Xenharmonic Wiki

41edo solfege: Difference between revisions

← Older edit
VisualWikitext
TallKite (talk | contribs)
autopatrolled, Sysops
4,192 edits
Wilh3lm (talk | contribs)
20 edits
→Shasavistic harmononyms: Filled in missing harmononyms (though I really hope 3 and 38 have better approximations than Xcyli and Jus)
 
(12 intermediate revisions by 2 users not shown)
Line 1: Line 1:
==Kite Giedraitis's Solfege==
==Uniform Solfege==


===Overview ===
===Overview ===
[[Kite Giedraitis|Kite]]'s solfege is nicknamed "Da Ra Mo" after harmonics 8, 9 and 10. It uses the conventional consonants D, R, M, F, S, L and T. But most consonants have an alternate form that indicates flattening or sharpening. The vowels are unconventional: u = '''u'''p, a = pl'''a'''in, o = d'''o'''wn and i = m'''i'''d.
See [[Uniform solfege]] for a full explanation.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
|+
|+
![[41edo]]
![[41edo]]
! colspan="2" |solfege names
!edosteps
! colspan="2" |[[Ups and downs notation|ups and downs]] names
! colspan="2" |solfege
! colspan="4" |[[Ups and downs notation|ups and downs]] names
|-
|-
!unisons
!unisons
|0-1
| colspan="2" |Da Du
| colspan="2" |Da Du
| colspan="2" |P1 ^1
| colspan="2" |P1 ^1
| colspan="2" |C ^C
|-
|-
!2nds
!2nds
|2-8
|Fro Fra Fru
|Fro Fra Fru
|Ri Ro Ra Ru
|Ri Ro Ra Ru
|vm2 m2 ^m2
| vm2 m2 ^m2
|~2 vM2 M2 ^M2
|~2 vM2 M2 ^M2
|vDb Db ^Db
|vvD vD D ^D
|-
|-
!3rds
!3rds
|9-15
|No Na Nu
|No Na Nu
|Mi Mo Ma Mu
|Mi Mo Ma Mu
|vm3 m3 ^m3
|vm3 m3 ^m3
|~3 vM3 M3 ^M3
|~3 vM3 M3 ^M3
|vEb Eb ^Eb
|vvE vE E ^E
|-
|-
!4ths
!4ths
| colspan="2" |Fo Fa Fu
|16-18
| colspan="2" |v4 P4 ^4
| colspan="2" | Fo Fa Fu
| colspan="2" | v4 P4 ^4
| colspan="2" |vF F ^F
|-
|-
!tritones
!tritones
| colspan="2" |Fi/Sho Po/Sha Pa/Shu Pu/Si
|19-22
| colspan="2" |~4/vd5 vA4/d5 A4/^d5 ^A4/~5
| colspan="2" | Fi/Sho Po/Sha Pa/Shu Pu/Si
| colspan="2" | ~4/vd5 vA4/d5 A4/^d5 ^A4/~5
| colspan="2" |^^F/vGb  vF#/Gb  F#/^Gb  ^F#/vvG
|-
|-
!5ths
!5ths
| colspan="2" |So Sa Su
|23-25
| colspan="2" |v5 P5 ^5
| colspan="2" | So Sa Su
| colspan="2" | v5 P5 ^5
| colspan="2" |vG G ^G
|-
|-
!6ths
!6ths
|26-32
|Flo Fla Flu
|Flo Fla Flu
|Li Lo La Lu
|Li Lo La Lu
|vm6 m6 ^m6
|vm6 m6 ^m6
|~6 vM6 M6 ^M6
|~6 vM6 M6 ^M6
|vAb Ab ^Ab
|vvA vA A ^A
|-
|-
!7ths
!7ths
|33-39
|Tho Tha Thu
|Tho Tha Thu
|Ti To Ta Tu
|Ti To Ta Tu
|vm7 m7 ^m7
|vm7 m7 ^m7
|~7 vM7 M7 ^M7
|~7 vM7 M7 ^M7
|vBb Bb ^Bb
|vvB vB B ^B
|-
|-
!8ves
!8ves
| colspan="2" |Do Da (Du)
|40-41
| colspan="2" |v8 P8 (^8)
| colspan="2" |Do Da
| colspan="2" |v8 P8
| colspan="2" |vC C
|}
|}
This is a subset of Kite's [[53edo solfege]]. Th- is unvoiced as in <u>th</u>ink. The idea of 12 consonants is inspired by Erv Wilson's solfege (see http://www.anaphoria.com/41notes.pdf). However Kite added a 13th consonant P- to indicate a sharpened 4th. Mnemonic: Sha sharpens to Sa, and Tha sharpens to Ta, so if Fa were spelled Pha, it would sharpen to Pa.
The seven 2nds illustrate the solfege's logic:
The seven 2nds illustrate the solfege's logic:


