Nelinda - Revision history

Overthink: /* Xenharmonic systems for nelinda */ added note on temperament

2025-11-29T21:01:55Z

Xenharmonic systems for nelinda: added note on temperament

← Older revision		Revision as of 21:01, 29 November 2025
Line 8:		Line 8:
	4:7:10:13 would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 4.7.10.13 JI subgroup, of which [[640/637]] is a notable comma.		4:7:10:13 would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 4.7.10.13 JI subgroup, of which [[640/637]] is a notable comma.

	The {{nowrap\| 20 & 27 }} (with respect to the tetratave) [https://sintel.pythonanywhere.com/result?subgroup=4.7.10.13&reduce=on&weights=weil&target=&edos=20%2C27&submit_edo=submit&commas= linear temperament] is a notable entry that tempers out the said comma, which we could call ''nelindic''. It has an approximate 16/13 as its generator and forms [[mos]] of 6, 7, and 13 notes for starters, the latter of which yields a good albitonic scale. [[27ed4]] is an okay tuning for nelindic (especially with compression), but [[47ed4]] ''really'' knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5). Note that 20ed4 is just 10edo, where 5/4 (and possibly also 7/4) is tuned too flat,.		The {{nowrap\| 20 & 27 }} (with respect to the tetratave) [https://sintel.pythonanywhere.com/result?subgroup=4.7.10.13&reduce=on&weights=weil&target=&edos=20%2C27&submit_edo=submit&commas= linear temperament] is a notable entry that tempers out the said comma, which we could call ''nelindic'', and corresponds to [[huntington]] excluding every other peiod. It has an approximate 16/13 as its generator and forms [[mos]] of 6, 7, and 13 notes for starters, the latter of which yields a good albitonic scale. [[27ed4]] is an okay tuning for nelindic (especially with compression), but [[47ed4]] ''really'' knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5). Note that 20ed4 is just 10edo, where 5/4 (and possibly also 7/4) is tuned too flat,.

	[[Category:Instruments]]		[[Category:Instruments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Subgroup]]		[[Category:Subgroup]]

Overthink: /* Xenharmonic systems for nelinda */

2025-10-26T04:42:03Z

Xenharmonic systems for nelinda

← Older revision		Revision as of 04:42, 26 October 2025
Line 8:		Line 8:
	4:7:10:13 would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 4.7.10.13 JI subgroup, of which [[640/637]] is a notable comma.		4:7:10:13 would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 4.7.10.13 JI subgroup, of which [[640/637]] is a notable comma.

	The {{nowrap\| 20 & 27 }} (with respect to the tetratave) [https://sintel.pythonanywhere.com/result?subgroup=4.7.10.13&reduce=on&weights=weil&target=&edos=20%2C27&submit_edo=submit&commas= linear temperament] is a notable entry that tempers out the said comma, which we could call ''nelindic''. It has an approximate 16/13 as its generator and forms [[mos]] of 6, 7, and 13 notes for starters, the latter of which yields a good albitonic scale. [[27ed4]] is an okay tuning for nelindic (especially with compression), but [[47ed4]] ''really'' knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).		The {{nowrap\| 20 & 27 }} (with respect to the tetratave) [https://sintel.pythonanywhere.com/result?subgroup=4.7.10.13&reduce=on&weights=weil&target=&edos=20%2C27&submit_edo=submit&commas= linear temperament] is a notable entry that tempers out the said comma, which we could call ''nelindic''. It has an approximate 16/13 as its generator and forms [[mos]] of 6, 7, and 13 notes for starters, the latter of which yields a good albitonic scale. [[27ed4]] is an okay tuning for nelindic (especially with compression), but [[47ed4]] ''really'' knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5). Note that 20ed4 is just 10edo, where 5/4 (and possibly also 7/4) is tuned too flat,.

	[[Category:Instruments]]		[[Category:Instruments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Subgroup]]		[[Category:Subgroup]]

FloraC: Wording. Fix heading levels. + category.

2025-09-29T04:10:20Z

Wording. Fix heading levels. + category.

