Father - Revision history

Vector at 01:14, 29 May 2026

2026-05-29T01:14:59Z

← Older revision		Revision as of 01:14, 29 May 2026
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	'''Father''' (3 & 5) is a very inaccurate exotemperament that makes 3:4:5 equidistant, in other words equating 5/4 and 4/3 to a single "fourth-third" interval (which the name 'Father' originates from). As a result, it serves as a simplification of 3:4:5-based ([[naiadic]]) harmony, in much the same way that [[Dicot (temperament)\|Dicot]] simplifies [[tertian harmony]] or [[Semaphore]] simplifies [[Chthonic harmony\|chthonic]] harmony.		'''Father''' (3 & 5) is a very inaccurate exotemperament that makes 3:4:5 equidistant, in other words equating 5/4 and 4/3 to a single "fourth-third" interval (which the name 'Father' originates from). As a result, it serves as a simplification of 3:4:5-based ([[naiadic]]) harmony, in much the same way that [[Dicot (temperament)\|Dicot]] simplifies [[tertian harmony]] or [[Semaphore]] simplifies [[Chthonic harmony\|chthonic]] harmony.

	Due to tempering out such a large and simple interval as 16/15, there is no accurate tuning for Father. One structurally justifiable tuning, somewhat equivalent to tuning Dicot's 5/4 to a perfect neutral third, involves splitting a just 5/3 in half, resulting in a fourth-third of 442 cents (or a fifth-sixth of 758 cents). However, as with Dicot, it is somewhat preferable to lean the tuning of the generator towards one of the two simple intervals it represents - as flat as about 400 cents to favor 5/4 (as in 3edo), or as sharp as about 480 cents to favor 4/3 (as in 5edo). Another notable tuning is the golden tuning, about 458 cents, which sets the logarithmic ratio of 4/3 and 3/2 to the golden ratio.		Due to tempering out such a large and simple interval as 16/15, there is no accurate tuning for Father. A sharper 5/4 implies a flatter 3/2, with the just tuning of 5/4 setting 3/2 to 8/5, and the just tuning of 3/2 setting 5/4 to 4/3. One structurally justifiable tuning, somewhat equivalent to tuning Dicot's 5/4 to a perfect neutral third, involves splitting a just 5/3 in half, resulting in a fourth-third of 442 cents (or a fifth-sixth of 758 cents). However, as with Dicot, it is somewhat preferable to lean the tuning of the generator towards one of the two simple intervals it represents - as flat as about 400 cents to favor 5/4 (as in 3edo), or as sharp as about 480 cents to favor 4/3 (as in 5edo). Another notable tuning is the golden tuning, about 458 cents, which sets the logarithmic ratio of 4/3 and 3/2 to the golden ratio.

	In the 5-limit, due to equating two reduced prime (sub)harmonics, it is found in a number of small edos; the simplest edo join, 1 & 2, is an extension of Father, meaning Father can be arguably seen as the simplest 'real' 5-limit temperament. The edo join that gives the best impression of its tuning range is 3 & 5.		In the 5-limit, due to equating two reduced prime (sub)harmonics, it is found in a number of small edos; the simplest edo join, 1 & 2, is an extension of Father, meaning Father can be arguably seen as the simplest 'real' 5-limit temperament. The edo join that gives the best impression of its tuning range is 3 & 5.
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	=== Melodic interpretation ===		=== Melodic interpretation ===
	Father can be thought of as replacing pairs of 5-limit JI intervals with "interordinal" intervals between them, having an interval (around 450 cents) that's 5/4~4/3, a 6/5~9/8 about 300 cents, an 8/5~3/2 of about 750 cents, a 5/3~16/9 of about 900 cents, and 15/8 being equated to the octave (meaning it might be beneficial to flatten the octave about 20-30 cents or so). ~~In this example above, it posseses a secret~~ 10/9 ~~tempered down~~ to 150 cents which ~~defines the difference between its intervals. Due to~~ the ~~new equivalences, a sharper "5/4" condemns a flatter "3/2" (~~the ~~same is true for for 6/5 ~ 9/8 and 5/3 ~ 16/9~~.)		Father can be thought of as replacing pairs of 5-limit JI intervals with "interordinal" intervals between them, having an interval (around 450 cents) that's 5/4~4/3, a 6/5~9/8 about 300 cents, an 8/5~3/2 of about 750 cents, a 5/3~16/9 of about 900 cents, and 15/8 being equated to the octave (meaning it might be beneficial to flatten the octave about 20-30 cents or so). 10/9 in father collapses to 32/27, which is set to about 150 cents in the above tuning, which is one of the more accurate products of the temperament.

