Alternative symbols for ups and downs notation: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Expansion
m Cleanup
Line 10: Line 10:


== Detail ==
== Detail ==
Below is a table showing the characteristics of each edo in the context of heptatonic ups and downs notation.  
Below is a table showing the characteristics of each ET in the context of heptatonic ups and downs notation.  


Each row represents the step size of a sharp/flat, to be called "sharp value" below. The sharp value is the basic category to determine the symbol set to be used.  
Each row represents the step size of a sharp/flat, to be called "sharp value" below. The sharp value is the basic category to determine the symbol set to be used.  
Line 18: Line 18:
{| class="wikitable"
{| class="wikitable"
|+Sharp value \ step size of a small tone
|+Sharp value \ step size of a small tone
|
!|
|'''-2'''
!|-2
|'''-1'''
!|-1
|'''0'''
!|0
|'''1'''
!|1
|'''2'''
!|2
|'''3'''
!|3
|'''4'''
!|4
|'''5'''
!|5
|'''6'''
!|6
|'''7'''
!|7
|'''8'''
!|8
|-
|-
|'''-3'''
!|-3
|
|
|
|
Line 44: Line 44:
|
|
|-
|-
|'''-2'''
!|-2
|
|
|
|
Line 57: Line 57:
|
|
|-
|-
|'''-1'''
!|-1
|
|
|
|
Line 70: Line 70:
|
|
|-
|-
|'''0'''
!|0
|
|
|
|
Line 83: Line 83:
|
|
|-
|-
|'''1'''
!|1
|
|
|
|
Line 96: Line 96:
|
|
|-
|-
|'''2'''
!|2
|
|
|3
|3
Line 109: Line 109:
|
|
|-
|-
|'''3'''
!|3
|1
|1
|8
|8
Line 122: Line 122:
|71b
|71b
|-
|-
|'''4'''
!|4
|6
|6
|13
|13
Line 135: Line 135:
|…
|…
|-
|-
|'''5'''
!|5
|11b
|11b
|18
|18
Line 148: Line 148:
|
|
|-
|-
|'''6'''
!|6
|
|
|23b
|23b
Line 161: Line 161:
|
|
|-
|-
|'''7'''
!|7
|
|
|
|
Line 174: Line 174:
|
|
|-
|-
|'''8'''
!|8
|
|
|
|
Line 187: Line 187:
|
|
|-
|-
|'''9'''
!|9
|
|
|
|
Line 200: Line 200:
|
|
|-
|-
|'''10'''
!|10
|
|
|
|
Line 223: Line 223:


{| class="wikitable"
{| class="wikitable"
|Step offset
!|Step offset
| '''+2'''
| +2
| '''+1'''
| +1
| '''0'''
| 0
| '''-1'''
| -1
| '''-2'''
| -2
|-
|-
|Symbol
!|Symbol
|[[File:accidental doublesharp.png]]
|[[File:accidental doublesharp.png]]
|[[File:accidental sharp.png]]
|[[File:accidental sharp.png]]
Line 243: Line 243:


{| class="wikitable"
{| class="wikitable"
|Step offset
!|Step offset
| '''+4'''
| +4
| +3
| +3
| '''+2'''
| +2
| +1
| +1
| '''0'''
| 0
| -1
| -1
| '''-2'''
| -2
| -3
| -3
| '''-4'''
| -4
|-
|-
|Symbol
!|Symbol
|[[File:accidental doublesharp.png]]
|[[File:accidental doublesharp.png]]
|[[File:accidental sesquisharp.png]]
|[[File:accidental sesquisharp.png]]
Line 271: Line 271:


{| class="wikitable"
{| class="wikitable"
|Step offset
!|Step offset
| 7
| 7
| '''6'''
| '''6'''
Line 281: Line 281:
| '''0'''
| '''0'''
|-
|-
|Sharp symbol
!|Sharp symbol
|[[File:accidental doublesharp up.png]]
|[[File:accidental doublesharp up.png]]
|[[File:accidental doublesharp.png]]
|[[File:accidental doublesharp.png]]
Line 289: Line 289:
|[[File:accidental sharp down.png]]
|[[File:accidental sharp down.png]]
|[[File:accidental natural up.png]]
|[[File:accidental natural up.png]]
|[[File:accidental natural.png]]
| rowspan="2" |[[File:accidental natural.png]]
|-
|-
|Flat symbol
!|Flat symbol
|[[File:accidental doubleflat down.png]]
|[[File:accidental doubleflat down.png]]
|[[File:accidental doubleflat.png]]
|[[File:accidental doubleflat.png]]
Line 299: Line 299:
|[[File:accidental flat up.png]]
|[[File:accidental flat up.png]]
|[[File:accidental natural down.png]]
|[[File:accidental natural down.png]]
|
|}
|}


