User:TromboneBoi9: Difference between revisions
TromboneBoi9 (talk | contribs) No edit summary |
TromboneBoi9 (talk | contribs) No edit summary |
||
| Line 5: | Line 5: | ||
'''[https://akahler.w3spaces.com/ I have a website!!]''' | '''[https://akahler.w3spaces.com/ I have a website!!]''' | ||
== An idea for notation I had == | |||
Something I noticed in regular EDO notation, | Something I noticed in [[Ups and downs notation|regular EDO notation]], relying on Pythagorean names with an extra layer of accidentals, is that the [Pythagorean] major third in a lot of temperaments is no longer the closest the EDO has to the [[5/4|just major third 5/4]]. So, with some thought from Just Intonation notations, I came up with something that I think might be promising. | ||
In essence, instead of solely relying on Pythaogrean names and arrows for edosteps in between (which can get unwieldy in larger EDOs), I considered making the arrow represent the [[syntonic comma]] instead. If your EDO has a different pitch for the just major third and the Pythagorean major third, then of course, it has syntonic comma that hasn't been tempered out. This won't change anything for EDOs with a syntonic comma less than or equal to one step, of course, but it could have an effect on even "sharper" systems like 37-EDO. | In essence, instead of solely relying on Pythaogrean names and arrows for edosteps in between (which can get unwieldy in larger EDOs, e.g. [[72edo#Intervals|72-EDO]]), I considered making the arrow represent the [[syntonic comma]] instead. If your EDO has a different pitch for the just major third and the Pythagorean major third, then of course, it has a syntonic comma that hasn't been tempered out. This won't change anything for EDOs with a syntonic comma less than or equal to one step, of course, but it could have an effect on even "sharper" systems like 37-EDO. | ||
For single edosteps, we can instead use a sort of slash-like symbol Bosanquet used in his notation, and perhaps stack them on top of each other to use less horizontal space. | For single edosteps, we can instead use a sort of slash-like symbol Bosanquet used in his notation, and perhaps stack them on top of each other to use less horizontal space. | ||
| Line 288: | Line 288: | ||
|D | |D | ||
|} | |} | ||
''I have also devised custom accidentals for quartertones in both diatonic and anti-diatonic systems, but the image uploading process is being weird so I'll have to figure that out at some point.'' | |||
== Cloudy scales == | |||
I don't know about you, but I love the seventh harmonic. These scales are named after the [[cloudy comma]], and use different [[7-limit]] intervals for generators. | I don't know about you, but I love the seventh harmonic. These scales are named after the [[cloudy comma]], and use different [[7-limit]] intervals for generators. | ||
=== Cumulus Alpha === | |||
'''''Cumulus Alpha''''' is a 5L6s [[MOS]] with [[7/4]] as the generator and [[2/1]] as the period. This appears to approximate a subset of [[26edo|26-EDO]]; it approximates the whole of 26-EDO when extended to a 5L21s MOS, which I dub '''''Cumulus Alpha Holo'''''. | '''''Cumulus Alpha''''' is a 5L6s [[MOS]] with [[7/4]] as the generator and [[2/1]] as the period. This appears to approximate a subset of [[26edo|26-EDO]]; it approximates the whole of 26-EDO when extended to a 5L21s MOS, which I dub '''''Cumulus Alpha Holo'''''. | ||
{| class="wikitable mw-collapsible" | {| class="wikitable mw-collapsible" | ||
| Line 359: | Line 361: | ||
|26 | |26 | ||
|} | |} | ||
=== Cumulus Beta === | |||
'''''Cumulus Beta''''' is an 4L5s MOS with [[7/6]] as the generator and [[2/1]] as the period. It approximates all intervals of [[9edo|9-EDO]] within a cent, proving 9-EDO's place as an exceptional 7-limit approximation. | '''''Cumulus Beta''''' is an 4L5s MOS with [[7/6]] as the generator and [[2/1]] as the period. It approximates all intervals of [[9edo|9-EDO]] within a cent, proving 9-EDO's place as an exceptional 7-limit approximation. | ||
{| class="wikitable mw-collapsible" | {| class="wikitable mw-collapsible" | ||
| Line 416: | Line 420: | ||
|0.000 | |0.000 | ||
|} | |} | ||
=== Cumulus Gamma === | |||
'''''Cumulus Gamma''''' is an 3L8s MOS with [[9/7]] as the generator and [[2/1]] as the period. It approximates all intervals of [[11edo|11-EDO]] within 10 cents. | '''''Cumulus Gamma''''' is an 3L8s MOS with [[9/7]] as the generator and [[2/1]] as the period. It approximates all intervals of [[11edo|11-EDO]] within 10 cents. | ||
{| class="wikitable mw-collapsible" | {| class="wikitable mw-collapsible" | ||
Revision as of 14:00, 22 May 2023
Hello! My name is Andrew and I like screwing around with xenharmony, especially notation.
