Porcupine - Revision history

Inthar at 15:20, 6 June 2026

2026-06-06T15:20:42Z

← Older revision		Revision as of 15:20, 6 June 2026
Line 2:		Line 2:
	'''Porcupine''', 2.3.5.11[15 & 22], is a temperament that splits 4/3 into three submajor seconds (approximately 11/10), representing 10/9~11/10~12/11. In the 5-limit, it equates 81/80 with 25/24. This makes it an excellent compromise between accuracy and simplicity on the side of simplicity while at the same time not fully exotempering (the intervals it detunes significantly, such as 10/9, can be seen as "connective" intervals rather than distinct harmonic identities, with the notable exception of 11/9). Porcupine is also notable for being inherently "un-Meantone" in the sense that rather than tempering out 81/80, it equates 81/80 to a fundamental 5-limit structural interval 25/24, the difference between 5/4 and 6/5; in fact, 7edo (essentially a trivial tuning of both) is the unique edo that is both Porcupine and Meantone.		'''Porcupine''', 2.3.5.11[15 & 22], is a temperament that splits 4/3 into three submajor seconds (approximately 11/10), representing 10/9~11/10~12/11. In the 5-limit, it equates 81/80 with 25/24. This makes it an excellent compromise between accuracy and simplicity on the side of simplicity while at the same time not fully exotempering (the intervals it detunes significantly, such as 10/9, can be seen as "connective" intervals rather than distinct harmonic identities, with the notable exception of 11/9). Porcupine is also notable for being inherently "un-Meantone" in the sense that rather than tempering out 81/80, it equates 81/80 to a fundamental 5-limit structural interval 25/24, the difference between 5/4 and 6/5; in fact, 7edo (essentially a trivial tuning of both) is the unique edo that is both Porcupine and Meantone.

	Note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7, thus [15 & 22], [22 & 29], and [29 & 7] represent three separate extensions in the full 7- and 11-limit. The extension ~~[15 & 22] in 2.3.5.7 or~~ 2.3.5.7.11, called Septimal Porcupine, is the extension historically most commonly assumed in many sources such as the Xen Wiki. This is the [[Archy]] extension. 2.3.5.7.11[29 & 7], on the other hand, is the [[Aberschismic]] extension, favored by Unque because of the inclusion of tunings with accurate 3rd harmonic.		Note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7, thus [15 & 22], [22 & 29], and [29 & 7] represent three separate extensions in the full 7- and 11-limit. The extension 2.3.5.7.11[15 & 22], called Septimal Porcupine, is the extension historically most commonly assumed in many sources such as the Xen Wiki. This is the [[Archy]] extension. 2.3.5.7.11[29 & 7], on the other hand, is the [[Aberschismic]] extension, favored by Unque because of the inclusion of tunings with accurate 3rd harmonic.

	The Porcupine generator generates 1L6s, 7L1s, and 7L8s.		The Porcupine generator generates 1L6s, 7L1s, and 7L8s.

Inthar at 15:20, 6 June 2026

2026-06-06T15:20:06Z

← Older revision		Revision as of 15:20, 6 June 2026
Line 2:		Line 2:
	'''Porcupine''', 2.3.5.11[15 & 22], is a temperament that splits 4/3 into three submajor seconds (approximately 11/10), representing 10/9~11/10~12/11. In the 5-limit, it equates 81/80 with 25/24. This makes it an excellent compromise between accuracy and simplicity on the side of simplicity while at the same time not fully exotempering (the intervals it detunes significantly, such as 10/9, can be seen as "connective" intervals rather than distinct harmonic identities, with the notable exception of 11/9). Porcupine is also notable for being inherently "un-Meantone" in the sense that rather than tempering out 81/80, it equates 81/80 to a fundamental 5-limit structural interval 25/24, the difference between 5/4 and 6/5; in fact, 7edo (essentially a trivial tuning of both) is the unique edo that is both Porcupine and Meantone.		'''Porcupine''', 2.3.5.11[15 & 22], is a temperament that splits 4/3 into three submajor seconds (approximately 11/10), representing 10/9~11/10~12/11. In the 5-limit, it equates 81/80 with 25/24. This makes it an excellent compromise between accuracy and simplicity on the side of simplicity while at the same time not fully exotempering (the intervals it detunes significantly, such as 10/9, can be seen as "connective" intervals rather than distinct harmonic identities, with the notable exception of 11/9). Porcupine is also notable for being inherently "un-Meantone" in the sense that rather than tempering out 81/80, it equates 81/80 to a fundamental 5-limit structural interval 25/24, the difference between 5/4 and 6/5; in fact, 7edo (essentially a trivial tuning of both) is the unique edo that is both Porcupine and Meantone.