Line 307: Line 306:


{| class="wikitable"
{| class="wikitable"
|Step offset
!|Step offset
| 9
| 9
| '''8'''
| '''8'''
Line 319: Line 318:
| '''0'''
| '''0'''
|-
|-
|Sharp symbol
!|Sharp symbol
|[[File:accidental doublesharp up.png]]
|[[File:accidental doublesharp up.png]]
|[[File:accidental doublesharp.png]]
|[[File:accidental doublesharp.png]]
Line 329: Line 328:
|[[File:accidental semisharp.png]]
|[[File:accidental semisharp.png]]
|[[File:accidental natural up.png]]
|[[File:accidental natural up.png]]
|[[File:accidental natural.png]]
| rowspan="2" |[[File:accidental natural.png]]
|-
|-
|Flat symbol
!|Flat symbol
|[[File:accidental doubleflat down.png]]
|[[File:accidental doubleflat down.png]]
|[[File:accidental doubleflat.png]]
|[[File:accidental doubleflat.png]]
Line 341: Line 340:
|[[File:accidental semiflat.png]]
|[[File:accidental semiflat.png]]
|[[File:accidental natural down.png]]
|[[File:accidental natural down.png]]
|
|}
|}


Line 354: Line 352:
'''Sharp-5'''
'''Sharp-5'''
{| class="wikitable"
{| class="wikitable"
|Step offset
!|Step offset
| 12
| 12
| 11
| 11
Line 369: Line 367:
| '''0'''
| '''0'''
|-
|-
|Sharp symbol
!|Sharp symbol
|[[File:accidental doublesharp up2.png]]
|[[File:accidental doublesharp up2.png]]
|[[File:accidental doublesharp up1.png]]
|[[File:accidental doublesharp up1.png]]
Line 382: Line 380:
|[[File:accidental natural up2.png]]
|[[File:accidental natural up2.png]]
|[[File:accidental natural up1.png]]
|[[File:accidental natural up1.png]]
|[[File:accidental natural.png]]
| rowspan="2" |[[File:accidental natural.png]]
|-
|-
|Flat symbol
!|Flat symbol
|[[File:accidental doubleflat down2.png]]
|[[File:accidental doubleflat down2.png]]
|[[File:accidental doubleflat down1.png]]
|[[File:accidental doubleflat down1.png]]
Line 397: Line 395:
|[[File:accidental natural down2.png]]
|[[File:accidental natural down2.png]]
|[[File:accidental natural down1.png]]
|[[File:accidental natural down1.png]]
|
|}
|}


'''Sharp-6'''
'''Sharp-6'''
{| class="wikitable"
{| class="wikitable"
|Step offset
!|Step offset
| 14
| 14
| 13
| 13
Line 419: Line 416:
| '''0'''
| '''0'''
|-
|-
|Sharp symbol
!|Sharp symbol
|[[File:accidental doublesharp up2.png]]
|[[File:accidental doublesharp up2.png]]
|[[File:accidental doublesharp up1.png]]
|[[File:accidental doublesharp up1.png]]
Line 434: Line 431:
|[[File:accidental natural up2.png]]
|[[File:accidental natural up2.png]]
|[[File:accidental natural up1.png]]
|[[File:accidental natural up1.png]]
|[[File:accidental natural.png]]
| rowspan="2" |[[File:accidental natural.png]]
|-
|-
|Flat symbol
!|Flat symbol
|[[File:accidental doubleflat down2.png]]
|[[File:accidental doubleflat down2.png]]
|[[File:accidental doubleflat down1.png]]
|[[File:accidental doubleflat down1.png]]
Line 451: Line 448:
|[[File:accidental natural down2.png]]
|[[File:accidental natural down2.png]]
|[[File:accidental natural down1.png]]
|[[File:accidental natural down1.png]]
|
|}
|}


'''Sharp-7'''
'''Sharp-7'''
{| class="wikitable"
{| class="wikitable"
|Step offset
!|Step offset
| 17
| 17
| 16
| 16
Line 476: Line 472:
| '''0'''
| '''0'''
|-
|-
|Sharp symbol
!|Sharp symbol
|[[File:accidental doublesharp up3.png]]
|[[File:accidental doublesharp up3.png]]
|[[File:accidental doublesharp up2.png]]
|[[File:accidental doublesharp up2.png]]
Line 494: Line 490:
|[[File:accidental natural up2.png]]
|[[File:accidental natural up2.png]]
|[[File:accidental natural up1.png]]
|[[File:accidental natural up1.png]]
|[[File:accidental natural.png]]
| rowspan="2" |[[File:accidental natural.png]]
|-
|-
|Flat symbol
!|Flat symbol
|[[File:accidental doubleflat down3.png]]
|[[File:accidental doubleflat down3.png]]
|[[File:accidental doubleflat down2.png]]
|[[File:accidental doubleflat down2.png]]
Line 514: Line 510:
|[[File:accidental natural down2.png]]
|[[File:accidental natural down2.png]]
|[[File:accidental natural down1.png]]
|[[File:accidental natural down1.png]]
|
|}
|}


