Blackjack 21-key mapping comparator

I had an email request for my Blackjack 21-key mapping comparator, so I have cleaned it up a lot, to be more self-explanatory, and I offer this minimal explanation:

It has a column where you enter the keyboard property you are interested in, e.g. whiteness of keys (0 for false, 1 for true), and a column where you enter the blackjack pitch-class property you are interested in, e.g. being notated as a natural. These two properties only need to be entered for one octave. Then it reproduces the pitch property column 20 more times, shifting it by one pitch each time. Then for each of these 21 mappings it calculates where the key property coincides with the pitch property, and at the top of each such column, gives counts of the number of times the properties coincide (one count for a 61-key board and another for an 88-key board). It flags those with the maximum number.

Examples are included for white naturals, white tetrads and white pentads.

You'll find it at
hyttp://uq.net.au/~zzdkeena/Music/Miracle/Blackjack21KeyMapComparator.xls.zip

It's a zipped Excel 97 spreadsheet (124 kB). Let me know if you need another format.

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

Sorry about that. The link should of course have been:
http://dkeenan.com/Music/Miracle/Blackjack21KeyMapComparator.xls.zip

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

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

/tuning/topicId_30846.html#30846

> I had an email request for my Blackjack 21-key mapping comparator,
so I have cleaned it up a lot, to be more self-explanatory, > >

hyttp://uq.net.au/~zzdkeena/Music/Miracle/Blackjack21KeyMapComparator.
xls.zip
>

Hello Dave!

Well, this is certainly ingenious, but I have to confess that I'm
having trouble with it. Could you please do a bit more *detailed*
explanation with cell reference numbers. Sorry to be so *dense*
about what is, possibly, self-explanatory...

Thanks!

Joseph

--- In tuning@y..., jpehrson@r... wrote:
> Hello Dave!
>
> Well, this is certainly ingenious, but I have to confess that I'm
> having trouble with it. Could you please do a bit more *detailed*
> explanation with cell reference numbers. Sorry to be so *dense*
> about what is, possibly, self-explanatory...
>
> Thanks!

I'm glad you asked, because I found mistakes in the white tetrads and white pentads parts. I've fixed these and added decimal notation alongside the 6x12 notation. I've also added a fourth comparison that counts decimal naturals falling on black keys. The new version is (145 KB) at

http://dkeenan.com/Music/Miracle/Blackjack21KeyMapComparator.xls.zip

I'm sorry I don't have time to explain it much more. Maybe someone else can help? But here's a bit more. Maybe you can ask specific questions after this.

The spreadsheet contains four (almost) identical blocks. Each one checks the 21 possible mappings, for the coincidence of a certain key property with a certain pitch property. e.g. The upper left one checks how many times whiteness of key coincides with naturalness of pitch in the 6x12 notation.

You describe the key and pitch properties by entering zeros and ones (in the blue regions) and then you read off the number of times they coincide for each mapping (from the yellow regions). The mappings are referred to by giving the blackjack pitch that falls on the middle-C key.

Ignore all the numbers in white cells (except for a few we'll mention later).

e.g. In H10 and H12 you can see that the mapping that puts a F#v on the middle-C key (so the middle-C pitch could be on either the D below middle-C key or the B above middle-C key) is the only mapping that gives maximum white naturals on both a 61-key and an 88-key keyboard. The overbars indicate a maximum.

In AD10 and AD12 you can see that the C on mid-C mapping has 4 less white naturals than the maximum possible, on both keyboards.

Now scroll right and look at BQ10 BQ12 CO10 CO12. You will see that by putting either a Bb^ or a F< on the middle-C key, we get the maximum number of 7-limit otonal tetrads on all white keys, irrespective of whether it is a 61-key or 88-key board (9 and 13 respectively).

If you want to know how many otonal tetrads (of any colour) there are in a given keyboard mapping, just look one cell below and to the left of the yellow square. e.g. looking at cells BQ12 and BP13 we learn that this (Bb^ on mid-C) mapping gives us 28 tetrads on an 88-key board, 13 of which are all-white.

Notice (in BX13) that the C on mid-C mapping gives two less tetrads on an 88-key board, (irrespective of their colour).

Now look at V131, V133, AT131, AT133. You'll see that the Bb^ and F< mappings give the maximum number of 4:5:6:7:9 chords on all white keys, however they don't give the maximum number of such chords (of any colour) on the keyboard. Look at E134 and I134 to see that it is the F] and G< mappings that do that.

Hope that helps.

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

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

/tuning/topicId_30846.html#30885

>
> You describe the key and pitch properties by entering zeros and
ones (in the blue regions) and then you read off the number of times
they coincide for each mapping (from the yellow regions). The
mappings are referred to by giving the blackjack pitch that falls on
the middle-C key.
>

Hi Dave!

For some reason, the entering of zeros and ones in the blue boxes to
gain different properties was confusing me... but it's perfectly
clear now, as was everything else in your explanatory post.

Thanks so much! This is quite a gadget...

Joseph