User:Overthink/13-limit interval flavors: Difference between revisions

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Created page with "In this article, we will cover the various flavors of 13-limit intervals. We consider intervals that differ by a pythagorean interval to have the same flavor. {| class="wikitable" |+13-limit flavors !D\N !1/3/9 !5 !7 !11 !13 |- |1/3/9 |1/1 | | | | |- |5 | |1/1 |7/5 |11/10 |13/10 |- |7 | | |1/1 | | |- |11 | | | |1/1 | |- |13 | | | | |1/1 |}"
 
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In this article, we will cover the various flavors of 13-limit intervals. We consider intervals that differ by a pythagorean interval to have the same flavor.
In this article, we will cover the various flavors of 13-limit intervals. We consider intervals that differ by a pythagorean interval to have the same flavor. The flavor of an interval depends on the primes higher than 3 in its prime factorization.
{| class="wikitable"
{| class="wikitable"
|+13-limit flavors
|+13-limit flavors
Line 9: Line 9:
!13
!13
|-
|-
|1/3/9
!1/3/9
|[[1/1]]
|[[1/1]] (wa)
|
|[[5/4]] (yo)
|
|[[7/4]] (zo)
|
|[[11/8]] (ilo)
|
|[[13/8]] (tho)
|-
|-
|5
!5
|
|[[8/5]] (gu)
|1/1
|1/1
|[[7/5]]
|[[7/5]] (zogu)
|[[11/10]]
|[[11/10]] (logu)
|13/10
|[[13/10]] (thogu)
|-
|-
|7
!7
|
|[[8/7]] (ru)
|
|[[10/7]] (yoru)
|1/1
|1/1
|
|[[11/7]] (loru)
|
|[[13/7]] (thoru)
|-
|-
|11
!11
|
|[[16/11]] (lu)
|
|[[20/11]] (yolu)
|
|[[14/11]] (zolu)
|1/1
|1/1
|
|[[13/11]] (tholu)
|-
|-
|13
!13
|
|[[16/13]] (thu)
|
|[[20/13]] (yothu)
|
|[[14/13]] (zothu)
|
|[[22/13]] (lothu)
|1/1
|1/1
|}
== The flavors of intervals ==
{| class="wikitable"
|+Pythagorean (wa)
!Cents
!Ratio
!FJS Name
!Color name
|-
|0.000
|1/1
|P1
|wa 1sn
|-
|90.225
|256/243
|m2
|sawa 2nd
|-
|203.910
|9/8
|M2
|wa 2nd
|-
|294.135
|32/27
|m3
|wa 3rd
|-
|407.820
|81/64
|M3
|lawa 3rd
|-
|498.045
|4/3
|P4
|wa 4th
|-
|588.270
|1024/729
|d5
|sawa 5th
|-
|611.730
|729/512
|A4
|lawa 4th
|-
|701.955
|3/2
|P5
|wa 5th
|-
|792.180
|128/81
|m6
|sawa 6th
|-
|905.865
|27/16
|M6
|wa 6th
|-
|996.090
|16/9
|m7
|wa 7th
|-
|1109.775
|243/128
|M7
|lawa 7th
|-
|1200.000
|2/1
|P8
|wa 8ve
|}
|}

Revision as of 23:35, 24 September 2025

In this article, we will cover the various flavors of 13-limit intervals. We consider intervals that differ by a pythagorean interval to have the same flavor. The flavor of an interval depends on the primes higher than 3 in its prime factorization.

13-limit flavors
D\N 1/3/9 5 7 11 13
1/3/9 1/1 (wa) 5/4 (yo) 7/4 (zo) 11/8 (ilo) 13/8 (tho)
5 8/5 (gu) 1/1 7/5 (zogu) 11/10 (logu) 13/10 (thogu)
7 8/7 (ru) 10/7 (yoru) 1/1 11/7 (loru) 13/7 (thoru)
11 16/11 (lu) 20/11 (yolu) 14/11 (zolu) 1/1 13/11 (tholu)
13 16/13 (thu) 20/13 (yothu) 14/13 (zothu) 22/13 (lothu) 1/1

The flavors of intervals

Pythagorean (wa)
Cents Ratio FJS Name Color name
0.000 1/1 P1 wa 1sn
90.225 256/243 m2 sawa 2nd
203.910 9/8 M2 wa 2nd
294.135 32/27 m3 wa 3rd
407.820 81/64 M3 lawa 3rd
498.045 4/3 P4 wa 4th
588.270 1024/729 d5 sawa 5th
611.730 729/512 A4 lawa 4th
701.955 3/2 P5 wa 5th
792.180 128/81 m6 sawa 6th
905.865 27/16 M6 wa 6th
996.090 16/9 m7 wa 7th
1109.775 243/128 M7 lawa 7th
1200.000 2/1 P8 wa 8ve
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