31edo solfege: Difference between revisions

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|Do

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The system shown preserved vowels in perfect fifths in any scale that only uses notes from meantone[7] modes, mohajira[7] modes, and substitutions of meantone intervals with corresponding septimal subminor or supermajor intervals, allowing for any diatonic type scale to be simple as easy to learn, as the inconsistencies of So-Ra and Te-Fo can be smoothed out by the fact that Ra can also be called Ro, for perfect second, or 9/8, and Fo is also Fe, as it's the "minor fourth", as 4/3 is tempered together with 27/20. These ~~commas~~ being tempered allows the system to preserve a surprising amount of consistency, being extremely easy to learn. Du is used for the up unison because it helps consistency, is generally used as a quartertone in scales like Centaurus, and because it allows the also common augmented and upaugmented unisons to be named, with Da and Di.

The system shown preserved vowels in perfect fifths in any scale that only uses notes from [[meantone]][7] modes, [[mohajira]][7] modes, and substitutions of meantone intervals with corresponding [[7-limit|septimal]] (7-limit) [[subminor]] or [[supermajor]] intervals, allowing for any diatonic type scale to be simple as easy to learn, as the inconsistencies of So-Ra and Te-Fo can be smoothed out by the fact that Ra can also be called Ro, for perfect second, or [[9/8]], and Fo is also Fe, as it's the "minor fourth", as [[4/3]] is tempered together with [[27/20]]. These [[comma]]s being [[tempered]] allows the system to preserve a surprising amount of consistency, being extremely easy to learn. Du is used for the up unison because it helps consistency, is generally used as a [[quartertone]] in scales like [[Centaurus]], and because it allows the also common augmented and upaugmented unisons to be named, with Da and Di.

The system is built on this consistency, and preserves the standard minor intervals names, as well as -a as the standard major from La, and Ti as the strongest leading tone, here being the upmajor seventh. The remaining vowels of -uh for sub and -u for neutral are used because they correspond to the vowel sounds from their respective words.

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To expand into intervals that surpass these, such as the ^A5, we will extend to Augmented, Diminished, Upaugmented, and Downdiminished intervals. The vowels for these are -ah (short a sound), -ih (for the short i in diminished), oy, and ow (for down) respectively. They work similarly to the others, and are first used in the second set of unisons, allowing the M7-A4 and d5-m2 perfect fifths and others of the sort to still use consistent vowels, as they show up in diatonic scales.

If intervals are used solely for their 3-limit role, such as the M2 or in some cases the M6, the names Ro and Lo may be used, for perfect second or perfect sixth, as Ra can be thought of to imply 10/9, while Ro would imply 9/8, similarly to Lo and 27/16. In other cases, Mo would be 32/27 and To would be 16/9. A situation where this naming scheme may be used would be in Harrison Major, P1 M2 ^M3 P4 P5 M6 ^M7 P8, where the M6 is used so that the ii chord has a perfect fifth, while the vi chord has a wolf fifth in order to be used as a "wolf tonic" to prevent tonicization.

If intervals are used solely for their 3-limit role, such as the M2 or in some cases the M6, the names Ro and Lo may be used, for perfect second or perfect sixth, as Ra can be thought of to imply 10/9, while Ro would imply 9/8, similarly to Lo and 27/16. In other cases, Mo would be 32/27 and To would be 16/9. A situation where this naming scheme may be used would be in Harrison Major, P1 M2 ^M3 P4 P5 M6 ^M7 P8, where the M6 is used so that the ii chord has a perfect fifth, while the vi chord has a [[Wolf interval|wolf fifth]] in order to be used as a "wolf tonic" to prevent tonicization.

==Kite Giedraitis's solfege==

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Once this is fully internalized, add in the other 4 vowels.

===The circle of fifths===

The 5 vowels create 5 chains of fifths. The 2 ~~tritones~~ with duplicate names each connect 2 pairs of chains. Thus there are only 3 fifths that don't rhyme:

The 5 vowels create 5 [[chain of fifths|chains of fifths]]. The 2 [[tritone]]s with duplicate names each connect 2 pairs of chains. Thus there are only 3 fifths that don't rhyme:

*Do - Se (P1 to P5)

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However going a 5th up from an aug or upaug 4th would go to an aug or upaug 8ve, which doesn't exist in this solfege. Therefore one must rename the 4th as a dim 5th, then go up to a minor 2nd. Thus Fe + 5th = Su + 5th = Ru. Dim 5ths may also need renaming: So + 4th = Fi + 4th = Ti.

