11/10 - Revision history

FloraC: Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

2025-11-03T13:07:00Z

Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

← Older revision		Revision as of 13:07, 3 November 2025
Line 10:		Line 10:
	== Approximation ==		== Approximation ==
	11/10 is approximated extremely precisely by [[80edo]] and its multiples, with a chain of 80 11/10's failing to close at the octave by a mere third of a [[cent]], close enough that you could theoretically tune an instrument to 80edo by ear using it if you had the patience. 11/10 is also approximated within 2 cents by [[22edo]], and is 4c sharp of an octave-reduced stack of 9 generators in [[BPS]].		11/10 is approximated extremely precisely by [[80edo]] and its multiples, with a chain of 80 11/10's failing to close at the octave by a mere third of a [[cent]], close enough that you could theoretically tune an instrument to 80edo by ear using it if you had the patience. 11/10 is also approximated within 2 cents by [[22edo]], and is 4c sharp of an octave-reduced stack of 9 generators in [[BPS]].
	{{~~Interval_Edo_Approximation~~ \| 11/10}}		{{Interval edo approximation\|11/10}}
	== Temperaments ==		== Temperaments ==
	Using 11/10 as a generator tempering out 4000/3993 (as previously mentioned) leads to scales that look like [[porcupine]] but whose harmonies can more accurately be explained. A half-octave period is exceptionally natural when 11/10 is a generator, because by virtue of making the (extremely accurate) approximation of the half-octave by [[99/70]], [[9/7]] is found as the period-complement of the generator. Taking this approach, this gives us temperaments in the [[stearnsmic clan]] such as [[pogo]], [[supers]], or [[echidna]], all of which detemper [[100/99]] ~ [[121/120]] and accurately find [[11-limit]] and (no-13's) [[17-limit]] harmonies. Of these, echidna's mapping of the no-13's 17-limit is the simplest, though all three have the same mapping of the 2.3.7.11/10.17 subgroup so that they only differ on the mapping of 5 and 11. The complexity of 5 and 11 in pogo are used to increase accuracy, being a weak schismic extension. That leaves supers as the odd one out; if you are using an edo tuning for it, 58edo supports echidna while 94edo supports pogo, so it seems to exist as a portable alternate way of finding primes 5 and 11 across systems, unless you use the 152edo tuning, which requires using the second-best mapping of 13 (the 152f [[val]]).		Using 11/10 as a generator tempering out 4000/3993 (as previously mentioned) leads to scales that look like [[porcupine]] but whose harmonies can more accurately be explained. A half-octave period is exceptionally natural when 11/10 is a generator, because by virtue of making the (extremely accurate) approximation of the half-octave by [[99/70]], [[9/7]] is found as the period-complement of the generator. Taking this approach, this gives us temperaments in the [[stearnsmic clan]] such as [[pogo]], [[supers]], or [[echidna]], all of which detemper [[100/99]] ~ [[121/120]] and accurately find [[11-limit]] and (no-13's) [[17-limit]] harmonies. Of these, echidna's mapping of the no-13's 17-limit is the simplest, though all three have the same mapping of the 2.3.7.11/10.17 subgroup so that they only differ on the mapping of 5 and 11. The complexity of 5 and 11 in pogo are used to increase accuracy, being a weak schismic extension. That leaves supers as the odd one out; if you are using an edo tuning for it, 58edo supports echidna while 94edo supports pogo, so it seems to exist as a portable alternate way of finding primes 5 and 11 across systems, unless you use the 152edo tuning, which requires using the second-best mapping of 13 (the 152f [[val]]).

