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| {{Idiosyncratic terms}} | | {{Idiosyncratic terms}} |
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| This is a user page, not one of the main wiki pages. | | This is a user page, '''not a real wiki page'''. |
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| This page is only opinion, not fact. | | '''This page is only opinion, not fact.''' |
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| This user page details how I personally assign each [[EDO]] to a [[subgroup]] of [[just intonation]].
| | Interpreting 12edo as a 2.3.5.17.19 system: |
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| == Types of subgroups == | | == Intervals == |
| * lim = [[Prime limit]]
| | <br> |
| * no-n = [[Subgroup|No-n subgroup]]
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| * dual = [[Dual-n|Dual-n subgroup]]
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| * EQ = [[Equalizer subgroup]]
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| * comp = [[Subgroup|Other composite subgroup]]
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| * nth-b [[Half-prime subgroup|Nth-basis subgroup]]
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| * frac = [[Subgroup|Other fractional subgroup]]
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| == How to choose a type ==
| | ; 0c (0 [[cents]]) |
| Remember: All of these rules are made to be broken. Bend the rules to fit the EDO. Don't bend the EDO to fit the rules.
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| === EDOs with 1 to 6 tones/octave ===
| | Behaves like: [[1/1|1:1]]. |
| # The subgroup should have 3 [[basis element]]s
| |
| # If the EDO approximates 3 or more [[prime]]s 11 or lower within 15 [[cents]], then choose the best 3 and use those as its subgroup
| |
| # If it approximates less than 3 such primes, then include all the ones it does approximate, and fill the remaining spots with odd harmonics smaller than 40 that it approximates within 15 cents (giving preference to the lowest harmonics first)
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| # If there are aren't enough of those to fill all 3 spots, fill the remaining spots with [[taxicab distance|taxicab-2]] intervals the edo approximates within 15 cents, giving preference to intervals with small primes and intervals that are approximated more precisely (use direction to decide which to value more on an edo-by-edo basis)
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| # If there are still spots left open, fill them with the smallest composite harmonics of any size that are approximated within 15 cents
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| === EDOs with 7 to 12 tones/octave ===
| |
| # The subgroup should have 5 basis elements
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| # If the EDO approximates any primes 11 or lower within 15 cents, then add all of those to its subgroup
| |
| # If there are still spots left over, and the EDO does not approximate prime 3, then check if it approximates any harmonics 6, 9, 12 or 15 within 15 cents. If so, add them all to the subgroup starting with the smallest until all spots are filled or all harmonics have been added.
| |
| # If there are still spots left over, if the EDO does not approximate one or both of 5 or 3, check if it approximates 5/3 within 15 cents and if so, add that as a basis element
| |
| # If there are still spots left over, if the EDO does not approximate one or both of 7 or 3, check if it approximates 7/3 within 15 cents and if so, add that as a basis element
| |
| # If there are still spots left over, if the EDO does not approximate one or both of 7 or 5, check if it approximates 7/5 within 15 cents and if so, add that as a basis element
| |
| # Do the same as above for 11/3, then 11/5, then 11/7
| |
| # If there are still spots left over, check if the EDO approximates any primes 13, 17, 19 or 23 within 15 cents, if so, then add all of those to its subgroup giving preference to the lowest ones and to the ones approximated most closely (use discretion to choose which of those things to weight more heavily) until all spots have been filled or all primes have been added
| |
| # If there are still spots left open, choose either (A) or (B) at your discretion on an edo-by-edo basis, or combine both for edos where that makes sense:
| |
| ## (A) fill the remaining spots with odd harmonics smaller than 40 that it the edo approximates within 15 cents (giving preference to harmonics that are multiples of simple harmonics like 21 or 33)
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| ## (B) fill the remaining spots with taxicab-2 intervals the edo approximates within 15 cents, giving preference to intervals with small primes and intervals that are approximated more precisely (use direction to decide which to value more on an edo-by-edo basis)
| |
| # If there are still spots left open, fill them with the smallest remaining integer harmonics of any size that are approximated within 15 cents
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| === EDOs with 13 to 27 tones/octave ===
| | ; 100c |
| # The subgroup should have 6 basis elements
| | |
| # If the EDO approximates any primes 13 or lower within 15 cents, then add all of those to its subgroup
| | Depending on context, behaves like: [[20/19|20:19]], [[19/18|19:18]], [[18/17|18:17]], [[17/16|17:16]] or [[16/15|16:15]]. |
| # If there are still spots left over, and the EDO does not approximate prime 3, then check if it approximates any harmonics 6, 9, 12 or 15 within 15 cents. If so, add them all to the subgroup starting with the smallest until all spots are filled or all harmonics have been added.
