No-twos subgroup temperaments: Difference between revisions
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This is a collection of [[subgroup temperament]]s which omit the prime harmonic of 2. Because of the absence of octaves, these are all [[nonoctave]] scales using a period of a [[tritave]], or if harmonic 3 is also excluded, [[5/1]]. | This is a collection of [[subgroup temperament]]s which omit the prime harmonic of 2. Because of the absence of octaves, these are all [[nonoctave]] scales using a period of a [[tritave]], or if harmonic 3 is also excluded, [[5/1]]. | ||
= Overview by mapping of 5 = | |||
Classified by focusing on the mapping of 5th harmonic, similar to [[Rank-2 temperaments by mapping of 3]]. | Classified by focusing on the mapping of 5th harmonic, similar to [[Rank-2 temperaments by mapping of 3]]. | ||
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* Juggernaut uses half-pentave(~11/5) as a period, and has a ~7/5 generator. | * Juggernaut uses half-pentave(~11/5) as a period, and has a ~7/5 generator. | ||
= 3.5.7 subgroup temperaments = | |||
== Arcturus == | |||
{{main|Arcturus}} | {{main|Arcturus}} | ||
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[[Optimal ET sequence]]: [[2edt|b2]], [[11edt|b11]], [[13edt|b13]] | [[Optimal ET sequence]]: [[2edt|b2]], [[11edt|b11]], [[13edt|b13]] | ||
=== Polturus === | |||
This extension of Arcturus adds [[Polaris]]'s mapping for [[11/9]], mapping it to 5 generators down. | This extension of Arcturus adds [[Polaris]]'s mapping for [[11/9]], mapping it to 5 generators down. | ||
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[[EDT]]s: 15, 13e, 28e, 43dee | [[EDT]]s: 15, 13e, 28e, 43dee | ||
== BPS == | |||
{{main|Bohlen-Pierce-Stearns}} | {{main|Bohlen-Pierce-Stearns}} | ||
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Badness (Sintel): 0.066 | Badness (Sintel): 0.066 | ||
=== Mintra === | |||
''See also [[No-twos subgroup temperaments#Mintaka|Mintaka]] and [[No-twos subgroup temperaments#Deneb|Deneb]].'' | ''See also [[No-twos subgroup temperaments#Mintaka|Mintaka]] and [[No-twos subgroup temperaments#Deneb|Deneb]].'' | ||
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Badness (Sintel): 0.302 | Badness (Sintel): 0.302 | ||
==== Tridecimal Mintra ==== | |||
This temperament uses the canonical extension for prime 13 described at [[No-twos subgroup temperaments#Tridecimal Mintaka|Tridecimal Mintaka]]. | This temperament uses the canonical extension for prime 13 described at [[No-twos subgroup temperaments#Tridecimal Mintaka|Tridecimal Mintaka]]. | ||
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Badness (Sintel): 0.373 | Badness (Sintel): 0.373 | ||
=== Dubhe === | |||
This temperament is a simple 3.5.7.17 weak extension of BPS that splits the generator of 9/7 into two intervals of [[17/15]]. The name was suggested by MidnightBlue after Dubhe, a bright double star (the ninth brightest) and similarities to the word "double". | This temperament is a simple 3.5.7.17 weak extension of BPS that splits the generator of 9/7 into two intervals of [[17/15]]. The name was suggested by MidnightBlue after Dubhe, a bright double star (the ninth brightest) and similarities to the word "double". | ||
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Badness (Sintel): 0.177 | Badness (Sintel): 0.177 | ||
== Canopus == | |||
{{main|Canopus}} | {{main|Canopus}} | ||
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[[Optimal ET sequence]]: [[13edt|b13]], [[62edt|b62]], [[75edt|b75]], [[88edt|b88]], [[101edt|b101]], [[114edt|b114]], [[355edt|b355]], [[469edt|b469]], [[583edt|b583]], [[697edt|b697]] | [[Optimal ET sequence]]: [[13edt|b13]], [[62edt|b62]], [[75edt|b75]], [[88edt|b88]], [[101edt|b101]], [[114edt|b114]], [[355edt|b355]], [[469edt|b469]], [[583edt|b583]], [[697edt|b697]] | ||