	Note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7~~.11~~, thus [15 & 22], [22 & 29], and [29 & 7] represent three separate extensions in the full 7- and 11-limit. The extension [15 & 22] in 2.3.5.7 or 2.3.5.7.11, called Septimal Porcupine, is the extension historically most commonly assumed in many sources such as the Xen Wiki. This is the [[Archy]] extension. 2.3.5.7.11[29 & 7], on the other hand, is the [[Aberschismic]] extension, favored by Unque because of the inclusion of tunings with accurate 3rd harmonic.		Note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7, thus [15 & 22], [22 & 29], and [29 & 7] represent three separate extensions in the full 7- and 11-limit. The extension [15 & 22] in 2.3.5.7 or 2.3.5.7.11, called Septimal Porcupine, is the extension historically most commonly assumed in many sources such as the Xen Wiki. This is the [[Archy]] extension. 2.3.5.7.11[29 & 7], on the other hand, is the [[Aberschismic]] extension, favored by Unque because of the inclusion of tunings with accurate 3rd harmonic.

	The Porcupine generator generates 1L6s, 7L1s, and 7L8s.		The Porcupine generator generates 1L6s, 7L1s, and 7L8s.

Inthar at 15:19, 6 June 2026

2026-06-06T15:19:38Z

← Older revision		Revision as of 15:19, 6 June 2026
Line 2:		Line 2:
	'''Porcupine''', 2.3.5.11[15 & 22], is a temperament that splits 4/3 into three submajor seconds (approximately 11/10), representing 10/9~11/10~12/11. In the 5-limit, it equates 81/80 with 25/24. This makes it an excellent compromise between accuracy and simplicity on the side of simplicity while at the same time not fully exotempering (the intervals it detunes significantly, such as 10/9, can be seen as "connective" intervals rather than distinct harmonic identities, with the notable exception of 11/9). Porcupine is also notable for being inherently "un-Meantone" in the sense that rather than tempering out 81/80, it equates 81/80 to a fundamental 5-limit structural interval 25/24, the difference between 5/4 and 6/5; in fact, 7edo (essentially a trivial tuning of both) is the unique edo that is both Porcupine and Meantone.		'''Porcupine''', 2.3.5.11[15 & 22], is a temperament that splits 4/3 into three submajor seconds (approximately 11/10), representing 10/9~11/10~12/11. In the 5-limit, it equates 81/80 with 25/24. This makes it an excellent compromise between accuracy and simplicity on the side of simplicity while at the same time not fully exotempering (the intervals it detunes significantly, such as 10/9, can be seen as "connective" intervals rather than distinct harmonic identities, with the notable exception of 11/9). Porcupine is also notable for being inherently "un-Meantone" in the sense that rather than tempering out 81/80, it equates 81/80 to a fundamental 5-limit structural interval 25/24, the difference between 5/4 and 6/5; in fact, 7edo (essentially a trivial tuning of both) is the unique edo that is both Porcupine and Meantone.

	Note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7.11, thus [22 & 29] and [29 & 7] represent separate extensions ~~from [15 & 22]~~ in the full 11-limit. The extension [15 & 22] in 2.3.5.7 or 2.3.5.7.11, called Septimal Porcupine, is the extension historically most commonly assumed in many sources such as the Xen Wiki. This is the [[Archy]] extension. 2.3.5.7.11[29 & 7], on the other hand, is the [[Aberschismic]] extension, favored by Unque because of the inclusion of tunings with accurate 3rd harmonic.		Note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7.11, thus [15 & 22], [22 & 29], and [29 & 7] represent three separate extensions in the full 7- and 11-limit. The extension [15 & 22] in 2.3.5.7 or 2.3.5.7.11, called Septimal Porcupine, is the extension historically most commonly assumed in many sources such as the Xen Wiki. This is the [[Archy]] extension. 2.3.5.7.11[29 & 7], on the other hand, is the [[Aberschismic]] extension, favored by Unque because of the inclusion of tunings with accurate 3rd harmonic.

