MOS step ratio spectrum - Revision history

Inthar: shorter title

2021-06-04T18:46:13Z

shorter title

← Older revision		Revision as of 18:46, 4 June 2021
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	~~The melodic sound of a~~ [[MOS]] is not just affected by the tuning of its intervals, but by the sizes of its steps. MOSes with L more similar to s sound smoother and more mellow. MOSes with L much larger than s sound jagged and dramatic. The '''step ratio''', the ratio between the sizes of L and s, is thus important to the sound of the scale. The step ratio has also been called '''Blackwood's R''', after Easley Blackwood who described it for diatonic mosses.		#redirect [[Step ratio]]

	~~== Relative interval sizes ==~~

	Part of this perception stems from the fact that, as these L:s ratios change and pass certain critical rational values, the next MOS in the sequence changes structure entirely. For instance, when we have L:s > 2, the next MOS changes from "xLys" to "yLxs." As an example, with the "5L2s" diatonic MOS, if we have L/s < 2, the next MOS will be "7L5s," and if we have L/s > 2, the next MOS will be "5L7s." (At the point L/s = 2, we have that the next MOS is an equal temperament.)

	~~Similar things happen with all of these rational points. As the L:s~~ ratio decreases and passes 3/2, for instance, the MOS that is two steps after the current one changes. Again, as an example, with the familiar 5L2s diatonic MOS sequence, if we have 3:2 < L:s < 2:1, the next two MOS's have 19 and 31 notes, whereas if we have L:s < 3:2, the next two MOS's have 19 and 26 notes.

	~~Another way to look at this is using [[Rothenberg propriety~~]]: it so happens that, with one small exception, if a MOS has L:s < 2:1, it is "strictly proper", if it has L:s > 2:1, it is "improper", and if it has L:s = 2:1, it is "proper," all using Rothenberg's definition. The one exception is if the MOS has a single small step (e.g. it is of the form xL1s), at which point it is always "strictly proper." Similarly we pass the L:s 3:2 boundary, the next MOS changes from strictly proper to improper, and so on.

	~~The special ratio L:s = phi is unique in that it is the only ratio in which the MOS is strictly proper, and all of the following MOS's are also strictly proper.~~

	~~== TAMNAMS naming system for step ratios ==~~
	~~:{{main\|TAMNAMS#Step ratio spectrum}}~~

Inthar at 18:45, 4 June 2021

2021-06-04T18:45:37Z

← Older revision		Revision as of 18:45, 4 June 2021
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	The melodic sound of a [[MOS]] is not just affected by the tuning of its intervals, but by the sizes of its steps. MOSes with L more similar to s sound smoother and more mellow. MOSes with L much larger than s sound jagged and dramatic. The ''step ratio'', the ratio between the sizes of L and s, is thus important to the sound of the scale. The step ratio has also been called '''Blackwood's R''', after Easley Blackwood who described it for diatonic mosses.		The melodic sound of a [[MOS]] is not just affected by the tuning of its intervals, but by the sizes of its steps. MOSes with L more similar to s sound smoother and more mellow. MOSes with L much larger than s sound jagged and dramatic. The '''step ratio''', the ratio between the sizes of L and s, is thus important to the sound of the scale. The step ratio has also been called '''Blackwood's R''', after Easley Blackwood who described it for diatonic mosses.

	== Relative interval sizes ==		== Relative interval sizes ==

Inthar at 18:45, 4 June 2021

2021-06-04T18:45:22Z

← Older revision		Revision as of 18:45, 4 June 2021
Line 1:		Line 1:
	The melodic sound of a [[MOS]] is not just affected by the tuning of its intervals, but by the sizes of its steps. MOSes with L more similar to s sound smoother and more mellow. MOSes with L much larger than s sound jagged and dramatic. The ''step ratio'', the ratio between the sizes of L and s, is thus important to the sound of the scale.		The melodic sound of a [[MOS]] is not just affected by the tuning of its intervals, but by the sizes of its steps. MOSes with L more similar to s sound smoother and more mellow. MOSes with L much larger than s sound jagged and dramatic. The ''step ratio'', the ratio between the sizes of L and s, is thus important to the sound of the scale. The step ratio has also been called '''Blackwood's R''', after Easley Blackwood who described it for diatonic mosses.