← Older revision		Revision as of 04:10, 29 September 2025
Line 1:		Line 1:
	The '''nelinda''' is a hypothetical family of single-reed instruments developed by [https://www.youtube.com/user/TruncatedTriangle/ TruncatedTriangle]. In contrast to the conical-bore saxophone, which produces all ~~(1n+1)~~ harmonics, and the cylindrical-bore clarinet, which produces mostly odd-numbered ({{nowrap\|2''n'' + 1}}) harmonics, the nelinda has a taper opposite in direction to the saxophone (that is, wider at the mouthpiece end and narrower at the bell end) designed to highlight the {{nowrap\|3''n'' + 1}} harmonics (that is, harmonics 1, 4, 7, 10, 13, etc.)		The '''nelinda''' is a hypothetical family of single-reed instruments developed by [https://www.youtube.com/user/TruncatedTriangle/ TruncatedTriangle]. In contrast to the conical-bore saxophone, which produces all harmonics, and the cylindrical-bore clarinet, which produces mostly odd-numbered ({{nowrap\| 2''n'' + 1 }}) harmonics, the nelinda has a taper opposite in direction to the saxophone (that is, wider at the mouthpiece end and narrower at the bell end) designed to highlight the {{nowrap\| 3''n'' + 1 }} harmonics (that is, harmonics 1, 4, 7, 10, 13, etc.)

	This implies that it will overblow not at the octave/ditave (2/1) or the twelfth/tritave (3/1) like other single-reeds, but instead at the fifteenth or double octave (4/1), giving it a wide range.		This implies that it will overblow not at the octave/ditave (2/1) or the twelfth/tritave (3/1) like other single-reeds, but instead at the fifteenth or double octave (4/1), giving it a wide range.

	=Xenharmonic ~~Systems~~ for ~~Nelinda~~=		== Xenharmonic systems for nelinda ==
			Similar to the mutual affinity between the tritave-repeating [[Bohlen–Pierce]] scale and the clarinet, with its spectrum of odd harmonics, a tuning system specifically for a (3''n'' + 1) spectrum like the nelinda can be developed, repeating at the 4/1 ratio (or ''tetratave'').
	Similar to the mutual affinity between the tritave-repeating [[Bohlen–Pierce]] scale and the clarinet, with its spectrum of odd harmonics, a tuning system specifically for a 3n+1 spectrum like the nelinda can be developed, repeating at the 4/1 ratio (or ''tetratave'').

	4:7:10:13 would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 4.7.10.13 JI subgroup, of which [[640/637]] is a notable comma.		4:7:10:13 would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 4.7.10.13 JI subgroup, of which [[640/637]] is a notable comma.

	~~Searching in Graham Breed's temperament finder for said comma, we quickly find the~~ {{nowrap\|27 ~~& 20~~}} (with respect to the tetratave) [https://sintel.pythonanywhere.com/result?subgroup=4.7.10.13&reduce=on&weights=weil&target=&edos=20%2C27&submit_edo=submit&commas= linear temperament], which we could call ''~~Nelindic~~''. It has an approximate 16/13 as its generator and forms ~~MOS~~ of 6, 7, and 13 notes for starters, the latter of which yields a good albitonic scale.		The {{nowrap\| 20 & 27 }} (with respect to the tetratave) [https://sintel.pythonanywhere.com/result?subgroup=4.7.10.13&reduce=on&weights=weil&target=&edos=20%2C27&submit_edo=submit&commas= linear temperament] is a notable entry that tempers out the said comma, which we could call ''nelindic''. It has an approximate 16/13 as its generator and forms [[mos]] of 6, 7, and 13 notes for starters, the latter of which yields a good albitonic scale. [[27ed4]] is an okay tuning for nelindic (especially with compression), but [[47ed4]] ''really'' knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).

	[[27ed4]] is an okay tuning for ~~Nelindic~~ (especially with compression), but [[47ed4]] ''really'' knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).

			[[Category:Instruments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Subgroup]]		[[Category:Subgroup]]

Overthink: Changed link to go to sintel instead of x31eq which doesn't work

2025-09-29T00:12:55Z

Changed link to go to sintel instead of x31eq which doesn't work

← Older revision		Revision as of 00:12, 29 September 2025
Line 9:		Line 9:
	4:7:10:13 would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 4.7.10.13 JI subgroup, of which [[640/637]] is a notable comma.		4:7:10:13 would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 4.7.10.13 JI subgroup, of which [[640/637]] is a notable comma.

