TromboneBoi9: reorganization and added alt names columns to tables

2025-11-16T08:21:33Z

reorganization and added alt names columns to tables

TromboneBoi9: Created page with "'''General dual-fifth notation''' (or ''GDF'' notation) is a system of notation that is designed for use with dual-fifth temperaments, intended for use with smaller dual-fifth EDOs. It can perhaps be considered a form of ups and downs notation since it uses the same nominals, symbols, and general principles, and when used for EDOs, it often materializes as a subset notation. The main goal of GDF notation is to describe intervals closer to what they a..."

2025-11-15T07:59:00Z

Created page with "'''General dual-fifth notation''' (or ''GDF'' notation) is a system of notation that is designed for use with dual-fifth temperaments, intended for use with smaller dual-fifth EDOs. It can perhaps be considered a form of ups and downs notation since it uses the same nominals, symbols, and general principles, and when used for EDOs, it often materializes as a subset notation. The main goal of GDF notation is to describe intervals closer to what they a..."

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'''General dual-fifth notation''' (or ''GDF'' notation) is a system of notation that is designed for use with [[dual-fifth]] temperaments, intended for use with smaller dual-fifth [[EDO|EDOs]]. It can perhaps be considered a form of [[ups and downs notation]] since it uses the same nominals, symbols, and general principles, and when used for EDOs, it often materializes as a [[subset notation]].

The main goal of GDF notation is to describe intervals closer to what they actually "are," rather than notation systems like [[antidiatonic]] which make minor or neutral seconds look like major seconds.

The idea of GDF notation is to maintain some semblance of a [[Chain-of-fifths notation|chain of fifths]] as used in other approachable notation systems. To do this, it relies instead on the [[9/8|major second]], since a chain of 9/8 major seconds is the same as every other step in a chain of fifths (assuming octave equivalence). Every remaining step in between is split to accommodate the dual fifths, with the major fifths notated as raised fifths (^5) and minor fifths notated as lowered fifths (v5). This ensures that there is no fifth that resembles a ''perfect'' fifth, as dual-fifth systems do not have them.

That is to say, GDF relies on the logic that '''the major fifth and the minor fifth make a major ninth''' (major second when octave-reduced), or that <math>3^+ \cdot 3^- = 9</math>.


With split fifths, a chain of fifths would look something like this:

{|class="wikitable"
| rowspan="2" | G&flat; || ^D&flat;
| rowspan="2" | A&flat; || ^E&flat;
| rowspan="2" | B&flat; || ^F
| rowspan="2" | C || ^G
| rowspan="2" | D || ^A
| rowspan="2" | E || ^B
| rowspan="2" | F&sharp; || ^C&sharp;
|-
| vD&flat; || vE&flat; || vF || vG || vA || vB || vC&sharp;
|}

This also implies a converse system where the other set of fifths are split:
{|class="wikitable"
| ^G&flat;
| rowspan="2" | D&flat; || ^A&flat;
| rowspan="2" | E&flat; || ^B&flat;
| rowspan="2" | F || ^C
| rowspan="2" | G || ^D
| rowspan="2" | A || ^E
| rowspan="2" | B || ^F&sharp;
| rowspan="2" | C&sharp;
|-
| vG&flat; || vA&flat; || vB&flat; || vC || vD || vE || vF&sharp;
|}

==Tables==
For EDOs, it's usually the case that the GDF notation of <math>n</math>-edo is identical to the subset notation taken from <math>2n</math>-edo.

'''Please note''' that when GDF for EDOs, the symbols ''^'' and ''v'' do not represent single [[arrow|edosteps]] as they do in [[ups and downs notation]]. Instead, they refer to ''half''-edosteps; full edosteps are represented by ''^^'' and ''vv''.

