Blue notes and their "amber" complements

This is a question about informal terminology concerning 7-limit intervals in blues, jazz, rock, country and related musical genres. Also, I'm still not finished with that "fragtime" piano thing in 72-edo I've been working on, but I'm about two-thirds done now. It's actually my first major microtonal composition, so I'm experimenting a lot. I spent hours just trying how to deal with a simple I-vi-ii-V progression and work around the "comma pump" problem.

I've been describing blues minor intervals as "minor-in-major", since they're otonal in nature, having a 7 in the numerator when expressed as JI. I describe all augmented intervals beginning with the fourth by that color now:

1. Blue tritone (aug. fourth) = 7/5
2. Blue semitone/minor second (aug. prime) = 21/20 or 28/27*
3. Blue minor sixth (aug. fifth) = 14/9
4. Blue minor third (aug. second) = 7/6
5. Blue minor seventh (aug. sixth) = 7/4
6. Blue lowered fourth (aug. third) = 21/20
7. Blue lowered octave (aug. seventh) = 63/32 or 35/18
*also, "blue" minor ninth (aug. octave) = 21/10 or 56/27

This applies not only to JI, but extended meantone, Pythagorean, Miracle and so on.

So what would you call _utonal_ 7-limit intervals, the "major-in-minor" tonalities? Since the complement of the color blue is yellow (in the scientific red-blue-green primary color system) or orange (in the older red-blue-yellow scheme), it could be called either. I'll split the difference and call these "amber" notes. I also thought of another name, "Sabawi" (Arabic: ُ؟�ُ؟�ُ؟�ُ؟�ُ؟�), derived from Saba, the maqam that contains a diminished fourth and diminished octave: D Ed F Gb A Bb C Db E F.

So here are the "amber" (or "Sabawi") intervals, the octave-complements of the blue notes above:

1. Amber tritone (dim. fifth) = 10/7
2. Amber major seventh (dim. octave) = 40/21 or 27/14
3. Amber major third (dim. fourth) = 9/7
4. Amber major sixth (dim. seventh) = 12/7
5. Amber tone/major second (dim. third) = 8/7
6. Amber fifth (dim. sixth) = 32/21
7. Amber raised prime (dim. second) = 64/63 or 36/35*
*also, "amber" raised octave (dim. ninth)

Actually, I'm using six colors - black, red, yellow, white, green and blue/cyan - to describe six successive divisions of an ET semitone in 72-equal. Most of these "blue" notes would actually be mapped to a "green" note, since they're two moria flat of an unaltered 12-equal pitch (the "blues" tritone is still "blue").

~D.

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Mike Battaglia wrote:
> Interesting ideas. I like the 'amber' terminology. Why do you refer to > 7-limit utonalities as being "major-in-minor"? Usually the sound that > I hear with a major-in-minor tonality is either a simple major third > over the root of a minor chord, as in the chord D F+ B E A D F#- or an > 81/64 wide third, as in the case of the stacked-third chord D F+ A C+ > E G+ B D+ F#.

A lot of the weird terminology I use out of habit I came up with before I knew the "proper" terminology, so it's all _ad hoc_. I came up with the phrase "minor-in-major" to refer to the use of minor-like intervals in an overall major tonality, with the minor subordinate to the major. I tend to follow Partch in thinking of otonal ratios and their equivalents as "major" (and "augmented") while utonal ratios are "minor" and "dminished". For 7-limit, I calculate otonality/utonality by this formula: for a ratio 3^a * 5^b * 7^c, n = a + 4b + 10c. Or I could just map everything to 31-equal; it's a quick-and-dirty method.