	== Extensions ==		== Extensions ==

Inthar at 01:29, 28 May 2026

2026-05-28T01:29:35Z

← Older revision		Revision as of 01:29, 28 May 2026
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	In the 5-limit, due to equating two reduced prime (sub)harmonics, it is found in a number of small edos; the simplest edo join, 1 & 2, is an extension of Father, meaning Father can be arguably seen as the simplest 'real' 5-limit temperament. The edo join that gives the best impression of its tuning range is 3 & 5.		In the 5-limit, due to equating two reduced prime (sub)harmonics, it is found in a number of small edos; the simplest edo join, 1 & 2, is an extension of Father, meaning Father can be arguably seen as the simplest 'real' 5-limit temperament. The edo join that gives the best impression of its tuning range is 3 & 5.

	Another point of interest in father is its moment-of-symmetry scales. It is likely that Father was originally defined in order to give a simple JI interpretation to the [[oneirotonic]] scale, although there are also Father tunings that generate [[checkertonic]]..		Another point of interest in father is its moment-of-symmetry scales. It is likely that Father was originally defined in order to give a simple JI interpretation to the [[oneirotonic]] scale, although there are also Father tunings that generate [[checkertonic]].

	=== Melodic interpretation ===		=== Melodic interpretation ===

Kili: /* Melodic interpretation */

2026-05-27T15:56:13Z

Melodic interpretation

← Older revision		Revision as of 15:56, 27 May 2026
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	=== Melodic interpretation ===		=== Melodic interpretation ===
	Father can be thought of as replacing pairs of 5-limit JI intervals with "interordinal" intervals between them, having an interval (around 450 cents) that's 5/4~4/3, a 6/5~9/8 about 300 cents, an 8/5~3/2 of about 750 cents, a 5/3~16/9 of about 900 cents, and 15/8 being equated to the octave (meaning it might be beneficial to flatten the octave about 20-30 cents or so). Due to the new equivalences, a sharper "5/4" condemns a flatter "3/2" (the same is true for for 6/5 ~ 9/8 and 5/3 ~ 16/9)		Father can be thought of as replacing pairs of 5-limit JI intervals with "interordinal" intervals between them, having an interval (around 450 cents) that's 5/4~4/3, a 6/5~9/8 about 300 cents, an 8/5~3/2 of about 750 cents, a 5/3~16/9 of about 900 cents, and 15/8 being equated to the octave (meaning it might be beneficial to flatten the octave about 20-30 cents or so). In this example above, it posseses a secret 10/9 tempered down to 150 cents which defines the difference between its intervals. Due to the new equivalences, a sharper "5/4" condemns a flatter "3/2" (the same is true for for 6/5 ~ 9/8 and 5/3 ~ 16/9.)

	== Extensions ==		== Extensions ==

Kili: /* Melodic interpretation */

2026-05-27T12:57:16Z

Melodic interpretation

← Older revision		Revision as of 12:57, 27 May 2026
Line 5:		Line 5:
	In the 5-limit, due to equating two reduced prime (sub)harmonics, it is found in a number of small edos; the simplest edo join, 1 & 2, is an extension of Father, meaning Father can be arguably seen as the simplest 'real' 5-limit temperament. The edo join that gives the best impression of its tuning range is 3 & 5.		In the 5-limit, due to equating two reduced prime (sub)harmonics, it is found in a number of small edos; the simplest edo join, 1 & 2, is an extension of Father, meaning Father can be arguably seen as the simplest 'real' 5-limit temperament. The edo join that gives the best impression of its tuning range is 3 & 5.

	Another point of interest in father is its moment-of-symmetry scales. It is likely that Father was originally defined in order to give a simple JI interpretation to the [[oneirotonic]] scale, although there are also Father tunings that generate [[checkertonic]].		Another point of interest in father is its moment-of-symmetry scales. It is likely that Father was originally defined in order to give a simple JI interpretation to the [[oneirotonic]] scale, although there are also Father tunings that generate [[checkertonic]]..

