Re: propriety

>I think there's more to it than propriety, as my favourite "Blues Scale" as
>outlined on my website was designed to work melodically, but is improper.
>In that case, it sounds like either a 5-note scale with "quartertone"
>inflections, or an uneven 7-note scale, or an even more uneven 8-note scale
>if you have good pitch discrimination.

>Although I do think propriety is a more reasonable property than maximal
>evenness, I think it's too restrictive. My favorite example over the years
>has been the Pythagorean diatonic scale, which is not proper.

Propriety is the most basic measurement of accousto-scalar effects, the first thing you ask. It isn't meant to decide the value of a scale, at least not in so crude a way as these posts seem to assume.

Propriety also isn't a property of scales, it is a property of the mental map that a listener uses to extract a certain type of information from an audio stimulus. Only if you assume that the listener is doing the most efficient extraction possible, and that the stimulus is strictly tuned in the given scale, can you use propriety as a property of the scale.

Even then it will apply only to sensations that arise from the tracking of scale degrees. Sensations related to absolute pitch, and any myriad of other things, are an entirely different affair:

Graham, you say your scales work melodically despite being improper. Work melodically they might, but this need not include melodic modulation per se, and I hear very little of it in the examples on your web site. What melodic modulation I do hear, I hear as subsets of a diatonic scale, which is the only map I have learned as a listener. So my experience jives perfectly with Rothenberg's theory.

-C.

>I have advocated a weaker version of propriety which only enforces the
>non-contradiction between generic size and specific size when it involves
>consonant intervals.

I like this a lot. Much as the drone works in Indian music, harmony can work in western music --- when a harmony sounds, dissonant notes tend to be heard as passing tones, measured against the VF (and probably harmonics of the VF) of the chord wether or not they participate in a proper mapping.

So I look at this version as a way of applying propriety to scales that may be used harmonically. As long as there's enough acoustic material to establish a VF consistently fixed to scale degrees, the other notes don't matter.

-C.

I wrote,

>>I have advocated a weaker version of propriety which only enforces the
>>non-contradiction between generic size and specific size when it involves
>>consonant intervals.

Carl Lumma wrote,

>I like this a lot. Much as the drone works in Indian music, harmony can work in western music --- when a harmony sounds, dissonant notes tend to be heard as passing tones, measured against the VF (and probably harmonics of the VF) of the chord wether or not they participate in a proper mapping.

>So I look at this version as a way of applying propriety to scales that may be used harmonically. As long as there's enough acoustic material to establish a VF consistently fixed to scale degrees, the other notes don't matter.

How about the idea that every consonant interval is always subtended by the same number of scale degrees? I think that's what Kraig Grady calls "constant structures" (after Erv Wilson), and it's implied by rule (2) for generalized diatonicity according to my paper.

Carl Lumma (238.5) wrote:

> Graham, you say your scales work melodically despite being
> improper. Work melodically they might, but this need not
> include melodic modulation per se, and I hear very little of
> it in the examples on your web site. What melodic modulation
> I do hear, I hear as subsets of a diatonic scale, which is
> the only map I have learned as a listener. So my experience
> jives perfectly with Rothenberg's theory.

The scale works *because* it's improper! The contrast of large and small
intervals has an emotional affect. For the uninitiated, the scale is:

A---------E
\ / \
\ / \
\ / \
\ / \
C---------G---------D
/ \ / \ /
D/-/---\--A/-/---\--E/ /
/ \ / \ /

C D D/ E E/ G A A/ C
4 0 3 1 5 3 1 5 =22
5 1 3 2 6 4 2 6 =29

or see http://www.cix.co.uk/~gbreed/blues.htm

When heard as a 5-note scale, it is proper, so melodic modulation will work
for this mental map. The scale C-D-E/-G-A/-C happens to be very close to
5=. The scale C-D-E-E/-G-A-A/-C is completely improper, and you have to be
very aware of the inequality of the intervals when you play it.

I think it's useful to talk of a "propriety index". This is the ratio of
the largest to the smallest atomic interval in the scale. Atomic intervals
being scale steps, or those intervals that can't be divided. In this case,
the largest atomic intervals are A/-C and E/-G. In just intonation, these
are 7/6 or 267 cents. The smallest intervals are E-E/ and A-A/, which at
36/35 are 49 cents wide. That gives the 7-note scale a propriety index of
5.5. The scale C-D-E/-G-A/-C has an index of 1.3.

Scales tend to get stranger the higher the propriety index gets. Neutral
scales have an index of around 1.3, and so sound ambiguous. This affect can
be lessened by using a non-MOS arrangement. Pythagorean diatonic scales
have an index slightly over 2. 2 may be the crossover between proper and
improper, although I don't think it's as simple as that. Anyway,
Pythagorean scales are good melodically. Perhaps the strongest melodic
scales have an index between 2 and 2.5. 5.5 is probably as high as you can
push it before the scale becomes incomprehensible. Sure enough, a 10-note
major-third MOS scale with an index of 8 is fairly uninteresting. I think
the high index points to this. Such a high propriety index signifies a
dysfunctional scale. But this is a long way from saying that impropriety
itself is a bad thing. Although nobody is saying that any more.