Pailiaq at 06:51, 3 November 2025

2025-11-03T06:51:04Z

← Older revision		Revision as of 06:51, 3 November 2025
Line 10:		Line 10:
	== Approximation ==		== Approximation ==
	11/10 is approximated extremely precisely by [[80edo]] and its multiples, with a chain of 80 11/10's failing to close at the octave by a mere third of a [[cent]], close enough that you could theoretically tune an instrument to 80edo by ear using it if you had the patience. 11/10 is also approximated within 2 cents by [[22edo]], and is 4c sharp of an octave-reduced stack of 9 generators in [[BPS]].		11/10 is approximated extremely precisely by [[80edo]] and its multiples, with a chain of 80 11/10's failing to close at the octave by a mere third of a [[cent]], close enough that you could theoretically tune an instrument to 80edo by ear using it if you had the patience. 11/10 is also approximated within 2 cents by [[22edo]], and is 4c sharp of an octave-reduced stack of 9 generators in [[BPS]].
			{{Interval_Edo_Approximation \| 11/10}}
	== Temperaments ==		== Temperaments ==
	Using 11/10 as a generator tempering out 4000/3993 (as previously mentioned) leads to scales that look like [[porcupine]] but whose harmonies can more accurately be explained. A half-octave period is exceptionally natural when 11/10 is a generator, because by virtue of making the (extremely accurate) approximation of the half-octave by [[99/70]], [[9/7]] is found as the period-complement of the generator. Taking this approach, this gives us temperaments in the [[stearnsmic clan]] such as [[pogo]], [[supers]], or [[echidna]], all of which detemper [[100/99]] ~ [[121/120]] and accurately find [[11-limit]] and (no-13's) [[17-limit]] harmonies. Of these, echidna's mapping of the no-13's 17-limit is the simplest, though all three have the same mapping of the 2.3.7.11/10.17 subgroup so that they only differ on the mapping of 5 and 11. The complexity of 5 and 11 in pogo are used to increase accuracy, being a weak schismic extension. That leaves supers as the odd one out; if you are using an edo tuning for it, 58edo supports echidna while 94edo supports pogo, so it seems to exist as a portable alternate way of finding primes 5 and 11 across systems, unless you use the 152edo tuning, which requires using the second-best mapping of 13 (the 152f [[val]]).		Using 11/10 as a generator tempering out 4000/3993 (as previously mentioned) leads to scales that look like [[porcupine]] but whose harmonies can more accurately be explained. A half-octave period is exceptionally natural when 11/10 is a generator, because by virtue of making the (extremely accurate) approximation of the half-octave by [[99/70]], [[9/7]] is found as the period-complement of the generator. Taking this approach, this gives us temperaments in the [[stearnsmic clan]] such as [[pogo]], [[supers]], or [[echidna]], all of which detemper [[100/99]] ~ [[121/120]] and accurately find [[11-limit]] and (no-13's) [[17-limit]] harmonies. Of these, echidna's mapping of the no-13's 17-limit is the simplest, though all three have the same mapping of the 2.3.7.11/10.17 subgroup so that they only differ on the mapping of 5 and 11. The complexity of 5 and 11 in pogo are used to increase accuracy, being a weak schismic extension. That leaves supers as the odd one out; if you are using an edo tuning for it, 58edo supports echidna while 94edo supports pogo, so it seems to exist as a portable alternate way of finding primes 5 and 11 across systems, unless you use the 152edo tuning, which requires using the second-best mapping of 13 (the 152f [[val]]).

Lériendil: meow

2025-04-10T04:53:07Z

meow

← Older revision		Revision as of 04:53, 10 April 2025
Line 12:		Line 12:

	== Temperaments ==		== Temperaments ==
	Using 11/10 as a generator tempering out 4000/3993 (as previously mentioned) leads to scales that look like [[porcupine]] but whose harmonies can more accurately be explained. ~~With a~~ half-octave period, a generator of 11/~~10 leads to~~ temperaments in the [[stearnsmic clan]] such as [[pogo]], [[supers]], or [[echidna]], all of which detemper [[100/99]] ~~and~~ [[121/120]] and accurately find [[11-limit]] and (no-13's) [[17-limit]] harmonies. Of these, echidna's mapping of the no-13's 17-limit is the simplest, though all three have the same mapping of the 2.3.7.11/10.17 subgroup so that they only differ on the mapping of 5 and 11. The complexity of 5 and 11 in pogo are used to increase accuracy, being a weak schismic extension. That leaves supers as the odd one out; if you are using an edo tuning for it, 58edo supports echidna while 94edo supports pogo, so it seems to exist as a portable alternate way of finding primes 5 and 11 across systems, unless you use the 152edo tuning, which requires using the second-best mapping of 13 (the 152f [[val]]).		Using 11/10 as a generator tempering out 4000/3993 (as previously mentioned) leads to scales that look like [[porcupine]] but whose harmonies can more accurately be explained. A half-octave period is exceptionally natural when 11/10 is a generator, because by virtue of making the (extremely accurate) approximation of the half-octave by [[99/70]], [[9/7]] is found as the period-complement of the generator. Taking this approach, this gives us temperaments in the [[stearnsmic clan]] such as [[pogo]], [[supers]], or [[echidna]], all of which detemper [[100/99]] ~ [[121/120]] and accurately find [[11-limit]] and (no-13's) [[17-limit]] harmonies. Of these, echidna's mapping of the no-13's 17-limit is the simplest, though all three have the same mapping of the 2.3.7.11/10.17 subgroup so that they only differ on the mapping of 5 and 11. The complexity of 5 and 11 in pogo are used to increase accuracy, being a weak schismic extension. That leaves supers as the odd one out; if you are using an edo tuning for it, 58edo supports echidna while 94edo supports pogo, so it seems to exist as a portable alternate way of finding primes 5 and 11 across systems, unless you use the 152edo tuning, which requires using the second-best mapping of 13 (the 152f [[val]]).