>
> Also, I know everyone thinks of blue notes as being 7-limit intervals, > but those are far from the only blue notes they use when playing the > actual blues. They go up to the 11-limit a lot - 11/8 is used quite a > bit, as is 11/9 as a blue third. Good ol' 6/5 is sometimes used for > that minor third as well. Hell, sometimes they'll even start on 7/6 on > the beginning of a note and bend up to around 5/4 or even 9/7 by the > end of it - which blue note is that? And while 9 times out of ten that > minor 7 is going to be 7/4, they sometimes go even flatter to around > 950 cents, and sometimes go sharper to around 9/5, although the latter > is more common in later, jazz-inspired forms of the blues.
>

Well, 11/8 as a tritone would be a "deeper shade of blue" than 7/5. (The prime 11 could be thought of as either 18 fifths up or 13 fifths down, but I treat it as neutral in the whole major/minor tonality scheme.)

I also call the septimal subminor ratios "default blues" tuning, but what you're talking about could also be melisma, moving the pitch around to give the melody some life and passion, since flat, steady pitches aren't going to sound very exciting. (In Arabic music, it's one of the parts of _tarab_, the art of achieving musical ecstasy; blues, jazz, rock, soul and country have their own generally-unwritten rules of "tarab".)

Of course, singers generally don't try to sing exact JI ratios and shouldn't; I'm talking about fixed-pitch instruments here, and I'm only approximating JI with 72-et or whatever I'm using. You're stuck with the pitch bend wheel if you want melisma. ~D.

2008/7/29 Danny Wier <dawiertx@sbcglobal.net>:

> So what would you call _utonal_ 7-limit intervals, the "major-in-minor"
> tonalities? Since the complement of the color blue is yellow (in the
> scientific red-blue-green primary color system) or orange (in the older
> red-blue-yellow scheme), it could be called either. I'll split the
> difference and call these "amber" notes. I also thought of another name,
> "Sabawi" (Arabic: صباوي), derived from Saba, the maqam that contains a
> diminished fourth and diminished octave: D Ed F Gb A Bb C Db E F.

Yellow's a good counterpart to blue because yellow has some
connotations in Chinese culture that correspond to connotations of
blue that may have led to "the blues". But maybe you can define your
blue/amber notes this way and I'll define yellow notes a different way
one day.

Graham

That is strange because yellow and blue make green, but in Japan's
ancient times there wasn't such a green concept (green was a kind of
blue more towards yellow!)

Funny enough, today, while I was waiting for a traffic light (for the
green man) a grandma reminded me that the man was already BLUE since
I was not paying attention to it
In other words still not such a green concept for the old people in
Japan.

Sorry if I got a bit off the subject!

Tony

On 2008/07/30, at 19:16, Graham Breed wrote:

> 2008/7/29 Danny Wier <dawiertx@...>:
>
> > So what would you call _utonal_ 7-limit intervals, the "major-in-
> minor"
> > tonalities? Since the complement of the color blue is yellow (in the
> > scientific red-blue-green primary color system) or orange (in the
> older
> > red-blue-yellow scheme), it could be called either. I'll split the
> > difference and call these "amber" notes. I also thought of
> another name,
> > "Sabawi" (Arabic: صباوي), derived from Saba, the maqam that
> contains a
> > diminished fourth and diminished octave: D Ed F Gb A Bb C Db E F.
>
> Yellow's a good counterpart to blue because yellow has some
> connotations in Chinese culture that correspond to connotations of
> blue that may have led to "the blues". But maybe you can define your
> blue/amber notes this way and I'll define yellow notes a different way
> one day.
>
> Graham
>
>

The complementary color to blue is Orange. And to many of the Sufi's has the opposite meaning as the blues. (Henri Corbin is a good reference to this)
What can or cannot be used in blues is such a question of context though.

I have liked some of Ptolemy's chromatics though in this regard. that 7/6 12/11 22/21 tetrachord rocks for me( try all inversions too!). While the Dallesandro CPS is mapped to 31 pitches in the octave. these glisses inbetween the smaller intervals with the scale have held me for hours.
--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Kraig Grady wrote:
> The complementary color to blue is Orange. And to many of the Sufi's has > the opposite meaning as the blues. (Henri Corbin is a good reference to > this)
> What can or cannot be used in blues is such a question of context though.
> Hey, I was reading about colors and the Lata'if-i Sitta not too long ago. (Those are the six centers of the psyche in Sufi psychology, comparable to chakras, and they have different colors assigned to them.)