== Izar == | |||
[[Subgroup]]: 3.5.7 | [[Subgroup]]: 3.5.7 | ||
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[[Support]]ing [[ET]]s: {{EDs|b13, b11cd, b193, b15cd, b180, b24c, b167, b37c, b154, 141, b50c, b28cd, b128, b63c|equave=t}} | [[Support]]ing [[ET]]s: {{EDs|b13, b11cd, b193, b15cd, b180, b24c, b167, b37c, b154, 141, b50c, b28cd, b128, b63c|equave=t}} | ||
== Nekkar == | |||
This temperament is the no-twos restriction of [[squares]], and as such is named after a star that belonged to the obsolete constellation of Quadrans Muralis, whose name has to do with squares. However, seeing the sheer complexity and size of the commas, Nekkar is much more naturally thought of as 3.5.7.11 than 3.5.7, whereupon it becomes a strong extension of [[Mintaka]]. | This temperament is the no-twos restriction of [[squares]], and as such is named after a star that belonged to the obsolete constellation of Quadrans Muralis, whose name has to do with squares. However, seeing the sheer complexity and size of the commas, Nekkar is much more naturally thought of as 3.5.7.11 than 3.5.7, whereupon it becomes a strong extension of [[Mintaka]]. | ||
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[[Support]]ing [[ET]]s: 22, 49, 5c, 71, 27, 17c, 120, 93, 76c, 32cc, 169d, 115, 191d, 164d | [[Support]]ing [[ET]]s: 22, 49, 5c, 71, 27, 17c, 120, 93, 76c, 32cc, 169d, 115, 191d, 164d | ||
=== 3.5.7.11 subgroup === | |||
''See also [[No-twos subgroup temperaments#Mintaka|Mintaka]].'' | ''See also [[No-twos subgroup temperaments#Mintaka|Mintaka]].'' | ||
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[[Support]]ing [[ET]]s: 22, 49, 71, 5c, 27, 120, 93, 17c, 76c, 169d, 191d, 115, 164d, 125cd | [[Support]]ing [[ET]]s: 22, 49, 71, 5c, 27, 120, 93, 17c, 76c, 169d, 191d, 115, 164d, 125cd | ||
== Sirius == | |||
{{main|Sirius}} | {{main|Sirius}} | ||
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[[Optimal ET sequence]]: [[6edt|b6]], [[7edt|b7]], [[13edt|b13]], [[71edt|b71]], [[84edt|b84]], [[97edt|b97]], [[110edt|b110]], [[123edt|b123]], [[136edt|b136]] | [[Optimal ET sequence]]: [[6edt|b6]], [[7edt|b7]], [[13edt|b13]], [[71edt|b71]], [[84edt|b84]], [[97edt|b97]], [[110edt|b110]], [[123edt|b123]], [[136edt|b136]] | ||
= 3.5.11 subgroup temperaments = | |||
== Polaris == | |||
{{main|Polaris}} | {{main|Polaris}} | ||
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[[EDT]]s: 17, 15, 32, 49, 13[+11], 47, 19, 11[+11], 81, 66, 79[+11], 62[+11], 28[+11], 21[-11] | [[EDT]]s: 17, 15, 32, 49, 13[+11], 47, 19, 11[+11], 81, 66, 79[+11], 62[+11], 28[+11], 21[-11] | ||
== Deneb == | |||
{{main|Deneb}} | {{main|Deneb}} | ||
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[[EDT]]s: 28, 11, 17, 6, 39, 5, 67, 45, 50, 16, 23, 73, 61, 62 | [[EDT]]s: 28, 11, 17, 6, 39, 5, 67, 45, 50, 16, 23, 73, 61, 62 | ||
== Alnilam == | |||
Effectively a [[microtemperament]], Alnilam takes a generator of an 81/55 flat fifth and equates 9 of them with [[11/9]]. The name was given by [[User:CompactStar|CompactStar]] to continue with the theme of naming no-twos temperaments after proper star names, but also to indirectly reference [[mavila]]. | Effectively a [[microtemperament]], Alnilam takes a generator of an 81/55 flat fifth and equates 9 of them with [[11/9]]. The name was given by [[User:CompactStar|CompactStar]] to continue with the theme of naming no-twos temperaments after proper star names, but also to indirectly reference [[mavila]]. | ||