==Andrew Heathwaite's solfege==

[[Andrew Heathwaite]]'s solfege is a subset of his [[41edo]] solfege. It expands on the conventional Do - Di/Ra - Re - Ri/Me - Mi - Fa - Fi/Se - So - Si/Le - La - Li/Te - Ti - Do. As a result there are 6 different vowel sequences.

{| class="wikitable" style="text-align:center"

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See also: [[17edo Solfege]], [[22edo Solfege]], [[29edo solfege|29edo Solfege]] and [[41edo solfege|41edo Solfege]].

For intervals that appear in the diatonic scale, the traditional solfege names are grandfathered in. While this makes it easier to learn the new syllables as extensions of the old ones — if you are trained with the old ones to begin with — it also makes for many irregularities.

For intervals that appear in the [[diatonic scale]], the traditional solfege names are grandfathered in. While this makes it easier to learn the new syllables as extensions of the old ones — if you are trained with the old ones to begin with — it also makes for many irregularities.

The syllables '''do, re, mi, fa, so[l], la, ti''' have the same meaning as traditional major and perfect intervals. The names for minor intervals are also retained: '''ra, me, le, te''', as well as the augmented fourth, '''fi''', and diminished fifth, '''se'''. Some traditional names for chromatically-altered intervals appear here, but altered by a semisharp or semiflat, rather than a full sharp or flat: '''di''' for a semiaugmented unison, '''da''' for a semidiminished unison, '''ri''' for a semiaugmented second, '''fe''' for a semidiminished fourth, '''si''' for a semiaugmented fifth, and '''li''' for a semiaugmented sixth. The remaining syllables flesh out the septimal and undecimal intervals which are not represented in 12edo.

