User talk:Aura/Aura's Ideas on Tonality - Revision history

Aura at 19:17, 17 December 2020

2020-12-17T19:17:45Z

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	!\| Rastmic Name		!\| Rastmic Name
	\|-		\|-
	\| [[~~244~~/~~243~~]]		\| [[243/242]]
	\| [1 -5 0 0 2>		\| [1 -5 0 0 2>
	\| 7.139		\| 7.139

Aura at 17:54, 3 November 2020

2020-11-03T17:54:10Z

← Older revision		Revision as of 17:54, 3 November 2020
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	: "There should also be a simple process to get from the ratio to the name. Why are some ratios Alpharabian and some Betarabian? What simple test can be applied to say 729/704 to determine which category it falls into? What happens to the intervals that don't fit into either category?" The terms are "Alpharabian" and "Betarabian", and yes, there is a rudamentary test in place. Alpharabian intervals are generally either directly in the 2.11 subgroup, or, they differ from a nearby Pythagorean interval by either 33/32, 1331/1296, 8192/8019, 4096/3993, or 243/242. The system for denoting Betarabian intervals is less complete, but so far, Betarabian intervals usually differ from Alpharabian intervals by a rastma. When dealing with intervals that are distant by additionl rastmas, I would just use "Rastimic", "Birastmic", "Trirastmic", and so on.		: "There should also be a simple process to get from the ratio to the name. Why are some ratios Alpharabian and some Betarabian? What simple test can be applied to say 729/704 to determine which category it falls into? What happens to the intervals that don't fit into either category?" The terms are "Alpharabian" and "Betarabian", and yes, there is a rudamentary test in place. Alpharabian intervals are generally either directly in the 2.11 subgroup, or, they differ from a nearby Pythagorean interval by either 33/32, 1331/1296, 8192/8019, 4096/3993, or 243/242. The system for denoting Betarabian intervals is less complete, but so far, Betarabian intervals usually differ from Alpharabian intervals by a rastma. When dealing with intervals that are distant by additionl rastmas, I would just use "Rastimic", "Birastmic", "Trirastmic", and so on.

	: "As a practical matter, if some violinists or vocalists were performing 2.3.11 JI music, they would constantly be fudging the rastma. They might shift a pitch by 7¢, or let the tonic drift by 7¢. The neutral triad is an innate-comma chord (aka essentially tempered chord), and the 3rd might fall between 11/9 and 27/22. No listener would notice these slight discrepancies. The rastma would effectively be tempered out, and the notation could reflect this. Simply notate two notes only a rastma apart as the same note, and trust the performers' ears." On the contrary, I've met a music director who can hear a difference between 440 Hz and 438 Hz- a difference of less than 8¢, and I know that 7¢ is above the average JND, so performers fudging the rastma would likely drive this director batty ~~unless~~ it ~~actually accomplished something musically, such as~~ modulating to quartertone-based keys Jacob-Collier-style. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 11:03, 1 November 2020 (UTC)		: "As a practical matter, if some violinists or vocalists were performing 2.3.11 JI music, they would constantly be fudging the rastma. They might shift a pitch by 7¢, or let the tonic drift by 7¢. The neutral triad is an innate-comma chord (aka essentially tempered chord), and the 3rd might fall between 11/9 and 27/22. No listener would notice these slight discrepancies. The rastma would effectively be tempered out, and the notation could reflect this. Simply notate two notes only a rastma apart as the same note, and trust the performers' ears." On the contrary, I've met a music director who can hear a difference between 440 Hz and 438 Hz- a difference of less than 8¢, and I know that 7¢ is above the average JND, so performers fudging the rastma would likely drive this director batty. The main reason for me not tempering out the rastma is that it is useful in modulating to quartertone-based keys Jacob-Collier-style. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 11:03, 1 November 2020 (UTC)

