Template:MOS mode degrees/doc: Difference between revisions

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Updated to reflect closest-mode search returning the brightest and darkest closest matches
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=== Usage ===
=== Usage ===
The typical use of this template is for showing a table of scale degrees for each mode of a mos or modmos, a step pattern that deviates from the true mos pattern. Scale degrees are referred to as mosdegrees and are indexed starting at 0, per [[TAMNAMS]] parlance.
The typical use of this template is for showing a table of scale degrees for each mode of a mos or a modmos, a step pattern that deviates from the true mos pattern. Scale degrees are referred to as mosdegrees and are indexed starting at 0, per [[TAMNAMS]] parlance.
<pre>{{MOS mode degrees}}</pre>
<pre>{{MOS mode degrees}}</pre>


Line 30: Line 30:
| Scale Signature=5L 2s
| Scale Signature=5L 2s
| MOS Prefix=mos}}</pre>
| MOS Prefix=mos}}</pre>
==== Using a modmos's step pattern ====
The modes of a modified step pattern, or modmos, can be entered instead. This changes the table to display the closest true mos modes, as well as display the modes in rotational order rather than in decreasing modal brightness.
<pre>{{MOS mode degrees
| Scale Signature=5L 2s
| MODMOS Step Pattern=LsLLsAs}}</pre>
{{MOS mode degrees
| Scale Signature=5L 2s
| MODMOS Step Pattern=LsLLsAs}}


==== Using mode names ====
==== Using mode names ====
Line 55: Line 46:
| MODMOS Step Pattern=LsLLsAs}}
| MODMOS Step Pattern=LsLLsAs}}


=== Advanced use ===
=== For use with modmosses ===
==== Entering modmosses ====
==== Entering a modmos's step pattern ====
The modes of a modified step pattern, or modmos, can be entered instead. This changes the table to display the closest true mos modes, as well as display the modes in rotational order rather than in decreasing modal brightness.
<pre>{{MOS mode degrees
| Scale Signature=5L 2s
| MODMOS Step Pattern=LsLLsAs}}</pre>
{{MOS mode degrees
| Scale Signature=5L 2s
| MODMOS Step Pattern=LsLLsAs}}
 
The step pattern for a modmos uses the characters L and s, either arranged differently from the true mos pattern or may include the characters A, c, and d. Each character has a value represented in large and small steps. It is recommended to use a step pattern whose value of L's and s's matches that of the true mos pattern. The table below shows the sizes of each supported step type.
The step pattern for a modmos uses the characters L and s, either arranged differently from the true mos pattern or may include the characters A, c, and d. Each character has a value represented in large and small steps. It is recommended to use a step pattern whose value of L's and s's matches that of the true mos pattern. The table below shows the sizes of each supported step type.
{| class="wikitable center-all"
{| class="wikitable center-all"
Line 75: Line 74:
As an example, the step pattern "LsLLsAs" is a modmos of 5L 2s, containing 3 large steps, 3 small steps, and one augmented step. The size of an augmented step is equivalent to that of a large step and chroma, and adding a chroma to a small step makes it a large step. In other words, the step pair "sA" is equivalent to that of "LL", since they have the same value in L's and s's, meaning that "LsLLsAs" is equal to 5 large steps and 2 small steps.
As an example, the step pattern "LsLLsAs" is a modmos of 5L 2s, containing 3 large steps, 3 small steps, and one augmented step. The size of an augmented step is equivalent to that of a large step and chroma, and adding a chroma to a small step makes it a large step. In other words, the step pair "sA" is equivalent to that of "LL", since they have the same value in L's and s's, meaning that "LsLLsAs" is equal to 5 large steps and 2 small steps.


==== Caveats regarding closest-mode search ====
=== Caveats regarding closest-mode search ===
For each mode of a modmos, the template finds the closest mode, which is the closest mode that has the fewest alterations; that is, whichever mode of the true mos requires the fewest changes to reach a given modmos's mode. If more than one mode can reach the same modmos mode using the same number of alterations, then whichever closest mode is the brightest is selected instead.
For each mode of a modmos, the template finds whichever that has the fewest alterations.
 
In cases where there are are more than one closest modes, both the brightest and darkest closest modes are provided. This doesn't always produce the mode that one may expect; for example, melodic minor (step pattern LsLLLLs) can be thought of as the Aeolian mode with a natural-6 and natural-7, but the template calculates the closest mode to be both Dorian (UDP 3|3) or Ionian (UDP 5|1).


