Re: Notation of 16-tet?

If 16 tET were recast in quarter comma meantone*:

C
------------------
F 7 G 9
Bb 13 D 3
Eb 4 A 12
Ab 11 E 5
Db 2 B 14
Gb 8 F# 8
Cb 15 C# 1
Fb 6 G# 10
Bbb 12 D# 4
Ebb 3 A# 13
Abb 10 E# 6
Dbb 1 B# 15
Gbb 7 Fx 9
Cbb 14 Cx 2
Fbb 5 Gx 11
Bbbb 11 Dx 5

C
C#
Db
D
Eb/D#
E
Fb/E#
F
F#/Gb
G/FX
G#
Ab
A/Bbb
Bb/A#
B/Cbb
Cb/B#
C

The following changes (in scale degrees) would be necessary to maintain the
correct spelling of keys:

0 (C) 0 3 5 7 9 12 14 16

1. (C#) 0 3 5 7 9 12 14 16

2. (Db) 0 [2] 5 [6] 9 [11] 14 16

3. (D) 0 [2] 5 [6] 9 [11] 14 16

4. (Eb) 0 3 5 7 9 12 [15] 16

5. (E) 0 3 5 7 9 12 [15] 16

6. (Fb) 0 [2] 5 [6] 9 12 14 16

7. (F) 0 [2] 5 [6] 9 12 14 16

8. (F#) 0 [2] 5 [6] 9 12 14 16
(Gb) 0 3 5 7 [10] 12 [15] 16

9. (G) 0 3 5 7 [10] 12 [15] 16

10. (G#) 0 3 5 7 [10] 12 [15] 16

11. (Ab) 0 [2] 5 7 9 12 14 16

12. (A) 0 [2] 5 7 9 12 14 16

13. (Bb) 0 3 [6] 7 [10] 12 [15] 16

14. (B) 0 3 [6] 7 [10] 12 [15] 16

15. (Cb) 0 3 5 7 9 12 14 16

16. (C) 0 3 5 7 9 12 14 16

Of course if your calling 5 a 4th and 14 a 7th in 16tET, your also going to
call a modal #4th 7, and a b5th 9.........?

Dan Stearns

*This could be done by recasting "O" as 31 (and therefore 18 as "F" and 13
as "f").

-----Original Message-----
From: Herman Miller <hmiller@io.com>
To: tuning@onelist.com <tuning@onelist.com>
Date: Saturday, January 16, 1999 5:38 PM
Subject: [tuning] Re: Notation of n-tet?

Since the best fifth in 16-tET falls below Rasch's limits of
recognizability (between 4/7 and 3/5 of an octave) one might choose
a notation without it. A possibility is then taking every three out
of 48-tET:
C C#\ D\\ D/ D# E\ E// F/ F# G\ G// G#/ A A#\ B\\ B/ C
D#=Eb, etc.

Manuel Op de Coul coul@ezh.nl

16-equal as a neo-pelog

cents pc fifths notation

0 0 0 1. Panegul
75 1 -7 bGulu
150 2 +2 2. Gulu
225 3 -5 bDada/#Gulu
300 4 +4 3. Dada
375 5 -3 #Dada
450 6 +6 bPelog
525 7 -1 4. Pelog
600 8 +8/-8 bLima
675 9 +1 5. Lima
750 10 -6 bNem
825 11 +3 6. Nem
900 12 -4 #Nem
975 13 +5 7. Barang
1050 14 -2 #Barang
1125 15 +7 bPanegul
1200 16/0 1. Panegul

Note that flats are added with ascending fifths and sharps with descending.