	Using sqrt(11/10) (22/21[[~]]21/20) as a generator leads to the low-complexity [[Nautilus]] with one period to the octave, and if you use two periods to the octave with this generator you get the high-accuracy temperament [[Harry]]; using cbrt(11/10) as a generator leads to [[Escapade]] with one period to the octave.		Using sqrt(11/10) (22/21[[~]]21/20) as a generator leads to the low-complexity [[Nautilus]] with one period to the octave, and if you use two periods to the octave with this generator you get the high-accuracy temperament [[Harry]]; using cbrt(11/10) as a generator leads to [[Escapade]] with one period to the octave.

Godtone: it's harry which is high accuracy; also clarify the gen

2025-04-10T00:37:57Z

it's harry which is high accuracy; also clarify the gen

← Older revision		Revision as of 00:37, 10 April 2025
Line 14:		Line 14:
	Using 11/10 as a generator tempering out 4000/3993 (as previously mentioned) leads to scales that look like [[porcupine]] but whose harmonies can more accurately be explained. With a half-octave period, a generator of 11/10 leads to temperaments in the [[stearnsmic clan]] such as [[pogo]], [[supers]], or [[echidna]], all of which detemper [[100/99]] and [[121/120]] and accurately find [[11-limit]] and (no-13's) [[17-limit]] harmonies. Of these, echidna's mapping of the no-13's 17-limit is the simplest, though all three have the same mapping of the 2.3.7.11/10.17 subgroup so that they only differ on the mapping of 5 and 11. The complexity of 5 and 11 in pogo are used to increase accuracy, being a weak schismic extension. That leaves supers as the odd one out; if you are using an edo tuning for it, 58edo supports echidna while 94edo supports pogo, so it seems to exist as a portable alternate way of finding primes 5 and 11 across systems, unless you use the 152edo tuning, which requires using the second-best mapping of 13 (the 152f [[val]]).		Using 11/10 as a generator tempering out 4000/3993 (as previously mentioned) leads to scales that look like [[porcupine]] but whose harmonies can more accurately be explained. With a half-octave period, a generator of 11/10 leads to temperaments in the [[stearnsmic clan]] such as [[pogo]], [[supers]], or [[echidna]], all of which detemper [[100/99]] and [[121/120]] and accurately find [[11-limit]] and (no-13's) [[17-limit]] harmonies. Of these, echidna's mapping of the no-13's 17-limit is the simplest, though all three have the same mapping of the 2.3.7.11/10.17 subgroup so that they only differ on the mapping of 5 and 11. The complexity of 5 and 11 in pogo are used to increase accuracy, being a weak schismic extension. That leaves supers as the odd one out; if you are using an edo tuning for it, 58edo supports echidna while 94edo supports pogo, so it seems to exist as a portable alternate way of finding primes 5 and 11 across systems, unless you use the 152edo tuning, which requires using the second-best mapping of 13 (the 152f [[val]]).

	Using sqrt(11/10) as a generator leads to low-complexity [[Nautilus]] with one period to the octave and high-accuracy [[Harry]] ~~with two periods~~; using cbrt(11/10) as a generator leads to [[Escapade]] with one period to the octave.		Using sqrt(11/10) (22/21[[~]]21/20) as a generator leads to the low-complexity [[Nautilus]] with one period to the octave, and if you use two periods to the octave with this generator you get the high-accuracy temperament [[Harry]]; using cbrt(11/10) as a generator leads to [[Escapade]] with one period to the octave.

	== See also ==		== See also ==

Godtone: im not sure why i previously wrote that they are all find the (no-13's) 17-limit "efficiently"; this isnt true; echidna's 5 and 11 are much simpler than pogo's and supers'

2025-04-10T00:32:48Z

im not sure why i previously wrote that they are all find the (no-13's) 17-limit "efficiently"; this isnt true; echidna's 5 and 11 are much simpler than pogo's and supers'

← Older revision		Revision as of 00:32, 10 April 2025
Line 12:		Line 12:

	== Temperaments ==		== Temperaments ==
	Using 11/10 as a generator tempering out 4000/3993 (as previously mentioned) leads to scales that look like [[porcupine]] but whose harmonies can more accurately be explained. With a half-octave period, a generator of 11/10 leads to temperaments in the [[stearnsmic clan]] such as [[pogo]], [[supers]], or [[echidna]], all of which detemper [[100/99]] and [[121/120]] ~~and efficiently~~ and accurately find [[11-limit]] and (no-13's) [[17-limit]] harmonies.		Using 11/10 as a generator tempering out 4000/3993 (as previously mentioned) leads to scales that look like [[porcupine]] but whose harmonies can more accurately be explained. With a half-octave period, a generator of 11/10 leads to temperaments in the [[stearnsmic clan]] such as [[pogo]], [[supers]], or [[echidna]], all of which detemper [[100/99]] and [[121/120]] and accurately find [[11-limit]] and (no-13's) [[17-limit]] harmonies. Of these, echidna's mapping of the no-13's 17-limit is the simplest, though all three have the same mapping of the 2.3.7.11/10.17 subgroup so that they only differ on the mapping of 5 and 11. The complexity of 5 and 11 in pogo are used to increase accuracy, being a weak schismic extension. That leaves supers as the odd one out; if you are using an edo tuning for it, 58edo supports echidna while 94edo supports pogo, so it seems to exist as a portable alternate way of finding primes 5 and 11 across systems, unless you use the 152edo tuning, which requires using the second-best mapping of 13 (the 152f [[val]]).

	Using sqrt(11/10) as a generator leads to low-complexity [[Nautilus]] with one period to the octave and high-accuracy [[Harry]] with two periods; using cbrt(11/10) as a generator leads to [[Escapade]] with one period to the octave.		Using sqrt(11/10) as a generator leads to low-complexity [[Nautilus]] with one period to the octave and high-accuracy [[Harry]] with two periods; using cbrt(11/10) as a generator leads to [[Escapade]] with one period to the octave.

Lucius Chiaraviglio: Add links to 12/11 and 10/9

2025-04-09T17:07:02Z

Add links to 12/11 and 10/9

← Older revision		Revision as of 17:07, 9 April 2025
Line 4:		Line 4:
	\| Sound = jid_11_10_pluck_adu_dr220.mp3		\| Sound = jid_11_10_pluck_adu_dr220.mp3
	}}		}}
	'''11/10''', the '''large undecimal neutral second''' or '''undecimal submajor second''', is the simplest submajor second. It is 15 cents sharp of 12/11 and 17 cents flat of 10/9. When tuned [[just]] or near-just, it not only has the very exotic melodic role of being almost exactly a third of [[4/3]], leading to [[4000/3993]] being [[Fudging\|fudged]], but is also very close in size to a stack consisting of an [[apotome]] and [[33/32]], leading to the [[schisma]] being fudged. Keeping 11/10 distinct from 12/11 ensures that 11/10 bridges [[quartertone]]-based chords with more typical [[5-limit]] and [[Pythagorean tuning\|Pythagorean]] chords as a step between notes.		'''11/10''', the '''large undecimal neutral second''' or '''undecimal submajor second''', is the simplest submajor second. It is 15 cents sharp of [[12/11]] and 17 cents flat of [[10/9]]. When tuned [[just]] or near-just, it not only has the very exotic melodic role of being almost exactly a third of [[4/3]], leading to [[4000/3993]] being [[Fudging\|fudged]], but is also very close in size to a stack consisting of an [[apotome]] and [[33/32]], leading to the [[schisma]] being fudged. Keeping 11/10 distinct from 12/11 ensures that 11/10 bridges [[quartertone]]-based chords with more typical [[5-limit]] and [[Pythagorean tuning\|Pythagorean]] chords as a step between notes.

	11/10 is the [[octave-reduced]] form of [[11/5]], one of the three most [[concordant]] 11-limit intervals within the entire [[4/1\|first two octaves]] along with [[11/4]] and [[11/3]].		11/10 is the [[octave-reduced]] form of [[11/5]], one of the three most [[concordant]] 11-limit intervals within the entire [[4/1\|first two octaves]] along with [[11/4]] and [[11/3]].

Hkm: /* Approximation */

2025-04-02T18:51:47Z

Approximation

← Older revision		Revision as of 18:51, 2 April 2025
Line 9:		Line 9:

	== Approximation ==		== Approximation ==
	11/10 is approximated extremely precisely by [[80edo]] and its multiples, with a chain of 80 11/10's failing to close at the octave by a mere third of a [[cent]], close enough that you could theoretically tune an instrument to 80edo by ear using it if you had the patience. 11/10 is also approximated within 2 cents by [[22edo]], and is ~~about~~ 4c sharp of ~~the [[chroma]]~~ of [[BPS]].		11/10 is approximated extremely precisely by [[80edo]] and its multiples, with a chain of 80 11/10's failing to close at the octave by a mere third of a [[cent]], close enough that you could theoretically tune an instrument to 80edo by ear using it if you had the patience. 11/10 is also approximated within 2 cents by [[22edo]], and is 4c sharp of an octave-reduced stack of 9 generators in [[BPS]].