| | |
| # If there are still spots left over, if the EDO does not approximate one or both of 5 or 3, check if it approximates 5/3 within 15 cents and if so, add that as a basis element
| | |
| # If there are still spots left over, if the EDO does not approximate one or both of 7 or 3, check if it approximates 7/3 within 15 cents and if so, add that as a basis element
| | ; 200c |
| # If there are still spots left over, if the EDO does not approximate one or both of 7 or 5, check if it approximates 7/5 within 15 cents and if so, add that as a basis element
| | |
| # Do the same as above for 11/3, then 11/5, then 11/7, then 13/3, then 13/5, then 13/7, then 13/11
| | Depending on context, behaves like: [[10/9|10:9]], [[19/17|19:17]], [[9/8|9:8]] or [[17/15|17:15]]. |
| # If there are still spots left over, check if the EDO approximates any primes 17, 19 or 23 within 15 cents, if so, then add all of those to its subgroup giving preference to the lowest ones and to the ones approximated most closely (use discretion to choose which of those things to weight more heavily) until all spots have been filled or all primes have been added
| | |
| # If there are still spots left open, choose either (A) or (B) at your discretion on an edo-by-edo basis, or combine both for edos where that makes sense:
| | |
| ## (A) fill the remaining spots with odd harmonics smaller than 40 that it the edo approximates within 15 cents (giving preference to harmonics that are multiples of simple harmonics like 21 or 33)
| | ; 300c |
| ## (B) fill the remaining spots with taxicab-2 intervals the edo approximates within 15 cents, giving preference to intervals with small primes and intervals that are approximated more precisely (use direction to decide which to value more on an edo-by-edo basis)
| | |
| # If there are still spots left open, fill them with the smallest remaining integer harmonics of any size that are approximated within 15 cents
| | Depending on context, behaves like: [[20/17|20:17]], [[32/27|32:27]], [[19/16|19:16]] or [[6/5|6:5]]. |
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| === EDOs with 28 to 52 tones/octave ===
| | ; 400c |
| # The subgroup should have 7 basis elements
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| # Primes 3, 5, 7 and 11 must be added to the subgroup
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| # If any primes 3, 5, 7 or 11 have more than 40% relative error, then they should be made a dual prime
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| # If there are more than 2 dual-primes, then only the two lowest dual-primes should be kept dual, and the rest made single again
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| # If there are still spots left open, then they should be filled by every prime 13 and up which the EDO approximates with less than 35% relative error, preferencing the lowest primes first, until all spots are filled
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| === EDOs with 53 or more tones/octave ===
| | Depending on context, behaves like: [[5/4|5:4]], [[34/27|34:27]], [[24/19|24:19]] or [[19/15|19:15]]. |
| # The subgroup should have 8 basis elements
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| # Primes 3, 5, 7 and 11 must be added to the subgroup
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| # If any primes 3, 5, 7 or 11 have more than 40% relative error, then they should be made a dual prime
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| # If there are more than 3 dual-primes, then only the two lowest dual-primes should be kept dual, and the rest made single again
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| # If there are still spots left open, then they should be filled by every prime 13 and up which the EDO approximates with less than 35% relative error, preferencing the lowest primes first, until all spots are filled
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| == Subgroups by EDO size ==
| |
| Size categories taken from my [[human EDO size categorization]] (HUECAT).