Aura at 11:03, 1 November 2020

2020-11-01T11:03:23Z

← Older revision		Revision as of 11:03, 1 November 2020
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	: "There should also be a simple process to get from the ratio to the name. Why are some ratios Alpharabian and some Betarabian? What simple test can be applied to say 729/704 to determine which category it falls into? What happens to the intervals that don't fit into either category?" The terms are "Alpharabian" and "Betarabian", and yes, there is a rudamentary test in place. Alpharabian intervals are generally either directly in the 2.11 subgroup, or, they differ from a nearby Pythagorean interval by either 33/32, 1331/1296, 8192/8019, 4096/3993, or 243/242. The system for denoting Betarabian intervals is less complete, but so far, Betarabian intervals usually differ from Alpharabian intervals by a rastma. When dealing with intervals that are distant by additionl rastmas, I would just use "Rastimic", "Birastmic", "Trirastmic", and so on.		: "There should also be a simple process to get from the ratio to the name. Why are some ratios Alpharabian and some Betarabian? What simple test can be applied to say 729/704 to determine which category it falls into? What happens to the intervals that don't fit into either category?" The terms are "Alpharabian" and "Betarabian", and yes, there is a rudamentary test in place. Alpharabian intervals are generally either directly in the 2.11 subgroup, or, they differ from a nearby Pythagorean interval by either 33/32, 1331/1296, 8192/8019, 4096/3993, or 243/242. The system for denoting Betarabian intervals is less complete, but so far, Betarabian intervals usually differ from Alpharabian intervals by a rastma. When dealing with intervals that are distant by additionl rastmas, I would just use "Rastimic", "Birastmic", "Trirastmic", and so on.

	: "As a practical matter, if some violinists or vocalists were performing 2.3.11 JI music, they would constantly be fudging the rastma. They might shift a pitch by 7¢, or let the tonic drift by 7¢. The neutral triad is an innate-comma chord (aka essentially tempered chord), and the 3rd might fall between 11/9 and 27/22. No listener would notice these slight discrepancies. The rastma would effectively be tempered out, and the notation could reflect this. Simply notate two notes only a rastma apart as the same note, and trust the performers' ears." On the contrary, I've met a music director who can hear a difference between 440 Hz and 438 Hz- a difference of less than 8¢, and I know that 7¢ is above the average JND, so performers fudging the rastma would likely drive this director batty. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 10:19, 1 November 2020 (UTC)		: "As a practical matter, if some violinists or vocalists were performing 2.3.11 JI music, they would constantly be fudging the rastma. They might shift a pitch by 7¢, or let the tonic drift by 7¢. The neutral triad is an innate-comma chord (aka essentially tempered chord), and the 3rd might fall between 11/9 and 27/22. No listener would notice these slight discrepancies. The rastma would effectively be tempered out, and the notation could reflect this. Simply notate two notes only a rastma apart as the same note, and trust the performers' ears." On the contrary, I've met a music director who can hear a difference between 440 Hz and 438 Hz- a difference of less than 8¢, and I know that 7¢ is above the average JND, so performers fudging the rastma would likely drive this director batty unless it actually accomplished something musically, such as modulating to quartertone-based keys Jacob-Collier-style. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 11:03, 1 November 2020 (UTC)

Aura at 10:39, 1 November 2020

2020-11-01T10:39:48Z

← Older revision		Revision as of 10:39, 1 November 2020
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	: "There should also be a simple process to get from the ratio to the name. Why are some ratios Alpharabian and some Betarabian? What simple test can be applied to say 729/704 to determine which category it falls into? What happens to the intervals that don't fit into either category?" The terms are "Alpharabian" and "Betarabian", and yes, there is a rudamentary test in place. Alpharabian intervals are generally either directly in the 2.11 subgroup, or, they differ from a nearby Pythagorean interval by either 33/32, 1331/1296, 8192/8019, 4096/3993, or 243/242. The system for denoting Betarabian intervals is less complete, but so far, Betarabian intervals usually differ from Alpharabian intervals by a rastma. When dealing with intervals that are distant by additionl rastmas, I would just use "Rastimic", "Birastmic", "Trirastmic", and so on.		: "There should also be a simple process to get from the ratio to the name. Why are some ratios Alpharabian and some Betarabian? What simple test can be applied to say 729/704 to determine which category it falls into? What happens to the intervals that don't fit into either category?" The terms are "Alpharabian" and "Betarabian", and yes, there is a rudamentary test in place. Alpharabian intervals are generally either directly in the 2.11 subgroup, or, they differ from a nearby Pythagorean interval by either 33/32, 1331/1296, 8192/8019, 4096/3993, or 243/242. The system for denoting Betarabian intervals is less complete, but so far, Betarabian intervals usually differ from Alpharabian intervals by a rastma. When dealing with intervals that are distant by additionl rastmas, I would just use "Rastimic", "Birastmic", "Trirastmic", and so on.