	== Temperaments ==		== Temperaments ==

Hkm: cleanup

2025-04-02T18:49:17Z

cleanup

← Older revision		Revision as of 18:49, 2 April 2025
Line 4:		Line 4:
	\| Sound = jid_11_10_pluck_adu_dr220.mp3		\| Sound = jid_11_10_pluck_adu_dr220.mp3
	}}		}}
	~~{{Wikipedia\| Neutral interval #Second }}~~		'''11/10''', the '''large undecimal neutral second''' or '''undecimal submajor second''', is the simplest submajor second. It is 15 cents sharp of 12/11 and 17 cents flat of 10/9. When tuned [[just]] or near-just, it not only has the very exotic melodic role of being almost exactly a third of [[4/3]], leading to [[4000/3993]] being [[Fudging\|fudged]], but is also very close in size to a stack consisting of an [[apotome]] and [[33/32]], leading to the [[schisma]] being fudged. Keeping 11/10 distinct from 12/11 ensures that 11/10 bridges [[quartertone]]-based chords with more typical [[5-limit]] and [[Pythagorean tuning\|Pythagorean]] chords as a step between notes.
	'''11/10''', the '''large undecimal neutral second''' or '''undecimal submajor second''', is ~~an interval favored by {{w\|Ptolemy}}~~. ~~Depending on who you ask~~, ~~this interval~~, ~~on its own~~, is ~~either considerably more or considerably less exotic than~~ [[12/11]] ~~or a number of other simple~~ [[11-limit]] ~~intervals~~.

	If tempered sharp, however, one could make the argument that 11/10 functions a bit more like a narrowed [[10/9]] in light of its usage in such a capacity in systems like [[41edo]] and [[63edo]] where 11/10 and 10/9 are [[tempered]] together due to [[100/99]] being tempered out.		11/10 is the [[octave-reduced]] form of [[11/5]], one of the three most [[concordant]] 11-limit intervals within the entire [[4/1\|first two octaves]] along with [[11/4]] and [[11/3]].

	Meanwhile, when tuned [[just]] or near-just, it not only has the very exotic melodic role of being almost exactly a third of [[4/3]], leading to [[4000/3993]] being [[Fudging\|fudged]] or [[tempered out]], but is also very close in size to a stack consisting of an [[apotome]] and [[33/32]], leading to the [[schisma]] being fudged or tempered out.

	Assuming you go with either of the aforementioned options, keeping 11/10 distinct from 12/11 ensures that 11/10 has a way of bridging [[quartertone]]-based chords with more typical [[5-limit]] and [[Pythagorean tuning\|Pythagorean]] chords as a sort of step between notes, however, if you temper out [[121/120]], expect this ability to vanish.

	11/10 is the [[octave-reduced]] form of [[11/5]], one of the three most [[concordant]] 11-limit intervals within the entire [[4/1\|first two octaves]] along with [[11/4]] and [[11/3]]. In any [[Octave equivalence\|octave-repeating]] tuning, a good approximation of 11/10 indicates a good approximation of 11/5. So, it could be argued that 11/10 is a high priority for any octave-repeating 11-limit tuning.

	== Approximation ==		== Approximation ==
	11/10 is approximated extremely precisely by [[80edo]] and its multiples, with a chain of 80 11/10's failing to close at the octave by a mere third of a [[cent]], close enough that you could theoretically tune an instrument to 80edo by ear using it if you had the patience.		11/10 is approximated extremely precisely by [[80edo]] and its multiples, with a chain of 80 11/10's failing to close at the octave by a mere third of a [[cent]], close enough that you could theoretically tune an instrument to 80edo by ear using it if you had the patience. 11/10 is also approximated within 2 cents by [[22edo]], and is about 4c sharp of the [[chroma]] of [[BPS]].