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[[EDT]]s: 99, 17, 82, 116, 181, 65, 14[-5], 280, 48, 215, 31, 133, 314, 263 | [[EDT]]s: 99, 17, 82, 116, 181, 65, 14[-5], 280, 48, 215, 31, 133, 314, 263 | ||
= Other tritave-based subgroups = | |||
== Aldebaran == | |||
{{Main|Aldebaran}} | {{Main|Aldebaran}} | ||
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[[CTE tuning|CTE generator]]: ~[[5/3]] = 887.76 | [[CTE tuning|CTE generator]]: ~[[5/3]] = 887.76 | ||
== Mintaka == | |||
{{main|Mintaka}} | {{main|Mintaka}} | ||
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[[Support]]ing [[ET]]s: {{EDs|b22, b5, b17, b39, b12, b61, b27, b7, b83, b49, b56, b32, b29, b100|equave=t}} | [[Support]]ing [[ET]]s: {{EDs|b22, b5, b17, b39, b12, b61, b27, b7, b83, b49, b56, b32, b29, b100|equave=t}} | ||
=== Tridecimal Mintaka === | |||
This extension to prime 13 works in the sharper half of the Mintaka tuning range, where the most important pental extension is [[No-twos subgroup temperaments#Mintra|Mintra]]. | This extension to prime 13 works in the sharper half of the Mintaka tuning range, where the most important pental extension is [[No-twos subgroup temperaments#Mintra|Mintra]]. | ||
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[[Support]]ing [[ET]]s: {{EDs|b39, b22, b17, b5f, b61, b56, b100, b139f, b95, b178ef, b83f, b134, b73f, b217ef|equave=t}} | [[Support]]ing [[ET]]s: {{EDs|b39, b22, b17, b5f, b61, b56, b100, b139f, b95, b178ef, b83f, b134, b73f, b217ef|equave=t}} | ||
=== Minalzidar === | |||
This extension to prime 13 works in the flatter half of the Mintaka tuning range, where the most important pental extension is [[No-twos subgroup temperaments#3.5.7.11 subgroup|Nekkar]]. | This extension to prime 13 works in the flatter half of the Mintaka tuning range, where the most important pental extension is [[No-twos subgroup temperaments#3.5.7.11 subgroup|Nekkar]]. | ||
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[[Support]]ing [[ET]]s: {{EDs|b5, b27, b22, b32, b17f, b37f, b12ff, b49, b59, b42df, b76, b39ff, b86d, b71f|equave=t}} | [[Support]]ing [[ET]]s: {{EDs|b5, b27, b22, b32, b17f, b37f, b12ff, b49, b59, b42df, b76, b39ff, b86d, b71f|equave=t}} | ||
= No-twos-or-threes subgroup temperaments = | |||
== Antipyth == | |||
{{main|Antipyth}} | {{main|Antipyth}} | ||
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[[Support]]ing [[ET]]s: {{EDs|c14, c5, c19, c33, c47, c9e, c61, c75, c23e, c24e, c52e, c80e, c89e, c37e|equave=5}} | [[Support]]ing [[ET]]s: {{EDs|c14, c5, c19, c33, c47, c9e, c61, c75, c23e, c24e, c52e, c80e, c89e, c37e|equave=5}} | ||
== Juggernaut == | |||
{{main|Juggernaut}} | {{main|Juggernaut}} | ||
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[[Support]]ing [[ET]]s: {{EDs|c14, c10, c6, c18, c24, c22, c32, c16, c38, c8d, c34, c26d, c46, c52e|equave=5}} | [[Support]]ing [[ET]]s: {{EDs|c14, c10, c6, c18, c24, c22, c32, c16, c38, c8d, c34, c26d, c46, c52e|equave=5}} | ||
=== Tridecimal juggernaut === | |||
[[Subgroup]]: 5.7.11.13 | [[Subgroup]]: 5.7.11.13 | ||
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[[Support]]ing [[ET]]s: {{EDs|c10, c14, c6, c24, c34, c16f, c44, c18f, c38, c26f, c54, c64|equave=5}} | [[Support]]ing [[ET]]s: {{EDs|c10, c14, c6, c24, c34, c16f, c44, c18f, c38, c26f, c54, c64|equave=5}} | ||
= Graphs = | |||
{| class="wikitable" | {| class="wikitable" | ||
Revision as of 19:25, 30 September 2024
(WIP, catalog of 3.5.7 subgroup rank two temperaments will eventually be redirected here)
This is a collection of subgroup temperaments which omit the prime harmonic of 2. Because of the absence of octaves, these are all nonoctave scales using a period of a tritave, or if harmonic 3 is also excluded, 5/1.