Currently experimenting with anti-diatonic stuff like EDOs 9, 11, 13, 16, and 23.
An idea for notation I had
Something I noticed in regular EDO notation, relying on Pythagorean names with an extra layer of accidentals, is that the [Pythagorean] major third in a lot of temperaments is no longer the closest the EDO has to the just major third 5/4. So, with some thought from Just Intonation notations, I came up with something that I think might be promising.
In essence, instead of solely relying on Pythaogrean names and arrows for edosteps in between (which can get unwieldy in larger EDOs, e.g. 72-EDO), I considered making the arrow represent the syntonic comma instead. If your EDO has a different pitch for the just major third and the Pythagorean major third, then of course, it has a syntonic comma that hasn't been tempered out. This won't change anything for EDOs with a syntonic comma less than or equal to one step, of course, but it could have an effect on even "sharper" systems like 37-EDO.
For single edosteps, we can instead use a sort of slash-like symbol Bosanquet used in his notation, and perhaps stack them on top of each other to use less horizontal space.
Here's a full example in 37-EDO:
| Steps | Pythagorean notation | Old notation | New notation |
|---|---|---|---|
| 0 | D | D | D |
| 1 | Eb | Eb | Eb |
| 2 | Fb | ^Eb | ^D |
| 3 | Gbb | ^^Eb | ^Eb |
| 4 | Bx | vvD# | vD# |
| 5 | Cx | vD# | vE |
| 6 | D# | D# | D# |
| 7 | E | E | E |
| 8 | F | F | F |
| 9 | Gb | Gb | Gb |
| 10 | Abb | ^Gb | ^F |
| 11 | Bbbb | ^^Gb | ^Gb |
| 12 | Dx | vvF# | vF# |
| 13 | E# | vF# | vG |
| 14 | F# | F# | F# |
| 15 | G | G | G |
| 16 | Ab | Ab | Ab |
| 17 | Bbb | ^Ab | ^G |
| 18 | Cbb | ^^Ab | ^Ab |
| 19 | Ex | vvG# | vG# |
| 20 | Fx | vG# | vA |
| 21 | G# | G# | G# |
| 22 | A | A | A |
| 23 | Bb | Bb | Bb |
| 24 | Cb | ^Bb | ^A |
| 25 | Dbb | ^^Bb | vBb |
| 26 | F#x | vvA# | ^A# |
| 27 | Gx | vA# | vB |
| 28 | A# | A# | A# |
| 29 | B | B | B |
| 30 | C | C | C |
| 31 | Db | Db | Db |
| 32 | Ebb | ^Db | ^C |
| 33 | Fbb | ^^Db | ^Db |
| 34 | Ax | vvC# | vC# |
| 35 | B# | vC# | vD |
| 36 | C# | C# | C# |
| 37 | D | D | D |
And for anti-diatonic systems, use ( and ) instead of ^ and v, using harmonic notation.
