FKH Extended-diatonic Interval Names - Revision history

Lériendil: retroactive shefkhed

2025-04-09T14:36:13Z

retroactive shefkhed

← Older revision		Revision as of 14:36, 9 April 2025
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	FKH (Fokker/Keenan/Hearne) Extended-diatonic Interval Names is a diatonic-based system for interval naming developed after [[Extended-diatonic interval names\|a review of the historical development of Western interval names, and of current proposed schemes]], taking the best and leaving alone the worst aspects of the existing standards. In addition to the standard diatonic interval name qualifiers - 'M', 'm', 'P', 'A' and 'd', the three most commonly used microtonal qualifies, 'N', 'S' and 's' are used, along with interval-class degrees and the additional qualifiers 'k' and 'K'. Using this scheme almost all small to medium sized [[Equal Temperaments\|equal temperaments]] (ETs) can be named such that 'S' and 's' and/or 'K' and 'k' correspond to a displacement of an interval up or down a single degree of the ET, respectively. With the addition of two more qualifiers, 'W' and 'n', FKH can name all intervals from all edos. Many commonly used [[MOS scale\|MOS scales]] may also be described using this scheme such that these scales' interval names are expressed consistently in in any tuning that supports them. The scheme, which can also be easily mapped to many of the current interval naming standards, facilitating translation between them, should improve pedagogy and communication in microtonal music.		'''FKH (Fokker/Keenan/Hearne) Extended-diatonic Interval Names''' (formerly known as '''SHEFKHED Interval Names''') is a [[diatonic]]-based system for interval naming developed after [[Extended-diatonic interval names\|a review of the historical development of Western interval names, and of current proposed schemes]], taking the best and leaving alone the worst aspects of the existing standards. In addition to the standard diatonic interval name qualifiers - 'M', 'm', 'P', 'A' and 'd', the three most commonly used microtonal qualifies, 'N', 'S' and 's' are used, along with interval-class degrees and the additional qualifiers 'k' and 'K' (formerly 'c' and 'C'). Using this scheme almost all small to medium sized [[Equal Temperaments\|equal temperaments]] (ETs) can be named such that 'S' and 's' and/or 'K' and 'k' correspond to a displacement of an interval up or down a single degree of the ET, respectively. With the addition of two more qualifiers, 'W' and 'n', FKH can name all intervals from all edos. Many commonly used [[MOS scale\|MOS scales]] may also be described using this scheme such that these scales' interval names are expressed consistently in in any tuning that supports them. The scheme, which can also be easily mapped to many of the current interval naming standards, facilitating translation between them, should improve pedagogy and communication in microtonal music.

	After feedback, the author ([[User:Lhearne]]) has since updated this scheme as [[SKULO interval names#WOFED interval names\|WOFED interval names]], and the later re-imagining [[SKULO interval names]].		After feedback, the author ([[User:Lhearne]]) has since updated this scheme as [[SKULO interval names#WOFED interval names\|WOFED interval names]], and the later re-imagining [[SKULO interval names]].