	The Porcupine generator generates 1L6s, 7L1s, and 7L8s.		The Porcupine generator generates 1L6s, 7L1s, and 7L8s.

Inthar at 01:17, 6 June 2026

2026-06-06T01:17:56Z

← Older revision		Revision as of 01:17, 6 June 2026
Line 2:		Line 2:
	'''Porcupine''', 2.3.5.11[15 & 22], is a temperament that splits 4/3 into three submajor seconds (approximately 11/10), representing 10/9~11/10~12/11. In the 5-limit, it equates 81/80 with 25/24. This makes it an excellent compromise between accuracy and simplicity on the side of simplicity while at the same time not fully exotempering (the intervals it detunes significantly, such as 10/9, can be seen as "connective" intervals rather than distinct harmonic identities, with the notable exception of 11/9). Porcupine is also notable for being inherently "un-Meantone" in the sense that rather than tempering out 81/80, it equates 81/80 to a fundamental 5-limit structural interval 25/24, the difference between 5/4 and 6/5; in fact, 7edo (essentially a trivial tuning of both) is the unique edo that is both Porcupine and Meantone.		'''Porcupine''', 2.3.5.11[15 & 22], is a temperament that splits 4/3 into three submajor seconds (approximately 11/10), representing 10/9~11/10~12/11. In the 5-limit, it equates 81/80 with 25/24. This makes it an excellent compromise between accuracy and simplicity on the side of simplicity while at the same time not fully exotempering (the intervals it detunes significantly, such as 10/9, can be seen as "connective" intervals rather than distinct harmonic identities, with the notable exception of 11/9). Porcupine is also notable for being inherently "un-Meantone" in the sense that rather than tempering out 81/80, it equates 81/80 to a fundamental 5-limit structural interval 25/24, the difference between 5/4 and 6/5; in fact, 7edo (essentially a trivial tuning of both) is the unique edo that is both Porcupine and Meantone.

	Note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7.11, thus [22 & 29] and [29 & 7] represent separate extensions from [15 & 22] in the full 11-limit. The extension [15 & 22] in 2.3.5.7 or 2.3.5.7.11, called Septimal Porcupine, is the extension historically most commonly assumed in many sources such as the Xen Wiki. This is the [[Archy]] extension. 2.3.5.7.11[29 & 7], on the other hand, is the [[Aberschismic]] extension, favored by Unque.		Note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7.11, thus [22 & 29] and [29 & 7] represent separate extensions from [15 & 22] in the full 11-limit. The extension [15 & 22] in 2.3.5.7 or 2.3.5.7.11, called Septimal Porcupine, is the extension historically most commonly assumed in many sources such as the Xen Wiki. This is the [[Archy]] extension. 2.3.5.7.11[29 & 7], on the other hand, is the [[Aberschismic]] extension, favored by Unque because of the inclusion of tunings with accurate 3rd harmonic.

	The Porcupine generator generates 1L6s, 7L1s, and 7L8s.		The Porcupine generator generates 1L6s, 7L1s, and 7L8s.