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| === Picnic EDOs (1-4) ===
| | ; 500c |
| * [[1edo]]: 2.125.127 (comp)
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| * [[2edo]]: 2.7/5.17/3 (nth-b) (15th)
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| * [[3edo]]: 2.5.17/3 (nth-b) (3rd)
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| * [[4edo]]: 2.5/3.7/5 (nth-b) (15th)
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| === Birthday EDOs (5-19) ===
| | Depending on context, behaves like: [[4/3|4:3]] or [[27/20|27:20]]. |
| * [[5edo]]: 2.3.7 (no-n)
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| * [[6edo]]: 2.9.5 (comp)
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| * [[7edo]]: 2.3.11/3.11/5.13 (nth-b) (15th)
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| * [[8edo]]: 2.5/3.11/3.13/5.19 (nth-b) (15th)
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| * [[9edo]]: 2.5.7/3.11.13/7 (nth-b) (3rd)
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| * [[10edo]]: 2.3.7.13.17 (no-n)
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| * [[11edo]]: 2.9.15.7.11 (comp)
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| * [[12edo]]: 2.3.5.17.19 (no-n)
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| * [[13edo]]: 2.9.5.11.13.17 (comp)
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| * [[14edo]]: 2.3.7/5.9/5.11/5.13 (nth-b) (5th)
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| * [[15edo]]: 2.3.5.7.11 (lim)
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| * [[16edo]]: 2.5.7.13.19 (no-n)
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| * [[17edo]]: 2.3.7.11.13 (no-n)
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| * [[18edo]]: 2.9.5.7/3.11 (nth-b) (3rd)
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| * [[19edo]]: 2.3.5.7.11.13 (lim)
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| === Carousel EDOs (20-34) ===
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| * [[20edo]]: 2.3.7.11.13.17 (no-n)
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| * [[21edo]]: 2.3.5.7.13.17 (no-n)
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| * [[22edo]]: 2.3.5.7.11.17 (no-n)
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| * [[23edo]]: 2.9.15.21.33.13 (comp)
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| * [[24edo]]: 2.3.5.7.11.13 (lim)
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| * [[25edo]]: 2.3.5.7.17.19 (no-n)
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| * [[26edo]]: 2.3.5.7.11.13 (lim)
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| * [[27edo]]: 2.3.5.7.11.13 (lim)
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| * [[28edo]]: 2.3.5.7.11.13.19 (no-n)
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| * [[29edo]]: 2.3.5.7.11.13.19 (no-n)
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| * [[30edo]]: 2.3+.3-.5.7.11.13 (dual)
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| * [[31edo]]: 2.3.5.7.11.13.17 (lim)
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| * [[32edo]]: 2.3.5.7.11.17.19 (no-n)
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| * [[33edo]]: 2.3.5.7.11.13.17 (lim)
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| * [[34edo]]: 2.3.5.7+.7-.11.13 (dual)
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|
| === Schoolbus EDOs (35-54) ===
| | ; 600c |
| * [[35edo]]: 2.3+.3-.5.7.11.17 (dual)
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| * [[36edo]]: 2.3.5+.5-.7.11+.11- (dual)
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| * [[37edo]]: 2.3.5.7.11.13.17 (lim)
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| * [[38edo]]: 2.3.5.7.11+.11-.13 (dual)
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| * [[39edo]]: 2.3.5+.5-.7+.7-.11 (dual)
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| * [[40edo]]: 2.3+.3-.5.7.11.13 (dual)
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| * [[41edo]]: 2.3.5.7.11.13.17 (lim)
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| * [[42edo]]: 2.3+.3-.5+.5-.7.11 (dual)
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| * [[43edo]]: 2.3.5.7.11.13.17 (lim)
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| * [[44edo]]: 2.3.5.7+.7-.11.13 (dual)
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| * [[45edo]]: 2.3.5+.5-.7.11.17 (dual)
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| * [[46edo]]: 2.3.5.7.11.13.17 (lim)
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| * [[47edo]]: 2.3+.3-.5.7.11+.11- (dual)
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| * [[48edo]]: 2.3.5+.5-.7.11.13 (dual)
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| * [[49edo]]: 2.3.5.7+.7-.11+.11- (dual)
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| * [[50edo]]: 2.3.5.7.11.13.17 (lim)
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| * [[51edo]]: 2.3.5+.5-.7.11+.11- (dual)
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| * [[52edo]]: 2.3+.3-.5.7.11.19 (dual)
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| * [[53edo]]: 2.3.5.7.11.13.17.19 (lim)
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| * [[54edo]]: 2.3+.3-.5+.5-.7+.7-.11 (dual)
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|
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|
| === Double-decker EDOs (55-74) ===
| | Depending on context, behaves like: [[24/17|24:17]], [[17/12|17:12]] or [[27/19|27:19]]. |
| ''(May complete later.)''