===13edo===
GDF notation of [[13edo]] is identical to [[26edo]] subset notation.
{|class="wikitable"
! Steps !! Cents !! Name(s)
|-
| 0 || 0.00 || C, vC&sharp;
|-
| 1 || 92.31 || ^C&sharp;, vD&flat;
|-
| 2 || 184.62 || D, ^D&flat;
|-
| 3 || 276.92 || ^D&sharp;, vE&flat;
|-
| 4 || 369.23 || E, ^E&flat;
|-
| 5 || 461.54 || ^E&sharp;, vF
|-
| 6 || 553.85 || F&sharp;, ^F
|-
| 7 || 646.15 || G&flat;, vG
|-
| 8 || 738.46 || G&sharp;, ^G
|-
| 9 || 830.77 || A&flat;, vA
|-
| 10 || 923.08 || A&sharp;, ^A
|-
| 11 || 1015.38 || B&flat;, vB
|-
| 12 || 1107.69 || ^B, vC&flat;
|-
| 13 || 1200.00 || C, vC&sharp;
|}

===18edo===
GDF notation of [[18edo]] is identical to [[36edo]] subset notation.
{|class="wikitable"
! Steps !! Cents !! Name(s)
|-
| 0 || 0.00 || C
|-
| 1 || 66.67 || vC&sharp;, vD&flat;
|-
| 2 || 133.33 || ^C&sharp;, ^D&flat;
|-
| 3 || 200.00 || D
|-
| 4 || 266.67 || vD&sharp;, vE&flat;
|-
| 5 || 333.33 || ^D&sharp;, ^E&flat;
|-
| 6 || 400.00 || E
|-
| 7 || 466.67 || vF
|-
| 8 || 533.33 || ^F
|-
| 9 || 600.00 || F&sharp;, G&flat;
|-
| 10 || 666.67 || vG
|-
| 11 || 733.33 || ^G
|-
| 12 || 800.00 || G&sharp;, A&flat;
|-
| 13 || 866.67 || vA
|-
| 14 || 933.33 || ^A
|-
| 15 || 1000.00 || A&sharp;, B&flat;
|-
| 16 || 1066.67 || vB
|-
| 17 || 1133.33 || ^B
|-
| 18 || 1200.00 || C
|}

===23edo===
GDF notation of [[23edo]] is identical to [[46edo]] subset notation.
{|class="wikitable"
! Steps !! Cents !! Name(s)
|-
| 0 || 0.00 || C
|-
| 1 || 52.17 || ^^C, vD&flat;
|-
| 2 || 104.35 || vC&sharp;, ^D&flat;
|-
| 3 || 156.52 || ^C&sharp;, vvD
|-
| 4 || 208.70 || D
|-
| 5 || 260.87 || ^^D, vE&flat;
|-
| 6 || 313.04 || vD&sharp;, ^E&flat;
|-
| 7 || 365.22 || ^D&sharp;, vvE
|-
| 8 || 417.39 || E
|-
| 9 || 469.57 || ^^E, vF
|-
| 10 || 521.74 || ^F, vvG&flat;
|-
| 11 || 573.91 || vvF&sharp;, G&flat;
|-
| 12 || 626.09 || F&sharp;, ^^G&flat;
|-
| 13 || 678.26 || ^^F&sharp;, vG
|-
| 14 || 730.43 || ^G, vvA&flat;
|-
| 15 || 782.61 || vvG&sharp;, A&flat;
|-
| 16 || 834.78 || G&sharp;, ^^A&flat;
|-
| 17 || 886.96 || ^^G&sharp;, vA
|-
| 18 || 939.13 || ^A, vvB&flat;
|-
| 19 || 991.30 || B&flat;
|-
| 20 || 1043.48 || ^^B&flat;, vC&flat;
|-
| 21 || 1095.65 || vB, ^C&flat;
|-
| 22 || 1147.83 || ^B
|-
| 23 || 1200.00 || C
|}

User:TromboneBoi9/Generalized Dual-Fifth Notation - Revision history

TromboneBoi9: reorganization and added alt names columns to tables