Inthar: temps, even ets, are usually not viewed as infinite-limit

2026-06-06T01:14:12Z

temps, even ets, are usually not viewed as infinite-limit

← Older revision		Revision as of 01:14, 6 June 2026
Line 2:		Line 2:
	'''Porcupine''', 2.3.5.11[15 & 22], is a temperament that splits 4/3 into three submajor seconds (approximately 11/10), representing 10/9~11/10~12/11. In the 5-limit, it equates 81/80 with 25/24. This makes it an excellent compromise between accuracy and simplicity on the side of simplicity while at the same time not fully exotempering (the intervals it detunes significantly, such as 10/9, can be seen as "connective" intervals rather than distinct harmonic identities, with the notable exception of 11/9). Porcupine is also notable for being inherently "un-Meantone" in the sense that rather than tempering out 81/80, it equates 81/80 to a fundamental 5-limit structural interval 25/24, the difference between 5/4 and 6/5; in fact, 7edo (essentially a trivial tuning of both) is the unique edo that is both Porcupine and Meantone.		'''Porcupine''', 2.3.5.11[15 & 22], is a temperament that splits 4/3 into three submajor seconds (approximately 11/10), representing 10/9~11/10~12/11. In the 5-limit, it equates 81/80 with 25/24. This makes it an excellent compromise between accuracy and simplicity on the side of simplicity while at the same time not fully exotempering (the intervals it detunes significantly, such as 10/9, can be seen as "connective" intervals rather than distinct harmonic identities, with the notable exception of 11/9). Porcupine is also notable for being inherently "un-Meantone" in the sense that rather than tempering out 81/80, it equates 81/80 to a fundamental 5-limit structural interval 25/24, the difference between 5/4 and 6/5; in fact, 7edo (essentially a trivial tuning of both) is the unique edo that is both Porcupine and Meantone.

	The simplest Porcupine edo join is [7 & 8], and surprisingly this correctly defines 11-limit Porcupine (implying 8edo technically supports [[Archy]]) — however, this results in an inaccurate extension to higher primes than 11. Also note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7.11, thus [22 & 29] and [29 & 7] represent separate extensions from [15 & 22] in the full 11-limit.		Note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7.11, thus [22 & 29] and [29 & 7] represent separate extensions from [15 & 22] in the full 11-limit. The extension [15 & 22] in 2.3.5.7 or 2.3.5.7.11, called Septimal Porcupine, is the extension historically most commonly assumed in many sources such as the Xen Wiki. This is the [[Archy]] extension. 2.3.5.7.11[29 & 7], on the other hand, is the [[Aberschismic]] extension, favored by Unque.

	The extension [15 & 22] in 2.3.5.7 or 2.3.5.7.11, called Septimal Porcupine, is the extension historically most commonly assumed in many sources such as the Xen Wiki. This is the [[Archy]] extension. 2.3.5.7.11[29 & 7], on the other hand, is the [[Aberschismic]] extension, favored by Unque.

	The Porcupine generator generates 1L6s, 7L1s, and 7L8s.		The Porcupine generator generates 1L6s, 7L1s, and 7L8s.

Inthar at 01:11, 6 June 2026

2026-06-06T01:11:30Z

← Older revision		Revision as of 01:11, 6 June 2026
Line 2:		Line 2:
	'''Porcupine''', 2.3.5.11[15 & 22], is a temperament that splits 4/3 into three submajor seconds (approximately 11/10), representing 10/9~11/10~12/11. In the 5-limit, it equates 81/80 with 25/24. This makes it an excellent compromise between accuracy and simplicity on the side of simplicity while at the same time not fully exotempering (the intervals it detunes significantly, such as 10/9, can be seen as "connective" intervals rather than distinct harmonic identities, with the notable exception of 11/9). Porcupine is also notable for being inherently "un-Meantone" in the sense that rather than tempering out 81/80, it equates 81/80 to a fundamental 5-limit structural interval 25/24, the difference between 5/4 and 6/5; in fact, 7edo (essentially a trivial tuning of both) is the unique edo that is both Porcupine and Meantone.		'''Porcupine''', 2.3.5.11[15 & 22], is a temperament that splits 4/3 into three submajor seconds (approximately 11/10), representing 10/9~11/10~12/11. In the 5-limit, it equates 81/80 with 25/24. This makes it an excellent compromise between accuracy and simplicity on the side of simplicity while at the same time not fully exotempering (the intervals it detunes significantly, such as 10/9, can be seen as "connective" intervals rather than distinct harmonic identities, with the notable exception of 11/9). Porcupine is also notable for being inherently "un-Meantone" in the sense that rather than tempering out 81/80, it equates 81/80 to a fundamental 5-limit structural interval 25/24, the difference between 5/4 and 6/5; in fact, 7edo (essentially a trivial tuning of both) is the unique edo that is both Porcupine and Meantone.