'''Sharp-8'''
'''Sharp-8'''
{| class="wikitable"
{| class="wikitable"
|Step offset
!|Step offset
| 19
| 19
| 18
| 18
Line 541: Line 536:
| '''0'''
| '''0'''
|-
|-
|Sharp symbol
!|Sharp symbol
|[[File:accidental doublesharp up3.png]]
|[[File:accidental doublesharp up3.png]]
|[[File:accidental doublesharp up2.png]]
|[[File:accidental doublesharp up2.png]]
Line 561: Line 556:
|[[File:accidental natural up2.png]]
|[[File:accidental natural up2.png]]
|[[File:accidental natural up1.png]]
|[[File:accidental natural up1.png]]
|[[File:accidental natural.png]]
| rowspan="2" |[[File:accidental natural.png]]
|-
|-
|Flat symbol
!|Flat symbol
|[[File:accidental doubleflat down3.png]]
|[[File:accidental doubleflat down3.png]]
|[[File:accidental doubleflat down2.png]]
|[[File:accidental doubleflat down2.png]]
Line 583: Line 578:
|[[File:accidental natural down2.png]]
|[[File:accidental natural down2.png]]
|[[File:accidental natural down1.png]]
|[[File:accidental natural down1.png]]
|
|}
|}


Line 593: Line 587:


{| class="wikitable"
{| class="wikitable"
|Step offset
!|Step offset
| '''+2'''
| +2
| '''+1'''
| +1
| '''0'''
| 0
| '''-1'''
| -1
| '''-2'''
| -2
|-
|-
|Symbol
!|Symbol
|[[File:accidental doubleflat.png]]
|[[File:accidental doubleflat.png]]
|[[File:accidental flat.png]]
|[[File:accidental flat.png]]
Line 611: Line 605:


{| class="wikitable"
{| class="wikitable"
|Step offset
!|Step offset
| '''+4'''
| +4
| +3
| +3
| '''+2'''
| +2
| +1
| +1
| '''0'''
| 0
| -1
| -1
| '''-2'''
| -2
| -3
| -3
| '''-4'''
| -4
|-
|-
|Symbol
!|Symbol
|[[File:accidental doubleflat.png]]
|[[File:accidental doubleflat.png]]
|[[File:accidental sesquiflat.png]]
|[[File:accidental sesquiflat.png]]
Line 642: Line 636:
'''14- and 21-ET'''
'''14- and 21-ET'''
{| class="wikitable"
{| class="wikitable"
|Step offset
!|Step offset
| +1
| +1
| '''0'''
| 0
| -1
| -1
|-
|-
|Symbol
!|Symbol
|[[File:accidental natural up.png]]
|[[File:accidental natural up.png]]
|[[File:accidental natural.png]]
|[[File:accidental natural.png]]
Line 655: Line 649:
'''28- and 35-ET'''
'''28- and 35-ET'''
{| class="wikitable"
{| class="wikitable"
|Step offset
!|Step offset
| +2
| +2
| +1
| +1
| '''0'''
| 0
| -1
| -1
| -2
| -2
|-
|-
|Symbol
!|Symbol
|[[File:accidental natural up2.png]]
|[[File:accidental natural up2.png]]
|[[File:accidental natural up1.png]]
|[[File:accidental natural up1.png]]
Line 676: Line 670:
Sharp value higher than 9 cannot be notated at all.  
Sharp value higher than 9 cannot be notated at all.  


Sometimes the symbols available are not sufficient for every key of an ET. When the max step offset of an ET exceeds its accidental symbol set, some of the keys are capped from its full strength.  
Sometimes the symbols available are not sufficient for every key of an ET. When the max step offset of an ET exceeds its accidental symbol set, some of the keys are capped from its full strength. This occurs with ETs that have a very flat fifth. 


[[Category:Notation]]
[[Category:Notation]]

Revision as of 08:49, 5 May 2020

This article discusses about an alternative set of symbols based on current practice of microtonal music with some experimental extrapolation. The notation is, in essence, ups and downs notation with a different look.

Alternative symbols may be useful for the following reasons:

  1. One may prefer a more conventional look of the score;
  2. The up and down symbols may not be quite accessible in computer-aided score typing.

All symbols proposed in this article are available in MuseScore 3. (Feel free to address others.)

What It Resolves

How is the conventional notation for 31-ET related to that for 22-ET? Is there a logical unity despite the apparent differences?

