Harmonotonic tuning - Revision history

Cmloegcmluin: /* Categorization */ address Flora's recent concerns about rationality vs. irrationality in this system

2023-03-28T21:40:45Z

Categorization: address Flora's recent concerns about rationality vs. irrationality in this system

← Older revision		Revision as of 21:40, 28 March 2023
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	# '''arithmetic & irrational''' (e.g. EDO)		# '''arithmetic & irrational''' (e.g. EDO)
	# '''non-arithmetic & irrational'''		# '''non-arithmetic & irrational'''

			Because different acronyms are used to distinguish rational (JI) tunings from general tunings which include irrational (non-JI) tunings, while the acronyms used for general tunings technically include the JI tunings, these general acronyms are more useful when reserved for non-JI tunings, and this is what is typically done. So when "irrational" is used on this page, it more accurately means "probably irrational".

	== Arithmetic tunings ==		== Arithmetic tunings ==

FloraC: FloraC moved page Harmonotonic tunings to Harmonotonic tuning: WP:PLURAL

2023-02-14T19:40:45Z

FloraC moved page Harmonotonic tunings to Harmonotonic tuning: WP:PLURAL

← Older revision	Revision as of 19:40, 14 February 2023
(No difference)

Wolftune: fixed inconsistent use of harmonic vs "overtone"

2022-01-22T20:30:03Z

fixed inconsistent use of harmonic vs "overtone"

Show changes

Cmloegcmluin: fix broken links

2021-11-11T19:37:43Z

fix broken links

← Older revision		Revision as of 19:37, 11 November 2021
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	\|-		\|-
	! rowspan="2" \|division		! rowspan="2" \|division
	\|[[Overtone scale#Over-n ~~Scales~~\|'''overtone mode, or over-n scale''' ''(equivalent to n-ODO)'']]		\|[[Overtone scale#Over-n scales\|'''overtone mode, or over-n scale''' ''(equivalent to n-ODO)'']]
	! rowspan="2" \|		! rowspan="2" \|
	\| rowspan="2" \|[[EFD\|'''n-EFDp:''' <u>n</u> <u>e</u>qual <u>f</u>requency <u>d</u>ivisions of irrational interval <u>p</u>]]		\| rowspan="2" \|[[EFD\|'''n-EFDp:''' <u>n</u> <u>e</u>qual <u>f</u>requency <u>d</u>ivisions of irrational interval <u>p</u>]]
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	\|-		\|-
	! rowspan="2" \|division		! rowspan="2" \|division
	\|[[Overtone scale#Next ~~Steps~~\|'''undertone mode, or under-n scale''' ''(equivalent to n-UDO)'']]		\|[[Overtone scale#Next steps\|'''undertone mode, or under-n scale''' ''(equivalent to n-UDO)'']]
	! rowspan="2" \|		! rowspan="2" \|
	\| rowspan="2" \|[[ELD\|'''n-ELDp:''' <u>n</u> <u>e</u>qual <u>l</u>ength <u>d</u>ivisions of irrational interval <u>p</u>]]		\| rowspan="2" \|[[ELD\|'''n-ELDp:''' <u>n</u> <u>e</u>qual <u>l</u>ength <u>d</u>ivisions of irrational interval <u>p</u>]]

Fredg999: Categories

2021-08-30T04:00:02Z

Cmloegcmluin: note to emphasize harmonic series

2021-03-23T17:43:38Z

note to emphasize harmonic series

← Older revision		Revision as of 17:43, 23 March 2021
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	<span>[[File:Diatonic scale not monotonic.svg\|400px]]</span><span>[[File:Overtone series segment monotonic.svg\|400px]]</span><span>[[File:EDO monotonic.svg\|400px]]</span>		<span>[[File:Diatonic scale not monotonic.svg\|400px]]</span><span>[[File:Overtone series segment monotonic.svg\|400px]]</span><span>[[File:EDO monotonic.svg\|400px]]</span>

			Essentially, "harmonotonic" references the mathematical concept of monotonicity to form an umbrella term for tunings which are closely related to the harmonic series.