	== Relative interval sizes ==		== Relative interval sizes ==

Inthar: /* TAMNAMS naming system for step ratios */

2021-04-16T02:32:19Z

TAMNAMS naming system for step ratios

Show changes

Inthar at 02:20, 16 April 2021

2021-04-16T02:20:58Z

← Older revision		Revision as of 02:20, 16 April 2021
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	The two extremes, equalized and paucitonic, are degenerate cases. An equalized MOS has L equal to s, so the MOS pattern is no longer apparent. A paucitonic MOS has s = 0, merging adjacent tones s apart into a single tone. In both cases, the MOS structure is no longer valid.		The two extremes, equalized and paucitonic, are degenerate cases. An equalized MOS has L equal to s, so the MOS pattern is no longer apparent. A paucitonic MOS has s = 0, merging adjacent tones s apart into a single tone. In both cases, the MOS structure is no longer valid.

	In between the nine specific ratios there are eight ranges of ratios. Each range has a name. These names are useful for classifying MOS tunings which don't match any of the nine simple step ratios. ''Hypohard'' could be used for tunings that are harder than basic but not as hard as the 3:1 tuning; similarly, ''hyposoft'' can be used for the range between soft and basic. Finally, there is ''~~kiki~~'' and ''~~bouba~~'' for the whole 'hard-of-basic' range and the whole 'soft-of-basic' range,respectively ~~(to minimize confusion with ''hard'' = exactly 3:1 and ''soft'' = exactly 3:2)~~.		In between the nine specific ratios there are eight ranges of ratios. Each range has a name. These names are useful for classifying MOS tunings which don't match any of the nine simple step ratios. ''Hypohard'' could be used for tunings that are harder than basic but not as hard as the 3:1 tuning; similarly, ''hyposoft'' can be used for the range between soft and basic. Finally, there is ''pan-hard'' and ''pan-soft'' for the whole 'hard-of-basic' range and the whole 'soft-of-basic' range,respectively.

	By default, all ranges include their endpoints. For example, a hard tuning is considered a quasihard tuning. To exclude endpoints, the modifier "strict" can be used, for example "strict hyposoft".		By default, all ranges include their endpoints. For example, a hard tuning is considered a quasihard tuning. To exclude endpoints, the modifier "strict" can be used, for example "strict hyposoft".
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	!Range		!Range
	\|-		\|-
	\|~~Bouba~~		\|Pansoft
	\|1:1 ≤ L:s ≤ 2:1		\|1:1 ≤ L:s ≤ 2:1
	\|-		\|-
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	\|4:1 ≤ L:s ≤ 1:0		\|4:1 ≤ L:s ≤ 1:0
	\|-		\|-
	\|~~Kiki~~		\|Panhard
	\|2:1 ≤ L:s ≤ 1:0		\|2:1 ≤ L:s ≤ 1:0
	\|}		\|}

Inthar: /* Ratio spectrum */

2021-04-16T02:19:35Z

Ratio spectrum

← Older revision		Revision as of 02:19, 16 April 2021
Line 69:		Line 69:
	!Range		!Range
	\|-		\|-
	\|~~bouba~~		\|Bouba
	\|1:1 ≤ L:s ≤ 2:1		\|1:1 ≤ L:s ≤ 2:1
	\|-		\|-

Inthar: /* Ratio spectrum */

2021-04-16T02:19:13Z

Ratio spectrum

← Older revision		Revision as of 02:19, 16 April 2021
Line 61:		Line 61:
	The two extremes, equalized and paucitonic, are degenerate cases. An equalized MOS has L equal to s, so the MOS pattern is no longer apparent. A paucitonic MOS has s = 0, merging adjacent tones s apart into a single tone. In both cases, the MOS structure is no longer valid.		The two extremes, equalized and paucitonic, are degenerate cases. An equalized MOS has L equal to s, so the MOS pattern is no longer apparent. A paucitonic MOS has s = 0, merging adjacent tones s apart into a single tone. In both cases, the MOS structure is no longer valid.