Lhearne: added reference and links in first paragraph to updates of this scheme

2024-03-18T11:06:04Z

added reference and links in first paragraph to updates of this scheme

← Older revision		Revision as of 11:06, 18 March 2024
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	FKH (Fokker/Keenan/Hearne) Extended-diatonic Interval Names is a diatonic-based system for interval naming developed after [[Extended-diatonic interval names\|a review of the historical development of Western interval names, and of current proposed schemes]], taking the best and leaving alone the worst aspects of the existing standards. In addition to the standard diatonic interval name qualifiers - 'M', 'm', 'P', 'A' and 'd', the three most commonly used microtonal qualifies, 'N', 'S' and 's' are used, along with interval-class degrees and the additional qualifiers 'k' and 'K'. Using this scheme almost all small to medium sized [[Equal Temperaments\|equal temperaments]] (ETs) can be named such that 'S' and 's' and/or 'K' and 'k' correspond to a displacement of an interval up or down a single degree of the ET, respectively. With the addition of two more qualifiers, 'W' and 'n', FKH can name all intervals from all edos. Many commonly used [[MOS scale\|MOS scales]] may also be described using this scheme such that these scales' interval names are expressed consistently in in any tuning that supports them. The scheme, which can also be easily mapped to many of the current interval naming standards, facilitating translation between them, should improve pedagogy and communication in microtonal music.		FKH (Fokker/Keenan/Hearne) Extended-diatonic Interval Names is a diatonic-based system for interval naming developed after [[Extended-diatonic interval names\|a review of the historical development of Western interval names, and of current proposed schemes]], taking the best and leaving alone the worst aspects of the existing standards. In addition to the standard diatonic interval name qualifiers - 'M', 'm', 'P', 'A' and 'd', the three most commonly used microtonal qualifies, 'N', 'S' and 's' are used, along with interval-class degrees and the additional qualifiers 'k' and 'K'. Using this scheme almost all small to medium sized [[Equal Temperaments\|equal temperaments]] (ETs) can be named such that 'S' and 's' and/or 'K' and 'k' correspond to a displacement of an interval up or down a single degree of the ET, respectively. With the addition of two more qualifiers, 'W' and 'n', FKH can name all intervals from all edos. Many commonly used [[MOS scale\|MOS scales]] may also be described using this scheme such that these scales' interval names are expressed consistently in in any tuning that supports them. The scheme, which can also be easily mapped to many of the current interval naming standards, facilitating translation between them, should improve pedagogy and communication in microtonal music.

			After feedback, the author ([[User:Lhearne]]) has since updated this scheme as [[SKULO interval names#WOFED interval names\|WOFED interval names]], and the later re-imagining [[SKULO interval names]].

	==Introduction==		==Introduction==

Lhearne at 10:56, 18 March 2024

2024-03-18T10:56:52Z

← Older revision		Revision as of 10:56, 18 March 2024
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	''FKH (Fokker/Keenan/Hearne) Extended-diatonic Interval Names'' is a diatonic-based system for interval naming developed after [[Extended-diatonic interval names\|a review of the historical development of Western interval names, and of current proposed schemes]], taking the best and leaving alone the worst aspects of the existing standards. In addition to the standard diatonic interval name qualifiers - 'M', 'm', 'P', 'A' and 'd', the three most commonly used microtonal qualifies, 'N', 'S' and 's' are used, along with interval-class degrees and the additional qualifiers 'k' and 'K'. Using this scheme almost all small to medium sized [[Equal Temperaments\|equal temperaments]] (ETs) can be named such that 'S' and 's' and/or 'K' and 'k' correspond to a displacement of an interval up or down a single degree of the ET, respectively. With the addition of two more qualifiers, 'W' and 'n', FKH can name all intervals from all edos. Many commonly used [[MOS scale\|MOS scales]] may also be described using this scheme such that these scales' interval names are expressed consistently in in any tuning that supports them. The scheme, which can also be easily mapped to many of the current interval naming standards, facilitating translation between them, should improve pedagogy and communication in microtonal music.		FKH (Fokker/Keenan/Hearne) Extended-diatonic Interval Names is a diatonic-based system for interval naming developed after [[Extended-diatonic interval names\|a review of the historical development of Western interval names, and of current proposed schemes]], taking the best and leaving alone the worst aspects of the existing standards. In addition to the standard diatonic interval name qualifiers - 'M', 'm', 'P', 'A' and 'd', the three most commonly used microtonal qualifies, 'N', 'S' and 's' are used, along with interval-class degrees and the additional qualifiers 'k' and 'K'. Using this scheme almost all small to medium sized [[Equal Temperaments\|equal temperaments]] (ETs) can be named such that 'S' and 's' and/or 'K' and 'k' correspond to a displacement of an interval up or down a single degree of the ET, respectively. With the addition of two more qualifiers, 'W' and 'n', FKH can name all intervals from all edos. Many commonly used [[MOS scale\|MOS scales]] may also be described using this scheme such that these scales' interval names are expressed consistently in in any tuning that supports them. The scheme, which can also be easily mapped to many of the current interval naming standards, facilitating translation between them, should improve pedagogy and communication in microtonal music.

	==Introduction==		==Introduction==

Lhearne: copied text from Intro from SHEFKHED page which is almost exactly the same but has had some small edits made.