	: "As a practical matter, if some violinists or vocalists were performing 2.3.11 JI music, they would constantly be fudging the rastma. They might shift a pitch by 7¢, or let the tonic drift by 7¢. The neutral triad is an innate-comma chord (aka essentially tempered chord), and the 3rd might fall between 11/9 and 27/22. No listener would notice these slight discrepancies. The rastma would effectively be tempered out, and the notation could reflect this. Simply notate two notes only a rastma apart as the same note, and trust the performers' ears." On the contrary, I've met a music director who can hear a difference between 440 Hz and 438 Hz- a difference of less than 8¢, and I know that 7¢ is above the average JND, so performers fudging the rastma would drive this director batty. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 10:19, 1 November 2020 (UTC)		: "As a practical matter, if some violinists or vocalists were performing 2.3.11 JI music, they would constantly be fudging the rastma. They might shift a pitch by 7¢, or let the tonic drift by 7¢. The neutral triad is an innate-comma chord (aka essentially tempered chord), and the 3rd might fall between 11/9 and 27/22. No listener would notice these slight discrepancies. The rastma would effectively be tempered out, and the notation could reflect this. Simply notate two notes only a rastma apart as the same note, and trust the performers' ears." On the contrary, I've met a music director who can hear a difference between 440 Hz and 438 Hz- a difference of less than 8¢, and I know that 7¢ is above the average JND, so performers fudging the rastma would likely drive this director batty. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 10:19, 1 November 2020 (UTC)

Aura at 10:39, 1 November 2020

2020-11-01T10:39:28Z

← Older revision		Revision as of 10:39, 1 November 2020
Line 783:		Line 783:
	: "There should also be a simple process to get from the ratio to the name. Why are some ratios Alpharabian and some Betarabian? What simple test can be applied to say 729/704 to determine which category it falls into? What happens to the intervals that don't fit into either category?" The terms are "Alpharabian" and "Betarabian", and yes, there is a rudamentary test in place. Alpharabian intervals are generally either directly in the 2.11 subgroup, or, they differ from a nearby Pythagorean interval by either 33/32, 1331/1296, 8192/8019, 4096/3993, or 243/242. The system for denoting Betarabian intervals is less complete, but so far, Betarabian intervals usually differ from Alpharabian intervals by a rastma. When dealing with intervals that are distant by additionl rastmas, I would just use "Rastimic", "Birastmic", "Trirastmic", and so on.		: "There should also be a simple process to get from the ratio to the name. Why are some ratios Alpharabian and some Betarabian? What simple test can be applied to say 729/704 to determine which category it falls into? What happens to the intervals that don't fit into either category?" The terms are "Alpharabian" and "Betarabian", and yes, there is a rudamentary test in place. Alpharabian intervals are generally either directly in the 2.11 subgroup, or, they differ from a nearby Pythagorean interval by either 33/32, 1331/1296, 8192/8019, 4096/3993, or 243/242. The system for denoting Betarabian intervals is less complete, but so far, Betarabian intervals usually differ from Alpharabian intervals by a rastma. When dealing with intervals that are distant by additionl rastmas, I would just use "Rastimic", "Birastmic", "Trirastmic", and so on.

	: "As a practical matter, if some violinists or vocalists were performing 2.3.11 JI music, they would constantly be fudging the rastma. They might shift a pitch by 7¢, or let the tonic drift by 7¢. The neutral triad is an innate-comma chord (aka essentially tempered chord), and the 3rd might fall between 11/9 and 27/22. No listener would notice these slight discrepancies. The rastma would effectively be tempered out, and the notation could reflect this. Simply notate two notes only a rastma apart as the same note, and trust the performers' ears." On the contrary, I've met ~~people~~ who can hear a difference between 440 Hz and 438 Hz, and I know that 7¢ is above the average JND. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 10:19, 1 November 2020 (UTC)		: "As a practical matter, if some violinists or vocalists were performing 2.3.11 JI music, they would constantly be fudging the rastma. They might shift a pitch by 7¢, or let the tonic drift by 7¢. The neutral triad is an innate-comma chord (aka essentially tempered chord), and the 3rd might fall between 11/9 and 27/22. No listener would notice these slight discrepancies. The rastma would effectively be tempered out, and the notation could reflect this. Simply notate two notes only a rastma apart as the same note, and trust the performers' ears." On the contrary, I've met a music director who can hear a difference between 440 Hz and 438 Hz- a difference of less than 8¢, and I know that 7¢ is above the average JND, so performers fudging the rastma would drive this director batty. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 10:19, 1 November 2020 (UTC)

