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User:Romeolz/Isomorphic layouts/Harmonic Table extensions: Difference between revisions

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tables
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=== Orwell (fifths ver.) ===
=== Orwell (fifths ver.) ===
Orwell offers good approximations of even 11-limit intervals, using its generator of about 272 cents to split 3/1 into seven. The generator can be interpreted as 7/6.
Orwell offers good approximations of even 11-limit intervals, using its generator of about 272 cents to split 3/1 into seven. The generator can be interpreted as 7/6.
[[File:"HT" (3-1)^(1-7).png|none|thumb|600x600px|A powerful temperament for even 11-limit just intonation, but the layout is quite spread apart...]]To be continued... (alternate sixths etc., fourths, hemififths...)
[[File:"HT" (3-1)^(1-7).png|none|thumb|600x600px|A powerful temperament for even 11-limit just intonation, but the layout is quite spread apart...]]


== Alternate sixths/seconds (this is where it starts to get weird) ==
== Alternate sixths/seconds (this is where it starts to get weird) ==
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=== Porcupine ===
=== Porcupine ===
Porcupine is a powerful 11-limit system with a distinctive sound. Here, with a pure 3/1, the sixth is quite flat at 868 cents. The 3/1 can be sharpened to improve other intervals.
Porcupine is a powerful 11-limit system with a distinctive sound. Here, with a pure 3/1, the sixth is quite flat at 868 cents. The 3/1 can be sharpened to improve other intervals.
[[File:"HT" (9-2)^(1-3).png|none|thumb|600x600px|aghsdjfkhdfgasd]]
[[File:"HT" (9-2)^(1-3).png|none|thumb|600x600px|basically porcupine[7] melodic mode]]


=== Negri ===
=== Negri ===
A coooooooooooooool temperament?? I don't want to type these out anymore
A coooooooooooooool temperament?? I don't want to type these out anymore
[[File:"HT" (27-4)^(1-4).png|none|thumb|600x600px|abcdefg]]
[[File:"HT" (27-4)^(1-4).png|none|thumb|600x600px|basically negri[9] melodic mode]]


=== Blackwood ===
=== Blackwood ===
i love blackwood 10
i love blackwood
[[File:"HT" (243-16)^(1-5).png|none|thumb|600x600px|heyy this one's pretty neat it splits the octave into 5]]
[[File:"HT" (243-16)^(1-5).png|none|thumb|600x600px|heyy this one's pretty neat it splits the octave into 5]]


=== I don't even know what this one is but it has a good 11/7 lol ===
=== I don't even know what this one is but it has a good 11/7 lol ===
yea
...
[[File:"HT" (243-16)^(1-6).png|none|thumb|600x600px|i've had enough for now]]
[[File:"HT" (243-16)^(1-6).png|none|thumb|600x600px|idk if anyone is ever gonna use this]]
ok
...


== Alternate fourths/fifths ==
== Alternate fourths/fifths ==
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==== Magi ====
==== Magi ====
[[File:"HT" fourths 440cent.png|none|thumb|600x600px|fgdfjhfgds]]
[[File:"HT" fourths 440cent.png|none|thumb|600x600px|fgdfjhfgds]]
table
Coming up with an equivalence continuum is tough for this one because the generator varies so much. If one were to choose a single JI interval all these should be approximating, the simple temperaments would be unrecognizable.
{| class="wikitable"
|+Continuation of fourths-axial augmented "HT" into various equivalence continua
!
!m
! colspan="3" |temperament,
comma
|-
!approximated interval,
location in genchain
!
!5/4
1
!9/7
1
!5/3
2
|-
!
!-2
|Yo
10/9
|???
8/7
|
|-
!
!-1
|Dicot
25/24
|Ruru
54/49
|
|-
!
!0
|Augmented
128/125
|Triru
729/686
|Father
16/15
|-
!
!1
|Symbolic
2048/1875
|Squares
19683/19208
|Dicot
25/24
|-
!
!2
|???
32768/28125
|Magi
537824/531441
|Magic
3125/3072
|-
!
!3
|
|Satribizo
[7 -15 6
|Augmented
128/125
|-
!
!4
|
|???
[9 -18 7
|???
[18 -1 -7
|-
!
!5
|
|
|
|}


==== Sixix/Amity ====
==== Sixix/Amity ====
[[File:"HT" fourths amity.png|none|thumb|600x600px|sthdhfsfdha]]
[[File:"HT" fourths amity.png|none|thumb|600x600px|When using amity, the best approximation of 5-limit thirds is further away from the root]]


==== Lemba ====
==== Lemba ====
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==== Orwell/Orson (fourths ver.) ====
==== Orwell/Orson (fourths ver.) ====
[[File:"HT" fourths orwell.png|none|thumb|600x600px|hfhdgfsh]]
[[File:"HT" fourths orwell.png|none|thumb|600x600px|hfhdgfsh]]
table
Same thing as with the above table.
{| class="wikitable"
|+
!
!m
! colspan="2" |temperament,
comma
|-
!approximated interval,
location in genchain
!
!6/5
1
!5/4
1
|-
!
!-2
|???
32/25
|
|-
!
!-1
|University
144/125
|
|-
!
!0
|Diminished
648/625
|???
625/512
|-
!
!1
|todo
|Lemba
140625/131072
|-
!
!2
|
|Orson
[-21 3 7
|-
!
!3
|
|
|-
!
!4
|
|
|}


=== Alternative thirds outside the continua ===
=== Alternative thirds outside the continua ===
Retrieved from "https://en.xen.wiki/w/User:Romeolz/Isomorphic_layouts/Harmonic_Table_extensions"