	== Categorization ==		== Categorization ==

Cmloegcmluin: /* History */

2021-03-23T16:48:30Z

History

← Older revision		Revision as of 16:48, 23 March 2021
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	== History ==		== History ==

	Harmonotonic tunings are not at all new concepts. However, the classifications and manners of specification for harmonotonic and arithmetic tunings described here were developed by Douglas Blumeyer in March 2021, incorporating existing ideas and further significant input and guidance from Billy Stiltner, [[Shaahin Mohajeri]], [[Paul Erlich]], Joakim Bang Larsen, ~~and~~ [[Dave Keenan]]. Discussion mostly occurred on Facebook on [https://www.facebook.com/groups/497105067092502/permalink/1980938532042474 this comment thread].		Harmonotonic tunings are not at all new concepts. However, the classifications and manners of specification for harmonotonic and arithmetic tunings described here were developed by Douglas Blumeyer in March 2021, incorporating existing ideas and further significant input and guidance from Billy Stiltner, [[Shaahin Mohajeri]], [[Paul Erlich]], Joakim Bang Larsen, [[Dave Keenan]], and [[Mike Battaglia]]. Discussion mostly occurred on Facebook on [https://www.facebook.com/groups/497105067092502/permalink/1980938532042474 this comment thread]. Other discussion occurred over email and private Facebook messages.

			Dave and Mike independently suggested the term "step-monotonic" and prefer it to "harmonotonic" because it is more descriptive and mathematically accurate. Douglas does not disagree with those motivations or facts, but nonetheless prefers the name "harmonotonic" because it is friendly for non-mathematicians: it references the harmonic series, which is the core of this umbrella naming effort (with monotonicity merely happening-to-be-the-case, providing a convenient etymological root to reference).

	[[Category:Otonality and utonality]]		[[Category:Otonality and utonality]]

Cmloegcmluin: /* Notes on monotonicity */ suggestion from Dave Keenan for correction of characterization of strict and absolute monotonicity

2021-03-23T16:19:34Z

Notes on monotonicity: suggestion from Dave Keenan for correction of characterization of strict and absolute monotonicity

← Older revision		Revision as of 16:19, 23 March 2021
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	Monotonicity must also be restricted to within the interval of repetition to have much value. Otherwise, only scales with equal step sizes would qualify as monotonic, because any increase or decrease in step size would be countered with an opposite change once the scale repeated.		Monotonicity must also be restricted to within the interval of repetition to have much value. Otherwise, only scales with equal step sizes would qualify as monotonic, because any increase or decrease in step size would be countered with an opposite change once the scale repeated.

	In mathematics, monotonicity is sometimes distinguished as strictly monotonic, when it is not permitted for a value to stay the same ~~if the values are increasing or decreasing~~. In this sense, all monotonic tunings classified here are strictly monotonic.		In mathematics, monotonicity is sometimes distinguished as strictly monotonic, when it is not permitted for a value to stay the same. In this sense, all tunings are strictly monotonic. But only some tunings are strictly step-monotonic. Of the tunings classified here, only those with increasing or decreasing step size are strictly step-monotonic.

	~~Sometimes also absolutely~~ monotonic ~~sequences are distinguished~~, whose ~~derivatives~~ are ~~all also~~ monotonic~~. This~~ is ~~true for all tunings classified here~~. ~~So all~~ tunings here are absolutely ~~and strictly~~ monotonic ~~by step size~~.		The sequence of step-sizes is the "first difference" of the sequence of pitches. If you were to list the differences between the sizes of successive steps, that would be the second difference. A monotonic sequence, all of whose differences are monotonic, is called "absolutely monotonic". All tunings categorized here are absolutely monotonic.