2024-03-18T10:50:10Z

copied text from Intro from SHEFKHED page which is almost exactly the same but has had some small edits made.

Show changes

Fredg999 category edits: Moving from Category:Naming to Category:Interval naming using Cat-a-lot

2023-05-29T04:21:33Z

Moving from Category:Naming to Category:Interval naming using Cat-a-lot

← Older revision		Revision as of 04:21, 29 May 2023
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	P1 S1 1-2 Km2 kM2 2-3 Km3 kM3 3-4 s4 P4 S4 s5 P5 S5 5-6 Km6 kM6 6-7 Km7 kM7 7-8 s8 P8, from which we can see it is a Barbados tuning.		P1 S1 1-2 Km2 kM2 2-3 Km3 kM3 3-4 s4 P4 S4 s5 P5 S5 5-6 Km6 kM6 6-7 Km7 kM7 7-8 s8 P8, from which we can see it is a Barbados tuning.
	[[Category:~~Naming~~]]		[[Category:Interval naming]]
	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave]]

BudjarnLambeth: Categorised this uncategorised page

2023-04-25T12:06:51Z

Categorised this uncategorised page

← Older revision		Revision as of 12:06, 25 April 2023
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	P1 S1 1-2 Km2 kM2 2-3 Km3 kM3 3-4 s4 P4 S4 s5 P5 S5 5-6 Km6 kM6 6-7 Km7 kM7 7-8 s8 P8, from which we can see it is a Barbados tuning.		P1 S1 1-2 Km2 kM2 2-3 Km3 kM3 3-4 s4 P4 S4 s5 P5 S5 5-6 Km6 kM6 6-7 Km7 kM7 7-8 s8 P8, from which we can see it is a Barbados tuning.
			[[Category:Naming]]
			[[Category:Equal divisions of the octave]]

Gareth.hearne: /* TUSK-INtervals */ this bit is an unfinished new idea, so I cut it off here and put it on a word doc

2018-10-22T15:47:06Z

TUSK-INtervals: this bit is an unfinished new idea, so I cut it off here and put it on a word doc

@@ Line 178: / Line 178: @@
 edo: P1 S1 sm2 m2 M2 SM2 sm3 m3 M3 SM3 s4 P4 A4 SA4/sd5 d5 P5 S5 sm6 m6 M6 SM6 sm7 m7 M7 SM7 s8 P8
-edo: P1 m2 N1 N2 kM2 M2 m3 Km3 N3 kM3 M3 P4 N4 skA4/Kd5 kA4/SKd5 N5 P5 m6 Km6 N6 kM6 M6 m7 Km7 N7 N8 M7 P8
+edo: P1 m2 hA1 N2 kM2 M2 m3 Km3 N3 kM3 M3 P4 hA4 skA4/Kd5 kA4/SKd5 hd5 P5 m6 Km6 N6 kM6 M6 m7 Km7 N7 hd8 M7 P8
 edo: P1 K1/S1/sm2 m2 Km2 kM2 M2 SM2/sm3 m3 Km3 kM3 M3 SM3/s4 P4 K4 kA4/d5 A4/Kd5 k5 P5 S5/sm6 m6 Km6 kM6 M6 SM6/sm7 m7 Km7 kM7 M7 SM7/S8/k8 P8
@@ Line 1,162: / Line 1,162: @@
 P1 S1 1-2 Km2 kM2 2-3 Km3 kM3 3-4 s4 P4 S4 s5 P5 S5 5-6 Km6 kM6 6-7 Km7 kM7 7-8 s8 P8, from which we can see it is a Barbados tuning.

Gareth.hearne at 15:12, 22 October 2018

2018-10-22T15:12:35Z

← Older revision		Revision as of 15:12, 22 October 2018
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	'''T'''ridecimal - 1053/1024, via T/t = turnt/tanked (greater/lesser tridecimal middle)		'''T'''ridecimal - 1053/1024, via T/t = turnt/tanked (greater/lesser tridecimal middle)

	'''U'''ndecimal - 99/98, via U/u = up/under		'''U'''ndecimal - 896/891, via U/u = up/under