Line 62: Line 83:
*Ri = '''R'''e-m'''i'''d = ~2
*Ri = '''R'''e-m'''i'''d = ~2
*Ro = '''R'''e-d'''o'''wn = vM2
*Ro = '''R'''e-d'''o'''wn = vM2
*Ra = '''R'''e-pl'''a'''in = M2
* Ra = '''R'''e-pl'''a'''in = M2
*Ru = '''R'''e-'''u'''p = ^M2
* Ru = '''R'''e-'''u'''p = ^M2


The vowels relate to [[color notation]]: -a = w'''a''', -o = y'''o''' or z'''o''', -u = g'''u''' or r'''u''', and -i = '''i'''la. The zogu 5th is Sha because the -o and -u in zogu cancel to make -a.
The vowels relate to [[color notation]]: -a = w'''a''', -o = y'''o''' or z'''o''' = '''o'''ver/'''o'''tonal, -u = g'''u''' or r'''u''' = '''u'''nder/'''u'''tonal, and -i = '''i'''la. The zogu 5th is Sha because the -o and -u in zogu cancel to make -a.


===Example scales & tags===
===Example scales & tags===
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
|+
|+
! rowspan="2" |3-limit
!Plain major scale
!Plain major scale
|Da
|Da
Line 76: Line 98:
|Fa
|Fa
|Sa
|Sa
| La
|La
|Ta
|Ta
|Da
|Da
Line 85: Line 107:
|Na
|Na
|Fa
|Fa
| Sa
|Sa
|Fla
|Fla
|Tha
|Tha
|Da
|Da
|-
|-
! rowspan="2" |5-limit
!Downmajor scale
!Downmajor scale
|Da
|Da
Line 110: Line 133:
|Da
|Da
|-
|-
!Upmajor scale
! rowspan="2" |7-limit
! Upmajor scale
|Da
|Da
|Ra
|Ra
Line 122: Line 146:
!Downminor scale
!Downminor scale
|Da
|Da
| Ra
|Ra
|No
|No
|Fa
|Fa
|Sa
|Sa
|Flo
| Flo
|Tho
|Tho
|Da
|Da
|-
|-
! 11-limit
!Mid scale
!Mid scale
|Da
|Da
|Ra
|Ra
|Mi
|Mi
|Fa
| Fa
|Sa
|Sa
|Li
|Li
Line 142: Line 167:
See also these barbershop tags: [[Kite Guitar Originals by Kite Giedraitis#Sweet%20Sweet%20Harmony%20.28barbershop%20tag.29|Sweet Sweet Harmony]] (original tag) and [[Kite Guitar Translations by Kite Giedraitis#Barbershop%20tags|Kite's translations of barbershop tags]].
See also these barbershop tags: [[Kite Guitar Originals by Kite Giedraitis#Sweet%20Sweet%20Harmony%20.28barbershop%20tag.29|Sweet Sweet Harmony]] (original tag) and [[Kite Guitar Translations by Kite Giedraitis#Barbershop%20tags|Kite's translations of barbershop tags]].


