Xenharmonic Wiki

46edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
Fredg999 (talk | contribs)
autopatrolled, Interface administrators, Sysops
6,129 edits
m Add interwiki
TallKite (talk | contribs)
autopatrolled, Sysops
3,990 edits
→Intervals: added a uniform solfege
Line 28: Line 28:
! Approximate Ratios<nowiki>*</nowiki>
! Approximate Ratios<nowiki>*</nowiki>
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" | [[Ups and Downs Notation]]
! Solfege
! colspan="2" |[[Solfege|Solfeges]]
|-
|-
| 0
| 0
Line 36: Line 36:
| P1
| P1
| D
| D
|da
| do
| do
|-
|-
Line 44: Line 45:
| ^1
| ^1
| ^D
| ^D
|du
| di
| di
|-
|-
Line 52: Line 54:
| vm2
| vm2
| vEb
| vEb
|fro
| ro
| ro
|-
|-
Line 60: Line 63:
| m2
| m2
| Eb
| Eb
|fra
| rih
| rih
|-
|-
Line 68: Line 72:
| ^m2
| ^m2
| ^Eb
| ^Eb
|fru
| ra
| ra
|-
|-
Line 76: Line 81:
| v~2
| v~2
| ^^Eb
| ^^Eb
| ru (as in supraminor)
|fri
| ru **
|-
|-
| 6
| 6
Line 84: Line 90:
| ^~2
| ^~2
| vvE
| vvE
| ruh (as in submajor)
|ri
| ruh ***
|-
|-
| 7
| 7
Line 92: Line 99:
| vM2
| vM2
| vE
| vE
|ro
| reh
| reh
|-
|-
Line 100: Line 108:
| M2
| M2
| E
| E
|ra
| re
| re
|-
|-
Line 108: Line 117:
| ^M2
| ^M2
| ^E
| ^E
|ru
| ri
| ri
|-
|-
Line 116: Line 126:
| vm3
| vm3
| vF
| vF
|no
| ma
| ma
|-
|-
Line 124: Line 135:
| m3
| m3
| F
| F
|na
| meh
| meh
|-
|-
Line 132: Line 144:
| ^m3
| ^m3
| ^F
| ^F
|nu
| me
| me
|-
|-
Line 140: Line 153:
| v~3
| v~3
| ^^F
| ^^F
| mu
|ni
| mu **
|-
|-
| 14
| 14
Line 148: Line 162:
| ^~3
| ^~3
| vvF#
| vvF#
| muh
|mi
| muh ***
|-
|-
| 15
| 15
Line 156: Line 171:
| vM3
| vM3
| vF#
| vF#
|mo
| mi
| mi
|-
|-
Line 164: Line 180:
| M3
| M3
| F#
| F#
|ma
| maa
| maa
|-
|-
Line 172: Line 189:
| ^M3
| ^M3
| ^F#
| ^F#
|mu
| mo
| mo
|-
|-
Line 180: Line 198:
| v4
| v4
| vG
| vG
|fo
| fe
| fe
|-
|-
Line 188: Line 207:
| P4
| P4
| G
| G
|fa
| fa
| fa
|-
|-
Line 196: Line 216:
| ^4
| ^4
| ^G
| ^G
|fu
| fih
| fih
|-
|-
Line 204: Line 225:
| v~4
| v~4
| ^^G
| ^^G
|fi/sho
| fu
| fu
|-
|-
Line 212: Line 234:
| ^~4, d5
| ^~4, d5
| vvG#, Ab
| vvG#, Ab
|pi/sha
| fi
| fi
|-
|-
Line 220: Line 243:
| vA4, ^d5
| vA4, ^d5
| vG#, ^Ab
| vG#, ^Ab
|po/shu
| seh
| seh
|-
|-
Line 228: Line 252:
| A4, v~5
| A4, v~5
| G#, ^^Ab
| G#, ^^Ab
|pa/shi
| se
| se
|-
|-
Line 236: Line 261:
| ^~5
| ^~5
| vvA
| vvA
|pu/si
| su
| su
|-
|-
Line 244: Line 270:
| v5
| v5
| vA
| vA
|so
| sih
| sih
|-
|-
Line 252: Line 279:
| P5
| P5
| A
| A
|sa
| sol
| sol
|-
|-
Line 260: Line 288:
| ^5
| ^5
| ^A
| ^A
|su
| si
| si
|-
|-
Line 268: Line 297:
| vm6
| vm6
| vBb
| vBb
|flo
| lo
| lo
|-
|-
Line 276: Line 306:
| m6
| m6
| Bb
| Bb
|fla
| leh
| leh
|-
|-
Line 284: Line 315:
| ^m6
| ^m6
| ^Bb
| ^Bb
|flu
| le
| le
|-
