Template:MOS degrees/doc: Difference between revisions

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→Using different notation and UDP: Note names column can now be omitted
Ganaram inukshuk (talk | contribs)
autopatrolled
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Mos-ordinals support dropped; Degree Notation param deprecated
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| <pre>Genchain Extend</pre> || No (optional) || Additional intervals corresponding to the number of additional generators going up and/or down after those represented by the UDP. This value is per period, and the default value is the number of large steps per period.
| <pre>Genchain Extend</pre> || No (optional) || Additional intervals corresponding to the number of additional generators going up and/or down after those represented by the UDP. This value is per period, and the default value is the number of large steps per period.
|-
|-
| <pre>Degree Notation</pre> || No (optional) || How should degrees be named? Options include TAMNAMS mosdegree naming and ordinal naming (EG, the unison is either called the 0-mosstep or 1st).
| <pre>Degree Notation</pre> || Deprecated || How should degrees be named? Options include TAMNAMS mosdegree naming and ordinal naming (EG, the unison is either called the 0-mosstep or 1st).
|-
|-
| <pre>MOS Prefix</pre> || No (optional) || If using TAMNAMS mosdegree naming, does the mos have a prefix?
| <pre>MOS Prefix</pre> || No (optional) || If using TAMNAMS mosdegree naming, does the mos have a prefix?
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<pre>{{MOS degrees|Scale Signature=5L 2s|Genchain Extend=0,4}}</pre>
<pre>{{MOS degrees|Scale Signature=5L 2s|Genchain Extend=0,4}}</pre>
{{MOS degrees|Scale Signature=5L 2s|Genchain Extend=0,4}}
{{MOS degrees|Scale Signature=5L 2s|Genchain Extend=0,4}}
=== Changing the degree notation ===
There are currently two ways of naming scale degrees supported by this template: using TAMNAMS numbering (which starts at 0 for the unison) and ordinal numbering (which starts at the 1st for the unison). The default is TAMNAMS degree notation, but this can be changed to ordinal notation as shown below.
<pre>{{MOS degrees|Scale Signature=2L 5s|UDP=1,5|Notation=CDEFGAB;#;b|Degree Notation=ordinal}}</pre>
{{MOS degrees|Scale Signature=2L 5s|UDP=1,5|Notation=CDEFGAB;#;b|Degree Notation=ordinal}}
=== Changing the mos prefix ===
=== Changing the mos prefix ===
It may be beneficial to change the prefix in cases where more than one nondiatonic mos is being discussed. The default is "mos", but this can be changed as shown below, using the previous section's example. (Do not add a hyphen to the end of the prefix, as the template will do that automatically.)
It may be beneficial to change the prefix in cases where more than one nondiatonic mos is being discussed. The default is "mos", but this can be changed as shown below, using the previous section's example. (Do not add a hyphen to the end of the prefix, as the template will do that automatically.)
<pre>{{MOS degrees|Scale Signature=2L 5s|UDP=1,5|Notation=CDEFGAB;#;b|Degree Notation=ordinal|MOS Prefix=pel}}</pre>
<pre>{{MOS degrees|Scale Signature=2L 5s|UDP=1,5|Notation=CDEFGAB;#;b|MOS Prefix=pel}}</pre>
{{MOS degrees|Scale Signature=2L 5s|UDP=1,5|Notation=CDEFGAB;#;b|Degree Notation=ordinal|MOS Prefix=pel}}
{{MOS degrees|Scale Signature=2L 5s|UDP=1,5|Notation=CDEFGAB;#;b|MOS Prefix=pel}}
Typing in "NONE" for the prefix will not show any prefixes, for both ordinal names and TAMNAMS-named scale degrees.
Typing in "NONE" for the prefix will not show any prefixes, for both ordinal names and TAMNAMS-named scale degrees.
<pre>{{MOS degrees|Scale Signature=4L 3s|MOS Prefix=NONE}}</pre>
<pre>{{MOS degrees|Scale Signature=4L 3s|MOS Prefix=NONE}}</pre>
{{MOS degrees|Scale Signature=4L 3s|MOS Prefix=NONE}}
{{MOS degrees|Scale Signature=4L 3s|MOS Prefix=NONE}}