The "blue" _latifa_ ("subtlety") is the _nafs_, or passionate soul/ego, while the "yellow" _latifa_ is the _qalb_, the heart/conscience, which leads one to repent of things done out of passions in the _nafs_... but you might be thinking of something else entirely.

> I have liked some of Ptolemy's chromatics though in this regard. that > 7/6 12/11 22/21 tetrachord rocks for me( try all inversions too!). > While the Dallesandro CPS is mapped to 31 pitches in the octave. these > glisses inbetween the smaller intervals with the scale have held me for > hours.
> A tetrachord of 1/1-12/11-7/6-22/21 sounds a _little_ like what you have in Dastgah-e Chahargah: C Dp E F G Ap B C - if you treat the koron (p) as a 3/4 tone, and based on my limited knowledge of Iranian music, the koron is more like a 2/3 tone, maybe 13/12 or 14/13.

Which reminds me, I need to make that list of epimoric tetrachords again, the one where in an increasing set of integers a, b, c, d: a/b, a/c, a/d, b/c, b/d and c/d are epimoric (superparticular ratios), and d/a = 4/3. Didn't Aristoxenus do this kind of study?

I'm going OT twice in one post, so I'll shut up now... ~D.

Hi Danny!
The Persians explored all the permutations of the Greeks so i would not be surprised at any similarity, actually the contrary. likewise i enjoyed the permutations which one can find with the CPS which serves as a great pitch base. i have often been impressed by what one can find in it, that it wasn't designed to have per se.

John Chalmers did a list of all the epimoric tetrachords in his book, "The Divisions of the Tetrachord)
--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Kraig Grady wrote:
> Hi Danny!
> The Persians explored all the permutations of the Greeks so i would not > be surprised at any similarity, actually the contrary. likewise i > enjoyed the permutations which one can find with the CPS which serves as > a great pitch base. i have often been impressed by what one can find in > it, that it wasn't designed to have per se.
>
> John Chalmers did a list of all the epimoric tetrachords in his book, > "The Divisions of the Tetrachord)
> Thanks for reminding me to read that. I found the text online, scanned in PDF in ten files; I thought someone posted the link before; but here it is again:

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

I decided to go a different direction than what I said I'd do: make a list of tetrachords from simple sets of overtones, a:b:c:d where d/a = 4/3, then pentachords a:b:c:d:e, and e/a = 3/2. The first one on the list is 9:10:11:12, which is vaguely like Rast.

~D.

Danny,
 
Your mention of the sufi word "qalb" being "the heart/conscience" surprised me - when I was in Morocco in the early 1970's I heard that "kalb" was arabic for "dog", and surmised that it was related to the Biblical name Caleb. 

Mark Rankin
 

--- On Thu, 7/31/08, Danny Wier <dawiertx@...> wrote:

From: Danny Wier <dawiertx@...>
Subject: Re: [tuning] Re: Blue notes and their "amber" complements
To: tuning@yahoogroups.com
Date: Thursday, July 31, 2008, 2:15 PM

Kraig Grady wrote:
> The complementary color to blue is Orange. And to many of the Sufi's has
> the opposite meaning as the blues. (Henri Corbin is a good reference to
> this)
> What can or cannot be used in blues is such a question of context though.
>

Hey, I was reading about colors and the Lata'if-i Sitta not too long
ago. (Those are the six centers of the psyche in Sufi psychology,
comparable to chakras, and they have different colors assigned to them.)

The "blue" _latifa_ ("subtlety") is the _nafs_, or passionate soul/ego,
while the "yellow" _latifa_ is the _qalb_, the heart/conscience, which
leads one to repent of things done out of passions in the _nafs_... but
you might be thinking of something else entirely.