	=== Melodic interpretation ===		=== Melodic interpretation ===
	Father can be thought of as replacing pairs of 5-limit JI intervals with "interordinal" intervals between them, having an interval (around 450 cents) that's 5/4~4/3, a 6/5~9/8 about 300 cents, an 8/5~3/2 of about 750 cents, a 5/3~16/9 of about 900 cents, and 15/8 being equated to the octave (meaning it might be beneficial to flatten the octave about 20-30 cents or so).		Father can be thought of as replacing pairs of 5-limit JI intervals with "interordinal" intervals between them, having an interval (around 450 cents) that's 5/4~4/3, a 6/5~9/8 about 300 cents, an 8/5~3/2 of about 750 cents, a 5/3~16/9 of about 900 cents, and 15/8 being equated to the octave (meaning it might be beneficial to flatten the octave about 20-30 cents or so). Due to the new equivalences, a sharper "5/4" condemns a flatter "3/2" (the same is true for for 6/5 ~ 9/8 and 5/3 ~ 16/9)

	== Extensions ==		== Extensions ==

Vector at 00:44, 27 May 2026

2026-05-27T00:44:55Z

@@ Line 9: / Line 9: @@
 === Melodic interpretation ===
 Father can be thought of as replacing pairs of 5-limit JI intervals with "interordinal" intervals between them, having an interval (around 450 cents) that's 5/4~4/3, a 6/5~9/8 about 300 cents, an 8/5~3/2 of about 750 cents, a 5/3~16/9 of about 900 cents, and 15/8 being equated to the octave (meaning it might be beneficial to flatten the octave about 20-30 cents or so).
 == Extensions ==

Vector at 00:44, 27 May 2026

2026-05-27T00:44:41Z

← Older revision		Revision as of 00:44, 27 May 2026
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	Another point of interest in father is its moment-of-symmetry scales. It is likely that Father was originally defined in order to give a simple JI interpretation to the [[oneirotonic]] scale, although there are also Father tunings that generate [[checkertonic]].		Another point of interest in father is its moment-of-symmetry scales. It is likely that Father was originally defined in order to give a simple JI interpretation to the [[oneirotonic]] scale, although there are also Father tunings that generate [[checkertonic]].

			=== Melodic interpretation ===
			Father can be thought of as replacing pairs of 5-limit JI intervals with "interordinal" intervals between them, having an interval (around 450 cents) that's 5/4~4/3, a 6/5~9/8 about 300 cents, an 8/5~3/2 of about 750 cents, a 5/3~16/9 of about 900 cents, and 15/8 being equated to the octave (meaning it might be beneficial to flatten the octave about 20-30 cents or so).

	== Melodic Meaning ==		== Melodic Meaning ==

Kili at 19:00, 26 May 2026

2026-05-26T19:00:28Z

← Older revision		Revision as of 19:00, 26 May 2026
Line 6:		Line 6:

	Another point of interest in father is its moment-of-symmetry scales. It is likely that Father was originally defined in order to give a simple JI interpretation to the [[oneirotonic]] scale, although there are also Father tunings that generate [[checkertonic]].		Another point of interest in father is its moment-of-symmetry scales. It is likely that Father was originally defined in order to give a simple JI interpretation to the [[oneirotonic]] scale, although there are also Father tunings that generate [[checkertonic]].

			== Melodic Meaning ==
			The obliteration of 16/15 has various obvious consequences for the development of melodies in Father Temparament---some of which are as follows.

			The 5/4 is conflated with the 4/3,

			The 6/5 is conflated with the 9/8,

			The 3/2 is conflated with the 8/5,

			The 5/3 is conflated with the 16/9,

			and the 15/8 is now 2/1.

	== Extensions ==		== Extensions ==

Kili: no one knows what chthonic harmony is so there has to be a link to the chthonic page

2026-05-04T17:11:14Z

no one knows what chthonic harmony is so there has to be a link to the chthonic page

← Older revision		Revision as of 17:11, 4 May 2026
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	'''Father''' (3 & 5) is a very inaccurate exotemperament that makes 3:4:5 equidistant, in other words equating 5/4 and 4/3 to a single "fourth-third" interval (which the name 'Father' originates from). As a result, it serves as a simplification of 3:4:5-based ([[naiadic]]) harmony, in much the same way that [[Dicot (temperament)\|Dicot]] simplifies tertian harmony or [[Semaphore]] simplifies chthonic harmony.		'''Father''' (3 & 5) is a very inaccurate exotemperament that makes 3:4:5 equidistant, in other words equating 5/4 and 4/3 to a single "fourth-third" interval (which the name 'Father' originates from). As a result, it serves as a simplification of 3:4:5-based ([[naiadic]]) harmony, in much the same way that [[Dicot (temperament)\|Dicot]] simplifies [[tertian harmony]] or [[Semaphore]] simplifies [[Chthonic harmony\|chthonic]] harmony.

