this
for your all prime minor:

11/7--------------33/28

,7/4.-------------21/16
,' `. ,' `.
1/1'-------------`3/2'-------------`9/8

Though I'm just dying to hitch up those poor disembodied 8:11s --
forgive me...

11/7.------------,33/28
`. , ' `.
,7/4.-------------21/16
,' `. ,' `.
1/1'-------------`3/2'-------------`9/8

Oh, what the hell -- might as well try and milk that phantom
12:14:18:21 for all its got!

11/7.------------,33/28
/ `. , ' / `.
/ ,7/4.--------/----21/16
/ ,' `. / ,' `.
1/1'-------------`3/2'-------------`9/8

ds

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:

http://www.egroups.com/message/tuning/12508

> Jacky Ligon wrote,
>
> > I describe my musical examples being in a major and minor diatonic
> scales
>
> OK, neat, I think I got it all now. Does Joseph Pehrson know about
the mislabeled Tuning Lab examples yet -- Joe?
>

Yes! I did read about it, but I am right in the middle of a couple
of other things. (I actually had to do a little "work work" today,
drat...) Am I to assume that the correct ratios are listed in this
post #12508...(??)

Is there a "breakdown" with the appropriate "cents value, etc." in a
post here... or, could you please send me updated text for the
experiment, Jacky??

I'm right in the middle of a big "bulk mail" project for our
composers group as well, so may be slightly more "incommunicato" than
usual. (What a break for y'all!)
__________ ____ ___ __ _
Joseph Pehrson

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:

Dan,

Hi!

I want to thank you profusely for analyzing and latticing the prime
scale. I would like to ask if it is appropriate to apply the kind of
analysis to the "overlapping" properties of the diatonic scale
degrees that you demonstrated yesterday with the modal grid? Perhaps
working with this as an example, I can grasp better the idea.

I would like to state that this type of scale is something that is
quite a bit off the beaten trail for me - something kind of new. The
primary scales that I'm most familiar with, in a compositional sense,
are much more oriented/derived from the harmonic series . When I was
confronted with the question of "what may I contribute to our Tuning
Lab?", something came to mind that I remember reading that Varese
said: "I don't write experimental music". Which I think I remember
him meaning, that by the time the music is written, the
experimentation is long over. Definitely an idea that resonates with
me, because way before I record one midi or audio track, I have made
great effort to internalize the tuning that I'm working with, by
improvising and trying out allot of different timbres. But there is
always that moment when you try something new - when you are hearing
a unique scale for the first time, that is the "experimental" phase
of a composition. This is the essence of what I was trying to
demonstrate with this first trip to the Lab and the All Prime Scale.
At first I wasn't even sure if were possible to find ratios that
would meet the two criteria, but was pleased to find that there are a
plenty of them that would work. Sometimes a huge difficulty that I
have about considering something "experimental" is that I've had so
many years of satisfying and successful compositional experiences
working within Just Intonation, that I find myself often without -
and perfectly empty of - anything to prove in an experimental sense.
The vocabulary is ingrained, to the point that I may take it for
granted, and not see it as an experiment any longer - even to the
point of accepting and using compositionally, many JI phenomenon that
might not rest easy on all ears. But this week, from the listening
test that we had around your composition, I am compelled toward
probing into the questions that arise from the experiencing Neutral
intervals.

Infinite Thanks,

Jacky Ligon

>
> Here's a couple of quick analytical type ruminations for whatever
> they're worth... I think that the 1/1 19/17 29/23 17/13 3/2 5/3 13/7
> 2/1 all prime major scale, with its near 4:5:6:7 V, could be said to
> most resemble (at it's simplest interpretation) some variation of a:
>
> 5/3-------5/4------15/8
> \ / \ /|\
> \ / \ / | \
> \ / \ /21/16\
> \ / \ / ,' `. \
> 1/1-------3/2'-----`9/8
>
> The 1/1 19/17 13/11 17/13 3/2 11/7 23/13 2/1 all prime minor -- ?
> Though once again, with it's nearly septimal minor sevenths,
probably
> something on the order of this 7-limit scale:
>
> 14/9------7/6-------7/4------21/16
> `. ,' `. ,' `.
> `1/1'-----`3/2'-----`9/8