41edo solfege: Difference between revisions

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*change the '''degree''' as usual: 2nd <--> 7th, 3rd <--> 6th, and 4th <--> 5th

*change the '''quality''' as usual: major <--> minor, aug <--> dim, but perfect and mid are unchanged

*get the new '''consonant''' from the degree and quality

* change the '''vowel''' as expected: -o <--> -u, but -a and -i are unchanged

For example, Fru = minor-Re-up becomes major-Ti-down = To.

For example, Fru = minor-Re-up becomes major-Ti-down = To. Likewise, Si becomes Fi.

===The Circle of Fifths===

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Because the aforementioned 4 chains connect up, it's very easy to find the note a 4th or 5th above any note. It always rhymes, and the consonant is as would be expected from conventional interval arithmetic. Ra plus a 4th is Sa, Fro plus a 5th is Flo, etc. Thus in the example scales above, the 3rd, 6th and 7th always rhyme, as do the tonic, 2nd, 4th and 5th.

However, consider the 4 tritones Fi, Po, Pa and Pu. The note a 5th above any of these would be some sort of augmented or mid 8ve, which doesn't exist in this solfege. Therefore one must rename the tritone as a dim or mid 5th. Thus Po + 5th = Sha + 5th = Fra. Likewise, Sho, Sha, Shu and Si need renaming when adding a 4th: Shu + 4th = Pa + 4th = Ta.

However, consider the four tritones Fi, Po, Pa and Pu. The note a 5th above any of these would be some sort of augmented or mid 8ve, which doesn't exist in this solfege. Therefore one must rename the tritone as a dim or mid 5th. Thus Po + 5th = Sha + 5th = Fra. Likewise, Sho, Sha, Shu and Si need renaming when adding a 4th: Shu + 4th = Pa + 4th = Ta.

One minor exception arises with Ti and Fi. Conventionally, M7 + 5th = A4, and indeed Tu/Ta/To + 5th = Pu/Pa/Po. But Ti + 5th = Fi not Pi. Likewise Fu/Fa/Fo + 4th = Thu/Tha/Tho, minor 7ths as expected, but Fi + 4th = Ti not Thi. These exceptions are not an issue as long as you remember that there is no Pi or Thi in the solfege.

One minor exception arises with Ti and Fi. Conventionally, M7 + 5th = A4, and indeed Tu/Ta/To + 5th = Pu/Pa/Po. But Ti + 5th = Fi not Pi. Likewise Fu/Fa/Fo + 4th = Thu/Tha/Tho, minor 7ths as expected, but Fi + 4th = Ti not Thi. These exceptions are not an issue as long as you remember that there is no Pi or Thi in the solfege. (What if we fix this by renaming Fi as Pi? Another issue arises: one would expect that Pi's octave complement would be Shi, but instead it's Si. What if Si were renamed Shi? Then Shi plus a 5th would make not Fri but rather Ri. So some sort of minor exception is inevitable.)

===Adding/subtracting other intervals===

@@ Line 210: / Line 210: @@
 *change the '''degree''' as usual: 2nd <--> 7th, 3rd <--> 6th, and 4th <--> 5th
 *change the '''quality''' as usual: major <--> minor, aug <--> dim, but perfect and mid are unchanged
+*get the new '''consonant''' from the degree and quality
 * change the '''vowel''' as expected: -o <--> -u,  but -a and -i are unchanged
-For example, Fru = minor-Re-up becomes major-Ti-down = To.
+For example, Fru = minor-Re-up becomes major-Ti-down = To. Likewise, Si becomes Fi.
 ===The Circle of Fifths===
@@ Line 303: / Line 304: @@
 Because the aforementioned 4 chains connect up, it's very easy to find the note a 4th or 5th above any note. It always rhymes, and the consonant is as would be expected from conventional interval arithmetic. Ra plus a 4th is Sa, Fro plus a 5th is Flo, etc. Thus in the example scales above, the 3rd, 6th and 7th always rhyme, as do the tonic, 2nd, 4th and 5th.
-However, consider the 4 tritones Fi, Po, Pa and Pu. The note a 5th above any of these would be some sort of augmented or mid 8ve, which doesn't exist in this solfege. Therefore one must rename the tritone as a dim or mid 5th. Thus Po + 5th = Sha + 5th = Fra. Likewise, Sho, Sha, Shu and Si need renaming when adding a 4th: Shu + 4th = Pa + 4th = Ta.
+However, consider the four tritones Fi, Po, Pa and Pu. The note a 5th above any of these would be some sort of augmented or mid 8ve, which doesn't exist in this solfege. Therefore one must rename the tritone as a dim or mid 5th. Thus Po + 5th = Sha + 5th = Fra. Likewise, Sho, Sha, Shu and Si need renaming when adding a 4th: Shu + 4th = Pa + 4th = Ta.
-One minor exception arises with Ti and Fi. Conventionally, M7 + 5th = A4, and indeed Tu/Ta/To + 5th = Pu/Pa/Po. But Ti + 5th = Fi not Pi. Likewise Fu/Fa/Fo + 4th = Thu/Tha/Tho, minor 7ths as expected, but Fi + 4th = Ti not Thi. These exceptions are not an issue as long as you remember that there is no Pi or Thi in the solfege.
+One minor exception arises with Ti and Fi. Conventionally, M7 + 5th = A4, and indeed Tu/Ta/To + 5th = Pu/Pa/Po. But Ti + 5th = Fi not Pi. Likewise Fu/Fa/Fo + 4th = Thu/Tha/Tho, minor 7ths as expected, but Fi + 4th = Ti not Thi. These exceptions are not an issue as long as you remember that there is no Pi or Thi in the solfege. (What if we fix this by renaming Fi as Pi? Another issue arises: one would expect that Pi's octave complement would be Shi, but instead it's Si. What if Si were renamed Shi? Then Shi plus a 5th would make not Fri but rather Ri. So some sort of minor exception is inevitable.)
 ===Adding/subtracting other intervals===