	== History ==		== History ==

Cmloegcmluin: /* Non-arithmetic harmonotonic tunings */ correct operation

2021-03-23T16:09:51Z

Non-arithmetic harmonotonic tunings: correct operation

← Older revision		Revision as of 16:09, 23 March 2021
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	!shifting		!shifting
	\|addition		\|addition
	\|[[wikipedia:Gaussian_logarithm\|Gaussian ~~logarithm~~]]		\|[[wikipedia:Gaussian_logarithm\|Gaussian logarithmic addition]]
	\|-		\|-
	!transposition		!transposition

Cmloegcmluin at 02:57, 23 March 2021

2021-03-23T02:57:25Z

← Older revision		Revision as of 02:57, 23 March 2021
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	A '''harmonotonic tuning''' is one whose ''step sizes'' are [https://en.wikipedia.org/wiki/Monotonic_function monotonic]: they do not both increase and decrease.		A '''harmonotonic tuning''', or '''step-monotonic tuning''', is one whose ''step sizes'' are [https://en.wikipedia.org/wiki/Monotonic_function monotonic]: they do not both increase and decrease.

	* A diatonic tuning is ''not'' harmonotonic because it goes back and forth between whole and half steps.		* A diatonic tuning is ''not'' harmonotonic because it goes back and forth between whole and half steps.

← Older revision		Revision as of 19:37, 11 November 2021
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	\|-		\|-
	! rowspan="2" \|division		! rowspan="2" \|division
	\|[[Overtone scale#Over-n ~~Scales~~\|'''overtone mode, or over-n scale''' ''(equivalent to n-ODO)'']]		\|[[Overtone scale#Over-n scales\|'''overtone mode, or over-n scale''' ''(equivalent to n-ODO)'']]
	! rowspan="2" \|		! rowspan="2" \|
	\| rowspan="2" \|[[EFD\|'''n-EFDp:''' <u>n</u> <u>e</u>qual <u>f</u>requency <u>d</u>ivisions of irrational interval <u>p</u>]]		\| rowspan="2" \|[[EFD\|'''n-EFDp:''' <u>n</u> <u>e</u>qual <u>f</u>requency <u>d</u>ivisions of irrational interval <u>p</u>]]
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	\|-		\|-
	! rowspan="2" \|division		! rowspan="2" \|division
	\|[[Overtone scale#Next ~~Steps~~\|'''undertone mode, or under-n scale''' ''(equivalent to n-UDO)'']]		\|[[Overtone scale#Next steps\|'''undertone mode, or under-n scale''' ''(equivalent to n-UDO)'']]
	! rowspan="2" \|		! rowspan="2" \|
	\| rowspan="2" \|[[ELD\|'''n-ELDp:''' <u>n</u> <u>e</u>qual <u>l</u>ength <u>d</u>ivisions of irrational interval <u>p</u>]]		\| rowspan="2" \|[[ELD\|'''n-ELDp:''' <u>n</u> <u>e</u>qual <u>l</u>ength <u>d</u>ivisions of irrational interval <u>p</u>]]

← Older revision		Revision as of 04:00, 30 August 2021
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	[[Category:Otonality and utonality]]		[[Category:Otonality and utonality]]
	~~[[Category:Overtone]]~~
	~~[[Category:Overtone‏‎ series]]~~
	[[Category:Otonality]]		[[Category:Otonality]]
	[[Category:Harmonic]]		[[Category:Harmonic]]
	[[Category:Harmonic series‏‎]]		[[Category:Harmonic series‏‎]]

	~~[[Category:Otonality and utonality]]~~
	~~[[Category:Undertone]]~~
	~~[[Category:Undertone series]]~~
	[[Category:Utonality]]		[[Category:Utonality]]
	[[Category:Subharmonic]]		[[Category:Subharmonic]]
	[[Category:Subharmonic series‏‎]]		[[Category:Subharmonic series‏‎]]

	[[Category:Equal-step tuning‏‎]]		[[Category:Equal-step tuning‏‎]]
	[[Category:Equal divisions of the octave‏‎ ]]		[[Category:Equal divisions of the octave‏‎]]