	The simplest Porcupine edo join is [7 & 8], and surprisingly this correctly defines 11-limit Porcupine (implying 8edo technically supports [[Archy]]) — however, this results in an inaccurate extension to higher primes than 11. Also note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7.11, thus [22 & 29] ~~represents a~~ separate ~~extension~~ from [15 & 22] in the full 11-limit.		The simplest Porcupine edo join is [7 & 8], and surprisingly this correctly defines 11-limit Porcupine (implying 8edo technically supports [[Archy]]) — however, this results in an inaccurate extension to higher primes than 11. Also note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7.11, thus [22 & 29] and [29 & 7] represent separate extensions from [15 & 22] in the full 11-limit.

	The extension [15 & 22] in 2.3.5.7 or 2.3.5.7.11, called Septimal Porcupine, is the extension historically most commonly assumed in many sources such as the Xen Wiki. This is the [[Archy]] extension. 2.3.5.7.11[29 & 7], on the other hand, is the [[Aberschismic]] extension, favored by Unque.		The extension [15 & 22] in 2.3.5.7 or 2.3.5.7.11, called Septimal Porcupine, is the extension historically most commonly assumed in many sources such as the Xen Wiki. This is the [[Archy]] extension. 2.3.5.7.11[29 & 7], on the other hand, is the [[Aberschismic]] extension, favored by Unque.

Inthar at 01:06, 6 June 2026

2026-06-06T01:06:54Z

← Older revision		Revision as of 01:06, 6 June 2026
Line 1:		Line 1:
	[[File:Porcupine7.png\|thumb\|Porcupine[7] MOS scale]]		[[File:Porcupine7.png\|thumb\|Porcupine[7] MOS scale]]
	'''Porcupine''', ~~[15 & 22] (usually defined in~~ 2.3.5.11 ~~or 2.3.5.7.11)~~, is a temperament that splits 4/3 into three submajor seconds (approximately 11/10), representing 10/9~11/10~12/11. In the 5-limit, it equates 81/80 with 25/24. This makes it an excellent compromise between accuracy and simplicity on the side of simplicity while at the same time not fully exotempering (the intervals it detunes significantly, such as 10/9, can be seen as "connective" intervals rather than distinct harmonic identities, with the notable exception of 11/9). Porcupine is also notable for being inherently "un-Meantone" in the sense that rather than tempering out 81/80, it equates 81/80 to a fundamental 5-limit structural interval 25/24, the difference between 5/4 and 6/5; in fact, 7edo (essentially a trivial tuning of both) is the unique edo that is both Porcupine and Meantone.		'''Porcupine''', 2.3.5.11[15 & 22], is a temperament that splits 4/3 into three submajor seconds (approximately 11/10), representing 10/9~11/10~12/11. In the 5-limit, it equates 81/80 with 25/24. This makes it an excellent compromise between accuracy and simplicity on the side of simplicity while at the same time not fully exotempering (the intervals it detunes significantly, such as 10/9, can be seen as "connective" intervals rather than distinct harmonic identities, with the notable exception of 11/9). Porcupine is also notable for being inherently "un-Meantone" in the sense that rather than tempering out 81/80, it equates 81/80 to a fundamental 5-limit structural interval 25/24, the difference between 5/4 and 6/5; in fact, 7edo (essentially a trivial tuning of both) is the unique edo that is both Porcupine and Meantone.

	The simplest Porcupine edo join is [7 & 8], and surprisingly this correctly defines 11-limit Porcupine (implying 8edo technically supports [[Archy]]) — however, this results in an inaccurate extension to higher primes than 11. Also note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7.11, thus [22 & 29] represents a separate extension from [15 & 22] in the full 11-limit.		The simplest Porcupine edo join is [7 & 8], and surprisingly this correctly defines 11-limit Porcupine (implying 8edo technically supports [[Archy]]) — however, this results in an inaccurate extension to higher primes than 11. Also note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7.11, thus [22 & 29] represents a separate extension from [15 & 22] in the full 11-limit.