===Octave Complements===
===Kite Guitar fretboard===
The various rainbows run either -o -u -o -u or else -a -i -a.
{| class="wikitable" style="text-align:center;"
|+
<-- nut                                                                                                                                    bridge -->
|'''Pa'''
|So
|Su
|Fla
|Li
|La
|'''Tho'''
|'''Thu'''
|'''To'''
|'''Tu'''
|'''Da'''
! colspan="9" |
|-
|'''Ru'''
|Na
|Mi
|Ma
|Fo
|Fu
|'''Sha'''
|'''Si'''
|'''Sa'''
|'''Flo'''
|'''Flu'''
|'''Lo'''
|'''Lu'''
|'''Tha'''
|Ti
|Ta
|Do
|Du
|Fra
|Ri
|-
|Ti
|Ta
|Do
|Du
|Fra
|Ri
| '''Ra'''
|'''No'''
| '''Nu'''
| '''Mo'''
|'''Mu'''
| '''Fa'''
| '''Fi'''
|'''Pa'''
|So
|Su
|Fla
|Li
|La
|'''Tho'''
|-
! colspan="9" |
|'''Da'''
| '''Fro'''
|'''Fru'''
|'''Ro'''
|'''Ru'''
|Na
|Mi
|Ma
|Fo
|Fu
|'''Sha'''
|}
 
===Suggestion for learning===
Even with many familiar consonants and a consistent vowel sequence, it can take a while to master 45 syllables. One might want to take a divide-and-conquer approach. Start with replacing Do Re Mi etc. with this solfege:
 
Da - Ra - Ma - Fa - Sa - La - Ta - Da
 
This helps with <u>un</u>learning the syllables Do, Mi, So and Ti, which are still present but have a changed meaning. (For those familiar with the full 17-name solfege, note that Ra, Ri, Fi, Si and Li are also present but changed.)
 
Once this solfege feels natural, add in the 6 altered consonants, making a 12-edo-like solfege:
 
Da - '''Fra''' - Ra - '''Na''' - Ma - Fa - '''Pa/Sha''' - Sa - '''Fla''' - La - '''Tha''' - Ta - Da
 
Once this is fully memorized, add in the other 3 vowels.
 
===Octave Complements ===
To find the [[octave complement]] of any interval:
To find the [[octave complement]] of any interval:


*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
*change the '''vowel''' as expected: -o <--> -u,  but -a and -i 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. The rule for changing the quality means the ~4 and the ~5 must be either Fi & Si or else Pi & Shi. The former is chosen to ensure that the 6 mid intervals Ri Mi Fi Si Li Ti all use the conventional (unaltered) consonants.
For example, Fru = minor-Re-up becomes major-Ti-down = To. Likewise, Si becomes Fi.  


===The Circle of Fifths===
===The Circle of Fifths===
Line 158: Line 271:
The aug 4th Pa is also the updim 5th Shu, which is the starting point for another 13-note chain of 5ths, all -u notes. Since the ending point Pu is also Si, this leads to a 6-note chain of -i notes. This in turn leads to a 13-note -o chain, which leads back to the -a chain. 13 -a notes + 13 -u notes + 6 -i notes + 13 -o notes = 45 names = 41 notes with duplicate names for the 4 tritones.  
The aug 4th Pa is also the updim 5th Shu, which is the starting point for another 13-note chain of 5ths, all -u notes. Since the ending point Pu is also Si, this leads to a 6-note chain of -i notes. This in turn leads to a 13-note -o chain, which leads back to the -a chain. 13 -a notes + 13 -u notes + 6 -i notes + 13 -o notes = 45 names = 41 notes with duplicate names for the 4 tritones.  


