Comparison of mode notation systems: Difference between revisions

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Several people have attempted to generalize the [[mode]]s of the [[5L 2s|diatonic]] scale by designing a system to notate or number the modes of any given scale, or at least any scale with certain properties such as [[MOS]]:
Several mode numbering or notation systems have been designed in an attempt to generalize the [[mode]]s of the [[5L 2s|diatonic]] scale. These systems aim to work for given scale, or at least any scale with certain properties such as [[MOS]].


* [[Mike Battaglia]]'s system: [[Modal UDP notation]];
Here are the most common systems used proposed by the xenharmonic community:
* [[Kite Giedraitis]]' system: [[Kite's Method of Naming Rank-2 Scales using Mode Numbers]];
* [[Modal UDP notation]];
* [[Jake Freivald]]'s system: [[Jake Freivald's mode numbering system]].
* [[Genchain mode numbering]] (GMN);
* [[Jake Freivald's mode numbering system]].


== Comparison tables ==
== Comparison tables ==
This section compares the different notations enumerated above. As an example, the seven diatonic modes (Ionian, Dorian, Phrygian, etc) will be used.
This section compares the different notations enumerated above. As an example, the seven diatonic modes (Ionian, Dorian, Phrygian, etc) will be used, first using the tempered meantone[7] scale and then using the abstract 5L 2s scale.
{| class="wikitable sortable"
{| class="wikitable sortable center-all"
|+ Comparison for diatonic (5L 2s) modes
|+ Comparison for meantone[7] modes
!Mode name
!Mode name
!Step pattern
!Step pattern
!Battaglia's method
!Modal UDP notation
(or UDP notation)
!Genchain mode numbering
!Kite's method
!Freivald's method
!Freivald's method
|-
|-
|Lydian
|Lydian
|LLLsLLs
|LLLsLLs
|<nowiki>6|0</nowiki>
|meantone[7] <nowiki>6|0</nowiki>
|1st meantone[7]
|1st meantone[7]
|Mode 4
|meantone[7] mode 4
|-
|-
|Ionian
|Ionian
|LLsLLLs
|LLsLLLs
|<nowiki>5|1</nowiki>
|meantone[7] <nowiki>5|1</nowiki>
|2nd meantone[7]
|2nd meantone[7]
|Mode 1
|meantone[7] mode 1
|-
|-
|Mixolydian
|Mixolydian
|LLsLLsL
|LLsLLsL
|<nowiki>4|2</nowiki>
|meantone[7] <nowiki>4|2</nowiki>
|3rd meantone[7]
|3rd meantone[7]
|Mode 5
|meantone[7] mode 5
|-
|-
|Dorian
|Dorian
|LsLLLsL
|LsLLLsL
|<nowiki>3|3</nowiki>
|meantone[7] <nowiki>3|3</nowiki>
|4th meantone[7]
|4th meantone[7]
|Mode 2
|meantone[7] mode 2
|-
|-
|Aeolian
|Aeolian
|LsLLsLL
|LsLLsLL
|<nowiki>2|4</nowiki>
|meantone[7] <nowiki>2|4</nowiki>
|5th meantone[7]
|5th meantone[7]
|Mode 6
|meantone[7] mode 6
|-
|-
|Phrygian
|Phrygian
|sLLLsLL
|sLLLsLL
|<nowiki>1|5</nowiki>
|meantone[7] <nowiki>1|5</nowiki>
|6th meantone[7]
|6th meantone[7]
|Mode 3
|meantone[7] mode 3
|-
|-
|Locrian
|Locrian
|sLLsLLL
|sLLsLLL
|<nowiki>0|6</nowiki>
|meantone[7] <nowiki>0|6</nowiki>
|7th meantone[7]
|7th meantone[7]
|Mode 7
|meantone[7] mode 7
|}
 
{| class="wikitable sortable center-all"
|+ Comparison for 5L 2s modes
!Mode name
!Step pattern
!Modal UDP notation
!Genchain mode numbering
!Freivald's method
|-
|Lydian
|LLLsLLs
|5L 2s <nowiki>6|0</nowiki>
|1st 5L 2s
|5L 2s mode 4
|-
|Ionian
|LLsLLLs
|5L 2s <nowiki>5|1</nowiki>
|2nd 5L 2s
|5L 2s mode 1
|-
|Mixolydian
|LLsLLsL
|5L 2s <nowiki>4|2</nowiki>
|3rd 5L 2s
|5L 2s mode 5
|-
|Dorian
|LsLLLsL
|5L 2s <nowiki>3|3</nowiki>
|4th 5L 2s
|5L 2s mode 2
|-
|Aeolian
|LsLLsLL
|5L 2s <nowiki>2|4</nowiki>
|5th 5L 2s
|5L 2s mode 6
|-
|Phrygian
|sLLLsLL
|5L 2s <nowiki>1|5</nowiki>
|6th 5L 2s
|5L 2s mode 3
|-
|Locrian
|sLLsLLL
|5L 2s <nowiki>0|6</nowiki>
|7th 5L 2s
|5L 2s mode 7
|}
|}


Latest revision as of 08:44, 5 June 2025

Several mode numbering or notation systems have been designed in an attempt to generalize the modes of the diatonic scale. These systems aim to work for given scale, or at least any scale with certain properties such as MOS.

Here are the most common systems used proposed by the xenharmonic community:

Comparison tables

This section compares the different notations enumerated above. As an example, the seven diatonic modes (Ionian, Dorian, Phrygian, etc) will be used, first using the tempered meantone[7] scale and then using the abstract 5L 2s scale.

Comparison for meantone[7] modes
Mode name Step pattern Modal UDP notation Genchain mode numbering Freivald's method
Lydian LLLsLLs meantone[7] 6|0 1st meantone[7] meantone[7] mode 4
Ionian LLsLLLs meantone[7] 5|1 2nd meantone[7] meantone[7] mode 1
Mixolydian LLsLLsL meantone[7] 4|2 3rd meantone[7] meantone[7] mode 5
Dorian LsLLLsL meantone[7] 3|3 4th meantone[7] meantone[7] mode 2
Aeolian LsLLsLL meantone[7] 2|4 5th meantone[7] meantone[7] mode 6
Phrygian sLLLsLL meantone[7] 1|5 6th meantone[7] meantone[7] mode 3
Locrian sLLsLLL meantone[7] 0|6 7th meantone[7] meantone[7] mode 7
Comparison for 5L 2s modes
Mode name Step pattern Modal UDP notation Genchain mode numbering Freivald's method
Lydian LLLsLLs 5L 2s 6|0 1st 5L 2s 5L 2s mode 4
Ionian LLsLLLs 5L 2s 5|1 2nd 5L 2s 5L 2s mode 1
Mixolydian LLsLLsL 5L 2s 4|2 3rd 5L 2s 5L 2s mode 5
Dorian LsLLLsL 5L 2s 3|3 4th 5L 2s 5L 2s mode 2
Aeolian LsLLsLL 5L 2s 2|4 5th 5L 2s 5L 2s mode 6
Phrygian sLLLsLL 5L 2s 1|5 6th 5L 2s 5L 2s mode 3
Locrian sLLsLLL 5L 2s 0|6 7th 5L 2s 5L 2s mode 7

It should be noted that the MOS pattern 5L 2s is supported by multiple temperaments, and as such, the name "meantone" is not meant to exclusively describe 5L 2s.

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