	'''S'''eptimal - 64/63 via S/s = super/sub		'''S'''eptimal - 64/63 via S/s = super/sub
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	3/2 - P5, 5/4 - kM3, 7/4 - sm7, 9/8 - M2, 11/8 - hA4 or sud5 13/8 - Tm6, 15/8 - kM7		3/2 - P5, 5/4 - kM3, 7/4 - sm7, 9/8 - M2, 11/8 - hA4 or sud5 13/8 - Tm6, 15/8 - kM7

	5/3 - kM6, 7/6 - sm3, 11/6 - N7 or ~~su8~~, 13/12 - Tm2		5/3 - kM6, 7/6 - sm3, 11/6 - N7 or sud8, 13/12 - Tm2

	7/5 - sKd5, 11/10 - KN2 or sKud3, 9/5 - Km7, 13/10 - 3-4 or kTd4		7/5 - sKd5, 11/10 - KN2 or sKud3, 9/5 - Km7, 13/10 - 3-4 or kTd4
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	9/7 - SM3, 11/7 - um6 or shA5, 13/7 - STm7, 15/14 - SkA1		9/7 - SM3, 11/7 - um6 or shA5, 13/7 - STm7, 15/14 - SkA1

	11/9 - N3 or ~~su4~~, 13/9 - Td5,		11/9 - N3 or sud4, 13/9 - Td5,

			13/11 - Thd3 or TSUM2, 15/11 - khA4 or SkUA3

			15/13 - 2-3 or kM7 - Tm6 = tkA2

			well... it's possible! Neutrals and intermediates certainly help, when you look at the other options for some things...

	* k shifts 81/80, the syntonic comma, for classic or comma-wide/comma-narrow, to get 5/4		* k shifts 81/80, the syntonic comma, for classic or comma-wide/comma-narrow, to get 5/4

Gareth.hearne at 14:42, 22 October 2018

2018-10-22T14:42:13Z

← Older revision		Revision as of 14:42, 22 October 2018
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	There are edos whose best fifth is flatter even than 4\7. In such edos major intervals are smaller than minor intervals, augmented smaller than major and diminished larger than minor. We expand our definition of well-ordered intervals to include that within each degree... ≤ dd ≤ d ≤ m ≤ M ≤ A ≤ AA ≤ ... or ... ≤ dd ≤ d ≤ P ≤ A ≤ AA ≤ ..., and where sk _ ≤ s/k_ ≤ _ ≤ S/K_ ≤ SK _ (where '_' represents any of ... dd, d, m, (P), M, A, AA ...). In order to obtain well-ordered interval-name sets, we use enharmonic equivalences, replacing diatonic intervals with altered intervals.		There are edos whose best fifth is flatter even than 4\7. In such edos major intervals are smaller than minor intervals, augmented smaller than major and diminished larger than minor. We expand our definition of well-ordered intervals to include that within each degree... ≤ dd ≤ d ≤ m ≤ M ≤ A ≤ AA ≤ ... or ... ≤ dd ≤ d ≤ P ≤ A ≤ AA ≤ ..., and where sk _ ≤ s/k_ ≤ _ ≤ S/K_ ≤ SK _ (where '_' represents any of ... dd, d, m, (P), M, A, AA ...). In order to obtain well-ordered interval-name sets, we use enharmonic equivalences, replacing diatonic intervals with altered intervals.

	In super flat edos, the fifths are so flat that the major third, from four fifths approximates the classic minor third, 6/5 and the minor third approximates the classic major third, 5/4, tempering out 135/128, resulting in [[Mavila temperament]]. Mavila temperament can be defined in the 5-limit using the enharmonic equivalence ~~cla M~~ = m, where meantone can be defined by cM = M, and schismatic by cM''n'' = d''n+1'' (superpyth in 2.3.7 can be defined by SM = M). Mavila[7] 3\|3 reads the same as Meantone[7] 3\|3: P1 M2 m3 P4 P5 M6 m7 P8, however Mavila[9] 4\|4 has diatonic interval names:		In super flat edos, the fifths are so flat that the major third, from four fifths approximates the classic minor third, 6/5 and the minor third approximates the classic major third, 5/4, tempering out 135/128, resulting in [[Mavila temperament]]. Mavila temperament can be defined in the 5-limit using the enharmonic equivalence kM = m, where meantone can be defined by kM = M, and schismatic by kM''n'' = d''n+1'' (superpyth in 2.3.7 can be defined by SM = M). Mavila[7] 3\|3 reads the same as Meantone[7] 3\|3: P1 M2 m3 P4 P5 M6 m7 P8, however Mavila[9] 4\|4 has diatonic interval names:

	P1 M2 M3 m3 P4 P5 M6 m6 m7 P8.		P1 M2 M3 m3 P4 P5 M6 m6 m7 P8.
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	P1 M2 M3 m2 m3 P4 P5 M6 M7 m6 m7 P8.		P1 M2 M3 m2 m3 P4 P5 M6 M7 m6 m7 P8.

	Adding neutrals and applying enharmonic replacements our primary well-ordered interval names are:		Even though major is now below minor, we may still give the name 'neural' to an interval half way between major and minor with an interval class. Adding neutrals and applying enharmonic replacements our primary well-ordered interval names are:

	P1 Km2 N2 N3 kM3 P4 P5 Km6 N6 N7 kM7 P8, in which we can see Neutral[7] 3\|3.		P1 Km2 N2 N3 kM3 P4 P5 Km6 N6 N7 kM7 P8, in which we can see Neutral[7] 3\|3.

			Where 11edo's best fifth is 47c flat, most would not really call it a P5. Accordingly we may wish instead to label 11edo as every second step of 22edo, where we still get major seconds and thirds, and minor sixths and sevenths:

			P1 Km2 M2 Km3 M3 K4 k5 m6 kM6 m7 kM7 P8.

			Since this labeling is based on a much more accurate fifth, the interval names mach their size much more closely, e.g. using 11edo's fifth, 2\11 was labelled a N2, but at 218c, is much closer to a M2, as it is labeled using 22edo's fifth. Since 11edo is abnormally flat even for Mavila, I suggest labeling using 22edo's fifth.

	16edo has diatonic interval names:		16edo has diatonic interval names:

Gareth.hearne: /* Prefixes */

2018-10-22T12:54:28Z

Prefixes

← Older revision		Revision as of 12:54, 22 October 2018
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	*The unison is labelled P1 for perfect unison, and the octave P8 for perfect octave.		*The unison is labelled P1 for perfect unison, and the octave P8 for perfect octave.
	*A tuning's best approximation to 3/2 is labelled P5, for perfect fifth, and it's octave-complement labelled P4, for perfect fourth.		*A tuning's best approximation to 3/2 is labelled P5, for perfect fifth, and it's octave-complement labelled P4, for perfect fourth.
	*From the Pythagorean diatonic scale ~~using~~ a tuning's best 3/2 fifth, the two sizes of second, third, sixth and seventh are labelled major, or 'M', for the larger, and minor, or 'm' for the smaller.		*From the Pythagorean diatonic scale generated by a tuning's best 3/2 fifth, the two sizes of second, third, sixth and seventh are labelled major, or 'M', for the larger, and minor, or 'm' for the smaller.
	*Any perfect or major interval raised by the apotome, the interval between the major and minor intervals of a single interval-class is labelled 'A' for augmented, and any perfect or minor interval lowered by the same is labelled 'd' for diminished.		*Any perfect or major interval raised by the apotome, the interval between the major and minor intervals of a single interval-class is labelled 'A' for augmented, and any perfect or minor interval lowered by the same is labelled 'd' for diminished.
	*Any augmented interval may be made doubly augmented, with short-hand 'AA' by the further raising of an apotome and any diminished interval made doubly diminished, with short-hand 'dd' by the further lowering of an apotome. This process may be iterated ad nauseum. At this stage we have simply rigorously defined diatonic interval names. Thankfully what remains of the definition leads to more desirable alternatives for most occasions in which one might find these iteratively diminished and augmented intervals.		*Any augmented interval may be made doubly augmented, with short-hand 'AA' by the further raising of an apotome and any diminished interval made doubly diminished, with short-hand 'dd' by the further lowering of an apotome. This process may be iterated ad nauseum. At this stage we have simply rigorously defined diatonic interval names. Thankfully what remains of the definition leads to more desirable alternatives for most occasions in which one might find these iteratively diminished and augmented intervals.