This doesn't always produce the mode that one may expect; for example, melodic minor (step pattern LsLLLLs) can be thought of as the Aeolian mode with a natural-6 and natural-7 (or major 5- and 6-mosdegrees, in TAMNAMS parlance), but the template calculates the closest mode to be Dorian (UDP 3|3) with a major 7th (6-mosstep).
{{MOS mode degrees
{{MOS mode degrees
| Scale Signature=5L 2s
| Scale Signature=5L 2s
| MODMOS Step Pattern=LsLLLLs
| MODMOS Step Pattern=LsLLLLs
| Mode Names=Aeolian ♮6 ♮7 (Melodic minor); Dorian b2; Lydian #5 (Lydian augmented); Lydian b7 (Lydian dominant); Mixolydian b6; Locrian ♮2 (Half-diminished); Locrian bb4 (Altered dominant, super-locrian)
}}
}}


The use of the brightest mode is a tradeoff between using the brightest mode as a tiebreaker versus the darkest mode.
=== Default mode names ===
{| class="wikitable"
 
|+ Comparison of UDP and alterations of LsLLLLs
Modes of 5L 2s and some of its modmosses are automatically provided by the template, notably:
! Brightest mode as tiebreaker !! Darkest mode as tiebreaker !! Step pattern !! Common names || Which tiebreaker is correct?
* Harmonic minor and its modes
|-
* Harmonic major and its modes
| 5<nowiki>|</nowiki>1 m2md || 3<nowiki>|</nowiki>3 M6md || LsLLLLs || Aeolian ♮6 ♮7 (Melodic minor) || Neither
* Melodic minor and its modes
|-
* Neapolitan minor and its modes
| 3<nowiki>|</nowiki>3 m1md || 1<nowiki>|</nowiki>5 M5md || sLLLLsL || Dorian b2 || Brightest
* Neapolitan major and its modes
|-
| 6<nowiki>|</nowiki>0 A4md || 6<nowiki>|</nowiki>0 A4md || LLLLsLs || Lydian #5 (Lydian augmented) || Brightest
|-
| 6<nowiki>|</nowiki>0 m6md || 4<nowiki>|</nowiki>2 A3md || LLLsLsL || Lydian b7 (Lydian dominant)} || Brightest
|-
| 4<nowiki>|</nowiki>2 m5md || 2<nowiki>|</nowiki>4 M2md || LLsLsLL || Mixolydian b6 || Brightest
|-
| 2<nowiki>|</nowiki>4 d4md || 0<nowiki>|</nowiki>6 M1md || LsLsLLL || Locrian ♮2 (Half-diminished) || Brightest
|-
| 0<nowiki>|</nowiki>6 d3md || 0<nowiki>|</nowiki>6 d3md || sLsLLLL || Locrian bb4 (Altered dominant, super-locrian) || Brightest
|}
{| class="wikitable"
|+ Comparison of UDP and alterations of sLLLLLs
! Brightest mode as tiebreaker !! Darkest mode as tiebreaker !! Step pattern !! Attested name(s) || Which tiebreaker is correct?
|-
| 5<nowiki>|</nowiki>1 m1md m2md || 1<nowiki>|</nowiki>5 M5md M6md || sLLLLLs || Ionian b2 b3 (Neapolitan major) || Brightest
|-
| 6<nowiki>|</nowiki>0 A4md A5md || 6<nowiki>|</nowiki>0 A4md A5md || LLLLLss || Lydian #5 #6 (Leading whole-tone) || Brightest
|-
| 6<nowiki>|</nowiki>0 A4md m6md || 4<nowiki>|</nowiki>2 A3md A4md || LLLLssL || Lydian #5 b7 (Lydian dominant augmented), Mixolydian #5 #11 || Depends on name
|-
| 6<nowiki>|</nowiki>0 m5md m6md || 2<nowiki>|</nowiki>4 M2md A3md || LLLssLL || Lydian b6 b7, Mixolydian #11 #13 || Depends on name
|-
| 4<nowiki>|</nowiki>2 d4md m5md || 0<nowiki>|</nowiki>6 M1md M2md || LLssLLL || Locrian ♮2 ♮3 (Major locrian), Mixolydian b5 b6 || Depends on name
|-
| 2<nowiki>|</nowiki>4 d3md d4md || 0<nowiki>|</nowiki>6 M1md d3md || LssLLLL || Locrian ♮2 b4 (Semilocrian b4) || Darkest
|-
| 0<nowiki>|</nowiki>6 d2md d3md || 0<nowiki>|</nowiki>6 d2md d3md || ssLLLLL || Locrian bb3 b4 (Superlocrian bb3) || Darkest
|}


=== Names ===
The names as suggested by closest-mode search are provided, as well as some of its common names.
The names for the modes and degrees are pulled from the following sources:
* https://www.guitarmasterclass.net/ls/exotic-scales-neapolitan-major/?part=main
* http://ftp.labdoo.org/download/Public/manuals/manuals-ubuntu/EN/Solfege/docs.solfege.org/3.22/C/scales/nea.html


=== See also ===
=== See also ===
* {{modlink}}
* {{modlink}}

Revision as of 07:52, 23 July 2024

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. 
MOS Prefix
 No (optional) If using TAMNAMS mosdegree naming, does the mos have a prefix? 
MODMOS Step Pattern
 No (optional) Step pattern of a MODMOS. 
Mode Names
 No (optional) Names for the modes of a mos.