> I have liked some of Ptolemy's chromatics though in this regard. that
> 7/6 12/11 22/21 tetrachord rocks for me( try all inversions too!).
> While the Dallesandro CPS is mapped to 31 pitches in the octave. these
> glisses inbetween the smaller intervals with the scale have held me for
> hours.
>

A tetrachord of 1/1-12/11-7/ 6-22/21 sounds a _little_ like what you have
in Dastgah-e Chahargah: C Dp E F G Ap B C - if you treat the koron (p)
as a 3/4 tone, and based on my limited knowledge of Iranian music, the
koron is more like a 2/3 tone, maybe 13/12 or 14/13.

Which reminds me, I need to make that list of epimoric tetrachords
again, the one where in an increasing set of integers a, b, c, d: a/b,
a/c, a/d, b/c, b/d and c/d are epimoric (superparticular ratios), and
d/a = 4/3. Didn't Aristoxenus do this kind of study?

I'm going OT twice in one post, so I'll shut up now... ~D.

Danny,
 
Your mention of the sufi word "qalb" being "the heart/conscience" surprised me - when I was in Morocco in the early 1970's I heard that "kalb" was arabic for "dog", and surmised that it was related to the Biblical name Caleb. 

Mark Rankin
 

--- On Thu, 7/31/08, Danny Wier <dawiertx@...> wrote:

From: Danny Wier <dawiertx@...>
Subject: Re: [tuning] Re: Blue notes and their "amber" complements
To: tuning@yahoogroups.com
Date: Thursday, July 31, 2008, 2:15 PM

Kraig Grady wrote:
> The complementary color to blue is Orange. And to many of the Sufi's has
> the opposite meaning as the blues. (Henri Corbin is a good reference to
> this)
> What can or cannot be used in blues is such a question of context though.
>

Hey, I was reading about colors and the Lata'if-i Sitta not too long
ago. (Those are the six centers of the psyche in Sufi psychology,
comparable to chakras, and they have different colors assigned to them.)

The "blue" _latifa_ ("subtlety") is the _nafs_, or passionate soul/ego,
while the "yellow" _latifa_ is the _qalb_, the heart/conscience, which
leads one to repent of things done out of passions in the _nafs_... but
you might be thinking of something else entirely.

> I have liked some of Ptolemy's chromatics though in this regard. that
> 7/6 12/11 22/21 tetrachord rocks for me( try all inversions too!).
> While the Dallesandro CPS is mapped to 31 pitches in the octave. these
> glisses inbetween the smaller intervals with the scale have held me for
> hours.
>

A tetrachord of 1/1-12/11-7/ 6-22/21 sounds a _little_ like what you have
in Dastgah-e Chahargah: C Dp E F G Ap B C - if you treat the koron (p)
as a 3/4 tone, and based on my limited knowledge of Iranian music, the
koron is more like a 2/3 tone, maybe 13/12 or 14/13.

Which reminds me, I need to make that list of epimoric tetrachords
again, the one where in an increasing set of integers a, b, c, d: a/b,
a/c, a/d, b/c, b/d and c/d are epimoric (superparticular ratios), and
d/a = 4/3. Didn't Aristoxenus do this kind of study?

I'm going OT twice in one post, so I'll shut up now... ~D.

--- In tuning@yahoogroups.com, Mark Rankin <markrankin95511@...> wrote:
>
> Danny,
>  
> Your mention of the sufi word "qalb" being "the heart/conscience"
> surprised me - when I was in Morocco in the early 1970's I heard
> that "kalb" was arabic for "dog", and surmised that it was related to
> the Biblical name Caleb. 
>

I don't know about Caleb - but AFAIK, "kalb" is indeed "dog". And, also
AFAIK, "qalb" and "kalb" are two separate things, with different
pronounciation.
--
Hans Straub