An example in 13-EDO:
| Steps | Pythagorean/old notation | 26-EDO Subset | New notation |
|---|---|---|---|
| 0 | D | D | D |
| 1 | E | Dx, Ebb | E, (C |
| 2 | Eb | E | Eb, (D |
| 3 | Fx | Ex, Fb | (E, )F |
| 4 | F# | F# | F#, )G |
| 5 | F | Gb | F, )A |
| 6 | G | G# | G, )B |
| 7 | A | Ab | A, (F |
| 8 | B | A# | B, (G |
| 9 | Bb | Bb | Bb, (A |
| 10 | Cx | B# | (B, )C |
| 11 | C# | C | C#, )D |
| 12 | C | Cx, Dbb | C, )E |
| 13 | D | D | D |
I have also devised custom accidentals for quartertones in both diatonic and anti-diatonic systems, but the image uploading process is being weird so I'll have to figure that out at some point.
Cloudy scales
I don't know about you, but I love the seventh harmonic. These scales are named after the cloudy comma, and use different 7-limit intervals for generators.
Cumulus Alpha
Cumulus Alpha is a 5L6s MOS with 7/4 as the generator and 2/1 as the period. This appears to approximate a subset of 26-EDO; it approximates the whole of 26-EDO when extended to a 5L21s MOS, which I dub Cumulus Alpha Holo.
| Steps | Ratio | Cents | Approx. 26-EDO Degree |
|---|---|---|---|
| 0 | 1/1 | 0.000 | 0 |
| 1 | 16807/16384 | 43.130 | 1 |
| 2 | 8/7 | 231.174 | 5 |
| 3 | 2401/2048 | 275.304 | 6 |
| 4 | 64/49 | 462.348 | 10 |
| 5 | 343/256 | 506.478 | 11 |
| 6 | 512/343 | 693.522 | 15 |
| 7 | 49/32 | 737.652 | 16 |
| 8 | 4096/2401 | 924.696 | 20 |
| 9 | 7/4 | 968.826 | 21 |
| 10 | 32768/16807 | 1155.870 | 25 |
| 11 | 2/1 | 1200.000 | 26 |
Cumulus Beta
Cumulus Beta is an 4L5s MOS with 7/6 as the generator and 2/1 as the period. It approximates all intervals of 9-EDO within a cent, proving 9-EDO's place as an exceptional 7-limit approximation.
| Steps | Ratio | Cents | 9-EDO Difference |
|---|---|---|---|
| 0 | 1/1 | 0.000 | 0.000 |
| 1 | 2592/2401 | 132.516 | -0.817 |
| 2 | 7/6 | 266.871 | 0.204 |
| 3 | 432/343 | 399.387 | -0.613 |
| 4 | 49/36 | 533.742 | 0.409 |
| 5 | 72/49 | 666.258 | -0.409 |
| 6 | 343/216 | 800.613 | 0.613 |
| 7 | 12/7 | 933.129 | -0.204 |
| 8 | 2401/1296 | 1067.484 | 0.817 |
| 9 | 7/4 | 1200.000 | 0.000 |
Cumulus Gamma
Cumulus Gamma is an 3L8s MOS with 9/7 as the generator and 2/1 as the period. It approximates all intervals of 11-EDO within 10 cents.
| Steps | Ratio | Cents | 11-EDO Difference |
|---|---|---|---|
| 0 | 1/1 | 0.000 | 0.000 |
| 1 | 729/686 | 105.252 | 3.839 |
| 2 | 67228/59049 | 224.580 | -6.398 |
| 3 | 98/81 | 329.832 | -2.559 |
| 4 | 9/7 | 435.084 | 1.280 |
| 5 | 6561/4802 | 540.336 | 5.119 |
| 6 | 9604/6561 | 659.664 | -5.119 |
| 7 | 14/9 | 764.916 | -1.280 |
| 8 | 81/49 | 870.168 | 2.559 |
| 9 | 59049/33614 | 975.420 | 6.398 |
| 10 | 1372/729 | 1094.748 | -3.839 |
| 11 | 2/1 | 1200.000 | 0.000 |