	Searching in Graham Breed's temperament finder for said comma, we quickly find the {{nowrap\|27 & 20}} (with respect to the tetratave) [~~http~~://~~x31eq~~.com/~~cgi-bin/rt~~.~~cgi?ets~~=~~14qddrrrfff_10p~~&~~limit~~=~~4_7_10_13~~ linear temperament], which we could call ''Nelindic''. It has an approximate 16/13 as its generator and forms MOS of 6, 7, and 13 notes for starters, the latter of which yields a good albitonic scale.		Searching in Graham Breed's temperament finder for said comma, we quickly find the {{nowrap\|27 & 20}} (with respect to the tetratave) [https://sintel.pythonanywhere.com/result?subgroup=4.7.10.13&reduce=on&weights=weil&target=&edos=20%2C27&submit_edo=submit&commas= linear temperament], which we could call ''Nelindic''. It has an approximate 16/13 as its generator and forms MOS of 6, 7, and 13 notes for starters, the latter of which yields a good albitonic scale.

	[[27ed4]] is an okay tuning for Nelindic (especially with compression), but [[47ed4]] ''really'' knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).		[[27ed4]] is an okay tuning for Nelindic (especially with compression), but [[47ed4]] ''really'' knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).

Sintel at 16:18, 4 April 2025

2025-04-04T16:18:27Z

← Older revision		Revision as of 16:18, 4 April 2025
Line 1:		Line 1:
	The '''nelinda''' is a ~~conceptual~~ family of single-reed instruments developed by [https://www.youtube.com/user/TruncatedTriangle/ TruncatedTriangle]. In contrast to the conical-bore saxophone, which produces all (1n+1) harmonics, and the cylindrical-bore clarinet, which produces mostly odd-numbered ({{nowrap\|2''n'' + 1}}) harmonics, the nelinda has a taper opposite in direction to the saxophone (that is, wider at the mouthpiece end and narrower at the bell end) designed to highlight the {{nowrap\|3''n'' + 1}} harmonics (that is, harmonics 1, 4, 7, 10, 13, etc.)		The '''nelinda''' is a hypothetical family of single-reed instruments developed by [https://www.youtube.com/user/TruncatedTriangle/ TruncatedTriangle]. In contrast to the conical-bore saxophone, which produces all (1n+1) harmonics, and the cylindrical-bore clarinet, which produces mostly odd-numbered ({{nowrap\|2''n'' + 1}}) harmonics, the nelinda has a taper opposite in direction to the saxophone (that is, wider at the mouthpiece end and narrower at the bell end) designed to highlight the {{nowrap\|3''n'' + 1}} harmonics (that is, harmonics 1, 4, 7, 10, 13, etc.)

	This implies that it will overblow not at the octave/ditave (2/1) or the twelfth/tritave (3/1) like other single-reeds, but instead at the fifteenth or double octave (4/1), giving it a wide range.		This implies that it will overblow not at the octave/ditave (2/1) or the twelfth/tritave (3/1) like other single-reeds, but instead at the fifteenth or double octave (4/1), giving it a wide range.

Sintel: remove MMTM section

2025-04-04T16:02:29Z

remove MMTM section

@@ Line 12: / Line 12: @@
 [[27ed4]] is an okay tuning for Nelindic (especially with compression), but [[47ed4]] ''really'' knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).
 [[Category:Nonoctave]]
 [[Category:Subgroup]]

ArrowHead294 at 18:44, 13 March 2025

2025-03-13T18:44:40Z

Dummy index: +categories

2022-01-14T16:22:31Z

+categories

← Older revision		Revision as of 16:22, 14 January 2022
Line 34:		Line 34:

	17ed of either tenth is an okay tuning for either Decimophonic (especially with stretching), but 25ed of either tenth knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).		17ed of either tenth is an okay tuning for either Decimophonic (especially with stretching), but 25ed of either tenth knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).

			[[Category:Nonoctave]]
			[[Category:Subgroup]]

Moremajorthanmajor: /* Xenharmonic Systems for Decimophone */

2022-01-12T02:19:41Z

Xenharmonic Systems for Decimophone

← Older revision		Revision as of 02:19, 12 January 2022
Line 21:		Line 21:
	Similar to the mutual affinity between the tritave-repeating [[Bohlen-Pierce]] scale and the clarinet, with its spectrum of odd harmonics, a tuning system specifically for a 3n+2 spectrum like the decimophone can be developed, repeating at the 5/2 ratio (or ''major decade'').		Similar to the mutual affinity between the tritave-repeating [[Bohlen-Pierce]] scale and the clarinet, with its spectrum of odd harmonics, a tuning system specifically for a 3n+2 spectrum like the decimophone can be developed, repeating at the 5/2 ratio (or ''major decade'').