Usage

The typical use of this template is for showing a table of scale degrees for each mode of a mos or a modmos, a step pattern that deviates from the true mos pattern. Scale degrees are referred to as mosdegrees and are indexed starting at 0, per TAMNAMS parlance. 

{{MOS mode degrees}}

Using a different scale signature

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

{{MOS mode degrees
| Scale Signature=5L 2s}}
Scale degrees of the modes of 5L 2s
UDP Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
6|0 1 LLLsLLs Perf. Maj. Maj. Aug. Perf. Maj. Maj. Perf.
5|1 5 LLsLLLs Perf. Maj. Maj. Perf. Perf. Maj. Maj. Perf.
4|2 2 LLsLLsL Perf. Maj. Maj. Perf. Perf. Maj. Min. Perf.
3|3 6 LsLLLsL Perf. Maj. Min. Perf. Perf. Maj. Min. Perf.
2|4 3 LsLLsLL Perf. Maj. Min. Perf. Perf. Min. Min. Perf.
1|5 7 sLLLsLL Perf. Min. Min. Perf. Perf. Min. Min. Perf.
0|6 4 sLLsLLL Perf. Min. Min. Perf. Dim. Min. Min. Perf.

Using a different mos prefix

By default, the mos prefix is "mos". For TAMNAMS-named mosses, the mos prefix will be automatically added. For non-TAMNAMS mosses that have prefixes, enter it using the parameter "MOS Prefix", as shown. 

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

Using mode names

The mode names can be entered as shown below. The number of names must exactly match the number of modes, and each mode must be separated with a semicolon. 

{{MOS mode degrees
| Scale Signature=4L 3s
| Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic}}
Scale degrees of the modes of 4L 3s
UDP Cyclic
order 		Step
pattern 		Scale degree (smidegree)
0 1 2 3 4 5 6 7
6|0 1 LLsLsLs Perf. Maj. Aug. Maj. Maj. Perf. Maj. Perf.
5|1 6 LsLLsLs Perf. Maj. Perf. Maj. Maj. Perf. Maj. Perf.
4|2 4 LsLsLLs Perf. Maj. Perf. Maj. Min. Perf. Maj. Perf.
3|3 2 LsLsLsL Perf. Maj. Perf. Maj. Min. Perf. Min. Perf.
2|4 7 sLLsLsL Perf. Min. Perf. Maj. Min. Perf. Min. Perf.
1|5 5 sLsLLsL Perf. Min. Perf. Min. Min. Perf. Min. Perf.
0|6 3 sLsLsLL Perf. Min. Perf. Min. Min. Dim. Min. Perf.

Mode names for 5L 2s and its modmos LLsLsAs are provided by the template automatically.

Scale degrees of the modes of 5L 2s
UDP Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
6|0 1 LLLsLLs Perf. Maj. Maj. Aug. Perf. Maj. Maj. Perf.
5|1 5 LLsLLLs Perf. Maj. Maj. Perf. Perf. Maj. Maj. Perf.
4|2 2 LLsLLsL Perf. Maj. Maj. Perf. Perf. Maj. Min. Perf.
3|3 6 LsLLLsL Perf. Maj. Min. Perf. Perf. Maj. Min. Perf.
2|4 3 LsLLsLL Perf. Maj. Min. Perf. Perf. Min. Min. Perf.
1|5 7 sLLLsLL Perf. Min. Min. Perf. Perf. Min. Min. Perf.
0|6 4 sLLsLLL Perf. Min. Min. Perf. Dim. Min. Min. Perf.
Scale degrees of the modes of 5L 2s (LsLLsAs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
2|4 M6md 1 LsLLsAs Perf. Maj. Min. Perf. Perf. Min. Maj. Perf.
0|6 M5md 2 sLLsAsL Perf. Min. Min. Perf. Dim. Maj. Min. Perf.
5|1 A4md 3 LLsAsLs Perf. Maj. Maj. Perf. Aug. Maj. Maj. Perf.
3|3 A3md 4 LsAsLsL Perf. Maj. Min. Aug. Perf. Maj. Min. Perf.
1|5 M2md 5 sAsLsLL Perf. Min. Maj. Perf. Perf. Min. Min. Perf.
6|0 A1md 6 AsLsLLs Perf. Aug. Maj. Aug. Perf. Maj. Maj. Perf.
0|6 d3md d6md 7 sLsLLsA Perf. Min. Min. Dim. Dim. Min. Dim. Perf.