Revision as of 21:05, 10 July 2023

Parameters

Parameters Required? Description 
Scale Signature
 Yes (optional on mos pages) The mos's scale signature in the form "xL ys", or for non-octave mosses, "xL ys<p/q>", "xL ys⟨p/q⟩", or "xL ys (p/q-equivalent)". If left blank and used on a mos page, then the page's title will be used. 
Step Ratio
 No (optional) The step ratio of the mos, denoted as a fraction p/q and separated with a slash. If left blank, then the step ratio "2/1" is used by default. 
UDP
 No (optional) The UDP representing the mode for which notation is applied. Due to technical limitations, using the pipe symbol is not advised and the "," character (comma) should be used instead. 
Notation
 No (optional) The notation for note names, consisting of the naturals (written without separators), sharp symbol, and flat symbol, each separated by semicolons. For example, standard notation is entered as "CDEFGAB; #; b". If left blank, the default is diamond-MOS notation (JKLMNOP for naturals, & for the sharp symbol, and @ for the flat symbol), or if the scale signature is 5L 2s, the default is standard notation. 
Genchain Extend
 No (optional) Additional intervals corresponding to the number of additional generators going up and/or down after those represented by the UDP. This value is per period, and the default value is the number of large steps per period. 
Degree Notation
 Deprecated How should degrees be named? Options include TAMNAMS mosdegree naming and ordinal naming (EG, the unison is either called the 0-mosstep or 1st). 
MOS Prefix
 No (optional) If using TAMNAMS mosdegree naming, does the mos have a prefix?

Usage

The typical use of this template is for showing a table of scale degrees for a specific step ratio. 

{{MOS degrees}}

Using a different scale signature

A scale signature different from the page's title can be entered as shown. 

{{MOS degrees|Scale Signature=5L 2s}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 5L 2s
Scale degree 12edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-diadegree (unison) 0 0 1/1 (exact)
Minor 1-diadegree 1 100
Major 1-diadegree 2 200
Minor 2-diadegree 3 300
Major 2-diadegree 4 400
Perfect 3-diadegree 5 500
Augmented 3-diadegree 6 600
Diminished 4-diadegree 6 600
Perfect 4-diadegree 7 700
Minor 5-diadegree 8 800
Major 5-diadegree 9 900
Minor 6-diadegree 10 1000
Major 6-diadegree 11 1100
Perfect 7-diadegree (octave) 12 1200 2/1 (exact)

Using a different step ratio

By default, cent and step values will be calculated for a step ratio of 2:1. A different step ratio can be entered as shown below. Up to 5 step ratios can be entered, written as p/q and with each ratio separated by semicolons. 

{{MOS degrees|Scale Signature=5L 2s|Step Ratio=2/1; 3/1; 3/2}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 5L 2s
Scale degree 12edo (Basic, L:s = 2:1) 17edo (Hard, L:s = 3:1) 19edo (Soft, L:s = 3:2) Approx. JI Ratios
Steps Cents Steps Cents Steps Cents
Perfect 0-diadegree (unison) 0 0 0 0 0 0 1/1 (exact)
Minor 1-diadegree 1 100 1 70.6 2 126.3
Major 1-diadegree 2 200 3 211.8 3 189.5
Minor 2-diadegree 3 300 4 282.4 5 315.8
Major 2-diadegree 4 400 6 423.5 6 378.9
Perfect 3-diadegree 5 500 7 494.1 8 505.3
Augmented 3-diadegree 6 600 9 635.3 9 568.4
Diminished 4-diadegree 6 600 8 564.7 10 631.6
Perfect 4-diadegree 7 700 10 705.9 11 694.7
Minor 5-diadegree 8 800 11 776.5 13 821.1
Major 5-diadegree 9 900 13 917.6 14 884.2
Minor 6-diadegree 10 1000 14 988.2 16 1010.5
Major 6-diadegree 11 1100 16 1129.4 17 1073.7
Perfect 7-diadegree (octave) 12 1200 17 1200 19 1200 2/1 (exact)

Using different notation and UDP

By default, diamond-mos notation is used, or if the scale signature is 5L 2s, standard notation is used. Different notation can be entered as shown below, with semicolons separating the note names, sharp symbol, and flat symbol. 