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| == Subgroups by subgroup type ==
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| === Full prime limit ===
| | ; 700c |
| * [[15edo]]: 2.3.5.7.11 (lim)
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| * [[19edo]]: 2.3.5.7.11.13 (lim)
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| * [[24edo]]: 2.3.5.7.11.13 (lim)
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| * [[26edo]]: 2.3.5.7.11.13 (lim)
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| * [[27edo]]: 2.3.5.7.11.13 (lim)
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| * [[31edo]]: 2.3.5.7.11.13.17 (lim)
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| * [[33edo]]: 2.3.5.7.11.13.17 (lim)
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| * [[37edo]]: 2.3.5.7.11.13.17 (lim)
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| * [[41edo]]: 2.3.5.7.11.13.17 (lim)
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| * [[43edo]]: 2.3.5.7.11.13.17 (lim)
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| * [[46edo]]: 2.3.5.7.11.13.17 (lim)
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| * [[50edo]]: 2.3.5.7.11.13.17 (lim)
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| * [[53edo]]: 2.3.5.7.11.13.17.19 (lim)
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| === No-n ===
| | Behaves like: [[3/2|3:2]]. |
| * [[5edo]]: 2.3.7 (no-n)
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| * [[10edo]]: 2.3.7.13.17 (no-n)
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| * [[12edo]]: 2.3.5.17.19 (no-n)
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| * [[16edo]]: 2.5.7.13.19 (no-n)
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| * [[17edo]]: 2.3.7.11.13 (no-n)
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| * [[20edo]]: 2.3.7.11.13.17 (no-n)
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| * [[21edo]]: 2.3.5.7.13.17 (no-n)
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| * [[25edo]]: 2.3.5.7.17.19 (no-n)
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| * [[22edo]]: 2.3.5.7.11.17 (no-n)
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| * [[28edo]]: 2.3.5.7.11.13.19 (no-n)
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| * [[29edo]]: 2.3.5.7.11.13.19 (no-n)
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| * [[32edo]]: 2.3.5.7.11.17.19 (no-n)
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| === Dual-n (dual-fifth) ===
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| * [[30edo]]: 2.3+.3-.5.7.11.13 (dual)
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| * [[35edo]]: 2.3+.3-.5.7.11.17 (dual)
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| * [[40edo]]: 2.3+.3-.5.7.11.13 (dual)
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| * [[42edo]]: 2.3+.3-.5+.5-.7.11 (dual)
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| * [[47edo]]: 2.3+.3-.5.7.11+.11- (dual)
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| * [[52edo]]: 2.3+.3-.5.7.11.19 (dual)
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| * [[54edo]]: 2.3+.3-.5+.5-.7+.7-.11 (dual)
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| === Dual-n (other)===
| | ; 800c |
| * [[34edo]]: 2.3.5.7+.7-.11.13 (dual)
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| * [[36edo]]: 2.3.5+.5-.7.11+.11- (dual)
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| * [[38edo]]: 2.3.5.7.11+.11-.13 (dual)
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| * [[39edo]]: 2.3.5+.5-.7+.7-.11 (dual)
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| * [[44edo]]: 2.3.5.7+.7-.11.13 (dual)
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| * [[45edo]]: 2.3.5+.5-.7.11.17 (dual)
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| * [[48edo]]: 2.3.5+.5-.7.11.13 (dual)
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| * [[49edo]]: 2.3.5.7+.7-.11+.11- (dual)
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| * [[51edo]]: 2.3.5+.5-.7.11+.11- (dual)
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| === Equalizer ===
| | Depending on context, behaves like: [[30/19|30:19]], [[19/12|19:12]], [[27/17|27:17]] or [[8/5|8:5]]. |
| No edos really fit this category.
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| === Other composite ===
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| * [[6edo]]: 2.9.5 (comp)
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| * [[11edo]]: 2.9.15.7.11 (comp)
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| * [[13edo]]: 2.9.5.11.13.17 (comp)
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| * [[23edo]]: 2.9.15.21.33.13 (comp)
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|
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|
| === Nth-basis ===
| | ; 900c |
| Interestingly, all of these can be seen as 15th-basis. It might just be because in EDOs 2 is always pure, and 3 and 5 are the next simplest harmonics, so it just makes sense for them to show up as simple subgroup denominators.
| |
| * [[7edo]]: 2.3.11/3.11/5.13 (nth-b) (15th)
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| * [[8edo]]: 2.11/3.13/5.19 (nth-b) (15th)
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| * [[9edo]]: 2.5.7/3.11 (nth-b) (3rd)
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| * [[14edo]]: 2.3.7/5.9/5.11/5.13 (nth-b) (5th)
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| * [[18edo]]: 2.9.5.7/3.11 (nth-b) (3rd)
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|
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| === Other fractional ===
| | Depending on context, behaves like: [[5/3|5:3]], [[32/19|32:19]], [[27/16|27:16]] or [[17/10|17:10]]. |
| No edos really fit this category.
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|
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|
| (''Technically any fractional subgroup can be said to be nth-basis, but if it were something absurdly big like 200th-basis, then it would belong in this category, not nth-basis, for the purpose of this list.''