Aura at 10:20, 1 November 2020

2020-11-01T10:20:11Z

← Older revision		Revision as of 10:20, 1 November 2020
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	: "There should also be a simple process to get from the ratio to the name. Why are some ratios Alpharabian and some Betarabian? What simple test can be applied to say 729/704 to determine which category it falls into? What happens to the intervals that don't fit into either category?" The terms are "Alpharabian" and "Betarabian", and yes, there is a rudamentary test in place. Alpharabian intervals are generally either directly in the 2.11 subgroup, or, they differ from a nearby Pythagorean interval by either 33/32, 1331/1296, 8192/8019, 4096/3993, or 243/242. The system for denoting Betarabian intervals is less complete, but so far, Betarabian intervals usually differ from Alpharabian intervals by a rastma. When dealing with intervals that are distant by additionl rastmas, I would just use "Rastimic", "Birastmic", "Trirastmic", and so on.		: "There should also be a simple process to get from the ratio to the name. Why are some ratios Alpharabian and some Betarabian? What simple test can be applied to say 729/704 to determine which category it falls into? What happens to the intervals that don't fit into either category?" The terms are "Alpharabian" and "Betarabian", and yes, there is a rudamentary test in place. Alpharabian intervals are generally either directly in the 2.11 subgroup, or, they differ from a nearby Pythagorean interval by either 33/32, 1331/1296, 8192/8019, 4096/3993, or 243/242. The system for denoting Betarabian intervals is less complete, but so far, Betarabian intervals usually differ from Alpharabian intervals by a rastma. When dealing with intervals that are distant by additionl rastmas, I would just use "Rastimic", "Birastmic", "Trirastmic", and so on.

	: "As a practical matter, if some violinists or vocalists were performing 2.3.11 JI music, they would constantly be fudging the rastma. They might shift a pitch by 7¢, or let the tonic drift by 7¢. The neutral triad is an innate-comma chord (aka essentially tempered chord), and the 3rd might fall between 11/9 and 27/22. No listener would notice these slight discrepancies. The rastma would effectively be tempered out, and the notation could reflect this. Simply notate two notes only a rastma apart as the same note, and trust the performers' ears." On the contrary, I've met people who can hear a difference between 440 Hz and ~~438Hz~~, and I know that 7¢ is above the average JND. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 10:19, 1 November 2020 (UTC)		: "As a practical matter, if some violinists or vocalists were performing 2.3.11 JI music, they would constantly be fudging the rastma. They might shift a pitch by 7¢, or let the tonic drift by 7¢. The neutral triad is an innate-comma chord (aka essentially tempered chord), and the 3rd might fall between 11/9 and 27/22. No listener would notice these slight discrepancies. The rastma would effectively be tempered out, and the notation could reflect this. Simply notate two notes only a rastma apart as the same note, and trust the performers' ears." On the contrary, I've met people who can hear a difference between 440 Hz and 438 Hz, and I know that 7¢ is above the average JND. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 10:19, 1 November 2020 (UTC)

Aura at 10:19, 1 November 2020

2020-11-01T10:19:18Z

← Older revision		Revision as of 10:19, 1 November 2020
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	I'm not a fan of using large edos to measure everything else, so I'll skip the 159edo vs. 205edo discussion.		I'm not a fan of using large edos to measure everything else, so I'll skip the 159edo vs. 205edo discussion.

			: "Conventionally, there is an aug unison but not a dim unison. So it seems a Paramajor Unison would be valid? What ratio would that be?" Well, Major and Minor never occur unpaired in conventional music, and "Paramajor" and "Paraminor" are coined in analogy to Major and Minor respectively. This is why I reject the idea of a "Paramajor Unison". Rather, I refer to a "Parasuperprime", which, ideally, has 33/32 as the ratio.

			: "Seems like dividing 9/8 into a diatonic quartertone and 3 ''identical'' chromatic quartertones will always make huge ratios. Maybe better to have unequal steps." Nope. Why? Because the Apotome has a ratio of 2187/2048- that's four digits for each number, just like with the ratios in my current system.

			: "Greater/Lesser is a problem because one can always add or subtract a rastma and get a new ratio slightly larger or smaller. I guess you solve this with Betarabic vs Alpharabic? This is the problem with cents-based nomenclatures. There's always more ratios in that cents range to deal with, and the nomenclature eventually breaks. I prefer monzo-based nomenclatures that don't break." I can understand that.

			: "There should also be a simple process to get from the ratio to the name. Why are some ratios Alpharabian and some Betarabian? What simple test can be applied to say 729/704 to determine which category it falls into? What happens to the intervals that don't fit into either category?" The terms are "Alpharabian" and "Betarabian", and yes, there is a rudamentary test in place. Alpharabian intervals are generally either directly in the 2.11 subgroup, or, they differ from a nearby Pythagorean interval by either 33/32, 1331/1296, 8192/8019, 4096/3993, or 243/242. The system for denoting Betarabian intervals is less complete, but so far, Betarabian intervals usually differ from Alpharabian intervals by a rastma. When dealing with intervals that are distant by additionl rastmas, I would just use "Rastimic", "Birastmic", "Trirastmic", and so on.