	2:5:8:11 would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 2.5.8.11 JI subgroup, of which ~~[[128~~/~~125]]~~ is a notable comma.		2:5:8:11(:14) would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 2.5.8.11(.14) JI subgroup, of which 125/121 is a notable comma.

	Searching in Graham Breed's temperament finder for said comma, we quickly find the 4n (with respect to the major decade) [http://x31eq.com/cgi-bin/uv.cgi linear temperament], which we call ''[[~~Augmented family\|augmented~~]].'' It is ~~clear this is not~~ a ~~very interesting result~~, ~~being nothing~~ more ~~than a less intuitively useful way~~ of ~~looking at~~ [[~~12edo~~]].		Searching in Graham Breed's temperament finder for said comma, we quickly find the 9&8/7 (with respect to the major decade) [http://x31eq.com/cgi-bin/uv.cgi?uvs=125%3A121&page=2&limit=2_5_8_11 linear temperament], which we could call ''Major Decimophonic.'' It has an approximate 19/17 or 4/3 as its generator and forms MOS of 7 or 8, 9 and 16 or 17 notes for starters, the latter of which yields a good albitonic scale.

			Unlike the nelinda, the decimophone has branches. The most important one beside that already mentioned will have a taper designed to highlight the ''4n+3'' harmonics (that is, the other harmonics of the clarinet.)

			Similar to the mutual affinity between the tritave-repeating [[Bohlen-Pierce]] scale and the clarinet, with its spectrum of odd harmonics, a tuning system specifically for a 4n+3 spectrum like the decimophone can be developed, repeating at the 7/3 ratio (or ''minor decade'').

			3:7:11:15(:19) would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 3.7.11.15(.19) JI subgroup, of which 135/133 is a notable comma.

			Searching in Graham Breed's temperament finder for said comma, we quickly find, beside more convoluted definitions of [[Bohlen-Pierce]], in top-down order, the 8&3, 17&8, 10&8, 8&7, and 14&8 (with respect to the minor decade) [http://x31eq.com/cgi-bin/uv.cgi?uvs=125%3A121&page=2&limit=2_5_8_11 linear temperaments], which we could call ''Minor Decimophonic.'' They have either the 7/3 or an approximate 14/9 as their period and form MOS of 5 through 7, or 8, 9 through 11, 13 through 15 and 17 or 18 notes for starters, the latter of which yield good albitonic scales.

			17ed of either tenth is an okay tuning for either Decimophonic (especially with stretching), but 25ed of either tenth knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).

Moremajorthanmajor at 12:51, 11 January 2022

2022-01-11T12:51:01Z

← Older revision		Revision as of 12:51, 11 January 2022
Line 12:		Line 12:

	[[27ed4]] is an okay tuning for Nelindic (especially with compression), but [[47ed4]] ''really'' knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).		[[27ed4]] is an okay tuning for Nelindic (especially with compression), but [[47ed4]] ''really'' knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).

			= Decimophone =
			Unlike the saxophone, the nelinda is still viable as an instrument with its taper reversed (that is, narrower at the mouthpiece end and wider at the bell end). This will be the branch of the '''decimophone''' which highlights the 3n+''2'' harmonics (that is, harmonics 2, 5, 8, 11, 14 etc.)

			This implies that overblowing at the major tenth, unlike other common full tubes, but instead like partial-tube trumpets, does not highlight the fundamental.

			= Xenharmonic Systems for Decimophone =
			Similar to the mutual affinity between the tritave-repeating [[Bohlen-Pierce]] scale and the clarinet, with its spectrum of odd harmonics, a tuning system specifically for a 3n+2 spectrum like the decimophone can be developed, repeating at the 5/2 ratio (or ''major decade'').

			2:5:8:11 would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 2.5.8.11 JI subgroup, of which [[128/125]] is a notable comma.