For use with modmosses

Entering a modmos's step pattern

The modes of a modified step pattern, or modmos, can be entered instead. This changes the table to display the closest true mos modes, as well as display the modes in rotational order rather than in decreasing modal brightness. 

{{MOS mode degrees
| Scale Signature=5L 2s
| MODMOS Step Pattern=LsLLsAs}}
Scale degrees of the modes of 5L 2s (LsLLsAs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
2|4 M6md 1 LsLLsAs Perf. Maj. Min. Perf. Perf. Min. Maj. Perf.
0|6 M5md 2 sLLsAsL Perf. Min. Min. Perf. Dim. Maj. Min. Perf.
5|1 A4md 3 LLsAsLs Perf. Maj. Maj. Perf. Aug. Maj. Maj. Perf.
3|3 A3md 4 LsAsLsL Perf. Maj. Min. Aug. Perf. Maj. Min. Perf.
1|5 M2md 5 sAsLsLL Perf. Min. Maj. Perf. Perf. Min. Min. Perf.
6|0 A1md 6 AsLsLLs Perf. Aug. Maj. Aug. Perf. Maj. Maj. Perf.
0|6 d3md d6md 7 sLsLLsA Perf. Min. Min. Dim. Dim. Min. Dim. Perf.

The step pattern for a modmos uses the characters L and s, either arranged differently from the true mos pattern or may include the characters A, c, and d. Each character has a value represented in large and small steps. It is recommended to use a step pattern whose value of L's and s's matches that of the true mos pattern. The table below shows the sizes of each supported step type.

Character Case-sensitive? Step name Size in L's and s's
L Yes (uppercase) The large step of a mos L
s No (uppercase or lowercase) The small step of a mos s
c Yes (lowercase) The difference between a large and small step; the interval needed to add to a small step to make it a large step L − s
A Yes (uppercase) An augmented step; a large step plus a chroma 2L − s
d Yes (lowercase) A diminished step (or diesis in some contexts); a small step minus a chroma −L + 2s

As an example, the step pattern "LsLLsAs" is a modmos of 5L 2s, containing 3 large steps, 3 small steps, and one augmented step. The size of an augmented step is equivalent to that of a large step and chroma, and adding a chroma to a small step makes it a large step. In other words, the step pair "sA" is equivalent to that of "LL", since they have the same value in L's and s's, meaning that "LsLLsAs" is equal to 5 large steps and 2 small steps.

Caveats regarding closest-mode search

For each mode of a modmos, the template finds whichever that has the fewest alterations.

In cases where there are are more than one closest modes, both the brightest and darkest closest modes are provided. This doesn't always produce the mode that one may expect; for example, melodic minor (step pattern LsLLLLs) can be thought of as the Aeolian mode with a natural-6 and natural-7, but the template calculates the closest mode to be both Dorian (UDP 3|3) or Ionian (UDP 5|1).


Scale degrees of the modes of 5L 2s (LsLLLLs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
5|1 m2md
3|3 M6md 		1 LsLLLLs Perf. Maj. Min. Perf. Perf. Maj. Maj. Perf.
3|3 m1md
1|5 M5md 		2 sLLLLsL Perf. Min. Min. Perf. Perf. Maj. Min. Perf.
6|0 A4md 3 LLLLsLs Perf. Maj. Maj. Aug. Aug. Maj. Maj. Perf.
6|0 m6md
4|2 A3md 		4 LLLsLsL Perf. Maj. Maj. Aug. Perf. Maj. Min. Perf.
4|2 m5md
2|4 M2md 		5 LLsLsLL Perf. Maj. Maj. Perf. Perf. Min. Min. Perf.
2|4 d4md
0|6 M1md 		6 LsLsLLL Perf. Maj. Min. Perf. Dim. Min. Min. Perf.
0|6 d3md 7 sLsLLLL Perf. Min. Min. Dim. Dim. Min. Min. Perf.

Default mode names

Modes of 5L 2s and some of its modmosses are automatically provided by the template, notably:

  • Harmonic minor and its modes
  • Harmonic major and its modes
  • Melodic minor and its modes
  • Neapolitan minor and its modes
  • Neapolitan major and its modes

The names as suggested by closest-mode search are provided, as well as some of its common names.

See also

Retrieved from "https://en.xen.wiki/index.php?title=Template:MOS_mode_degrees/doc&oldid=148382"