To summarize, the 4 vowels create 4 separate chains of 5ths, and the 4 tritones with duplicate names connect those 4 chains into one 41-note circle. This is one rationale for the 13th consonant, for it supplies most of the duplicate names.
To summarize, the 4 vowels create 4 separate chains of 5ths, and the 4 tritones with duplicate names connect those 4 chains into one 41-note circle. This is one rationale for the 13th consonant P-, for it supplies most of the duplicate names.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
|+The 45 note names in circle-of-5ths order <br>
|+The 45 note names in circle-of-5ths order <br>
Line 170: Line 283:
!P4
!P4
!P1
!P1
!P5
! P5
!M2
!M2
!M6
!M6
!M3
!M3
!M7
! M7
!A4 (d5)
! A4 (d5)
|-
|-
!-a
!-a
| colspan="6" |
| colspan="6" |
|Da
| Da
|Sa
| Sa
|Ra
|Ra
|La
|La
Line 195: Line 308:
|Fu
|Fu
|Du
|Du
|Su
| Su
|Ru
|Ru
|Lu
| Lu
|Mu
| Mu
|Tu
| Tu
|Pu (Si)
|Pu (Si)
|-
|-
!-i
! -i
| colspan="7" |
| colspan="7" |
|Si
|Si
| Ri
|Ri
|Li
|Li
|Mi
|Mi
| Ti
|Ti
| Fi (Sho)
|Fi (Sho)
|-
|-
!-o
!-o
|Sho
|Sho
| Fro
|Fro
|Flo
|Flo
|No
| No
|Tho
| Tho
|Fo
|Fo
|Do
| Do
|So
|So
|Ro
|Ro
| Lo
|Lo
| Mo
|Mo
|To
|To
|Po (Sha)
| Po (Sha)
|-
|-
!-a
!-a
|Sha
|Sha
|Fra
|Fra
|Fla
| Fla
|Na
|Na
|Tha
| Tha
|Fa
|Fa
|Da
|Da
Line 237: Line 350:
|}
|}


=== Adding/subtracting 4ths, 5ths and major 2nds===
=== Adding/subtracting 4ths and 5ths===
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.


A few minor exceptions arise with the -i notes. Conventionally, M7 + 5th = A4, and indeed Ta + 5th = Pa. But Ti + 5th = Fi not Pi. Likewise Fa + 4th = Tha, a minor 7th 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.)


The same rule for 4ths and 5ths mostly holds for plain major 2nds. Keep the vowel, and change the consonant as expected. Ra + M2 = Ma. But the 4 tritones must be named as 5ths not 4ths: Fi + M2 = Sho + M2 = Flo. Note that Fi to Si is a <u>minor</u> 2nd. Beware, this rule breaks down entirely for major-ish and mid 7ths (the four T- notes), due to the lack of aug and mid 8ves:
===Adding/subtracting other intervals===
The same rule for 4ths and 5ths mostly holds for plain major 2nds. Keep the vowel, and change the consonant as expected. Ra + M2 = Ma. But again the 4 tritones must be named as 5ths not 4ths: Fi + M2 = Sho + M2 = Flo. Note that Fi to Si is a <u>minor</u> 2nd. Beware, this rule breaks down entirely for major and mid 7ths (the four T- notes), due to the lack of aug and mid 8ves:


*Tu + M2 = Ri (^M7 + M2 = ~9)
* Tu + M2 = Ri (^M7 + M2 = ~9)
*Ta + M2 = Fru (M7 + M2 = ^m9)
*Ta + M2 = Fru (M7 + M2 = ^m9)
*To + M2 = Fra (vM7 + M2 = m9)
*To + M2 = Fra (vM7 + M2 = m9)
*Ti + M2 = Fro (~7 + M2 = vm9)
*Ti + M2 = Fro (~7 + M2 = vm9)
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. However 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 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-upmionor 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.)
 
=== Learning suggestion===
Even with many familiar consonants and a consistent vowel sequence, it can take a while to master 45 syllables. One might want to divide-and-conquer. Start with using this simple solfege:
 
Da - Ra - Ma - Fa - Sa - La - Ta - Da
 
This helps with <u>un</u>learning the syllables Do, Mi, So and Ti, which are still present but have a changed meaning. (For those familiar with the full 17-name solfege, note that Ra, Ri, Fi, Si and Li are also present but changed.)
 
Next add in the 6 altered consonants, making a 12-edo-like solfege:
 
Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - Sa - Fla - La - Tha - Ta - Da
 
Once this is fully internalized, add in the other 3 vowels.