Overview by mapping of 5
Classified by focusing on the mapping of 5th harmonic, similar to Rank-2 temperaments by mapping of 3.
- Arcturus, Aldebaran and Polaris have a 3/1 period and ~5/3 generator. There is one-to-one correspondence between the 3.5 subgroup and mapped intervals.
- BPS has a ~9/7 generator, two of which give the ~5/3.
- Sirius has a ~25/21 generator, three of which give the ~5/3.
- Deneb has a ~11/9 generator, three of which give the ~9/5.
- Canopus has a ~7/5 generator, five of which give the ~27/5 (9/5 up a tritave).
- Alnilam has a ~81/55 generator, ten of which give the ~243/5 (9/5 up three tritaves).
- Izar has a ~16807/10125 generator, twelve of which give the ~2187/5 (9/5 up five tritaves).
- Nekkar has a ~16807/10935 generator, sixteen of which give the ~6561/5 (9/5 up six tritaves).
- Mintaka does not include the 5th harmonic, and has an ~11/7 generator, two of which give the ~27/11, and three of which give the ~27/7 (9/7 and a tritave).
- Antipyth uses 5/1 as a period, and has a ~7/5 generator. There is one-to-one correspondence between the 5.7 subgroup and mapped intervals.
- Juggernaut uses half-pentave(~11/5) as a period, and has a ~7/5 generator.
3.5.7 subgroup temperaments
Arcturus
As for extensions of this temperament that include the prime 2, see opossum, crepuscular, catalan, bunya, bohpier, and superkleismic.
Subgroup: 3.5.7
Comma list: 15625/15309
Sval mapping: [⟨1 0 -7], ⟨0 1 6]]
Sval mapping generators: ~3, ~5
POTE generator: ~5/3 = 878.042
Optimal ET sequence: b2, b11, b13
Polturus
This extension of Arcturus adds Polaris's mapping for 11/9, mapping it to 5 generators down.
Subgroup: 3.5.7.11
Comma list: 15625/15309, 177147/171875
Gencom: [3/1 5/3; 15625/15309 177147/171875]
Mapping: [⟨1 1 -1 5], ⟨0 1 6 -6]]
POTE generator: ~5/3 = 884.268
EDTs: 15, 13e, 28e, 43dee
BPS
For extensions to this temperament that include the prime 2, see Sensamagic clan. No-twos extensions will be documented below.
Subgroup: 3.5.7
Comma list: 245/243
Sval mapping: [⟨1 1 2], ⟨0 -2 1]]
Sval mapping generators: ~3, ~9/7
Optimal tuning (POTE): ~3 = 1\1edt, ~9/7 = 440.4881
Optimal ET sequence: b4, b9, b13, b56, b69, b82, b95
Badness (Sintel): 0.066
Mintra
This temperament splits 27/7 (the BPS generator up a tritave) into three by means of 11/7, and is the intersection of BPS, Deneb, and Mintaka temperaments as well as the most natural temperament satisfied in the 3.5.7.11 subgroup in 39edt.
Subgroup: 3.5.7.11
Comma list: 245/243, 1331/1323
Subgroup-val mapping: [⟨1 5 0 1], ⟨0 -6 3 2]]
Sval mapping generators: ~3, ~21/11
Optimal tuning (CWE): ~3 = 1\1edt, ~11/7 = 780.752
Supporting ETs: 39, 17, 56, 22, 5, 95, 12, 61, 73, 134, 27c, 151e, 100, 90
Badness (Sintel): 0.302
Tridecimal Mintra
This temperament uses the canonical extension for prime 13 described at Tridecimal Mintaka.
Subgroup: 3.5.7.11.13
Comma list: 245/243, 275/273, 1575/1573
Subgroup-val mapping: [⟨1 5 0 1 10], ⟨0 -6 3 2 -13]]
Sval mapping generators: ~3, ~21/11
Optimal tuning (CWE): ~3 = 1\1edt, ~11/7 = 780.428
Supporting ETs: 39, 17, 22, 56, 5f, 61, 95, 100, 134, 73f, 139cf, 83cf, 173e, 178cef
Badness (Sintel): 0.373
Dubhe
This temperament is a simple 3.5.7.17 weak extension of BPS that splits the generator of 9/7 into two intervals of 17/15. The name was suggested by MidnightBlue after Dubhe, a bright double star (the ninth brightest) and similarities to the word "double".