Detail

Below is a table showing the characteristics of each ET in the context of heptatonic ups and downs notation.

Each row represents the step size of a sharp/flat, to be called "sharp value" below. The sharp value is the basic category to determine the symbol set to be used.

Each column represents the step size of a small tone, located between E–F and B–C.

Sharp value \ step size of a small tone
-2 -1 0 1 2 3 4 5 6 7 8
-3 6b
-2 4 11 18b
-1 2 9 16 23 30b
0 7 14 21 28 35 42b
1 5 12 19 26 33 40 47 54b
2 3 10 17 24 31 38 45 52 59b
3 1 8 15 22 29 36 43 50 57 64 71b
4 6 13 20 27 34 41 48 55 62 69 …
5 11b 18 25 32 39 46 53 60 67 …
6 23b 30 37 44 51 58 65 72 …
7 35b 42 49 56 63 70 …
8 47b 54 61 68 …
9 52b 59 66 …
10 64b 71 …

The symbol set comprises traditional sharps, flats, semisharps, semiflats, and up and down arrows attached to sharps and flats. Semisharps and semiflats apply to even sharp values only.

Sharp Value 1 to 4

Sharp-1 ETs have a sharp that raises 1 step. ETs of this category include 5, 12, 19, 26, etc.

Traditional notation can be used since an up is exactly equivalent to a sharp.

Step offset +2 +1 0 -1 -2
Symbol

Sharp-2 ETs have a sharp that raises 2 steps. ETs of this category include 10, 17, 24, 31, etc.

As are commonly seen in 24-edo and 31-edo, semisharps and semiflats could be used for a substitution of the tilde.

Step offset +4 +3 +2 +1 0 -1 -2 -3 -4
Symbol

Sharp-3 ETs have a sharp that raises 3 steps. ETs of this category include 22, 29, 36, 43, etc.

This is where you really want to use ups and downs.

Step offset 7 6 5 4 3 2 1 0
Sharp symbol
Flat symbol

Sharp-4 ETs have a sharp that raises 4 steps. ETs of this category include 27, 34, 41, 48, etc.

A full combination of semisharps, semiflats, ups and downs looks very neat.

Step offset 9 8 7 6 5 4 3 2 1 0
Sharp symbol
Flat symbol

Sharp Value 5 to 8

Starting with sharp-5, which includes the famous 53-ET, you'll have to use double ups and downs.

There's a small version of the arrow symbol available that can be stacked twice or thrice, termed raise/lower by one syntonic comma, for which the step size of 53-edo is a close approximation. These arrow symbols, possibly combined with semisharps and semiflats, could be used through sharp-5 to sharp-8 ETs.

It is basically another system, to be called the "complex system", in contrast to the "simple system" above. The complex system is compatible with lower sharp values. For example, you could use the sharp-8 68-ET for the notation of 34-ET, but the reason the former should not take priority is obvious. However you do, using arrow symbols of both systems should be definitely avoided, because they look too similar.

Sharp-5

Step offset 12 11 10 9 8 7 6 5 4 3 2 1 0
Sharp symbol
Flat symbol

Sharp-6

Step offset 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
Sharp symbol
Flat symbol

Sharp-7

Step offset 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
Sharp symbol
Flat symbol

Sharp-8

Step offset 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
Sharp symbol
Flat symbol

The rest will be discussed below.

Negative Sharp Values

Flat-1 ETs have a sharp that lowers 1 step. ETs of this category include 9, 16, and 23. To have a sharp that actually lowers the tone can be counter-intuitive, yet reasonable for the system. Regardless, you could just flip it around.

Step offset +2 +1 0 -1 -2
Symbol

Flat-2 ETs (virtually 11-ET only) have a sharp that lowers 2 steps. So besides the special flavor of the sharps and flats, there are also semisharps and semiflats to fill up the spaces between.

Step offset +4 +3 +2 +1 0 -1 -2 -3 -4
Symbol

Sharp Value 0

The zero row is even more special in that the conventional meaning of the sharp or flat does not apply.

One possible solution is to use the simple system for 14- and 21-ET, and the complex system for 28- and 35-ET.

14- and 21-ET

Step offset +1 0 -1
Symbol

28- and 35-ET

Step offset +2 +1 0 -1 -2
Symbol

Conclusively, this set of symbols cover all ETs below 72 except 59, 66, and 71.

Limitations

Sharp value higher than 9 cannot be notated at all.

Sometimes the symbols available are not sufficient for every key of an ET. When the max step offset of an ET exceeds its accidental symbol set, some of the keys are capped from its full strength. This occurs with ETs that have a very flat fifth.

Retrieved from "https://en.xen.wiki/index.php?title=Alternative_symbols_for_ups_and_downs_notation&oldid=44143"