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 |Do
 |}
-The system shown preserved vowels in perfect fifths in any scale that only uses notes from meantone[7] modes, mohajira[7] modes, and substitutions of meantone intervals with corresponding septimal subminor or supermajor intervals, allowing for any diatonic type scale to be simple as easy to learn, as the inconsistencies of So-Ra and Te-Fo can be smoothed out by the fact that Ra can also be called Ro, for perfect second, or 9/8, and Fo is also Fe, as it's the "minor fourth", as 4/3 is tempered together with 27/20. These commas being tempered allows the system to preserve a surprising amount of consistency, being extremely easy to learn. Du is used for the up unison because it helps consistency, is generally used as a quartertone in scales like Centaurus, and because it allows the also common augmented and upaugmented unisons to be named, with Da and Di.
+The system shown preserved vowels in perfect fifths in any scale that only uses notes from [[meantone]][7] modes, [[mohajira]][7] modes, and substitutions of meantone intervals with corresponding [[7-limit|septimal]] (7-limit) [[subminor]] or [[supermajor]] intervals, allowing for any diatonic type scale to be simple as easy to learn, as the inconsistencies of So-Ra and Te-Fo can be smoothed out by the fact that Ra can also be called Ro, for perfect second, or [[9/8]], and Fo is also Fe, as it's the "minor fourth", as [[4/3]] is tempered together with [[27/20]]. These [[comma]]s being [[tempered]] allows the system to preserve a surprising amount of consistency, being extremely easy to learn. Du is used for the up unison because it helps consistency, is generally used as a [[quartertone]] in scales like [[Centaurus]], and because it allows the also common augmented and upaugmented unisons to be named, with Da and Di.
 The system is built on this consistency, and preserves the standard minor intervals names, as well as -a as the standard major from La, and Ti as the strongest leading tone, here being the upmajor seventh. The remaining vowels of -uh for sub and -u for neutral are used because they correspond to the vowel sounds from their respective words.
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 To expand into intervals that surpass these, such as the ^A5, we will extend to Augmented, Diminished, Upaugmented, and Downdiminished intervals. The vowels for these are -ah (short a sound), -ih (for the short i in diminished), oy, and ow (for down) respectively. They work similarly to the others, and are first used in the second set of unisons, allowing the M7-A4 and d5-m2 perfect fifths and others of the sort to still use consistent vowels, as they show up in diatonic scales.
-If intervals are used solely for their 3-limit role, such as the M2 or in some cases the M6, the names Ro and Lo may be used, for perfect second or perfect sixth, as Ra can be thought of to imply 10/9, while Ro would imply 9/8, similarly to Lo and 27/16. In other cases, Mo would be 32/27 and To would be 16/9. A situation where this naming scheme may be used would be in Harrison Major, P1 M2 ^M3 P4 P5 M6 ^M7 P8, where the M6 is used so that the ii chord has a perfect fifth, while the vi chord has a wolf fifth in order to be used as a "wolf tonic" to prevent tonicization.
+If intervals are used solely for their 3-limit role, such as the M2 or in some cases the M6, the names Ro and Lo may be used, for perfect second or perfect sixth, as Ra can be thought of to imply 10/9, while Ro would imply 9/8, similarly to Lo and 27/16. In other cases, Mo would be 32/27 and To would be 16/9. A situation where this naming scheme may be used would be in Harrison Major, P1 M2 ^M3 P4 P5 M6 ^M7 P8, where the M6 is used so that the ii chord has a perfect fifth, while the vi chord has a [[Wolf interval|wolf fifth]] in order to be used as a "wolf tonic" to prevent tonicization.
 ==Kite Giedraitis's solfege==
@@ Line 312: / Line 312: @@
 Once this is fully internalized, add in the other 4 vowels.
 ===The circle of fifths===
-The 5 vowels create 5 chains of fifths. The 2 tritones with duplicate names each connect 2 pairs of chains. Thus there are only 3 fifths that don't rhyme:
+The 5 vowels create 5 [[chain of fifths|chains of fifths]]. The 2 [[tritone]]s with duplicate names each connect 2 pairs of chains. Thus there are only 3 fifths that don't rhyme:
 *Do - Se (P1 to P5)
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 However going a 5th up from an aug or upaug 4th would go to an aug or upaug 8ve, which doesn't exist in this solfege. Therefore one must rename the 4th as a dim 5th, then go up to a minor 2nd. Thus Fe + 5th = Su + 5th = Ru. Dim 5ths may also need renaming: So + 4th = Fi + 4th = Ti.
 ==Andrew Heathwaite's solfege==
 [[Andrew Heathwaite]]'s solfege is a subset of his [[41edo]] solfege. It expands on the conventional Do - Di/Ra - Re - Ri/Me - Mi - Fa - Fi/Se - So - Si/Le - La - Li/Te - Ti - Do. As a result there are 6 different vowel sequences.
 {| class="wikitable" style="text-align:center"
@@ Line 427: / Line 428: @@
 See also: [[17edo Solfege]], [[22edo Solfege]], [[29edo solfege|29edo Solfege]] and [[41edo solfege|41edo Solfege]].
-For intervals that appear in the diatonic scale, the traditional solfege names are grandfathered in. While this makes it easier to learn the new syllables as extensions of the old ones — if you are trained with the old ones to begin with — it also makes for many irregularities.
+For intervals that appear in the [[diatonic scale]], the traditional solfege names are grandfathered in. While this makes it easier to learn the new syllables as extensions of the old ones — if you are trained with the old ones to begin with — it also makes for many irregularities.
 The syllables '''do, re, mi, fa, so[l], la, ti''' have the same meaning as traditional major and perfect intervals. The names for minor intervals are also retained: '''ra, me, le, te''', as well as the augmented fourth, '''fi''', and diminished fifth, '''se'''. Some traditional names for chromatically-altered intervals appear here, but altered by a semisharp or semiflat, rather than a full sharp or flat: '''di''' for a semiaugmented unison, '''da''' for a semidiminished unison, '''ri''' for a semiaugmented second, '''fe''' for a semidiminished fourth, '''si''' for a semiaugmented fifth, and '''li''' for a semiaugmented sixth. The remaining syllables flesh out the septimal and undecimal intervals which are not represented in 12edo.