	In between the nine specific ratios there are eight ranges of ratios. Each range has a name. These names are useful for classifying MOS tunings which don't match any of the nine simple step ratios. ''Hypohard'' could be used for tunings that are harder than basic but not as hard as the 3:1 tuning; similarly, ''hyposoft'' can be used for the range between soft and basic. Finally, there is ''~~pan-hard~~'' and ''~~pan-soft~~'' for the whole 'hard-of-basic' range and the whole 'soft-of-basic' range,respectively.		In between the nine specific ratios there are eight ranges of ratios. Each range has a name. These names are useful for classifying MOS tunings which don't match any of the nine simple step ratios. ''Hypohard'' could be used for tunings that are harder than basic but not as hard as the 3:1 tuning; similarly, ''hyposoft'' can be used for the range between soft and basic. Finally, there is ''kiki'' and ''bouba'' for the whole 'hard-of-basic' range and the whole 'soft-of-basic' range,respectively (to minimize confusion with ''hard'' = exactly 3:1 and ''soft'' = exactly 3:2).

	By default, all ranges include their endpoints. For example, a hard tuning is considered a quasihard tuning. To exclude endpoints, the modifier "strict" can be used, for example "strict hyposoft".		By default, all ranges include their endpoints. For example, a hard tuning is considered a quasihard tuning. To exclude endpoints, the modifier "strict" can be used, for example "strict hyposoft".
Line 69:		Line 69:
	!Range		!Range
	\|-		\|-
	\|~~Pansoft~~		\|bouba
	\|1:1 ≤ L:s ≤ 2:1		\|1:1 ≤ L:s ≤ 2:1
	\|-		\|-
Line 96:		Line 96:
	\|4:1 ≤ L:s ≤ 1:0		\|4:1 ≤ L:s ≤ 1:0
	\|-		\|-
	\|~~Panhard~~		\|Kiki
	\|2:1 ≤ L:s ≤ 1:0		\|2:1 ≤ L:s ≤ 1:0
	\|}		\|}

Inthar: /* Ratio spectrum */ Added new panhard and pansoft ranges

2021-04-16T01:58:50Z

Ratio spectrum: Added new panhard and pansoft ranges

← Older revision		Revision as of 01:58, 16 April 2021
Line 61:		Line 61:
	The two extremes, equalized and paucitonic, are degenerate cases. An equalized MOS has L equal to s, so the MOS pattern is no longer apparent. A paucitonic MOS has s = 0, merging adjacent tones s apart into a single tone. In both cases, the MOS structure is no longer valid.		The two extremes, equalized and paucitonic, are degenerate cases. An equalized MOS has L equal to s, so the MOS pattern is no longer apparent. A paucitonic MOS has s = 0, merging adjacent tones s apart into a single tone. In both cases, the MOS structure is no longer valid.

	In between the nine specific ratios there are eight ranges of ratios. Each range has a name. These names are useful for classifying MOS tunings which don't match any of the nine simple step ratios. ''Hypohard'' could be used for tunings that are harder than basic but not as hard as the 3:1 tuning; similarly, ''hyposoft'' can be used for the range between soft and basic.		In between the nine specific ratios there are eight ranges of ratios. Each range has a name. These names are useful for classifying MOS tunings which don't match any of the nine simple step ratios. ''Hypohard'' could be used for tunings that are harder than basic but not as hard as the 3:1 tuning; similarly, ''hyposoft'' can be used for the range between soft and basic. Finally, there is ''pan-hard'' and ''pan-soft'' for the whole 'hard-of-basic' range and the whole 'soft-of-basic' range,respectively.