Inthar at 01:03, 6 June 2026

2026-06-06T01:03:06Z

← Older revision		Revision as of 01:03, 6 June 2026
Line 4:		Line 4:
	The simplest Porcupine edo join is [7 & 8], and surprisingly this correctly defines 11-limit Porcupine (implying 8edo technically supports [[Archy]]) — however, this results in an inaccurate extension to higher primes than 11. Also note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7.11, thus [22 & 29] represents a separate extension from [15 & 22] in the full 11-limit.		The simplest Porcupine edo join is [7 & 8], and surprisingly this correctly defines 11-limit Porcupine (implying 8edo technically supports [[Archy]]) — however, this results in an inaccurate extension to higher primes than 11. Also note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7.11, thus [22 & 29] represents a separate extension from [15 & 22] in the full 11-limit.

	The extension [15 & 22] in 2.3.5.7 or 2.3.5.7.11, called Septimal Porcupine, is the extension historically most commonly assumed in many sources such as the Xen Wiki. This is the Archy extension. 2.3.5.7.11[29 & 7], on the other hand, is the [[Aberschismic]] extension, favored by Unque.		The extension [15 & 22] in 2.3.5.7 or 2.3.5.7.11, called Septimal Porcupine, is the extension historically most commonly assumed in many sources such as the Xen Wiki. This is the [[Archy]] extension. 2.3.5.7.11[29 & 7], on the other hand, is the [[Aberschismic]] extension, favored by Unque.

	The Porcupine generator generates 1L6s, 7L1s, and 7L8s.		The Porcupine generator generates 1L6s, 7L1s, and 7L8s.

Inthar at 01:02, 6 June 2026

2026-06-06T01:02:16Z

← Older revision		Revision as of 01:02, 6 June 2026
Line 2:		Line 2:
	'''Porcupine''', [15 & 22] (usually defined in 2.3.5.11 or 2.3.5.7.11), is a temperament that splits 4/3 into three submajor seconds (approximately 11/10), representing 10/9~11/10~12/11. In the 5-limit, it equates 81/80 with 25/24. This makes it an excellent compromise between accuracy and simplicity on the side of simplicity while at the same time not fully exotempering (the intervals it detunes significantly, such as 10/9, can be seen as "connective" intervals rather than distinct harmonic identities, with the notable exception of 11/9). Porcupine is also notable for being inherently "un-Meantone" in the sense that rather than tempering out 81/80, it equates 81/80 to a fundamental 5-limit structural interval 25/24, the difference between 5/4 and 6/5; in fact, 7edo (essentially a trivial tuning of both) is the unique edo that is both Porcupine and Meantone.		'''Porcupine''', [15 & 22] (usually defined in 2.3.5.11 or 2.3.5.7.11), is a temperament that splits 4/3 into three submajor seconds (approximately 11/10), representing 10/9~11/10~12/11. In the 5-limit, it equates 81/80 with 25/24. This makes it an excellent compromise between accuracy and simplicity on the side of simplicity while at the same time not fully exotempering (the intervals it detunes significantly, such as 10/9, can be seen as "connective" intervals rather than distinct harmonic identities, with the notable exception of 11/9). Porcupine is also notable for being inherently "un-Meantone" in the sense that rather than tempering out 81/80, it equates 81/80 to a fundamental 5-limit structural interval 25/24, the difference between 5/4 and 6/5; in fact, 7edo (essentially a trivial tuning of both) is the unique edo that is both Porcupine and Meantone.

	The simplest Porcupine edo join is [7 & 8], and surprisingly this correctly defines 11-limit Porcupine (implying 8edo technically supports [[Archy]]) — however, this results in an inaccurate extension to higher primes than 11. Also note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7.11, thus [22 & 29] represents a separate extension from [15 & 22] in the full 11-limit. The extension [15 & 22] in 2.3.5.7 or 2.3.5.7.11, called Septimal Porcupine, is the extension historically most commonly assumed in many sources such as the Xen Wiki.		The simplest Porcupine edo join is [7 & 8], and surprisingly this correctly defines 11-limit Porcupine (implying 8edo technically supports [[Archy]]) — however, this results in an inaccurate extension to higher primes than 11. Also note that 29 agrees with 15 & 22 in 2.3.5.11 but not in 2.3.5.7.11, thus [22 & 29] represents a separate extension from [15 & 22] in the full 11-limit.