	== Temperaments ==		== Temperaments ==
	11/10 ~~may be treated implicitly~~ as a ~~[[comma]] in [[JI]] scales that for example do not find [[11~~/~~8]] and [[5/4]] above the same degree, but usually it makes much more sense to use it~~ as ~~a [[generator]], such as the aforementioned very accurate strategy of making it a third of [[4/3]], leading~~ to scales that look like [[porcupine]] but whose harmonies can more accurately be explained ~~in a number of ways depending partially on the exact tempering used~~. ~~If you use~~ a half-octave period ~~you get~~ temperaments in the [[stearnsmic clan]] such as [[pogo]], [[supers]], or [[echidna]], all of which detemper [[100/99]] and [[121/120]] and efficiently and accurately find [[11-limit]] and (no-13's) [[17-limit]] harmonies.		Using 11/10 as a generator tempering out 4000/3993 (as previously mentioned) leads to scales that look like [[porcupine]] but whose harmonies can more accurately be explained. With a half-octave period, a generator of 11/10 leads to temperaments in the [[stearnsmic clan]] such as [[pogo]], [[supers]], or [[echidna]], all of which detemper [[100/99]] and [[121/120]] and efficiently and accurately find [[11-limit]] and (no-13's) [[17-limit]] harmonies.

	~~=== Exotemperaments ===~~
	11/10 is tempered out in the [[patent val]]s of [[edo]]s 1, 2, 3 and 5. An example rank-2 [[exotemperament]] that treats it as a comma to be tempered out is [[very low accuracy temperaments #Antietam\|antietam]].

	~~== Trivia ==~~		Using sqrt(11/10) as a generator leads to low-complexity [[Nautilus]] with one period to the octave and high-accuracy [[Harry]] with two periods; using cbrt(11/10) as a generator leads to [[Escapade]] with one period to the octave.
	~~Coincidentally, the interval between the most common tuning frequency~~ (~~A440~~) and ~~the second most common AC electrical frequency~~ (~~50 Hz) is exactly 44/5, or three octaves above an~~ 11/10.

	== See also ==		== See also ==

BudjarnLambeth: Links

2024-12-24T06:27:33Z

Links

← Older revision		Revision as of 06:27, 24 December 2024
Line 7:		Line 7:
	'''11/10''', the '''large undecimal neutral second''' or '''undecimal submajor second''', is an interval favored by {{w\|Ptolemy}}. Depending on who you ask, this interval, on its own, is either considerably more or considerably less exotic than [[12/11]] or a number of other simple [[11-limit]] intervals.		'''11/10''', the '''large undecimal neutral second''' or '''undecimal submajor second''', is an interval favored by {{w\|Ptolemy}}. Depending on who you ask, this interval, on its own, is either considerably more or considerably less exotic than [[12/11]] or a number of other simple [[11-limit]] intervals.

	If tempered sharp, however, one could make the argument that 11/10 functions a bit more like a narrowed [[10/9]] in light of its usage in such a capacity in systems like [[41edo]] and [[63edo]] where 11/10 and 10/9 are tempered together due to [[100/99]] being tempered out.		If tempered sharp, however, one could make the argument that 11/10 functions a bit more like a narrowed [[10/9]] in light of its usage in such a capacity in systems like [[41edo]] and [[63edo]] where 11/10 and 10/9 are [[tempered]] together due to [[100/99]] being tempered out.

	Meanwhile, when tuned [[just]] or near-just, it not only has the very exotic melodic role of being almost exactly a third of [[4/3]], leading to [[4000/3993]] being [[Fudging\|fudged]] or [[tempered out]], but is also very close in size to a stack consisting of an [[apotome]] and [[33/32]], leading to the [[schisma]] being fudged or tempered out.		Meanwhile, when tuned [[just]] or near-just, it not only has the very exotic melodic role of being almost exactly a third of [[4/3]], leading to [[4000/3993]] being [[Fudging\|fudged]] or [[tempered out]], but is also very close in size to a stack consisting of an [[apotome]] and [[33/32]], leading to the [[schisma]] being fudged or tempered out.

	Assuming you go with either of the aforementioned options, keeping 11/10 distinct from 12/11 ensures that 11/10 has a way of bridging quartertone-based chords with more typical [[5-limit]] and [[Pythagorean tuning\|Pythagorean]] chords as a sort of step between notes, however, if you temper out [[121/120]], expect this ability to vanish.		Assuming you go with either of the aforementioned options, keeping 11/10 distinct from 12/11 ensures that 11/10 has a way of bridging [[quartertone]]-based chords with more typical [[5-limit]] and [[Pythagorean tuning\|Pythagorean]] chords as a sort of step between notes, however, if you temper out [[121/120]], expect this ability to vanish.

