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41edo solfege: Difference between revisions

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→Shasavistic harmononyms: Filled in missing harmononyms (though I really hope 3 and 38 have better approximations than Xcyli and Jus)
 
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!edosteps
!edosteps
! colspan="2" |solfege
! colspan="2" |solfege
! colspan="2" |[[Ups and downs notation|ups and downs]] names
! colspan="4" |[[Ups and downs notation|ups and downs]] names
|-
|-
!unisons
!unisons
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| colspan="2" |Da Du
| colspan="2" |Da Du
| colspan="2" |P1 ^1
| colspan="2" |P1 ^1
| colspan="2" |C ^C
|-
|-
!2nds
!2nds
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| vm2 m2 ^m2
| vm2 m2 ^m2
|~2 vM2 M2 ^M2
|~2 vM2 M2 ^M2
|vDb Db ^Db
|vvD vD D ^D
|-
|-
!3rds
!3rds
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|vm3 m3 ^m3
|vm3 m3 ^m3
|~3 vM3 M3 ^M3
|~3 vM3 M3 ^M3
|vEb Eb ^Eb
|vvE vE E ^E
|-
|-
!4ths
!4ths
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| colspan="2" | Fo Fa Fu
| colspan="2" | Fo Fa Fu
| colspan="2" | v4 P4 ^4
| colspan="2" | v4 P4 ^4
| colspan="2" |vF F ^F
|-
|-
!tritones
!tritones
|19-22
|19-22
| colspan="2" | Fi/Sho Po/Sha Pa/Shu Pu/Si
| colspan="2" | Fi/Sho Po/Sha Pa/Shu Pu/Si
| colspan="2" | ~4/vd5 vA4/d5 A4/^d5 ^A4/~5
| colspan="2" | ~4/vd5 vA4/d5 A4/^d5 ^A4/~5
| colspan="2" |^^F/vGb  vF#/Gb  F#/^Gb  ^F#/vvG
|-
|-
!5ths
!5ths
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| colspan="2" | So Sa Su
| colspan="2" | So Sa Su
| colspan="2" | v5 P5 ^5
| colspan="2" | v5 P5 ^5
| colspan="2" |vG G ^G
|-
|-
!6ths
!6ths
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|vm6 m6 ^m6
|vm6 m6 ^m6
|~6 vM6 M6 ^M6
|~6 vM6 M6 ^M6
|vAb Ab ^Ab
|vvA vA A ^A
|-
|-
!7ths
!7ths
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|vm7 m7 ^m7
|vm7 m7 ^m7
|~7 vM7 M7 ^M7
|~7 vM7 M7 ^M7
|vBb Bb ^Bb
|vvB vB B ^B
|-
|-
!8ves
!8ves
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| colspan="2" |Do Da
| colspan="2" |Do Da
| colspan="2" |v8 P8
| colspan="2" |v8 P8
| colspan="2" |vC C
|}
|}
The seven 2nds illustrate the solfege's logic:
The seven 2nds illustrate the solfege's logic:
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{| class="wikitable" style="text-align:center;"
{| class="wikitable" style="text-align:center;"
|+
|+
<-- nut                                       bridge -->
<-- nut                                                                                                                                     bridge -->
|Tho
|'''Pa'''
|Thu
|So
|To
|Su
|Tu
|Fla
|Da
|Li
! colspan="3" |
|La
|'''Tho'''
|'''Thu'''
|'''To'''
|'''Tu'''
|'''Da'''
! colspan="9" |
|-
|-
|Sha
|'''Ru'''
|Si
|Na
|Sa
|Mi
|Flo
|Ma
|Flu
|Fo
|Lo
|Fu
|Lu
|'''Sha'''
|Tha
|'''Si'''
|'''Sa'''
|'''Flo'''
|'''Flu'''
|'''Lo'''
|'''Lu'''
|'''Tha'''
|Ti
|Ta
|Do
|Du
|Fra
|Ri
|-
|-
| Ra
|Ti
|No
|Ta
| Nu
|Do
| Mo
|Du
|Mu
|Fra
| Fa
|Ri
| Fi
| '''Ra'''
|Pa
|'''No'''
| '''Nu'''
| '''Mo'''
|'''Mu'''
| '''Fa'''
| '''Fi'''
|'''Pa'''
|So
|Su
|Fla
|Li
|La
|'''Tho'''
|-
|-
! colspan="3" |
! colspan="9" |
|Da
|'''Da'''
| Fro
| '''Fro'''
|Fru
|'''Fru'''
|Ro
|'''Ro'''
|Ru
|'''Ru'''
|Na
|Mi
|Ma
|Fo
|Fu
|'''Sha'''
|}
|}