==Andrew Heathwaite's Solfege==
==Andrew Heathwaite's Solfege==
Line 274: Line 375:
!solfege names
!solfege names
![[Ups and downs notation|ups and downs]] names
![[Ups and downs notation|ups and downs]] names
!edosteps
|-
|-
!unisons
!unisons
| Do Di
|Do Di
|P1 ^1
|P1 ^1
|0-1
|-
|-
!2nds
!2nds
|Ro Rih Ra Ru Reh Re Ri
|Ro Rih Ra Ru Reh Re Ri
|vm2 m2 ^m2 ~2 vM2 M2 ^M2
|vm2 m2 ^m2 ~2 vM2 M2 ^M2
|2-8
|-
|-
!3rds
!3rds
|Ma Meh Me Mu Mi Maa Mo
|Ma Meh Me Mu Mi Maa Mo
|vm3 m3 ^m3 ~3 vM3 M3 ^M3
|vm3 m3 ^m3 ~3 vM3 M3 ^M3
|9-15
|-
|-
!4ths
!4ths
|Fe Fa Fih Fu Fi
|Fe Fa Fih Fu Fi
|v4 P4 ^4 ~4 vA4
|v4 P4 ^4 ~4 vA4
|16-20
|-
|-
!5ths
!5ths
|Se Su Sih So (or Sol) Si
|Se Su Sih So (or Sol) Si
|^d5 ~5 v5 P5 ^5
|^d5 ~5 v5 P5 ^5
|21-25
|-
|-
!6ths
!6ths
|Lo Leh Le Lu La Laa Li
|Lo Leh Le Lu La Laa Li
|vm6 m6 ^m6 ~6 vM6 M6 ^M6
|vm6 m6 ^m6 ~6 vM6 M6 ^M6
|26-32
|-
|-
!7ths
!7ths
|Ta Teh Te Tu Ti Taa To
|Ta Teh Te Tu Ti Taa To
|vm7 m7 ^m7 ~7 vM7 M7 ^M7
| vm7 m7 ^m7 ~7 vM7 M7 ^M7
|33-39
|-
|-
!8ves
!8ves
|Da Do (Di)
|Da Do (Di)
|v8 P8 (^8)
|v8 P8 (^8)
|40-41 (42)
|}
|}


See also Andrew's [[31edo solfege]], which is a subset of this solfege, and his [[53edo solfege]], which is very nearly a superset. (It names the M7 as Tih.)
See also Andrew's [[31edo|31edo solfege]], which is a subset of this solfege, and <bdi>Phylingual</bdi>‎'s [[53edo|53edo solfege]], which is very nearly a superset. (It names the M7 as Tih.)


===Example scales===
===Example scales===
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
|+
|+
! rowspan="2" |3- limit
!Plain major scale
!Plain major scale
|Do
|Do
Line 331: Line 442:
|Leh
|Leh
|Teh
|Teh
| Do
|Do
|-
|-
! rowspan="2" |5-limit
!Downmajor scale
!Downmajor scale
|Do
|Do
Line 344: Line 456:
|-
|-
!Upminor scale
!Upminor scale
| Do
|Do
|Re
|Re
|Me
|Me
Line 353: Line 465:
|Do
|Do
|-
|-
! rowspan="2" |7-limit
!Upmajor scale
!Upmajor scale
|Do
|Do
| Re
|Re
|Mo
|Mo
| Fa
|Fa
|Sol
|Sol
|Li
|Li
Line 366: Line 479:
|Do
|Do
|Re
|Re
| Ma
|Ma
| Fa
|Fa
|Sol
|Sol
|Lo
|Lo
Line 373: Line 486:
|Do
|Do
|-
|-
!11-limit
!Mid scale
!Mid scale
|Do
|Do
Line 380: Line 494:
|Sol
|Sol
|Lu
|Lu
| Tu
|Tu
|Do
|Do
|}
|}
The downmajor and upminor 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]]
Retrieved from "https://en.xen.wiki/w/41edo_solfege"