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| ''But, there aren't any edos where that kind of subgroup makes sense hence this category being empty.'')
| | ; 1000c |
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| == Notation of dual-3 EDOs ==
| | Depending on context, behaves like: [[30/17|30:17]], [[16/9|16:9]] or [[9/5|9:5]]. |
| Most EDO notation systems, including the near-universal [[ups and downs notation]], are built upon [[chain-of-fifths notation]]. How then should an EDO be notated if it’s dual-fifth, i.e. it has two mappings of 3: 3+ and 3-?
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| The most straightforward solution is to just choose whichever 3 is closer to just 3/1, and pretend that’s the "real 3" for notation purposes. Treat the other 3 as just another prime, like 5 or 7. In most cases, I advise to do that.
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| If you happen to be mainly using an EDO as a tuning for one specific non-dual [[regular temperament]] like meantone, mavila, etc., then pretend that temperament’s mapping of 3 is the ‘real’ one for the purpose of notation, and pretend the other 3 is just like any other larger prime.
| | ; 1100c |
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|
| Of course, this results in multiple notation systems for the same EDO, since different people use different temperaments or none at all, but that’s already the case. All of those notation systems already exist, I’m not adding any new ones, I’m just saying that the ones we already have all have a valid place and it’s okay to use one some day and another some other day on a project-by-project basis.
| | Depending on context, behaves like: [[15/8|15:8]], [[32/17|32:17]], [[17/9|17:9]], [[36/19|36:19]] or [[19/10|19:10]]. |
|
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| As long as you name and briefly explain your notation system at the start of your score, use whatever system you want. Use whichever one works in practice for you and the musicians collaborating with you. Invent one, if the existing ones don’t work. It’s fine. Not everything has to be standardized and homogenized.
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| Because I’m personally a fan of mixing and matching multiple temperaments, and other things that aren’t temperaments like approximated JI scales, MOS scales, MODMOS & inflected MOS scales and even randomly generated scales, I usually like to go with the first option: ups and downs notation, in particular using whichever 3 is closest to just for its chain of fifths, and the other 3 being treated as just another available prime like 5, 7 or 11.
| | ; 1200c |
|
| |
|
| == Interpreting 12edo as a 2.3.5.17.19 system==
| | Behaves like: [[2/1|2:1]]. |
| === Intervals ===
| |
| <br> | | <br> |
|
| |
|
| ; 0c (0 [[cents]])
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|
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| Behaves like: [[1/1|1:1]].
| | == Chords == |
| | <br> |
| | |
| | === Common chords === |
| | My interpretation of what the just harmonies are, hiding behind common practice chords. |
| | |
| | Note names and common practice titles assume C is the [[tonic]] but of course you can transpose to any other key. |
| | |
| | Harmonies from ''inversions'' of the chord are in ''italics''. |
| | |
| | |
| | ; Major chord |
| | |
| | Just harmonies approximated: |
| | * 4:5:6 |
| | * ''2:3:5'' |
| | * ''3:4:5'' |
| | |
| | Note numbers: 0, 4, 7 |
| | |
| | Note names: C, E, G |
| | |
| | Common practice title: C |
| | |
| | |
| | ; Minor chord |
| | |
| | Just harmonies: |
| | * 10:12:15 |
| | * 16:19:24 |
| | * ''12:16:19'' |
| | |
| | Note numbers: 0, 3, 7 |
| | |
| | Note names: C, Eb, G |
| | |
| | Common practice title: Cm |
| | |
| | |
| | ; Diminished chord |