Subgroup: 3.5.7.17
Comma list: 245/243, 2025/2023
Subgroup-val mapping: [⟨1 1 2 2], ⟨0 4 -2 3]]
Optimal tuning (CWE): ~3 = 1\1edt, ~17/15 = 220.142
Supporting ETs: 26, 9, 17, 43, 69, 8, 35, 95, 61, 60, 121, 25g, 112, 44
Badness (Sintel): 0.177
Canopus
For extensions to this temperament that include the prime 2, see Mirkwai clan. No-twos extensions will be documented below.
Subgroup: 3.5.7
Comma list: 16875/16807
Subgroup-val mapping: [⟨1 3 3], ⟨0 -5 -4]]
Sval mapping generators: ~3, ~7/5
Optimal ET sequence: b13, b62, b75, b88, b101, b114, b355, b469, b583, b697
Izar
Subgroup: 3.5.7
Comma list: 13841287201/13839609375
Subgroup-val mapping: [⟨1 7 5], ⟨0 -12 -7]]
Sval mapping generators: ~3, ~16807/10125
Optimal tuning (CTE): ~3 = 1\1edt, ~16807/10125 = 877.280
Supporting ETs: b13, b11cd, b193, b15cd, b180, b24c, b167, b37c, b154, 141, b50c, b28cd, b128, b63c
Nekkar
This temperament is the no-twos restriction of squares, and as such is named after a star that belonged to the obsolete constellation of Quadrans Muralis, whose name has to do with squares. However, seeing the sheer complexity and size of the commas, Nekkar is much more naturally thought of as 3.5.7.11 than 3.5.7, whereupon it becomes a strong extension of Mintaka.
Subgroup: 3.5.7
Comma list: 35303692060125/33232930569601
Subgroup-val mapping: [⟨1 8 3], ⟨0 -16 -3]]
Sval mapping generators: ~3, ~16807/10935
Optimal tuning (CWE): ~3 = 1\1edt, ~16807/10935 = 776.767
Supporting ETs: 22, 49, 5c, 71, 27, 17c, 120, 93, 76c, 32cc, 169d, 115, 191d, 164d
3.5.7.11 subgroup
See also Mintaka.
This continues the canonical 11-limit extension of squares.
Subgroup: 3.5.7.11
Comma list: 1331/1323, 120285/117649
Subgroup-val mapping: [⟨1 8 3 3], ⟨0 -16 -3 -2]]
Sval mapping generators: ~3, ~11/7
Optimal tuning (CWE): ~3 = 1\1edt, ~11/7 = 776.781
Supporting ETs: 22, 49, 71, 5c, 27, 120, 93, 17c, 76c, 169d, 191d, 115, 164d, 125cd
Sirius
For an overview of extensions to this temperament that include prime 2, see Gariboh clan#Overview to extensions.
Subgroup: 3.5.7
Comma list: 3125/3087
Subgroup-val mapping: [⟨1 1 1], ⟨0 3 5]]
- sval mapping generators: ~3, ~25/21
Optimal tuning (POTE): ~3 = 1\1edt, ~25/21 = 293.740
Optimal ET sequence: b6, b7, b13, b71, b84, b97, b110, b123, b136
3.5.11 subgroup temperaments
Polaris
Polaris tempers out the comma 177147/171875, and thus equates 7 5/3's with 15/11, or equivalently 7 9/5's with 11/9.
Subgroup: 3.5.11
Comma list: 177147/171875
Gencom: [3/1 5/3; 177147/171875]
Sval mapping: [⟨1 2 1], ⟨0 1 -6]]
POTE generator: ~5/3 = 892.6
EDTs: 17, 15, 32, 49, 13[+11], 47, 19, 11[+11], 81, 66, 79[+11], 62[+11], 28[+11], 21[-11]
Deneb
Subgroup: 3.5.11
Comma list: 6655/6561
Gencom: [3/1 11/9; 6655/6561]
Sval mapping: [⟨1 2 2], ⟨0 -3 1]]
POTE generator: ~11/9 = 340.242
EDTs: 28, 11, 17, 6, 39, 5, 67, 45, 50, 16, 23, 73, 61, 62
Alnilam
Effectively a microtemperament, Alnilam takes a generator of an 81/55 flat fifth and equates 9 of them with 11/9. The name was given by CompactStar to continue with the theme of naming no-twos temperaments after proper star names, but also to indirectly reference mavila.