	11/10 is the [[octave-reduced]] form of [[11/5]], one of the three most [[concordant]] 11-limit intervals within the entire [[4/1\|first two octaves]] along with [[11/4]] and [[11/3]]. In any [[Octave equivalence\|octave-repeating]] tuning, a good approximation of 11/10 indicates a good approximation of 11/5. So, it could be argued that 11/10 is a high priority for any octave-repeating 11-limit tuning.		11/10 is the [[octave-reduced]] form of [[11/5]], one of the three most [[concordant]] 11-limit intervals within the entire [[4/1\|first two octaves]] along with [[11/4]] and [[11/3]]. In any [[Octave equivalence\|octave-repeating]] tuning, a good approximation of 11/10 indicates a good approximation of 11/5. So, it could be argued that 11/10 is a high priority for any octave-repeating 11-limit tuning.

BudjarnLambeth at 22:55, 13 December 2024

2024-12-13T22:55:47Z

← Older revision		Revision as of 22:55, 13 December 2024
Line 7:		Line 7:
	'''11/10''', the '''large undecimal neutral second''' or '''undecimal submajor second''', is an interval favored by {{w\|Ptolemy}}. Depending on who you ask, this interval, on its own, is either considerably more or considerably less exotic than [[12/11]] or a number of other simple [[11-limit]] intervals.		'''11/10''', the '''large undecimal neutral second''' or '''undecimal submajor second''', is an interval favored by {{w\|Ptolemy}}. Depending on who you ask, this interval, on its own, is either considerably more or considerably less exotic than [[12/11]] or a number of other simple [[11-limit]] intervals.

	If tempered sharp, however, one could make the argument that 11/10 functions a bit more like a narrowed [[10/9]] in light of its usage in such a capacity in systems like [[41edo]] and [[63edo]] where 11/10 and 10/9 are tempered together due to [[100/99]] being tempered out. Meanwhile, when tuned [[just]] or near-just, it not only has the very exotic melodic role of being almost exactly a third of [[4/3]], leading to [[4000/3993]] being [[Fudging\|fudged]] or [[tempered out]], but is also very close in size to a stack consisting of an [[apotome]] and [[33/32]], leading to the [[schisma]] being fudged or tempered out.		If tempered sharp, however, one could make the argument that 11/10 functions a bit more like a narrowed [[10/9]] in light of its usage in such a capacity in systems like [[41edo]] and [[63edo]] where 11/10 and 10/9 are tempered together due to [[100/99]] being tempered out.

			Meanwhile, when tuned [[just]] or near-just, it not only has the very exotic melodic role of being almost exactly a third of [[4/3]], leading to [[4000/3993]] being [[Fudging\|fudged]] or [[tempered out]], but is also very close in size to a stack consisting of an [[apotome]] and [[33/32]], leading to the [[schisma]] being fudged or tempered out.

	Assuming you go with either of the aforementioned options, keeping 11/10 distinct from 12/11 ensures that 11/10 has a way of bridging quartertone-based chords with more typical [[5-limit]] and [[Pythagorean tuning\|Pythagorean]] chords as a sort of step between notes, however, if you temper out [[121/120]], expect this ability to vanish.		Assuming you go with either of the aforementioned options, keeping 11/10 distinct from 12/11 ensures that 11/10 has a way of bridging quartertone-based chords with more typical [[5-limit]] and [[Pythagorean tuning\|Pythagorean]] chords as a sort of step between notes, however, if you temper out [[121/120]], expect this ability to vanish.

← Older revision		Revision as of 06:27, 24 December 2024
Line 7:		Line 7:
	'''11/10''', the '''large undecimal neutral second''' or '''undecimal submajor second''', is an interval favored by {{w\|Ptolemy}}. Depending on who you ask, this interval, on its own, is either considerably more or considerably less exotic than [[12/11]] or a number of other simple [[11-limit]] intervals.		'''11/10''', the '''large undecimal neutral second''' or '''undecimal submajor second''', is an interval favored by {{w\|Ptolemy}}. Depending on who you ask, this interval, on its own, is either considerably more or considerably less exotic than [[12/11]] or a number of other simple [[11-limit]] intervals.

	If tempered sharp, however, one could make the argument that 11/10 functions a bit more like a narrowed [[10/9]] in light of its usage in such a capacity in systems like [[41edo]] and [[63edo]] where 11/10 and 10/9 are tempered together due to [[100/99]] being tempered out.		If tempered sharp, however, one could make the argument that 11/10 functions a bit more like a narrowed [[10/9]] in light of its usage in such a capacity in systems like [[41edo]] and [[63edo]] where 11/10 and 10/9 are [[tempered]] together due to [[100/99]] being tempered out.