|-
Line 292: Line 324:
| v~6
| v~6
| ^^Bb
| ^^Bb
| lu
|fli
| lu **
|-
|-
| 33
| 33
Line 300: Line 333:
| ^~6
| ^~6
| vvB
| vvB
| luh
|li
| luh ***
|-
|-
| 34
| 34
Line 308: Line 342:
| vM6
| vM6
| vB
| vB
|lo
| la
| la
|-
|-
Line 316: Line 351:
| M6
| M6
| B
| B
|la
| laa
| laa
|-
|-
Line 324: Line 360:
| ^M6
| ^M6
| ^B
| ^B
|lu
| li
| li
|-
|-
Line 332: Line 369:
| vm7
| vm7
| vC
| vC
|tho
| ta
| ta
|-
|-
Line 340: Line 378:
| m7
| m7
| C
| C
|tha
| teh
| teh
|-
|-
Line 348: Line 387:
| ^m7
| ^m7
| ^C
| ^C
|thu
| te
| te
|-
|-
Line 356: Line 396:
| v~7
| v~7
| ^^C
| ^^C
| tu
|thi
| tu **
|-
|-
| 41
| 41
Line 364: Line 405:
| ^~7
| ^~7
| vvC#
| vvC#
| tuh
|ti
| tuh ***
|-
|-
| 42
| 42
Line 372: Line 414:
| vM7
| vM7
| vC#
| vC#
|to
| ti
| ti
|-
|-
Line 380: Line 423:
| M7
| M7
| C#
| C#
|ta
| taa
| taa
|-
|-
Line 388: Line 432:
| ^M7
| ^M7
| ^C#
| ^C#
|tu
| to
| to
|-
|-
Line 396: Line 441:
| v8
| v8
| vD
| vD
|do
| da
| da
|-
|-
Line 404: Line 450:
| P8
| P8
| D
| D
|da
| do
| do
|}
|}
<nowiki>*</nowiki> Based on treating 46edo as a 2.3.5.7.11.13.17.23 subgroup, without ratios of 15 (except the superparticulars). 46edo has the 15th harmonic poorly approximated in general, because, while both the 3rd and 5th harmonics are sharp by a fair amount and they add up, all the other primes are flat, making the difference even larger, to the extent that it is not [[consistent]] in the [[15-odd-limit]]. This can be demonstrated with the discrepancy approximating [[15/13]] (and its inversion [[26/15]]). 9\46edo is closer to 15/13 by a hair; 10\46edo represents the difference between, for instance, 46edo's 15/8 and 13/8, and is more likely to appear in chords actually functioning as 15/13.  
<nowiki>*</nowiki> Based on treating 46edo as a 2.3.5.7.11.13.17.23 subgroup, without ratios of 15 (except the superparticulars). 46edo has the 15th harmonic poorly approximated in general, because, while both the 3rd and 5th harmonics are sharp by a fair amount and they add up, all the other primes are flat, making the difference even larger, to the extent that it is not [[consistent]] in the [[15-odd-limit]]. This can be demonstrated with the discrepancy approximating [[15/13]] (and its inversion [[26/15]]). 9\46edo is closer to 15/13 by a hair; 10\46edo represents the difference between, for instance, 46edo's 15/8 and 13/8, and is more likely to appear in chords actually functioning as 15/13.  
<nowiki>**</nowiki> -u as in s'''u'''praminor
<nowiki>***</nowiki> -uh as in s'''u'''bmajor


=== Interval quality and chord names in color notation ===
=== Interval quality and chord names in color notation ===
Retrieved from "https://en.xen.wiki/w/46edo"