Subgroup: 3.5.11
Comma list: [0 -35 9 0 10⟩
Gencom: [3/1 81/55; [0 -35 9 0 10⟩]
Sval mapping: [⟨1 5 -1], ⟨0 -10 9]]
CTE generator: ~81/55 = 672.410
EDTs: 99, 17, 82, 116, 181, 65, 14[-5], 280, 48, 215, 31, 133, 314, 263
Other tritave-based subgroups
Aldebaran
Subgroup: 3.5.13
Comma list: 3159/3125
Sval mapping: [⟨1 0 5], ⟨0 1 -2]]
Supporting ETs: 15, 17, 13, 32, 47, 28, 11[-13], 19[+13], 43, 9[-13], 7[-13], 49[+13], 21[+13], 41[-13]
CTE generator: ~5/3 = 887.76
Mintaka
Subgroup: 3.7.11
Comma list: 1331/1323
Sval mapping: [⟨1 0 1], ⟨0 3 2]]
Sval mapping generators: ~3, ~21/11
Supporting ETs: b22, b5, b17, b39, b12, b61, b27, b7, b83, b49, b56, b32, b29, b100
Tridecimal Mintaka
This extension to prime 13 works in the sharper half of the Mintaka tuning range, where the most important pental extension is Mintra.
Subgroup: 3.7.11.13
Comma list: 1331/1323, 218491/216513
Sval mapping: [⟨1 0 1 10], ⟨0 3 2 -13]]
Sval mapping generators: ~3, ~21/11
Supporting ETs: b39, b22, b17, b5f, b61, b56, b100, b139f, b95, b178ef, b83f, b134, b73f, b217ef
Minalzidar
This extension to prime 13 works in the flatter half of the Mintaka tuning range, where the most important pental extension is Nekkar.
Subgroup: 3.7.11.13
Comma list: 1331/1323, 351/343
Sval mapping: [⟨1 0 1 -3], ⟨0 3 2 9]]
Sval mapping generators: ~3, ~21/11
Supporting ETs: b5, b27, b22, b32, b17f, b37f, b12ff, b49, b59, b42df, b76, b39ff, b86d, b71f
No-twos-or-threes subgroup temperaments
Antipyth
Subgroup: 5.7.11
Comma list: 859375/823543
Subgroup-val mapping: [⟨1 2 7], ⟨0 1 7]]
Mapping generators: ~5, ~7/25
Optimal tuning (CTE): ~5 = 1\1ed5, ~7/5 = 592.728
Supporting ETs: c14, c5, c19, c33, c47, c9e, c61, c75, c23e, c24e, c52e, c80e, c89e, c37e
Juggernaut
Subgroup: 5.7.11
Comma list: 125/121
Subgroup-val mapping: [⟨2 4 3], ⟨0 1 0]]
Mapping generators: ~11/5, ~7/25
Optimal tuning (CTE): ~11/5 = 1\2ed5, ~7/5 = 582.512
Supporting ETs: c14, c10, c6, c18, c24, c22, c32, c16, c38, c8d, c34, c26d, c46, c52e
Tridecimal juggernaut
Subgroup: 5.7.11.13
Comma list: 125/121, 637/625
Subgroup-val mapping: [⟨2 4 3 0], ⟨0 1 0 -2]]
Mapping generators: ~11/5, ~7/25
Optimal tuning (CTE): ~11/5 = 1\2ed5, ~7/5 = 582.512
Supporting ETs: c10, c14, c6, c24, c34, c16f, c44, c18f, c38, c26f, c54, c64
Graphs
|
| Complexity vs. damage plot. z<1 corresponds to the "Middle Path" inclusion criterion. |
Projective tuning space diagrams
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| Temperaments with smaller commas, labeled by name |
|
| Temperaments with smaller commas, labeled by comma |
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| Temperaments with larger commas, labeled by name |
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| Temperaments with larger commas, labeled by comma |
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| Both sets, labeled by name |
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| Both sets, labeled by comma |