	Due to tempering out such a large and simple interval as 16/15, there is no accurate tuning for Father. One structurally justifiable tuning, somewhat equivalent to tuning Dicot's 5/4 to a perfect neutral third, involves splitting a just 5/3 in half, resulting in a fourth-third of 442 cents (or a fifth-sixth of 758 cents). However, as with Dicot, it is somewhat preferable to lean the tuning of the generator towards one of the two simple intervals it represents - as flat as about 400 cents to favor 5/4 (as in 3edo), or as sharp as about 480 cents to favor 4/3 (as in 5edo). Another notable tuning is the golden tuning, about 458 cents, which sets the logarithmic ratio of 4/3 and 3/2 to the golden ratio.		Due to tempering out such a large and simple interval as 16/15, there is no accurate tuning for Father. One structurally justifiable tuning, somewhat equivalent to tuning Dicot's 5/4 to a perfect neutral third, involves splitting a just 5/3 in half, resulting in a fourth-third of 442 cents (or a fifth-sixth of 758 cents). However, as with Dicot, it is somewhat preferable to lean the tuning of the generator towards one of the two simple intervals it represents - as flat as about 400 cents to favor 5/4 (as in 3edo), or as sharp as about 480 cents to favor 4/3 (as in 5edo). Another notable tuning is the golden tuning, about 458 cents, which sets the logarithmic ratio of 4/3 and 3/2 to the golden ratio.

Inthar at 02:01, 6 March 2026

2026-03-06T02:01:27Z

← Older revision		Revision as of 02:01, 6 March 2026
Line 1:		Line 1:
	'''Father''' (3 & 5) is a very inaccurate exotemperament that makes 3:4:5 equidistant, in other words equating 5/4 and 4/3 to a single "fourth-third" interval (which the name '~~father~~' originates from). As a result, it serves as a simplification of 3:4:5-based ([[naiadic]]) harmony, in much the same way that [[Dicot (temperament)\|Dicot]] simplifies tertian harmony or [[Semaphore]] simplifies chthonic harmony.		'''Father''' (3 & 5) is a very inaccurate exotemperament that makes 3:4:5 equidistant, in other words equating 5/4 and 4/3 to a single "fourth-third" interval (which the name 'Father' originates from). As a result, it serves as a simplification of 3:4:5-based ([[naiadic]]) harmony, in much the same way that [[Dicot (temperament)\|Dicot]] simplifies tertian harmony or [[Semaphore]] simplifies chthonic harmony.

	Due to tempering out such a large and simple interval as 16/15, there is no accurate tuning for Father. One structurally justifiable tuning, somewhat equivalent to tuning Dicot's 5/4 to a perfect neutral third, involves splitting a just 5/3 in half, resulting in a fourth-third of 442 cents (or a fifth-sixth of 758 cents). However, as with Dicot, it is somewhat preferable to lean the tuning of the generator towards one of the two simple intervals it represents - as flat as about 400 cents to favor 5/4 (as in 3edo), or as sharp as about 480 cents to favor 4/3 (as in 5edo). Another notable tuning is the golden tuning, about 458 cents, which sets the logarithmic ratio of 4/3 and 3/2 to the golden ratio.		Due to tempering out such a large and simple interval as 16/15, there is no accurate tuning for Father. One structurally justifiable tuning, somewhat equivalent to tuning Dicot's 5/4 to a perfect neutral third, involves splitting a just 5/3 in half, resulting in a fourth-third of 442 cents (or a fifth-sixth of 758 cents). However, as with Dicot, it is somewhat preferable to lean the tuning of the generator towards one of the two simple intervals it represents - as flat as about 400 cents to favor 5/4 (as in 3edo), or as sharp as about 480 cents to favor 4/3 (as in 5edo). Another notable tuning is the golden tuning, about 458 cents, which sets the logarithmic ratio of 4/3 and 3/2 to the golden ratio.

Inthar: /* Comparison to other temperaments */

2026-03-06T01:06:32Z

Comparison to other temperaments

← Older revision		Revision as of 01:06, 6 March 2026
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	== Comparison to other temperaments ==		== Comparison to other temperaments ==
	Father is distinct from temperaments such as [[Blackwood]] (5 & 15), [[Trienstonian]] (5 & 18), and [[Fendo]] (5 & 7, 2.3.13/5) that equate other major thirds to 4/3 and that are generally more accurate. It is also distinct from more accurate [[oneirotonic]] temperaments such as [[A-Team]] that are not generated by 4/3, and from the temperament-agnostic [[Golden generator\|golden tuning]].		Father is distinct from temperaments such as [[Blackwood]] (5 & 15), [[Trienstonian]] (5 & 18), and [[Fendo]] (5 & 7, 2.3.13/5) that equate other major thirds to 4/3 and that are generally more accurate. It is also distinct from more accurate [[oneirotonic]] temperaments such as [[A-Team]] that are not generated by 4/3, and from the temperament-agnostic [[Golden generator\|golden tuning]].

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