| | |
| | Just harmonies: |
| | * 17:20:24 |
| | * ''10:12:17'' |
| | * ''12:17:20'' |
| | |
| | Note numbers: 0, 3, 6 |
| | |
| | Note names: C, Eb, Gb |
| | |
| | Common practice title: Cdim |
| | |
| | |
| | ; Major seventh chord |
| | |
| | Just harmonies: |
| | * 8:10:12:15 |
| | * 20:25:30:38 |
| | * ''15:19:20:25'' |
| | |
| | Note numbers: 0, 4, 7, 11 |
| | |
| | Note names: C, E, G, B |
| | |
| | Common practice title: Cmaj7 |
| | |
| | |
| | ; Minor seventh chord |
| | |
| | Just harmonies: |
| | * 10:12:15:18 |
| | * ''9:10:12:15'' |
| | |
| | Note numbers: 0, 3, 7, 10 |
| | |
| | Note names: C, Eb, G, Bb |
| | |
| | Common practice title: Cmin7 |
| | |
| | |
| | ; Dominant seventh chord |
| | |
| | Just harmonies: |
| | * 20:25:30:36 |
| | * ''15:18:20:25'' |
| | |
| | Note numbers: 0, 4, 7, 10 |
| | |
| | Note names: C, E, G, Bb |
| | |
| | Common practice title: C7 |
| | |
| | |
| | ; Sus2 chord |
| | |
| | Just harmonies: |
| | * 8:9:12 |
| | * 18:20:27 |
| | * ''6:8:9'' |
| | |
| | Note numbers: 0, 2, 7 |
| | |
| | Note names: C, D, G |
| | |
| | Common practice title: Csus2 |
| | |
| | |
| | ; Sus4 chord |
| | |
| | Just harmonies: |
| | * 6:8:9 |
| | * 20:25:27 |
| | |
| | Note numbers: 0, 5, 7 |
| | |
| | Note names: C, F, G |
| | |
| | Common practice title: Csus4 |
| | |
| | |
| | ; Augmented chord |
| | |
| | Just harmonies: |
| | * 12:15:19 |
| | * 15:18:20 |
| | * ''9:10:15'' |
| | |
| | Note numbers: 0, 4, 8 |
| | |
| | Note names: C, E, G# |
| | |
| | Common practice title: Caug |
| | |
| | |
| | ; Dominant seventh chord |
| | |
| | Just harmonies: |
| | * 20:25:30:36 |
| | * ''15:18:20:25'' |
| | |
| | Note numbers: 0, 4, 7, 10 |
| | |
| | Note names: C, E, G, Bb |
| | |
| | Common practice title: C7 |
| | |
| | |
| | ; Major ninth chord |
| | |
| | Just harmonies: |
| | * 8:10:12:15:18 |
| | * ''8:9:10:12:15'' |
| | |
| | Note numbers: 0, 4, 7, 11, 14 |
| | |
| | Note names: C, E, G, B, D |
| | |
| | Common practice title: Cmaj9 |
| | |
| | |
| | ; Minor ninth chord |
|
| |
|
| | Just harmonies: |
| | * 40:48:60:72:85 |
|
| |
|
| ; 100c
| | Note numbers: 0, 3, 7, 10, 14 |
|
| |
|
| Depending on context, behaves like: [[20/19|20:19]], [[19/18|19:18]], [[18/17|18:17]], [[17/16|17:16]] or [[16/15|16:15]].
| | Note names: C, Eb, G, Bb, D |
|
| |
|
| | Common practice title: Cmin9 |
|
| |
|
| ; 200c
| |
|
| |
|
| Depending on context, behaves like: [[10/9|10:9]], [[19/17|19:17]], [[9/8|9:8]] or [[17/15|17:15]].
| | ; Dominant ninth chord |
|
| |
|
| | Just harmonies: |
| | * 40:50:60:72:85 |
|
| |
|
| ; 300c
| | Note numbers: 0, 4, 7, 10, 14 |
|
| |
|
| Depending on context, behaves like: [[20/17|20:17]], [[32/27|32:27]], [[19/16|19:16]] or [[6/5|6:5]].
| | Note names: C, E, G, Bb, D |
|
| |
|
| | Common practice title: C9 |
|
| |
|
| ; 400c
| |
|
| |
|
| Depending on context, behaves like: [[5/4|5:4]], [[34/27|34:27]], [[24/19|24:19]] or [[19/15|19:15]].
| | ; Major eleventh chord |
|
| |
|
| | Just harmonies: |
| | * 24:30:36:45:54:64 |
| | * ''24:28:30:32:36:45'' |
|
| |
|
| ; 500c
| | Note numbers: 0, 4, 7, 11, 14, 17 |
|
| |
|
| Depending on context, behaves like: [[4/3|4:3]] or [[27/20|27:20]].
| | Note names: C, E, G, B, D, F |
|
| |
|
| | Common practice title: Cmaj11 |
|
| |
|
| ; 600c
| |
|
| |
|
| Depending on context, behaves like: [[24/17|24:17]], [[17/12|17:12]] or [[27/19|27:19]].
| | ; Minor eleventh chord |
|
| |
|
| | Just harmonies: |
| | * 40:48:60:72:85:108 |
| | * ''40:48:54:60:72:85'' |
|
| |
|
| ; 700c
| | Note numbers: 0, 3, 7, 10, 14, 17 |
|
| |
|
| Behaves like: [[3/2|3:2]].
| | Note names: C, Eb, G, Bb, D, F |
|
| |
|
| | Common practice title: Cmin11 |
|
| |
|
| ; 800c
| |
|
| |
|
| Depending on context, behaves like: [[30/19|30:19]], [[19/12|19:12]], [[27/17|27:17]] or [[8/5|8:5]].
