Nowitzkian Note Names ("NNN") for 72tET and Blackjack

Hi gang!

Margo Schulter (AKA "Nicest Person In The World")
reminded me that I haven't contributed to the Tuning
List in ages. So I figured I'd throw my 16 2/3 cents
in on this 72tET notation topic. Actually, I created
a webpage about a year ago that touched on using
Nowitzkian Note Names ("NNN") for 72tET:

"Representing Meantone Tunings with Nowitzkian Note
Names"
http://nowitzky.hypermart.net/justint/nnnmt.htm

The above webpage showed only a small subset of the
72-note scale. So I'll elaborate here.

The following diagrams can be thought of as Rick
Tagawa's 6 keyboards stacked on top of each other.
They also correspond to Joe Monzo's 6-row mapping of
Harvey Starr's Ztar (see
http://www.ixpres.com/interval/dict/blackjack.htm ).

The Nowitzkian Note Names for all 72 scale degrees of
72tEt:

7C 7Db 7Ebb 7Eb 7Fb 7F 7Gb 7G 7Ab 7Bbb
7Bb 7Cb
2 8 14 20 26 32 38 44 50 56 62
68

6C 6Db 6D 6Eb 6Fb 6F 6Gb 6G 6Ab 6A
6Bb 6Cb
1 7 13 19 25 31 37 43 49 55 61
67

5C 5Db 5D 5Eb 5E 5F 5Gb 5G 5Ab 5A
5Bb 5B
0 6 12 18 24 30 36 42 48 54 60
66

4C# 4D 4Eb 4E 4F 4F# 4G 4G# 4A
4Bb 4B 4C
5 11 17 23 29 35 41 47 53 59
65 71

3C# 3D 3D# 3E 3F 3F# 3G 3G# 3A
3A# 3B 3C
4 10 16 22 28 34 40 46 52 58
64 70

2C# 2D 2D# 2E 2E# 2F# 2FX 2G# 2A
2A# 2B 2B#
3 9 15 21 27 33 39 45 51 57
63 69

I've omitted the octave values, in hopes that the
diagrams don't word-wrap (and God help you if you're
using a proportional font!). The comma values can be
thought of as Rick's keyboard number or Joe's row
number. They're numbered 2 thru 7 instead of 1 thru
6, because NNN uses 5 as the center (5C5 is middle C).
The comma values are actually approximations (see
http://nowitzky.hypermart.net/justint/nnnmt.htm ).

Notice that the letter names in each column are not
all the same; e.g., the second column has Db's and
C#'s. This is intentional (see
http://nowitzky.hypermart.net/justint/nnn.htm ); e.g.,
4C# is a little higher than 4Db. For each of the 72
notes, I show the letter name that keeps the
corresponding frequency closest (geometrically, AKA
logarithmically) to its 72tET counterpart. If scale
degree 0 is middle C at 264Hz, scale degree 5 is
277.019Hz. 4C#5 is 278.438Hz, and 4Db5 is 274.69Hz.
4C#5 is closest.

The Nowitzkian Note Names for Blackjack:

7C 7Ebb 7G 7Bbb
2 14 44 56
6Db 6Gb 6Ab
7 37 49
5C 5F 5G
0 30 42
4E 4F#
4B
23 35
65
3D# 3F
3A# 3C
16 28 58
70
2D 2E 2A
2B
9 21 51
63

Final note: NNN was originally designed for 5-Limit
Just Intonation. 4:5:6 is EXACTLY 5C 4E 5G. But it's
a little funky when used as-is for higher limits.
E.g., 4:5:6:7 is APPROXIMATELY 5C 4E 5G 3A#. A closer
approximation is 5C 4E 5G 7Ebbbbbb6. To represent
higher limit more precisely, consider additional
prefix values for the note names; e.g., 4:5:6:7 could
use something like 5&5C 5&4E 5&5G 4&5Bb (where the
number before the "&" provides the 7-limit dimension).

--Mark Nowitzky
nowitzky@alum.mit.edu, AKA
tuning-owner@yahoogroups.com

=====
+-------------------------------------------------------
| Mark Nowitzky
| email: nowitzky@alum.mit.edu
| www: http://nowitzky.hypermart.net
| "If you haven't visited Mark Nowitzky's home
| page recently, you haven't missed much..."
+-------------------------------------------------------

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--- In tuning@y..., Mark Nowitzky <mnowitzky@y...> wrote:

/tuning/topicId_22856.html#22856

> Hi gang!
>
> Margo Schulter (AKA "Nicest Person In The World")
> reminded me that I haven't contributed to the Tuning
> List in ages.

Hi Mark! Welcome back!

(... you elusive List Owner, you...)

And to Margo,

Thanks heaps for the detailed explanation of how to interpret
the ratios in the Benedetti example. I'm simply too busy
with other things, and too wrapped up in MIRACLE at this point,
to go into it further right now. It will have to be a
"future project"...

-monz
http://www.monz.org
"All roads lead to n^0"