			The extension [15 & 22] in 2.3.5.7 or 2.3.5.7.11, called Septimal Porcupine, is the extension historically most commonly assumed in many sources such as the Xen Wiki. This is the Archy extension. 2.3.5.7.11[29 & 7], on the other hand, is the [[Aberschismic]] extension, favored by Unque.

	The Porcupine generator generates 1L6s, 7L1s, and 7L8s.		The Porcupine generator generates 1L6s, 7L1s, and 7L8s.

Inthar: /* Interval chain */

2026-06-06T01:00:12Z

Interval chain

← Older revision		Revision as of 01:00, 6 June 2026
Line 9:		Line 9:
	In the following table, odd harmonics 1–15 and their inverses are in '''bold'''. Interpretations in parentheses are only found in the Septimal Porcupine (2.3.5.7.11.17 [15 & 22]) extension.		In the following table, odd harmonics 1–15 and their inverses are in '''bold'''. Interpretations in parentheses are only found in the Septimal Porcupine (2.3.5.7.11.17 [15 & 22]) extension.

	TODO: add [22 & 29]-specific interpretations		TODO: add [7 & 29]-specific interpretations
	{\| class="wikitable center-1 right-2 right-3"		{\| class="wikitable center-1 right-2 right-3"
	\|-		\|-
	! #		! #
	! Cents (Septimal Porcupine)*		! Cents (Septimal Porcupine)*
	! Cents (22 & 29)**		! Cents (29 & 7)**
	! Approximate ratios		! Approximate ratios
	\|-		\|-
Line 24:		Line 24:
	\| 1		\| 1
	\| 162.8		\| 162.8
	\| ~~164~~.5		\| 166.6
	\| 10/9, 11/10, 12/11		\| 10/9, 11/10, 12/11
	\|-		\|-
	\| 2		\| 2
	\| 325.6		\| 325.6
	\| ~~329~~.0		\| 331.9
	\| 6/5, 11/9, (17/14)		\| 6/5, 11/9, (17/14)
	\|-		\|-
	\| 3		\| 3
	\| 488.4		\| 488.4
	\| ~~493~~.5		\| 497.9
	\| '''4/3'''		\| '''4/3'''
	\|-		\|-
	\| 4		\| 4
	\| 651.3		\| 651.3
	\| ~~658~~.0		\| 663.9
	\| '''16/11'''		\| '''16/11'''
	\|-		\|-
	\| 5		\| 5
	\| 814.1		\| 814.1
	\| ~~822~~.5		\| 829.9
	\| '''8/5'''		\| '''8/5'''
	\|-		\|-
	\| 6		\| 6
	\| 976.9		\| 976.9
	\| ~~987~~.0		\| 995.8
	\| ('''7/4'''), '''16/9'''		\| ('''7/4'''), '''16/9'''
	\|-		\|-
	\| 7		\| 7
	\| 1139.7		\| 1139.7
	\| ~~1151~~.5		\| 1161.8
	\| 160/81, 64/33, 48/25		\| 160/81, 64/33, 48/25
	\|-		\|-
	\| 8		\| 8
	\| 102.5		\| 102.5
	\| ~~116~~.0		\| 127.8
	\| '''16/15''', ('''17/16''')		\| '''16/15''', ('''17/16''')
	\|-		\|-
	\| 9		\| 9
	\| 265.3		\| 265.3
	\| ~~280~~.5		\| 293.7
	\| (7/6)		\| (7/6)
	\|-		\|-
	\| 10		\| 10
	\| 428.2		\| 428.2
	\| ~~445~~.0		\| 459.7
	\| (14/11), 32/25		\| (14/11), 32/25
	\|-		\|-
	\| 11		\| 11
	\| 591.0		\| 591.0
	\| ~~609~~.5		\| 625.7
	\| (7/5, 17/12)		\| (7/5, 17/12)
	\|-		\|-
	\| 12		\| 12
	\| 753.8		\| 753.8
	\| ~~774~~.0		\| 791.7
	\| (14/9, 17/11)		\| (14/9, 17/11)
	\|-		\|-
	\| 13		\| 13
	\| 916.6		\| 916.6
	\| ~~938~~.5		\| 957.6
	\| (17/10)		\| (17/10)
	\|}		\|}