			: "As a practical matter, if some violinists or vocalists were performing 2.3.11 JI music, they would constantly be fudging the rastma. They might shift a pitch by 7¢, or let the tonic drift by 7¢. The neutral triad is an innate-comma chord (aka essentially tempered chord), and the 3rd might fall between 11/9 and 27/22. No listener would notice these slight discrepancies. The rastma would effectively be tempered out, and the notation could reflect this. Simply notate two notes only a rastma apart as the same note, and trust the performers' ears." On the contrary, I've met people who can hear a difference between 440 Hz and 438Hz, and I know that 7¢ is above the average JND. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 10:19, 1 November 2020 (UTC)

TallKite at 09:49, 1 November 2020

2020-11-01T09:49:42Z

Show changes

Xenwolf: addition about phone-number values

2020-10-19T09:14:01Z

addition about phone-number values

← Older revision		Revision as of 09:14, 19 October 2020
Line 10:		Line 10:
	I'd say that adding interval sizes could be of use, even cent precision would do, something like this:		I'd say that adding interval sizes could be of use, even cent precision would do, something like this:

	{\| class="wikitable center-1 right-2 mw-collapsible"		{\| class="wikitable center-1 right-2 mw-collapsible mw-collapsed"
	\|-		\|-
	! Ratio		! Ratio
Line 177:		Line 177:
	And finally let me add that a 6-decimal doesn't add anything if the minimal differences is more than 2 cents. It's only harder to separate significant information from the insignificant one when reading, IOW the excessive precision just adds noise here:		And finally let me add that a 6-decimal doesn't add anything if the minimal differences is more than 2 cents. It's only harder to separate significant information from the insignificant one when reading, IOW the excessive precision just adds noise here:

	{\| class="wikitable sortable center-1 right-2 mw-collapsible"		{\| class="wikitable sortable center-1 right-2 mw-collapsible mw-collapsed"
	\|-		\|-
	! class="unsortable" \| Interval		! class="unsortable" \| Interval
Line 358:		Line 358:

	:: There is consensus in the wiki that 6 decimals make sense on page [[Gallery og just intervals]]. The reason for this is that nobody has to worry about possible collisions when inserting a single interval. On individual interval pages we use 5 decimals, as a "canonical" reference. For EDO pages, such a consensus doesn't exist. --[[User:Xenwolf\|Xenwolf]] ([[User talk:Xenwolf\|talk]]) 08:02, 19 October 2020 (UTC)		:: There is consensus in the wiki that 6 decimals make sense on page [[Gallery og just intervals]]. The reason for this is that nobody has to worry about possible collisions when inserting a single interval. On individual interval pages we use 5 decimals, as a "canonical" reference. For EDO pages, such a consensus doesn't exist. --[[User:Xenwolf\|Xenwolf]] ([[User talk:Xenwolf\|talk]]) 08:02, 19 October 2020 (UTC)

			::: I'm personally against these "phone numbers". Here is why:
			::: When reading, nobody has anything of these decimal places, because they are size specifications. Also nobody will voluntarily calculate with them by hand. It is also unnecessary to copy and paste them into programs, because it is better to calculate the exact numbers there (how to do this is described on the Cent page, which we link to on all occasions in the Wiki). --[[User:Xenwolf\|Xenwolf]] ([[User talk:Xenwolf\|talk]]) 09:14, 19 October 2020 (UTC)

Xenwolf: /* table syntax and column alignment */ re

2020-10-19T08:02:44Z

table syntax and column alignment: re

← Older revision		Revision as of 08:02, 19 October 2020
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	: On one level, it does, and for that I thank you. However, when it comes to the precision in terms of cents, the precision in cent size is meant to be compatible with that found on the [[Gallery of just intervals]] page. That way, assuming there are no more errors in the table, you can take the info out of here and place it in the table on the [[Gallery of just intervals]] page. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 06:27, 19 October 2020 (UTC)		: On one level, it does, and for that I thank you. However, when it comes to the precision in terms of cents, the precision in cent size is meant to be compatible with that found on the [[Gallery of just intervals]] page. That way, assuming there are no more errors in the table, you can take the info out of here and place it in the table on the [[Gallery of just intervals]] page. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 06:27, 19 October 2020 (UTC)

			:: There is consensus in the wiki that 6 decimals make sense on page [[Gallery og just intervals]]. The reason for this is that nobody has to worry about possible collisions when inserting a single interval. On individual interval pages we use 5 decimals, as a "canonical" reference. For EDO pages, such a consensus doesn't exist. --[[User:Xenwolf\|Xenwolf]] ([[User talk:Xenwolf\|talk]]) 08:02, 19 October 2020 (UTC)