			Searching in Graham Breed's temperament finder for said comma, we quickly find the 4n (with respect to the major decade) [http://x31eq.com/cgi-bin/uv.cgi linear temperament], which we call ''[[Augmented family\|augmented]].'' It is clear this is not a very interesting result, being nothing more than a less intuitively useful way of looking at [[12edo]].

← Older revision		Revision as of 18:44, 13 March 2025
Line 1:		Line 1:
	The '''nelinda''' is a conceptual family of single-reed instruments developed by [https://www.youtube.com/user/TruncatedTriangle/ TruncatedTriangle]. In contrast to the conical-bore saxophone, which produces all (1n+1) harmonics, and the cylindrical-bore clarinet, which produces mostly odd-numbered (2n+1) harmonics, the nelinda has a taper opposite in direction to the saxophone (that is, wider at the mouthpiece end and narrower at the bell end) designed to highlight the ''3n+1'' harmonics (that is, harmonics 1, 4 ,7, 10, 13, etc.)		The '''nelinda''' is a conceptual family of single-reed instruments developed by [https://www.youtube.com/user/TruncatedTriangle/ TruncatedTriangle]. In contrast to the conical-bore saxophone, which produces all (1n+1) harmonics, and the cylindrical-bore clarinet, which produces mostly odd-numbered ({{nowrap\|2''n'' + 1}}) harmonics, the nelinda has a taper opposite in direction to the saxophone (that is, wider at the mouthpiece end and narrower at the bell end) designed to highlight the {{nowrap\|3''n'' + 1}} harmonics (that is, harmonics 1, 4, 7, 10, 13, etc.)

	This implies that it will overblow not at the octave/ditave (2/1) or the twelfth/tritave (3/1) like other single-reeds, but instead at the fifteenth or double octave (4/1), giving it a wide range.		This implies that it will overblow not at the octave/ditave (2/1) or the twelfth/tritave (3/1) like other single-reeds, but instead at the fifteenth or double octave (4/1), giving it a wide range.
Line 5:		Line 5:
	=Xenharmonic Systems for Nelinda=		=Xenharmonic Systems for Nelinda=

	Similar to the mutual affinity between the tritave-repeating [[~~Bohlen-Pierce~~]] scale and the clarinet, with its spectrum of odd harmonics, a tuning system specifically for a 3n+1 spectrum like the nelinda can be developed, repeating at the 4/1 ratio (or ''tetratave'').		Similar to the mutual affinity between the tritave-repeating [[Bohlen–Pierce]] scale and the clarinet, with its spectrum of odd harmonics, a tuning system specifically for a 3n+1 spectrum like the nelinda can be developed, repeating at the 4/1 ratio (or ''tetratave'').

	4:7:10:13 would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 4.7.10.13 JI subgroup, of which [[640/637]] is a notable comma.		4:7:10:13 would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 4.7.10.13 JI subgroup, of which [[640/637]] is a notable comma.

	Searching in Graham Breed's temperament finder for said comma, we quickly find the 27&20 (with respect to the tetratave) [http://x31eq.com/cgi-bin/rt.cgi?ets=14qddrrrfff_10p&limit=4_7_10_13 linear temperament], which we could call ''Nelindic''. It has an approximate 16/13 as its generator and forms MOS of 6, 7, and 13 notes for starters, the latter of which yields a good albitonic scale.		Searching in Graham Breed's temperament finder for said comma, we quickly find the {{nowrap\|27 & 20}} (with respect to the tetratave) [http://x31eq.com/cgi-bin/rt.cgi?ets=14qddrrrfff_10p&limit=4_7_10_13 linear temperament], which we could call ''Nelindic''. It has an approximate 16/13 as its generator and forms MOS of 6, 7, and 13 notes for starters, the latter of which yields a good albitonic scale.

	[[27ed4]] is an okay tuning for Nelindic (especially with compression), but [[47ed4]] ''really'' knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).		[[27ed4]] is an okay tuning for Nelindic (especially with compression), but [[47ed4]] ''really'' knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).
Line 19:		Line 19:

	= Xenharmonic Systems for Decimophone =		= Xenharmonic Systems for Decimophone =
	Similar to the mutual affinity between the tritave-repeating [[~~Bohlen-Pierce~~]] scale and the clarinet, with its spectrum of odd harmonics, a tuning system specifically for a 3n+2 spectrum like the decimophone can be developed, repeating at the 5/2 ratio (or ''major decade'').		Similar to the mutual affinity between the tritave-repeating [[Bohlen–Pierce]] scale and the clarinet, with its spectrum of odd harmonics, a tuning system specifically for a 3n+2 spectrum like the decimophone can be developed, repeating at the 5/2 ratio (or ''major decade'').

