Xenharmonic Wiki

5L 7s: Difference between revisions

← Older editNewer edit →
VisualWikitext
Xenllium (talk | contribs)
autopatrolled
4,516 edits
mNo edit summary
The chroma-positive generator is the fifth not the fourth
Line 3: Line 3:
| nLargeSteps = 5
| nLargeSteps = 5
| nSmallSteps = 7
| nSmallSteps = 7
| Equalized = 5
| Equalized = 7
| Paucitonic = 2
| Paucitonic = 3
| Pattern = ssLsLssLsLsL
| Pattern = ssLsLssLsLsL
| Name = p-chromatic
| Name = p-chromatic
}}
}}


'''5L 7s''' is the MOS pattern of the [[Pythagorean tuning|Pythagorean]]/[[Schismatic family|schismic]] chromatic scale, and also the [[superpyth]] chromatic scale. In contrast to the [[7L 5s|meantone chromatic scale]], in which diatonic semitones are larger than chromatic semitones, here the reverse is true: diatonic semitones are smaller than chromatic semitones, so the [[5L 2s|diatonic scale]] subset is actually [[Rothenberg propriety|improper]].
'''5L 7s''' is the MOS pattern of the [[Pythagorean tuning|Pythagorean]]/[[Schismatic family|schismic]] chromatic scale, and also the [[superpyth]] chromatic scale. In contrast to the [[7L 5s|meantone chromatic scale]], in which the diatonic semitone is larger than the chromatic semitone, here the reverse is true: the diatonic semitone is smaller than the chromatic semitone, so the [[5L 2s|diatonic scale]] subset is actually [[Rothenberg propriety|improper]].


The two distinct harmonic entropy minima with this MOS pattern are, on the one hand, scales very close to Pythagorean such that [[64/63]] is not tempered out, such as the schismatic temperaments known as "Helmholtz" and "Garibaldi", and on the other hand, the much simpler and less accurate scale known as "superpyth" in which 64/63 is tempered out.
The two distinct harmonic entropy minima with this MOS pattern are, on the one hand, scales very close to Pythagorean such that [[64/63]] is not tempered out, such as the schismatic temperaments known as Helmholtz and Garibaldi, and on the other hand, the much simpler and less accurate scale known as superpyth in which 64/63 is tempered out.


The Pythagorean/schismatic version is proper, but the superpyth version is improper (it doesn't become proper until you add 5 more notes to form the superpyth "enharmonic" scale, superpyth[17]).
The Pythagorean/schismatic version is proper, but the superpyth version is improper (it does not become proper until you add 5 more notes to form the superpyth enharmonic scale, superpyth[17]).


== Modes ==
== Modes ==
Line 40: Line 40:
{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="6" | Generator
! colspan="6" | Generator
! Fifth <br>(cents)
! Cents
! L
! L
! s
! s
Line 48: Line 48:
| 7\12 || || || || || || 700.000 || 1 || 1 || 1.000 ||  
| 7\12 || || || || || || 700.000 || 1 || 1 || 1.000 ||  
|-
|-
| || || || || || 38\65 || 701.539 || 6 || 5 || 1.200 || [[Photia]] / [[Pontiac]] / [[Grackle]]
| || || || || || 38\65 || 701.539 || 6 || 5 || 1.200 || [[Photia]] / [[pontiac]] / [[grackle]]↑
|-
|-
| || || || || 31\53 || || 701.887 || 5 || 4 || 1.250 || [[Helmholtz]] / [[Pythagorean]]
| || || || || 31\53 || || 701.887 || 5 || 4 || 1.250 || [[Helmholtz]], [[Pythagorean tuning]] (701.9550¢)
|-
|-
| || || || || || 55\94 || 702.128 || 9 || 7 || 1.286 || [[Garibaldi]] / [[Cassandra]]
| || || || || || 55\94 || 702.128 || 9 || 7 || 1.286 || [[Garibaldi]] / [[cassandra]]
|-
|-
| || || || 24\41 || || || 702.409 || 4 || 3 || 1.333 || Garibaldi / [[Andromeda]]
| || || || 24\41 || || || 702.409 || 4 || 3 || 1.333 || Garibaldi / [[andromeda]]
|-
|-
| || || || || || 65\111 || 702.703 || 11 || 8 || 1.375 || [[Kwai]]
| || || || || || 65\111 || 702.703 || 11 || 8 || 1.375 || [[Kwai]]
Line 68: Line 68:
| || || || || 44\75 || || 704.000 || 8 || 5 || 1.600 ||
| || || || || 44\75 || || 704.000 || 8 || 5 || 1.600 ||
|-
|-
| || || || || || 71\121 || 704.132 || 13 || 8 || 1.625 || Golden neogothic (Fifth = 704.0956 cents)
| || || || || || 71\121 || 704.132 || 13 || 8 || 1.625 || Golden neogothic (704.0956¢)
|-
|-
| || || || 27\46 || || || 704.348 || 5 || 3 || 1.667 || [[Leapday]] / [[Polypyth]]
| || || || 27\46 || || || 704.348 || 5 || 3 || 1.667 || [[Leapday]] / [[polypyth]]
|-
|-
| || || || || || 64\109 || 704.587 || 12 || 7 || 1.714 || [[Leapweek]]
| || || || || || 64\109 || 704.587 || 12 || 7 || 1.714 || [[Leapweek]]
Line 78: Line 78:
| || || || || || 47\80 || 705.000 || 9 || 5 || 1.800 ||
| || || || || || 47\80 || 705.000 || 9 || 5 || 1.800 ||
|-
|-
| || 10\17 || || || || || 705.882 || 2 || 1 || 2.000 || Basic p-chromatic <br>(Fifths smaller than this are proper)
| || 10\17 || || || || || 705.882 || 2 || 1 || 2.000 || Basic p-chromatic <br>(Generators smaller than this are proper)
|-
|-
| || || || || || 43\73 || 706.849 || 9 || 4 || 2.250 ||
| || || || || || 43\73 || 706.849 || 9 || 4 || 2.250 ||
Line 88: Line 88:
| || || || 23\39 || || || 707.692 || 5 || 2 || 2.500 ||  
| || || || 23\39 || || || 707.692 || 5 || 2 || 2.500 ||  
|-
|-
| || || || || || 59\100 || 708.000 || 13 || 5 || 2.600 || Golden supra (Fifth = 708.0539 cents)
| || || || || || 59\100 || 708.000 || 13 || 5 || 2.600 || Golden supra (708.0539¢)
|-
|-
| || || || || 36\61 || || 708.197 || 8 || 3 || 2.667 || [[Quasisuper]] / [[quasisupra]]
| || || || || 36\61 || || 708.197 || 8 || 3 || 2.667 || [[Quasisuper]] / [[quasisupra]]
Line 108: Line 108:
| || || || || 19\32 || || 712.500 || 5 || 1 || 5.000 ||
| || || || || 19\32 || || 712.500 || 5 || 1 || 5.000 ||
|-
|-
| || || || || || 22\37 || 713.514 || 6 || 1 || 6.000 || [[Oceanfront]] / [[Ultrapyth]]
| || || || || || 22\37 || 713.514 || 6 || 1 || 6.000 || [[Oceanfront]]↓ / [[ultrapyth]]↓
|-
|-
| 3\5 || || || || || || 720.000 || 1 || 0 || → inf ||
| 3\5 || || || || || || 720.000 || 1 || 0 || → inf ||
Retrieved from "https://en.xen.wiki/w/5L_7s"