Xenharmonic Wiki

8edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
TallKite (talk | contribs)
autopatrolled, Sysops
3,990 edits
cleanup
TallKite (talk | contribs)
autopatrolled, Sysops
3,990 edits
updated ups/down notation, general cleanup
Line 11: Line 11:
Another way of looking at 8-EDO is to treat a chord of 0-1-2-3-4 degrees (0-150-300-450-600 cents) as approximating harmonics 10:11:12:13:14 (~0-165-316-454-583 cents), which is not too implausible if you can buy that 12-EDO is a 5-limit temperament. This interpretation would imply that 121/120, 144/143, 169/168, and hence also 36/35 and 66/65, are tempered out.
Another way of looking at 8-EDO is to treat a chord of 0-1-2-3-4 degrees (0-150-300-450-600 cents) as approximating harmonics 10:11:12:13:14 (~0-165-316-454-583 cents), which is not too implausible if you can buy that 12-EDO is a 5-limit temperament. This interpretation would imply that 121/120, 144/143, 169/168, and hence also 36/35 and 66/65, are tempered out.


=Intervals=
=Notation=
 
[[File:8ed2-001.svg|alt=alt : Your browser has no SVG support.]]
 
[[:File:8ed2-001.svg|8ed2-001.svg]]


8-edo can be notated as a subset of 24-edo, using [[Ups_and_Downs_Notation|ups and downs]]. It can also be notated as a subset of 16-edo, but this is a less intuitive notation.
8-edo can be notated as a subset of 24-edo, using [[Ups_and_Downs_Notation|ups and downs]]. It can also be notated as a subset of 16-edo, but this is a less intuitive notation.
Line 100: Line 96:
|}
|}


8-edo chords are very ambiguous, with many chord homonyms. Even the major and minor triads are homonyms. Chord components usually default to M2, M3, P4, P5, M6, m7, M9, P11 and M13. Thus D7 has a M3, P5 and m7. 8-edo chord names using 24-edo subset names are greatly simplified by using different defaults: ~2, ^M3, v4, ^5, M6, ~7, ~9, v11 and M13. Thus D7 becomes ^M3, ^5 and ~7.
This is a heptatonic notation generated by 5ths (5th meaning 3/2). Alternative notations include pentatonic 5th-generated, octotonic, and heptatonic 2nd-generated.
 
'''<u>Pentatonic 5th-generated</u>: D * E G * A C * D'''  (generator = 5\8 = perfect 5thoid)
 
D - D#/Eb - E - G - G#/Ab - A - C - C#/Db - D
 
P1 - A1/ms3 - Ms3 - P4d - A4d/d5d - P5d - ms7 - Ms7/d8d - P8d  (s = sub-, d = -oid)
 
pentatonic genchain of 5ths: ...Cb - Gb - Db - Ab - Eb - C - G - D - A - E - C# - G# - D# - A# - E#...
 
pentatonic genchain of 5ths: ...d8d - d5d - ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d - A1... (s = sub-, d = -oid)
 
'''<u>Octatonic:</u>''' '''A B C D E F G H A'''  (every interval is a generator)
 
P1 - P2 - P3 - P4 - P5 - P6 - P7 - P8 - P9
 
'''<u>Heptatonic 2nd-generated</u>: D E F G * A B C D'''  (generator = 1\8 = perfect 2nd = 150¢)
 
D - E - F - G - G#/Ab - A -B - C - D
 
P1 - P2 - m3 - M3/m4 - M4/m5 - M5/m6 - M6 - P7 - P8
 
genchain of 2nds: ...D# - E# - F# - G# - A - B - C - D - E - F - G - Ab - Bb - Cb - Db...
 
genchain of 2nds: ...A1 - A2 - M3 - M4 - M5 - M6 - P7 - P1 - P2 - m3 - m4 - m5 - m6 - d7 - d8...
 
== Chord Names ==
8-edo chords are very ambiguous, with many chord homonyms. Even the major and minor triads are homonyms. Chord components usually default to M2, M3, P4, P5, M6, m7, M9, P11 and M13. Thus D7 has a M3, P5 and m7. 8-edo chord names using 24-edo subset names are greatly simplified by using different defaults: ~2, ^M3, v4, ^5, M6, ~7, ~9, v11 and M13. Thus D7 becomes ^M3, ^5 and ~7


{| class="wikitable"
{| class="wikitable"
Line 106: Line 129:
! | Chord edosteps
! | Chord edosteps
! | Chord notes
! | Chord notes
! | Proper name
! | Full name
! | Abbreviated name
! | Abbreviated name
! | Homonyms
! | Homonyms
Line 153: Line 176:
|}
|}


=Commas=
=JI Intervals=
8 EDO tempers out the following commas. (Note: This assumes val &lt; 8 13 19 22 28 30 |). ||~ Comma ||~ Monzo ||~ Cents ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
[[File:8ed2-001.svg|alt=alt : Your browser has no SVG support.]]
 
[[:File:8ed2-001.svg|8ed2-001.svg]]
 
= Commas =
8 EDO tempers out the following commas. (Note: This assumes val &lt; 8 13 19 22 28 30 |).  