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*change the '''degree''' as usual: 2nd <--> 7th, 3rd <--> 6th, and 4th <--> 5th
*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
*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
* 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===
===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.
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===
===Adding/subtracting other intervals===
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In general, one can add or subtract any conventional (i.e. plain) interval from any note, and the result will be as expected. But only if the expected answer exists in the solfege. It must exist on the 13-note chain of 5ths from dim5 to aug4. In other words, the expected answer must not be augmented or diminished, unless it's an aug4 or a dim5. (Otherwise, one must use an enharmonic equivalent.)  For example, one can easily add a M3 to any note other than a L-, M-, T- or P- note. Thus Ro + M3 = Po and Na + M3 = Sa, but La + M3 = Fru. Beware, because the -i chain is only 6 notes long, when adding to or subtracting from an -i note, the expected answer must exist on the P5-A4 chain.
In general, one can add or subtract any conventional (i.e. plain) interval from any note, and the result will be as expected. But only if the expected answer exists in the solfege. It must exist on the 13-note chain of 5ths from dim5 to aug4. In other words, the expected answer must not be augmented or diminished, unless it's an aug4 or a dim5. (Otherwise, one must use an enharmonic equivalent.)  For example, one can easily add a M3 to any note other than a L-, M-, T- or P- note. Thus Ro + M3 = Po and Na + M3 = Sa, but La + M3 = Fru. Beware, because the -i chain is only 6 notes long, when adding to or subtracting from an -i note, the expected answer must exist on the P5-A4 chain.


One can often easily add/subtract an unconventional (upped or downed) interval as well. The ups and downs add up and cancel out as expected. Thus Ra + vM2 = Mo and Ru + vM2 = Ma. Obviously the vowel will change. Again, the expected answer must exist in the solfege. No double-upmajor, double-upminor or double-downminor intervals! (Double-downmajor is mid, thus Ro + vM2 = Mi.)
One can often easily add/subtract an unconventional (upped or downed) interval as well. The ups and downs add up and cancel out as expected. Thus Ra + vM2 = Mo and Ru + vM2 = Ma. Obviously the vowel will change. Again, the expected answer must exist in the solfege. No dupmajor, dupminor or dudminor intervals! (Dudmajor is mid, thus Ro + vM2 = Mi.)


==Andrew Heathwaite's Solfege==
==Andrew Heathwaite's Solfege==
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The two 5-limit scales are the same as conventional solfege.
The two 5-limit scales are the same as conventional solfege.


== Shasavistic harmononyms ==
Harmononyms are the system of pitch names used in Shasavistic music theory, developed by [[L4MPLIGHT]].
Here are some harmononyms for each pitch class in 41-EDO, the temperament preferred by L4MPLIGHT. Note that multiple harmononyms may exist for different ratios that get tempered to the same pitch class.
{| class="wikitable"
|+
!41-edo steps
!Harmononym
!Ratio
|-
|0
|Ah
|1/1
|-
|1
|Schup
|64/63
|-
|2
|Chyzi
|33/32
|-
|3
|Xcyli
|135/128
|-
|4
|Fus
|16/15
|-
|5
|Chyk
|12/11
|-
|6
|Schuli
|10/9
|-
|7
|Scy
|9/8
|-
|8
|Pu
|8/7
|-
|9
|Fumi
|7/6
|-
|10
|Ju
|32/27
|-
|11
|Chys
|6/5
|-
|12
|Schuzi
|11/9
|-
|13
|Ly
|5/4
|-
|14
|Myk
|14/11
|-
|15
|Scyp
|9/7
|-
|16
|Chymi
|21/16
|-
|17
|Fu
|4/3
|-
|18
|Xcys
|27/20
|-
|19
|Zy
|11/8
|-
|20
|Sumi
|7/5
|-
|21
|Lyp
|10/7
|-
|22
|Tschu
|16/11
|-
|23
|Juli
|40/27
|-
|24
|Chy
|3/2
|-
|25
|Fup
|32/21
|-
|26
|Dry
|25/16
|-
|27
|Puzi
|11/7
|-
|28
|Su
|8/5
|-
|29
|Scyk
|18/11
|-
|30
|Fuli
|5/3
|-
|31
|Xcy
|27/16
|-
|32
|Chyp
|12/7
|-
|33
|My
|7/4
|-
|34
|Schu
|16/9
|-
|35
|Scys
|9/5
|-
|36
|Fuzi
|11/6
|-
|37
|Chyli
|15/8
|-
|38
|Jus
|256/135
|-
|39
|Fuk
|64/33
|-
|40
|Scymi
|63/32
|}
[[Category:41edo]]
[[Category:41edo]]
[[Category:Solfege]]
[[Category:Solfege]]
[[Category:Kite Guitar]]
[[Category:Kite Guitar]]
Retrieved from "https://en.xen.wiki/w/41edo_solfege"