| | ; Dominant eleventh chord |
|
| |
|
| | Just harmonies: |
| | * 40:50:60:72:85:108 |
| | * ''40:50:54:60:72:85'' |
|
| |
|
| ; 900c
| | Note numbers: 0, 4, 7, 10, 14, 17 |
|
| |
|
| Depending on context, behaves like: [[5/3|5:3]], [[32/19|32:19]], [[27/16|27:16]] or [[17/10|17:10]].
| | Note names: C, E, G, Bb, D, F |
|
| |
|
| | Common practice title: C11 |
| | <br> |
|
| |
|
| ; 1000c
| |
|
| |
|
| Depending on context, behaves like: [[30/17|30:17]], [[16/9|16:9]] or [[9/5|9:5]].
| | === Parent chords === |
| | My list of in my opinion the most harmonious 'parent chords' in 12edo, which you can use as palettes to build novel and pretty smaller chords. Choose one of these chords, take any subset of 2 or more notes from it, and you will make another, also harmonious chord. |
|
| |
|
| | These chords work particularly well if you drop the root note down an octave, better mimicking the shape of the [[harmonic series]]. (''For example you can play "chord 0-12-15-19-20-21-22-23" instead of "chord 0-3-7-8-9-10-11"''). |
|
| |
|
| ; 1100c
| | Note names and common practice titles assume C is the [[tonic]] but of course you can transpose to any other key. |
|
| |
|
| Depending on context, behaves like: [[15/8|15:8]], [[32/17|32:17]], [[17/9|17:9]], [[36/19|36:19]] or [[19/10|19:10]].
| |
|
| |
|
| | ; The over-9 parent chord of 12edo |
|
| |
|
| ; 1200c
| | Approximated [[just]] harmony: 9:10:12:16:17 |
|
| |
|
| Behaves like: [[2/1|2:1]].
| | Note numbers: 0, 2, 5, 10, 11 |
|
| |
|
| === Chords ===
| | (With octave): 0, 12, 15, 17, 22, 23 |
| These chords work particularly well if you drop the root note down an octave, better mimicking the shape of the [[harmonic series]].
| |
|
| |
|
| (e.g you can play "chord 0-15-19-20-21-22-23" instead of "chord 0-3-7-8-9-10-11")
| | Note names: C, D, F, A#/Bb, B |
|
| |
|
| You can also of course take any subset of 2 or more notes from one of these chords to make another, also harmonious chord.
| | Common practice title: Dm7#5/C add(b6) |
|
| |
|
| Notes and names here assume C is the [[tonic]] but of course you can transpose to any other key.
| |
|
| |
|
| | ; The over-10 parent chord of 12edo |
|
| |
|
| ; Chord 0-3-8-10
| | Just harmony: 10:12:15:16:17:18:19 |
|
| |
|
| (Approximate) [[just]] harmony: 5:6:8:9
| | Note numbers: 0, 3, 7, 8, 9, 10, 11 |
|
| |
|
| Notes: C, D#/Eb, G#/Ab, A#/Bb
| | (With octave): 0, 12, 15, 19, 20, 21, 22, 23 |
|
| |
|
| Name: Cm7#5
| | Note names: C, D#/Eb, G, G#/Ab, A, A#/Bb, B |
|
| |
|
|
| |
|
| ; Chord 0-5-7-9 | | ; The over-12 parent chord of 12edo |
|
| |
|
| Just harmony: 6:8:9:10 | | Just harmony: 12:15:16:17:18:19:20 |
|
| |
|
| Notes: C, F, G, A
| | Note numbers: 0, 4, 5, 6, 7, 8, 9 |
|
| |
|
| Name: Fadd9/C
| | (With octave): 0, 12, 16, 17, 18, 19, 20, 21 |
|
| |
|
| | Note names: C, E, F, F#/Gb, G, G#/Ab, A |
|
| |
|
| ; Chord 0-2-4-7-11
| |
|
| |
|
| Just harmony 8:9:10:12:15
| | ; The over-15 parent chord of 12edo |
|
| |
|