{| class="wikitable"
{| class="wikitable"
! style="text-align:center;" |[[Ratio]]
! style="text-align:center;" |[[Monzo]]
! style="text-align:center;" |Cents
! style="text-align:center;" |[[Color notation/Temperament Names|Color Name]]
! style="text-align:center;" |Name 1
! style="text-align:center;" |Name 2
! style="text-align:center;" |Name 3
|-
|-
| style="text-align:center;" | 648/625
| style="text-align:center;" | 648/625
| |<nowiki> | 3 4 -4 </nowiki>&gt;
| |<nowiki> | 3 4 -4 </nowiki>&gt;
| style="text-align:right;" | 62.57
| style="text-align:right;" | 62.57
| style="text-align:center;" |Quadgu
| style="text-align:center;" | Major Diesis
| style="text-align:center;" | Major Diesis
| style="text-align:center;" | Diminished Comma
| style="text-align:center;" | Diminished Comma
Line 168: Line 204:
| |<nowiki> | 1 -5 3 </nowiki>&gt;
| |<nowiki> | 1 -5 3 </nowiki>&gt;
| style="text-align:right;" | 49.17
| style="text-align:right;" | 49.17
| style="text-align:center;" |Triyo
| style="text-align:center;" | Maximal Diesis
| style="text-align:center;" | Maximal Diesis
| style="text-align:center;" | Porcupine Comma
| style="text-align:center;" | Porcupine Comma
Line 175: Line 212:
| |<nowiki> | 2 9 -7 </nowiki>&gt;
| |<nowiki> | 2 9 -7 </nowiki>&gt;
| style="text-align:right;" | 13.40
| style="text-align:right;" | 13.40
| style="text-align:center;" |Sepgu
| style="text-align:center;" | Medium Semi Comma
| style="text-align:center;" | Medium Semi Comma
| style="text-align:center;" | Sensipent Comma
| style="text-align:center;" | Sensipent Comma
Line 182: Line 220:
| |<nowiki> | 6 -2 0 -1 </nowiki>&gt;
| |<nowiki> | 6 -2 0 -1 </nowiki>&gt;
| style="text-align:right;" | 27.26
| style="text-align:right;" | 27.26
| style="text-align:center;" |Ru
| style="text-align:center;" | Septimal Comma
| style="text-align:center;" | Septimal Comma
| style="text-align:center;" | Archytas' Comma
| style="text-align:center;" | Archytas' Comma
Line 189: Line 228:
| |<nowiki> | -5 -3 3 1 </nowiki>&gt;
| |<nowiki> | -5 -3 3 1 </nowiki>&gt;
| style="text-align:right;" | 21.90
| style="text-align:right;" | 21.90
| style="text-align:center;" |Zotriyo
| style="text-align:center;" | Keema
| style="text-align:center;" | Keema
| |  
| |  
Line 196: Line 236:
| |<nowiki> | -9 8 -4 2 </nowiki>&gt;
| |<nowiki> | -9 8 -4 2 </nowiki>&gt;
| style="text-align:right;" | 8.04
| style="text-align:right;" | 8.04
| style="text-align:center;" |Labizogugu
| style="text-align:center;" | Varun Isma
| style="text-align:center;" | Varun Isma
| |  
| |  
Line 203: Line 244:
| |<nowiki> | 11 1 -3 -2 </nowiki>&gt;
| |<nowiki> | 11 1 -3 -2 </nowiki>&gt;
| style="text-align:right;" | 5.36
| style="text-align:right;" | 5.36
| style="text-align:center;" |Sarurutrigu
| style="text-align:center;" | Cornwell
| style="text-align:center;" | Cornwell
| |  
| |  
Line 210: Line 252:
| |<nowiki> | 2 -2 2 0 -1 </nowiki>&gt;
| |<nowiki> | 2 -2 2 0 -1 </nowiki>&gt;
| style="text-align:right;" | 17.40
| style="text-align:right;" | 17.40
| style="text-align:center;" |Luyoyo
| style="text-align:center;" | Ptolemies
| style="text-align:center;" | Ptolemies
| |  
| |  
Line 217: Line 260:
| |<nowiki> | -3 -1 -1 0 2 </nowiki>&gt;
| |<nowiki> | -3 -1 -1 0 2 </nowiki>&gt;
| style="text-align:right;" | 14.37
| style="text-align:right;" | 14.37
| style="text-align:center;" |Lologu
| style="text-align:center;" | Batista
| style="text-align:center;" | Batista
| |  
| |  
Line 224: Line 268:
| |<nowiki> | 4 0 -2 -1 1 </nowiki>&gt;
| |<nowiki> | 4 0 -2 -1 1 </nowiki>&gt;
| style="text-align:right;" | 9.86
| style="text-align:right;" | 9.86
| style="text-align:center;" |Lorugugu
| style="text-align:center;" | Valinor Mo
| style="text-align:center;" | Valinor Mo
| |  
| |  
Line 231: Line 276:
| |<nowiki> | 16 0 0 -2 -3 </nowiki>&gt;
| |<nowiki> | 16 0 0 -2 -3 </nowiki>&gt;
| style="text-align:right;" | 8.39
| style="text-align:right;" | 8.39
| style="text-align:center;" |Satrilu-aruru
| style="text-align:center;" | Organisms
| style="text-align:center;" | Organisms
| |  
| |  
Line 238: Line 284:
| |<nowiki> | -7 -1 1 1 1 </nowiki>&gt;
| |<nowiki> | -7 -1 1 1 1 </nowiki>&gt;
| style="text-align:right;" | 4.50
| style="text-align:right;" | 4.50
| style="text-align:center;" |Lozoyo
| style="text-align:center;" | Keenanisma
| style="text-align:center;" | Keenanisma
| |  
| |  
Line 245: Line 292:
| |<nowiki> | 5 -1 3 0 -3 </nowiki>&gt;
| |<nowiki> | 5 -1 3 0 -3 </nowiki>&gt;
| style="text-align:right;" | 3.03
| style="text-align:right;" | 3.03
| style="text-align:center;" |Triluyo
| style="text-align:center;" | Wizard Harry
| style="text-align:center;" | Wizard Harry
| |  
| |  
Retrieved from "https://en.xen.wiki/w/8edo"