Yahoo Tuning Groups Ultimate Backup tuning questions on Keenan color charts

Well here goes. Everybody who knows me knows that I don't hesitate
asking questions, regardless of how lame...

Here are some questions on the Keenan color keyboard charts. They're
quite beautiful, by the way...

1) I understand that the colors are the chains of secors. However,
what are the little black and white dots that also seem to go along
about a chain of 10, but they differ from the colors. That was never
quite explained on the diagram... or if it was, I'm not seeing it.

2) The various intervals below the keyboard indicate *samples* of
various intervals, yes?? They are not all of them, right... since I
know the smaller intervals, for instance, would include other colors
than the ones shown if they were all there, yes?

3) Why is it that, while the two keyboards changed the base note,
from B[ on Halberstadt A to B[ on Halberstadt Ab, and the colors
change on the keyboard, all the colors of the illustrated intervals
remain the same in both charts. That seemed a little "suspicious" to
me... Is that the way it's *supposed* to work out??

4) Even more importantly: I understand the idea of coloring chains
according to the string of secors, but does that make any sense from
a *concordance* standpoint? Generally, I have been coloring
concordant tetrads with the same color stickers. In this case,
though, even some of the most common and concordant tetrads would
have different colors, yes? So, although interesting, how does this
particular coloring help a person find the *concordances* in the
system??

Well, I guess that's all the questions for *now* :)

🔗Paul Erlich <paul@stretch-music.com>

🔗jpehrson@rcn.com

🔗David C Keenan <D.KEENAN@UQ.NET.AU>

--- In tuning@y..., jpehrson@r... wrote:
> Well here goes. Everybody who knows me knows that I don't hesitate
> asking questions, regardless of how lame...

Joseph, It is a quality that endears you to many; both to those who are afraid to ask the questions you ask, and to those who enjoy answering them.

By the way, Paul, don't hesitate to explain my stuff. No need to make folks wait, given the time zone differences etc.

> Here are some questions on the Keenan color keyboard charts.
They're
> quite beautiful, by the way...

Yes, but it would be a hell of a job to actually paint a keyboard like that, wouldn't it?

I've updated the middle-C on middle-C 21 key per octave keyboard chart. It's now called
http://dkeenan.com/Music/Miracle/BlackjackHalberstadt21C.doc

I've enlarged it to 88 keys as requested. I've added ratios for the 12-integer-limit intervals. I've corrected the decimal names to correspond to Graham's latest system.

> 1) I understand that the colors are the chains of secors. However,
> what are the little black and white dots that also seem to go along
> about a chain of 10, but they differ from the colors. That was
never
> quite explained on the diagram... or if it was, I'm not seeing it.

They correspond to what blackjack would look like on a generalised (or blackjack-specific) keyboard. Except they would all be squeezed much closer horizontally so that an octave was back to its usual 282 mm again.

Ignore the difference between black and white dots for the moment. Imagine them all red. Notice that each slanting line corresponds to a single key colour. If you were actually playing on the dots, this positional information would be superior to the key colours, since most people haven't internalised the order of colours in the rainbow. You would have to actually change your finger positions slightly (front-to-back) to play a 7:9 instead of a 4:5, while both span a perfect fifth on the Halberstadt.

If you are using coloured dots instead of painting the keys, you should arrange the dots in these slanting lines. Ignore whether they are black or white and instead make them the colour of the key they are shown on.

But why are they black and white? The white ones correspond to the naturals in the decimal notation.

> 2) The various intervals below the keyboard indicate *samples* of
> various intervals, yes?? They are not all of them, right... since I
> know the smaller intervals, for instance, would include other colors
> than the ones shown if they were all there, yes?

That's correct. You can shift the colurs up or down the rainbow provided you shift the colour of every note by the same amount. e.g. a perfect fifth on the keyboard will give a 4:5 if it goes green:cyan as shown or if it goes orange:yellow or yellow:green or cyan:blue or blue:magenta. Any other perfect fifths will give you a 7:9.

> 3) Why is it that, while the two keyboards changed the base note,
> from B[ on Halberstadt A to B[ on Halberstadt Ab, and the colors
> change on the keyboard, all the colors of the illustrated intervals
> remain the same in both charts. That seemed a little "suspicious"
to
> me... Is that the way it's *supposed* to work out??

Yes. That's the way it's supposed to work.