	Meanwhile, when tuned [[just]] or near-just, it not only has the very exotic melodic role of being almost exactly a third of [[4/3]], leading to [[4000/3993]] being [[Fudging\|fudged]] or [[tempered out]], but is also very close in size to a stack consisting of an [[apotome]] and [[33/32]], leading to the [[schisma]] being fudged or tempered out.		Meanwhile, when tuned [[just]] or near-just, it not only has the very exotic melodic role of being almost exactly a third of [[4/3]], leading to [[4000/3993]] being [[Fudging\|fudged]] or [[tempered out]], but is also very close in size to a stack consisting of an [[apotome]] and [[33/32]], leading to the [[schisma]] being fudged or tempered out.

	Assuming you go with either of the aforementioned options, keeping 11/10 distinct from 12/11 ensures that 11/10 has a way of bridging quartertone-based chords with more typical [[5-limit]] and [[Pythagorean tuning\|Pythagorean]] chords as a sort of step between notes, however, if you temper out [[121/120]], expect this ability to vanish.		Assuming you go with either of the aforementioned options, keeping 11/10 distinct from 12/11 ensures that 11/10 has a way of bridging [[quartertone]]-based chords with more typical [[5-limit]] and [[Pythagorean tuning\|Pythagorean]] chords as a sort of step between notes, however, if you temper out [[121/120]], expect this ability to vanish.

	11/10 is the [[octave-reduced]] form of [[11/5]], one of the three most [[concordant]] 11-limit intervals within the entire [[4/1\|first two octaves]] along with [[11/4]] and [[11/3]]. In any [[Octave equivalence\|octave-repeating]] tuning, a good approximation of 11/10 indicates a good approximation of 11/5. So, it could be argued that 11/10 is a high priority for any octave-repeating 11-limit tuning.		11/10 is the [[octave-reduced]] form of [[11/5]], one of the three most [[concordant]] 11-limit intervals within the entire [[4/1\|first two octaves]] along with [[11/4]] and [[11/3]]. In any [[Octave equivalence\|octave-repeating]] tuning, a good approximation of 11/10 indicates a good approximation of 11/5. So, it could be argued that 11/10 is a high priority for any octave-repeating 11-limit tuning.

← Older revision		Revision as of 22:55, 13 December 2024
Line 7:		Line 7:
	'''11/10''', the '''large undecimal neutral second''' or '''undecimal submajor second''', is an interval favored by {{w\|Ptolemy}}. Depending on who you ask, this interval, on its own, is either considerably more or considerably less exotic than [[12/11]] or a number of other simple [[11-limit]] intervals.		'''11/10''', the '''large undecimal neutral second''' or '''undecimal submajor second''', is an interval favored by {{w\|Ptolemy}}. Depending on who you ask, this interval, on its own, is either considerably more or considerably less exotic than [[12/11]] or a number of other simple [[11-limit]] intervals.

	If tempered sharp, however, one could make the argument that 11/10 functions a bit more like a narrowed [[10/9]] in light of its usage in such a capacity in systems like [[41edo]] and [[63edo]] where 11/10 and 10/9 are tempered together due to [[100/99]] being tempered out. Meanwhile, when tuned [[just]] or near-just, it not only has the very exotic melodic role of being almost exactly a third of [[4/3]], leading to [[4000/3993]] being [[Fudging\|fudged]] or [[tempered out]], but is also very close in size to a stack consisting of an [[apotome]] and [[33/32]], leading to the [[schisma]] being fudged or tempered out.		If tempered sharp, however, one could make the argument that 11/10 functions a bit more like a narrowed [[10/9]] in light of its usage in such a capacity in systems like [[41edo]] and [[63edo]] where 11/10 and 10/9 are tempered together due to [[100/99]] being tempered out.

			Meanwhile, when tuned [[just]] or near-just, it not only has the very exotic melodic role of being almost exactly a third of [[4/3]], leading to [[4000/3993]] being [[Fudging\|fudged]] or [[tempered out]], but is also very close in size to a stack consisting of an [[apotome]] and [[33/32]], leading to the [[schisma]] being fudged or tempered out.

	Assuming you go with either of the aforementioned options, keeping 11/10 distinct from 12/11 ensures that 11/10 has a way of bridging quartertone-based chords with more typical [[5-limit]] and [[Pythagorean tuning\|Pythagorean]] chords as a sort of step between notes, however, if you temper out [[121/120]], expect this ability to vanish.		Assuming you go with either of the aforementioned options, keeping 11/10 distinct from 12/11 ensures that 11/10 has a way of bridging quartertone-based chords with more typical [[5-limit]] and [[Pythagorean tuning\|Pythagorean]] chords as a sort of step between notes, however, if you temper out [[121/120]], expect this ability to vanish.