Another thing with my scale above is that, although the largest atomic
intervals are much bigger then the smallest intervals, there are plenty of
intermediate intervals. I think this is good when the propriety index gets
so high, although it contradicts the idea that scales should only have two
different atomic intervals.

>How about the idea that every consonant interval is always subtended by the >same number of scale degrees? I think that's what Kraig Grady calls "constant >structures" (after Erv Wilson), and it's implied by rule (2) for generalized >diatonicity according to my paper.

Yes, this is a good one too. We've discussed it before. Here's something...

s-> scalar interval
a-> acoustic interval
h-> harmonic function

(r)equires
(g)uaranteed by

1. Some s has only one a.
(r) strict propriety
3rds in 4-note symmetric 1.2.1.2

2. Every s has only one a.
(r)(g) equal steps
6tET

3. Some a has only one s.
(g) MOS
3/2 in 7-tone Pythagorean

4. Every a has only one s.
(r)(g) strict propriety
4-note symmetric scale (above)

5. Some s has only one h.
?
3rds are 5-function in meantone

6. Every s has only one h.
?
?

7. Some h has only one s.
?
?

8. Every h has only one s.
?
?

...so maybe a section should be added for "c", consonant intervals.

-C.

>> Graham, you say your scales work melodically despite being
>> improper. Work melodically they might, but this need not
>> include melodic modulation per se, and I hear very little of
>> it in the examples on your web site. What melodic modulation
>> I do hear, I hear as subsets of a diatonic scale, which is
>> the only map I have learned as a listener. So my experience
>> jives perfectly with Rothenberg's theory.
>
>The scale works *because* it's improper! The contrast of large and small
>intervals has an emotional affect.

Sure! This is an example of something that isn't melodic modulation. I've been hounding for 2 years on this list how commatic shifts in melody can be cool, even correct.

>For the uninitiated, the scale is:
>
> A---------E
> \ / \
> \ / \
> \ / \
> \ / \
> C---------G---------D
> / \ / \ /
> D/-/---\--A/-/---\--E/ /
> / \ / \ /

A nifty scale. If you remember the first mail I sent you, back in December...

>>Your website is also very cool. I really like some of the blues scales.

>When heard as a 5-note scale, it is proper, so melodic modulation will work
>for this mental map. The scale C-D-E/-G-A/-C happens to be very close to
>5=.

Right! And I tend to hear 5-note scales as subsets of 7-note scales.

>I think it's useful to talk of a "propriety index". This is the ratio of
>the largest to the smallest atomic interval in the scale. Atomic intervals
>being scale steps, or those intervals that can't be divided. In this case,
>the largest atomic intervals are A/-C and E/-G. In just intonation, these
>are 7/6 or 267 cents. The smallest intervals are E-E/ and A-A/, which at
>36/35 are 49 cents wide. That gives the 7-note scale a propriety index of
>5.5. The scale C-D-E/-G-A/-C has an index of 1.3.

Say, that's a very interesting idea, which I'd never thought of. I'll have to take a look at it tonight.

I'd always imagined two other measures, that could work together, 1. What percent of pitch-class space is filled? 2. What percent of pitch class space is more than singly-filled? It may be best to formulate this measure graphically, rather than worry about which numbers to show. If you take a tonality diamond, and look down the diagonals, you have the pitch classes. One could imagine a graph where each of the pitch classes would be color-coded strips, with overlapping areas florescent orange, or so. A little practice looking at these and the user would probably be able to tell more about the melodic properties of a scale, faster, than anybody else.

>But this is a long way from saying that impropriety itself is a bad thing. >Although nobody is saying that any more.

Who ever said that?

-C.

Carl Lumma wrote,

>I'd always imagined two other measures, that could work together, 1. What
percent of pitch-class space is filled? >2. What percent of pitch class
space is more than singly-filled? It may be best to formulate this measure
>graphically, rather than worry about which numbers to show. If you take a
tonality diamond, and look down the >diagonals, you have the pitch classes.
One could imagine a graph where each of the pitch classes would be
>color-coded strips, with overlapping areas florescent orange, or so. A
little practice looking at these and the user >would probably be able to
tell more about the melodic properties of a scale, faster, than anybody
else.

I don't get it.

>Well I'm just trying to better understand it really... and now that I
>feel that I have some confidence in the definition, I should probably
>go purge the TD archives to get a better handle on what propriety is
>defining _conceptually_. But for the sake of others whom might be
>interested and perhaps just picked up the thread here, I'll ask if
>anyone wants to offer an explanation of what these classes of
>propriety are really saying conceptually: When Paul says that "it
>depends what you're seeking to use propriety for or to discredit about
>it," I'm interested in what its best uses might be, what might
>discredit it, etc.

Dan, if you search the archives for the word, "paraphrase", you should come
across my post "Paraphrase of some Rothenberg" rather quickly (TD 262.14).
If the text doesn't display correctly on your machine, the next issue (263)
has three or four copies of the same post with different formatting. Most
of the stuff in this post is quoted directly from one of Rothenberg's
papers, and it is a section where he attempts to address what propriety
means for the perception of music.

-C.