	By default, all ranges include their endpoints. For example, a hard tuning is considered a quasihard tuning. To exclude endpoints, the modifier "strict" can be used, for example "strict hyposoft".		By default, all ranges include their endpoints. For example, a hard tuning is considered a quasihard tuning. To exclude endpoints, the modifier "strict" can be used, for example "strict hyposoft".
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	!TAMNAMS Name		!TAMNAMS Name
	!Range		!Range
			\|-
			\|Pansoft
			\|1:1 ≤ L:s ≤ 2:1
	\|-		\|-
	\|Ultrasoft		\|Ultrasoft
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	\|Ultrahard		\|Ultrahard
	\|4:1 ≤ L:s ≤ 1:0		\|4:1 ≤ L:s ≤ 1:0
			\|-
			\|Panhard
			\|2:1 ≤ L:s ≤ 1:0
	\|}		\|}

Inthar: /* TAMNAMS naming system for step ratios */

2021-04-14T21:32:23Z

TAMNAMS naming system for step ratios

← Older revision		Revision as of 21:32, 14 April 2021
Line 14:		Line 14:

	=== Ratio spectrum ===		=== Ratio spectrum ===
			The [[TAMNAMS]] system names nine specific simple L:s ratios.
	~~We in the discord have named~~ nine specific simple L:s ratios.
	{\| class="wikitable"		{\| class="wikitable"
	\|+Step ratio names		\|+Step ratio names

Inthar: using wikipedia styling

2021-04-14T21:29:49Z

using wikipedia styling

← Older revision		Revision as of 21:29, 14 April 2021
Line 1:		Line 1:
	The melodic sound of a [[MOS]] is not just affected by the tuning of its intervals, but by the sizes of its steps. MOSes with L more similar to s sound smoother and more mellow. MOSes with L much larger than s sound jagged and dramatic. The ''step ratio'', the ratio between the sizes of L and s, is thus important to the sound of the scale.		The melodic sound of a [[MOS]] is not just affected by the tuning of its intervals, but by the sizes of its steps. MOSes with L more similar to s sound smoother and more mellow. MOSes with L much larger than s sound jagged and dramatic. The ''step ratio'', the ratio between the sizes of L and s, is thus important to the sound of the scale.

	= Relative interval sizes =		== Relative interval sizes ==

	Part of this perception stems from the fact that, as these L:s ratios change and pass certain critical rational values, the next MOS in the sequence changes structure entirely. For instance, when we have L:s > 2, the next MOS changes from "xLys" to "yLxs." As an example, with the "5L2s" diatonic MOS, if we have L/s < 2, the next MOS will be "7L5s," and if we have L/s > 2, the next MOS will be "5L7s." (At the point L/s = 2, we have that the next MOS is an equal temperament.)		Part of this perception stems from the fact that, as these L:s ratios change and pass certain critical rational values, the next MOS in the sequence changes structure entirely. For instance, when we have L:s > 2, the next MOS changes from "xLys" to "yLxs." As an example, with the "5L2s" diatonic MOS, if we have L/s < 2, the next MOS will be "7L5s," and if we have L/s > 2, the next MOS will be "5L7s." (At the point L/s = 2, we have that the next MOS is an equal temperament.)
Line 11:		Line 11:
	The special ratio L:s = phi is unique in that it is the only ratio in which the MOS is strictly proper, and all of the following MOS's are also strictly proper.		The special ratio L:s = phi is unique in that it is the only ratio in which the MOS is strictly proper, and all of the following MOS's are also strictly proper.

	= TAMNAMS naming system for step ratios =		== TAMNAMS naming system for step ratios ==

	== Ratio spectrum ==		=== Ratio spectrum ===

	We in the discord have named nine specific simple L:s ratios.		We in the discord have named nine specific simple L:s ratios.