Template:MOS degrees/doc

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.
Show Abbreviations	No (optional)	Whether to show degree abbreviations. Abbreviations are shown without a mos prefix, and are intended to be an aid with entering JI ratios. Enter "1" to show abbreviations.
Number of Alterations	No (optional)	Whether to show alterations to a mos's specific interval sizes. One alteration shows the large size with +1 chroma and the small size with -1 chroma, or for periods (including the unison and equave), the perfect size with +1 and -1 chroma.
JI Ratios	No (optional)	Whether to include JI ratios for certain entries. For assistance with entering ratios, see below.
UDP	No (optional)	The UDP representing the mode for which notation is applied; this is to be used in conjunction with notation. 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". Notation will not be displayed unless entered.
MOS Prefix	No (optional)	If using TAMNAMS mosdegree naming, does the mos have a prefix?
Genchain Extend	Deprecated	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).

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)

Changing the mos prefix

A mos-prefix, if defined under TAMNAMS, is automatically added. For mosses outside of TAMNAMS that have a prefix, enter it as shown below.

{{MOS degrees
|Scale Signature=2L 5s
|MOS Prefix=pel}}

Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.

Scale degree of 2L 5s

Scale degree	9edo (Basic, L:s = 2:1)		Approx. JI Ratios
	Steps	Cents
Perfect 0-peldegree (unison)	0	0	1/1 (exact)
Minor 1-peldegree	1	133.3
Major 1-peldegree	2	266.7
Minor 2-peldegree	2	266.7
Major 2-peldegree	3	400
Diminished 3-peldegree	3	400
Perfect 3-peldegree	4	533.3
Perfect 4-peldegree	5	666.7
Augmented 4-peldegree	6	800
Minor 5-peldegree	6	800
Major 5-peldegree	7	933.3
Minor 6-peldegree	7	933.3
Major 6-peldegree	8	1066.7
Perfect 7-peldegree (octave)	9	1200	2/1 (exact)

Typing in "NONE" for the prefix will not show any prefixes.

{{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)

Using notation and UDP

By default, no notation is displayed unless entered as shown in the example below.

{{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)

The template will attempt to use default notation with a default UDP if the keyword "Default" is entered. The default is standard notation on C (for 5L 2s) and diamond-mos for any nondiatonic mosses.

{{MOS degrees
|Scale Signature=4L 3s
|Notation=Default
}}

Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.

Scale degree of 4L 3s

Scale degree	On J	11edo (Basic, L:s = 2:1)		Approx. JI Ratios
		Steps	Cents
Perfect 0-smidegree (unison)	J	0	0	1/1 (exact)
Minor 1-smidegree	K@	1	109.1
Major 1-smidegree	K	2	218.2
Perfect 2-smidegree	L	3	327.3
Augmented 2-smidegree	L&	4	436.4
Minor 3-smidegree	M@	4	436.4
Major 3-smidegree	M	5	545.5
Minor 4-smidegree	N	6	654.5
Major 4-smidegree	N&	7	763.6
Diminished 5-smidegree	O@	7	763.6
Perfect 5-smidegree	O	8	872.7
Minor 6-smidegree	P	9	981.8
Major 6-smidegree	P&	10	1090.9
Perfect 7-smidegree (octave)	J	11	1200	2/1 (exact)

Advanced usage

Adding JI ratios

JI ratios can be added by writing a semicolon-delimited list of entries, where each entry is an abbreviation for a scale degree, followed by a colon, followed by the JI ratio.

To help with entering ratios, set the parameter "Show Abbreviations" to 1 to show scale degrees.

{{MOS degrees
|Scale Signature=4L 3s
|Show Abbreviations=1
|JI Ratios=
M1md: 8/7;
P2md: 77/64, 6/5;
m3md: 14/11;
M3md:11/8;
m4md: 16/11;
M4md: 11/7;
P5md: 5/3;
m6md: 7/4;
}}

Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.

Scale degree of 4L 3s

Scale degree	Abbrev.	11edo (Basic, L:s = 2:1)		Approx. JI Ratios
		Steps	Cents
Perfect 0-smidegree (unison)	P0md	0	0	1/1 (exact)
Minor 1-smidegree	m1md	1	109.1
Major 1-smidegree	M1md	2	218.2	8/7
Perfect 2-smidegree	P2md	3	327.3	77/64, 6/5
Augmented 2-smidegree	A2md	4	436.4
Minor 3-smidegree	m3md	4	436.4	14/11
Major 3-smidegree	M3md	5	545.5	11/8
Minor 4-smidegree	m4md	6	654.5	16/11
Major 4-smidegree	M4md	7	763.6	11/7
Diminished 5-smidegree	d5md	7	763.6
Perfect 5-smidegree	P5md	8	872.7	5/3
Minor 6-smidegree	m6md	9	981.8	7/4
Major 6-smidegree	M6md	10	1090.9
Perfect 7-smidegree (octave)	P7md	11	1200	2/1 (exact)

Showing alterations

Alterations refer to raising scale degrees by a chroma beyond the large and small sizes of a mos. For the number of alterations added, an additional altered degree is shown from raising the large size of a scale degree and lowering the small size of a scale degree (or the perfect size for period, unison, and equaves).

{{MOS degrees
|Scale Signature=4L 3s
|Number of Alterations=1
}}

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-smidegree (unison)	0	0	1/1 (exact)
Augmented 0-smidegree	1	109.1
Diminished 1-smidegree	0	0
Minor 1-smidegree	1	109.1
Major 1-smidegree	2	218.2
Augmented 1-smidegree	3	327.3
Diminished 2-smidegree	2	218.2
Perfect 2-smidegree	3	327.3
Augmented 2-smidegree	4	436.4
2× Augmented 2-smidegree	5	545.5
Diminished 3-smidegree	3	327.3
Minor 3-smidegree	4	436.4
Major 3-smidegree	5	545.5
Augmented 3-smidegree	6	654.5
Diminished 4-smidegree	5	545.5
Minor 4-smidegree	6	654.5
Major 4-smidegree	7	763.6
Augmented 4-smidegree	8	872.7
2× Diminished 5-smidegree	6	654.5
Diminished 5-smidegree	7	763.6
Perfect 5-smidegree	8	872.7
Augmented 5-smidegree	9	981.8
Diminished 6-smidegree	8	872.7
Minor 6-smidegree	9	981.8
Major 6-smidegree	10	1090.9
Augmented 6-smidegree	11	1200
Diminished 7-smidegree	10	1090.9
Perfect 7-smidegree (octave)	11	1200	2/1 (exact)

Limitations

Setting the number of alterations to any value greater than 1 throws the following error:

Lua error: Internal error: The interpreter has terminated with signal "24".