{{MOS degrees|Scale Signature=7L 2s|Notation=123456789; #; b}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 7L 2s
Scale degree On 1 16edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-armdegree (unison) 1 0 0 1/1 (exact)
Minor 1-armdegree 2b 1 75
Major 1-armdegree 2 2 150
Minor 2-armdegree 3b 3 225
Major 2-armdegree 3 4 300
Minor 3-armdegree 4 5 375
Major 3-armdegree 4# 6 450
Perfect 4-armdegree 5 7 525
Augmented 4-armdegree 5# 8 600
Diminished 5-armdegree 6b 8 600
Perfect 5-armdegree 6 9 675
Minor 6-armdegree 7b 10 750
Major 6-armdegree 7 11 825
Minor 7-armdegree 8 12 900
Major 7-armdegree 8# 13 975
Minor 8-armdegree 9 14 1050
Major 8-armdegree 9# 15 1125
Perfect 9-armdegree (octave) 1 16 1200 2/1 (exact)

By default, the mode for which nominals are applied is the symmetric mode, corresponding to a UDP of n|n. In the case of a mos with an even number of modes and therefore two "middle" modes (n+1|n and n|n+1), the brighter of the two is used as the default instead. Since some notation schemes may use a different mode as its "default", the UDP can be changed, as shown below. (Use a comma instead of the pipe | symbol.) 

{{MOS degrees|Scale Signature=7L 2s|Notation=123456789; #; b|UDP=7,1}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 7L 2s
Scale degree On 1 16edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-armdegree (unison) 1 0 0 1/1 (exact)
Minor 1-armdegree 2b 1 75
Major 1-armdegree 2 2 150
Minor 2-armdegree 3b 3 225
Major 2-armdegree 3 4 300
Minor 3-armdegree 4b 5 375
Major 3-armdegree 4 6 450
Perfect 4-armdegree 5 7 525
Augmented 4-armdegree 5# 8 600
Diminished 5-armdegree 6b 8 600
Perfect 5-armdegree 6 9 675
Minor 6-armdegree 7b 10 750
Major 6-armdegree 7 11 825
Minor 7-armdegree 8b 12 900
Major 7-armdegree 8 13 975
Minor 8-armdegree 9b 14 1050
Major 8-armdegree 9 15 1125
Perfect 9-armdegree (octave) 1 16 1200 2/1 (exact)

Typing in "NONE" for notation omits the column for note names. This allows the table to be used to list out interval sizes. 

{{MOS degrees|Scale Signature=7L 5s|Notation=NONE|}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 7L 5s
Scale degree 19edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-mosdegree (unison) 0 0 1/1 (exact)
Minor 1-mosdegree 1 63.2
Major 1-mosdegree 2 126.3
Minor 2-mosdegree 3 189.5
Major 2-mosdegree 4 252.6
Minor 3-mosdegree 4 252.6
Major 3-mosdegree 5 315.8
Minor 4-mosdegree 6 378.9
Major 4-mosdegree 7 442.1
Diminished 5-mosdegree 7 442.1
Perfect 5-mosdegree 8 505.3
Minor 6-mosdegree 9 568.4
Major 6-mosdegree 10 631.6
Perfect 7-mosdegree 11 694.7
Augmented 7-mosdegree 12 757.9
Minor 8-mosdegree 12 757.9
Major 8-mosdegree 13 821.1
Minor 9-mosdegree 14 884.2
Major 9-mosdegree 15 947.4
Minor 10-mosdegree 15 947.4
Major 10-mosdegree 16 1010.5
Minor 11-mosdegree 17 1073.7
Major 11-mosdegree 18 1136.8
Perfect 12-mosdegree (octave) 19 1200 2/1 (exact)

Advanced usage

Changing the genchain lengths

The values in the table are calculated using a generator chain, or specifically by stacking its bright generator up from the root and down from the note one period up (usually down from the octave). The UDP described previously represents the lengths of the ascending and descending chains to reach all of the nominals, and extending further reaches pitches modified by accidentals.

The default extend value is the number of large steps per period. This means for multi-period mosses, there is an ascending and descending chain for each period.

As an example using 5L 2s, a value of 5 effectively shows the two possible note names for all of the black keys on a standard piano. 

