Dot-Guide for 16-EDD instruments


16-EDD Fretboard is based on the formula (Scale_Length/(2^(x/16))). Although the disputes generated by the presumption of advocate the best way for visualize a worthy 16-EDD fretboard, defending for place, in contra-natura, the same old 12-EDD 'sketch' over the 16-EDD fingerboard, in essence, Armodue dot-guide is the most suitable and consistent way for visualize a Hexadecaphonic fretboard.

WHY?

Because 2 worlds about theory referent to 16-EDD show us a same conclusion: David S. Goldsmith 16-EDO Theory and Armodue Esadecafonia Theory designs a layout of 9 white keys and 7 black keys for piano. What's mean? Means that each parallel conclusions in different times and different locations are summarized under the same scheme for graphics with the better intention their ideas and renew the "Unmovable (or abominable ;) 12-EDD universal music language", that actually is, still, overestimated and extremely SPENT!
Goldsmith, in summarized accounts, declaims the use of 16-EDD with a Notation based in the first 9 minuscules letters of the Greek alphabet, with their correspondents distribution of the accidental symbols and applying it over 2 hexagrams (a Bass hexagram and a Treeble Hexagram, like a it homologous duodecatonic transcription on pentagrams).
Armodue, on the other hand, declaims the use of 16-EDD with a notation based in 9 Numbers (obviating the number 0), with their respective distribution of the accidental symbols and applying it over Tetragrams distributed by 'Decaves' (Ditaves/'Octaves'), making of this last, the most EASY for transcription. But, BOTH are driven under the same Piano scheme: LLLsLLLLs (7L2s): 2 2 2 1 2 2 2 2 1 (2;1), called Superdiatonic or Mávila-9.

With respect to the Hexadecaphonic fretboard, this is a first way:
16-EDO_Dot-Guide_0.png
16-EDD Dot-Guide, Goldsmith/Armodue

The dots denote clearly the 16-Piano layout transposed to the fretboard, visualizing the 'black keys' in the dots and the 'white keys' in the blank spaces. Denotes too, the interval of 6th (blown 5th) with 2 dots, the 'Decave' ('Octave') with 3 dots, for differentiate 6ths and 10ths, making by logic the tuning on 7th fret by intervals of 5ths (Acute 4ths). A simplification for this dot-guide is:
16-EDO_Dot-Guide_1.png
16-EDD Dot-Guide, simplified form

The dots are in the places 3· 5· 7· 9· 11· 13· 16: 19· 21· 23· 25· 27· 29· 32: & 35· NOT LOSING THE CONSISTENCY with the superdiatonic scheme, and this is the better orientation for somebody that is beginning in the Goldsmith/Armodue theories over 16-EDD string Instruments, denoting a scale of 2L5s 3;2 Relation, 3 2 2 2 2 2 3 (aka Mávila-7 or simply Antidiatonic).
Step (form 1)
Purdal size
Cent size
|
Step (form 2)
Purdal size
Cent size
01
618,75
75
|
01
618,75
75
02
1237,5
150
|
02
1237,5
150
03·
1856,25
225
|
03·
1856,25
225
04
2475
300
|
04
2475
300
05·
3093,75
375
|
05·
3093,75
375
06
3712,5
450
|
06
3712,5
450
07·
4331,25
525
|
07·
4331,25
525
08
4950
600
|
08
4950
600
09··
5568,75
675
|
09·
5568,75
675
10
6187,5
750
|
10
6187,5
750
11
6806,25
825
|
11·
6806,25
825
12·
7425
900
|
12
7425
900
13
8043,75
975
|
13·
8043,75
975
14·
8662,5
1050
|
14
8662,5
1050
15
9281,25
1125
|
15
9281,25
1125
16\0···
9900\0
1200\0
|
16\0:
9900\0
1200\0
Another way for a 16-EDD dot-guide is like this:
16-EDO_Dot-Guide_2.png
16-EDD Dot-Guide, alterned form

The dots are in the places 3· 5· 8· 11· 13· 16: 19· 21· 24· 27· 29· 32: 35· denoting a consistent scale of 4L2s 3;2 Relation, 3 2 3 3 2 3, concluding with the total symmetry that 16-EDD have in its internal structure.

A last dot-guide for 16-EDD is it that FabrizioFulvioFaustoFiale puts on his 'Esadekachitarra', using the 4-EDD subset for that:
16-EDD Tetraf fretboard.png
16-EDD dot-guide, TetraF form

Step (form 3)
Purdal size
Cent size
|
Step (form 4)
Purdal size
Cent size
01
618,75
75
|
01
618,75
75
02
1237,5
150
|
02
1237,5
150
03·
1856,25
225
|
03
1856,25
225
04
2475
300
|
04·
2475
300
05·
3093,75
375
|
05
3093,75
375
06
3712,5
450
|
06
3712,5
450
07
4331,25
525
|
07
4331,25
525
08·
4950
600
|
08·
4950
600
09
5568,75
675
|
09
5568,75
675
10
6187,5
750
|
10
6187,5
750
11·
6806,25
825
|
11
6806,25
825
12
7425
900
|
12·
7425
900
13·
8043,75
975
|
13
8043,75
975
14
8662,5
1050
|
14
8662,5
1050
15
9281,25
1125
|
15
9281,25
1125
16\0:
9900\0
1200\0
|
16\0:
9900\0
1200\0