> 4) Even more importantly: I understand the idea of coloring chains
> according to the string of secors, but does that make any sense from
> a *concordance* standpoint? Generally, I have been coloring
> concordant tetrads with the same color stickers. In this case,
> though, even some of the most common and concordant tetrads would
> have different colors, yes? So, although interesting, how does this
> particular coloring help a person find the *concordances* in the
> system??

Your method will only work while you're only dealing with a few chords. If you're going to have a different colour for every consonant (or otherwise interesting) chord, you're going to run out of colours pretty soon, and some keys are going to have a _lot_ of different colours on them. There are eight h7 chords (7-limit tetrads 4:5:6:7) to start with. My colouring scheme is not specific to h7 or any other chords. It is guaranteed to work for everything, including chords that haven't even been invented yet!

But to take h7 chords as our first example. If we put together the required intervals from the chart we find that a h7 chord looks like a stack of P5|P4|P4 keyboard intervals and goes green:cyan:green:cyan. This means it could also go yellow:green:yellow:green or cyan:blue:cyan:blue. But if you try to play the same pattern of P5|P4|P4 with cyan:green:cyan:green etc. you will not get a h7 chord you'll get a supermajor wide minor seventh chord (SMWm7), which is an interesting 9-limit ASS, but not what you wanted.

Hope that helps. Feel free to ask more questions.

Regards,
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com

🔗jpehrson@rcn.com

--- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:

/tuning/topicId_30778.html#30789

Maybe the Yahoo server is tired of being a "Yahoo" and is actually
storing passwords again... I'll try to post again!

> I've enlarged it to 88 keys as requested. I've added ratios for the
12-integer-limit intervals. I've corrected the decimal names to
correspond to Graham's latest system.
>

As I mentioned, Dave, this keyboard is really terrific. I am
*definitely* going to use it!

> > 1) I understand that the colors are the chains of secors.
However, what are the little black and white dots that also seem to
go along about a chain of 10, but they differ from the colors. That
was never quite explained on the diagram... or if it was, I'm not
seeing it.
>
> They correspond to what blackjack would look like on a generalised
(or blackjack-specific) keyboard. Except they would all be squeezed
much closer horizontally so that an octave was back to its usual 282
mm again.
>

Got it! I was wondering, though, why the pattern broke and the dot
colors changed... but I *guess* that's the place the secor chain has
to break in order to fit into an octave, or something like that (??)

>
> If you are using coloured dots instead of painting the keys, you
should arrange the dots in these slanting lines. Ignore whether they
are black or white and instead make them the colour of the key they
are shown on.
>

I'm not certain they're going to fit like that, but I *certainly*
will use the color scheme...

> > 4) Even more importantly: I understand the idea of coloring
chains
> > according to the string of secors, but does that make any sense
from a *concordance* standpoint? Generally, I have been coloring
> > concordant tetrads with the same color stickers. In this case,
> > though, even some of the most common and concordant tetrads would
> > have different colors, yes? So, although interesting, how does
this
> > particular coloring help a person find the *concordances* in the
> > system??
>
> Your method will only work while you're only dealing with a few
chords. If you're going to have a different colour for every
consonant (or otherwise interesting) chord, you're going to run out
of colours pretty soon,

Actually, this already happened, so *your* suggestion will be *far*
superior... I believe I understand it now. In other words, the
*sequence* of colors for a particular chord will remain the same...
if it doesn't, it's a different chord! Right??

>
> Hope that helps.

It's just great!

Thanks so much again!

Joseph

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

--- In tuning@y..., jpehrson@r... wrote:
> Got it! I was wondering, though, why the pattern broke and the dot
> colors changed... but I *guess* that's the place the secor chain has
> to break in order to fit into an octave, or something like that (??)

No. The change from black to white in any given line purely depends on
where Graham has decided to put the naturals of the decimal notation,
not anything relevant to you at this stage.

Incidentally I have a rationale for Graham's current choice, that does
not depend on his 24-key mapping or any kind of C fetish. Briefly it
is to minimise the use of negative numbers in chord transposition
calculations (9> is -1, 0< is 10, 1< is 11 etc.) while not having any
double accidentals.

> Actually, this already happened, so *your* suggestion will be *far*
> superior... I believe I understand it now. In other words, the
> *sequence* of colors for a particular chord will remain the same...
> if it doesn't, it's a different chord! Right??

You got it! Except of course you can slide the whole chord up or down
the rainbow and it stays the same too.

-- Dave Keenan