	2:5:8:11(:14) would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 2.5.8.11(.14) JI subgroup, of which 125/121 is a notable comma.		2:5:8:11(:14) would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 2.5.8.11(.14) JI subgroup, of which 125/121 is a notable comma.

	Searching in Graham Breed's temperament finder for said comma, we quickly find the 9&8/7 (with respect to the major decade) [http://x31eq.com/cgi-bin/uv.cgi?uvs=125%3A121&page=2&limit=2_5_8_11 linear temperament], which we could call ''Major Decimophonic.'' It has an approximate 19/17 or 4/3 as its generator and forms MOS of 7 or 8, 9 and 16 or 17 notes for starters, the latter of which yields a good albitonic scale.		Searching in Graham Breed's temperament finder for said comma, we quickly find the {{nowrap\|9 & 8/7}} (with respect to the major decade) [http://x31eq.com/cgi-bin/uv.cgi?uvs=125%3A121&page=2&limit=2_5_8_11 linear temperament], which we could call ''Major Decimophonic.'' It has an approximate 19/17 or 4/3 as its generator and forms MOS of 7 or 8, 9 and 16 or 17 notes for starters, the latter of which yields a good albitonic scale.

	Unlike the nelinda, the decimophone has branches. The most important one beside that already mentioned will have a taper designed to highlight the ''4n+3'' harmonics (that is, the other harmonics of the clarinet.)		Unlike the nelinda, the decimophone has branches. The most important one beside that already mentioned will have a taper designed to highlight the ''4n+3'' harmonics (that is, the other harmonics of the clarinet.)

	Similar to the mutual affinity between the tritave-repeating [[~~Bohlen-Pierce~~]] scale and the clarinet, with its spectrum of odd harmonics, a tuning system specifically for a 4n+3 spectrum like the decimophone can be developed, repeating at the 7/3 ratio (or ''minor decade'').		Similar to the mutual affinity between the tritave-repeating [[Bohlen–Pierce]] scale and the clarinet, with its spectrum of odd harmonics, a tuning system specifically for a 4n+3 spectrum like the decimophone can be developed, repeating at the 7/3 ratio (or ''minor decade'').

	3:7:11:15(:19) would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 3.7.11.15(.19) JI subgroup, of which 135/133 is a notable comma.		3:7:11:15(:19) would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working within a 3.7.11.15(.19) JI subgroup, of which 135/133 is a notable comma.

	Searching in Graham Breed's temperament finder for said comma, we quickly find, beside more convoluted definitions of [[~~Bohlen-Pierce~~]], in top-down order, the 8&3, 17&8, 10&8, 8&7, and 14&8 (with respect to the minor decade) [http://x31eq.com/cgi-bin/uv.cgi?uvs=125%3A121&page=2&limit=2_5_8_11 linear temperaments], which we could call ''Minor Decimophonic.'' They have either the 7/3 or an approximate 14/9 as their period and form MOS of 5 through 7, or 8, 9 through 11, 13 through 15 and 17 or 18 notes for starters, the latter of which yield good albitonic scales.		Searching in Graham Breed's temperament finder for said comma, we quickly find, beside more convoluted definitions of [[Bohlen–Pierce]], in top-down order, the {{nowrap\|8 & 3\|17 & 8\|10 & 8\|8 & 7}}, and {{nowrap\|14 & 8}} (with respect to the minor decade) [http://x31eq.com/cgi-bin/uv.cgi?uvs=125%3A121&page=2&limit=2_5_8_11 linear temperaments], which we could call ''Minor Decimophonic.'' They have either the 7/3 or an approximate 14/9 as their period and form MOS of 5 through 7, or 8, 9 through 11, 13 through 15 and 17 or 18 notes for starters, the latter of which yield good albitonic scales.

	17ed of either tenth is an okay tuning for either Decimophonic (especially with stretching), but 25ed of either tenth knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).		17ed of either tenth is an okay tuning for either Decimophonic (especially with stretching), but 25ed of either tenth knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).