| Notes: C, D, E, G, B
| | Just harmony: 15:16:17:18:19:20:24:27 |
|
| |
|
| Name: Cmaj9
| | Note numbers: 1, 2, 3, 4, 5, 8, 10 |
|
| |
|
| | (With octave): 0, 12, 13, 14, 15, 16, 17, 20, 22 |
|
| |
|
| ; Chord 0-2-5-10-11
| | Note names: C, C#/Db, D, D#/Eb, E, F, G#/Ab, A#/Bb |
|
| |
|
| Just harmony: 9:10:12:16:17
| |
|
| |
|
| Notes: C, D, F, A#/Bb, B
| | ; The over-16 parent chord of 12edo |
|
| |
|
| Name: Dm7#5/C add(b6)
| | Just harmony: 16:17:18:19:20:24:30 |
|
| |
|
| | Note numbers: 0, 1, 2, 3, 4, 7, 11 |
|
| |
|
| ; Chord 0-3-7-8-9-10-11
| | (With octave): 0, 12, 13, 14, 15, 16, 19, 23 |
|
| |
|
| 10:12:15:16:17:18:19
| | Note names: C, C#/Db, D, D#/Eb, E, G, B |
|
| |
|
| Notes: C, D#/Eb, G, G#/Ab, A, A#/Bb, B
| | Common practice title: Cmaj9 add(m3,m9) |
|
| |
|
|
| |
|
| ; Chord 0-4-5-6-7-8-9 | | ; The over-17 parent chord of 12edo |
|
| |
|
| 12:15:16:17:18:19:20
| | Just harmony: 17:18:19:20:24:27:30:32 |
|
| |
|
| Notes: C, E, F, F#/Gb, G, G#/Ab, A
| | Note numbers: 0, 1, 2, 3, 6, 8, 10, 11 |
|
| |
|
| | (With octave): 0, 12, 13, 14, 15, 18, 20, 22, 23 |
|
| |
|
| ; Chord 0-1-2-3-4-5-8-10
| | Note names: C, C#/Db, D, D#/Eb, F#/Gb, G#/Ab, A#/Bb, B |
|
| |
|
| 15:16:17:18:19:20:24:27
| |
|
| |
|
| Notes: C, C#/Db, D, D#/Eb, E, F, G#/Ab, A#/Bb
| | ; The over-18 parent chord of 12edo |
|
| |
|
| | Just harmony: 18:19:20:24:27:30:32:34 |
|
| |
|
| ; Chord 0-1-2-3-4-7-11
| | Note numbers: 0, 1, 2, 5, 7, 9, 10, 11 |
|
| |
|
| 16:17:18:19:20:24:30
| | (With octave): 0, 12, 13, 14, 17, 19, 21, 22, 23 |
|
| |
|
| Notes: C, C#/Db, D, D#/Eb, E, G, B
| | Note names: C, C#/Db, D, F, G, A, A#/Bb, B |
|
| |
|
| Name: Cmaj9 add(m3,m9)
| |
|
| |
|
| | ; The over-19 parent chord of 12edo |
|
| |
|
| ; Chord 0-1-2-3-6-8-10-11
| | Just harmony: 19:20:24:27:30:32:36 |
|
| |
|
| 17:18:19:20:24:27:30:32
| | Note numbers: 0, 1, 4, 6, 8, 9, 11 |
|
| |
|
| Notes: C, C#/Db, D, D#/Eb, F#/Gb, G#/Ab, A#/Bb, B
| | (With octave): 0, 12, 13, 16, 18, 20, 21, 23 |
|
| |
|
| | Note names: C, C#/Db, E, F#/Gb, G#/Ab, A, B |
|
| |
|
| ; Chord 0-1-2-5-7-9-10-11
| |
|
| |
|
| 18:19:20:24:27:30:32:34
| | ; The over-20 parent chord of 12edo |
|
| |
|
| Notes: C, C#/Db, D, F, G, A, A#/Bb, B
| | Just harmony: 20:24:25:27:30:32:34:36:38 |
|
| |
|
| | Note numbers: 0, 3, 4, 5, 7, 8, 9, 10, 11 |
|
| |
|
| ; Chord 0-1-4-6-8-9-11
| | (With octave): 0, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23 |
|
| |
|
| 19:20:24:27:30:32:36
| | Note names: C, D#/Eb, E, F, G, G#/Ab, A, A#/Bb, B |
|
| |
|
| Notes: C, C#/Db, E, F#/Gb, G#/Ab, A, B
| |
|
| |
|
| | ; The over-24 parent chord of 12edo |
|
| |
|
| ; Chord 0-3-4-5-7-8-9-10-11
| | Just harmony: 24:27:30:32:34:36:38:40 |
|
| |
|
| 20:24:25:27:30:32:34:36:38
| | Note numbers: 0, 2, 4, 5, 6, 7, 8, 9 |
|
| |
|
| Notes: C, D#/Eb, E, F, G, G#/Ab, A, A#/Bb, B
| | (With octave): 0, 12, 14, 16, 17, 18, 19, 20, 21 |
|
| |
|
| [[Category:Impression]]
| | Note names: C, D, E, F, F#/Gb, G, G#/Ab, A |