{{MOS degrees|Scale Signature=5L 2s|Genchain Extend=5}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 5L 2s
Scale degree 12edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-diadegree (unison) 0 0 1/1 (exact)
Minor 1-diadegree 1 100
Major 1-diadegree 2 200
Minor 2-diadegree 3 300
Major 2-diadegree 4 400
Perfect 3-diadegree 5 500
Augmented 3-diadegree 6 600
Diminished 4-diadegree 6 600
Perfect 4-diadegree 7 700
Minor 5-diadegree 8 800
Major 5-diadegree 9 900
Minor 6-diadegree 10 1000
Major 6-diadegree 11 1100
Perfect 7-diadegree (octave) 12 1200 2/1 (exact)

Changing this value to 0 means only the naturals are shown. 

{{MOS degrees|Scale Signature=5L 2s|Genchain Extend=0}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 5L 2s
Scale degree 12edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-diadegree (unison) 0 0 1/1 (exact)
Minor 1-diadegree 1 100
Major 1-diadegree 2 200
Minor 2-diadegree 3 300
Major 2-diadegree 4 400
Perfect 3-diadegree 5 500
Augmented 3-diadegree 6 600
Diminished 4-diadegree 6 600
Perfect 4-diadegree 7 700
Minor 5-diadegree 8 800
Major 5-diadegree 9 900
Minor 6-diadegree 10 1000
Major 6-diadegree 11 1100
Perfect 7-diadegree (octave) 12 1200 2/1 (exact)

To show only the minor intervals, consider that the UDP here is 5|1, meaning that the ascending chain starts with 5 generators and the descending chain starts with 1 generator. Going up one more generator produces the augmented 4th, so it's not necessary to extend the ascending chain. Going down 4 more generators produces all of the minor intervals and one more after that produces the diminished 5th, so the descending chain should be extended further by 4.

This template supports entering separate values for the ascending and descending extend values; the first value is for the ascending chain, and the second for the descending chain, as shown below. 

{{MOS degrees|Scale Signature=5L 2s|Genchain Extend=0,4}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 5L 2s
Scale degree 12edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-diadegree (unison) 0 0 1/1 (exact)
Minor 1-diadegree 1 100
Major 1-diadegree 2 200
Minor 2-diadegree 3 300
Major 2-diadegree 4 400
Perfect 3-diadegree 5 500
Augmented 3-diadegree 6 600
Diminished 4-diadegree 6 600
Perfect 4-diadegree 7 700
Minor 5-diadegree 8 800
Major 5-diadegree 9 900
Minor 6-diadegree 10 1000
Major 6-diadegree 11 1100
Perfect 7-diadegree (octave) 12 1200 2/1 (exact)

Changing the mos prefix

It may be beneficial to change the prefix in cases where more than one nondiatonic mos is being discussed. The default is "mos", but this can be changed as shown below, using the previous section's example. (Do not add a hyphen to the end of the prefix, as the template will do that automatically.) 

{{MOS degrees|Scale Signature=2L 5s|UDP=1,5|Notation=CDEFGAB;#;b|MOS Prefix=pel}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 2L 5s
Scale degree On C 9edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-peldegree (unison) C 0 0 1/1 (exact)
Minor 1-peldegree D 1 133.3
Major 1-peldegree D# 2 266.7
Minor 2-peldegree E 2 266.7
Major 2-peldegree E# 3 400
Diminished 3-peldegree Fb 3 400
Perfect 3-peldegree F 4 533.3
Perfect 4-peldegree G 5 666.7
Augmented 4-peldegree G# 6 800
Minor 5-peldegree A 6 800
Major 5-peldegree A# 7 933.3
Minor 6-peldegree B 7 933.3
Major 6-peldegree B# 8 1066.7
Perfect 7-peldegree (octave) C 9 1200 2/1 (exact)

Typing in "NONE" for the prefix will not show any prefixes, for both ordinal names and TAMNAMS-named scale degrees. 

{{MOS degrees|Scale Signature=4L 3s|MOS Prefix=NONE}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 4L 3s
Scale degree 11edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-degree (unison) 0 0 1/1 (exact)
Minor 1-degree 1 109.1
Major 1-degree 2 218.2
Perfect 2-degree 3 327.3
Augmented 2-degree 4 436.4
Minor 3-degree 4 436.4
Major 3-degree 5 545.5
Minor 4-degree 6 654.5
Major 4-degree 7 763.6
Diminished 5-degree 7 763.6
Perfect 5-degree 8 872.7
Minor 6-degree 9 981.8
Major 6-degree 10 1090.9
Perfect 7-degree (octave) 11 1200 2/1 (exact)
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