Beep: Difference between revisions

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'''Beep''' is a remarkable low-complexity, though high-badness [[7-limit]] [[temperament]]. It is also called '''titanium''' by [[Mason Green]]. It [[tempering out|tempers out]] the [[21/20|septimal minor semitone (21/20)]], making it a [[septisemi temperaments|septisemi temperament]], and the [[49/48|slendro diesis (49/48)]], making it part of the [[slendro clan]]. As such, ~~[[6/5]],~~ [[7/6]], and [[8/7]] ~~are all represented by the same interval (which, in fact, is the [[generator]])~~. Two of these generators make a very sharp [[4/3|fourth]] (which is also a very flat [[7/5]]). Since three fifths make a minor ~~(not major) sixth~~, and four make a minor ~~(not major) third~~, it is also similar to the [[pelogic]] temperament ([[superpelog]] in particular~~). It also tempers out [[27/25]] and is part of the [[bug family]]; because of this, the generator also functions as [[10/9]] (meaning this tuning has a ''negative'' syntonic comma~~). Finally it can be also considered a sort of messed-up variant of [[orwell]] temperament as well, since the generator falls into the same range of sizes.

'''Beep''' is a remarkable low-complexity, though high-badness [[7-limit]] [[temperament]]. It is also called '''titanium''' by [[Mason Green]].

It [[tempering out|tempers out]] [[27/25]] and is part of the [[bug family]]; as such, [[6/5]] and [[10/9]] are represented by the same interval which, in fact, is the [[generator]]. It also tempers out the [[21/20|septimal minor semitone (21/20)]], making it a [[septisemi temperaments|septisemi temperament]], and the [[49/48|slendro diesis (49/48)]], making it part of the [[slendro clan]]. As such, the generator also represents [[7/6]] and [[8/7]]. Two of these generators make a very sharp [[4/3|fourth]] which is also a very flat [[7/5]]. Two fifths make a second that is neutral in [[interval quality|quality]], so a good tuning typically has a ''negative'' [[syntonic comma]]. Since three fifths make a sixth that sounds minor, and four make a third that sounds minor, it is also similar to the [[pelogic]] temperament ([[superpelog]] in particular). Finally it can be also considered a sort of messed-up variant of [[orwell]] temperament as well, since the generator falls into the same range of sizes.

The edos whose [[patent val]]s support beep are [[4edo]], [[5edo]], [[9edo]], and [[14edo]]. Many other edos can be used as non-patent vals, such as 13.

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<nowiki>*~~</nowiki> octave~~ reduced, in 7-limit CTE tuning

<nowiki />* Octave reduced, in 7-limit CTE tuning

== Chords and harmony ==

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|-

| 116

| -4

| −4

|-

| 271

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Line 62:

|-

| 387

| -3

| −3

|-

| 542

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|-

| 658

| -2

| −2

|-

| 813 (or 774)

| 3 (or -6)

| 3 (or −6)

|-

| 929

| -1

| −1

|-

| 1045

| -5

| −5

|}

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=== Suggested timbre ===

If using brittle ~~titanium~~ (23cd, 14edo, etc.), one might want to consider using this as a guideline. With this spectrum, no partials are more than 25 cents above or below their perfectly harmonic values, and when using 14edo, no intervals will be more than 26 cents out of tune. This is only a guideline, and only with synthesized tones would it be possible to achieve this perfectly. With physical idiophones (celestas, gamelans, etc.) it should still be possible to get a great approximation using CAD (or trial and error).

If using brittle beep (23cd, 14edo, etc.), one might want to consider using this as a guideline. With this spectrum, no partials are more than 25 cents above or below their perfectly harmonic values, and when using 14edo, no intervals will be more than 26 cents out of tune. This is only a guideline, and only with synthesized tones would it be possible to achieve this perfectly. With physical idiophones (celestas, gamelans, etc.) it should still be possible to get a great approximation using CAD (or trial and error).

Fundamental (1st): just

* Fundamental (1st): just

* Octave (2nd): just

* 3rd: −12.5

* 4th: just

* 5th: +25

* 6th: −12.5 cents

* 7th: −25 cents

* 8th: just

* 9th: −25 cents

* 10th: +25 cents

* 11th: −25 cents

* 12th: −12.5 cents

* 13th: +15 cents

* 14th: −25 cents

* 15th: +12.5 cents

* 16th: just

~~Octave~~ (~~2nd~~)~~: just~~

== Tunings ==

=== Tuning spectrum ===

~~3rd:~~ -12.5

{| class="wikitable center-all left-4"

|-

~~4th: just~~

! Edo<br>Generator !! Eigenmonzo<br>(Unchanged-interval) !! Generator (¢) !! Comments

|-

~~5th: +25~~

| || 5/3 || 884.3 ||

|-

~~6th: -12~~.5 ~~cents~~

| 3\4 || || 900.0 || Lower bound of 7-odd-limit diamond monotone

|-

~~7th:~~ -~~25 cents~~

| || 7/5 || 908.7 ||

|-

~~8th: just~~

| 10\13 || || 923.1 ||

|-

~~9th:~~ -~~25 cents~~

| || 5/4 || 928.8 || 5- and 7-odd-limit minimax

|-

~~10th: +25 cents~~

| || 7/6 || 933.1 ||

|-

~~11th:~~ -~~25 cents~~

| 7\9 || || 933.3 ||

|-

~~12th:~~ -12.~~5 cents~~

| 11\14 || || 942.9 ||

|-

~~13th: +15 cents~~

| || 9/7 || 945.0 || 9-odd-limit minimax

|-

~~14th:~~ -~~25 cents~~

| || 3/2 || 951.0 ||

|-

~~15th: +12~~.~~5 cents~~

| 4\5 || || 960.0 || Upper bound of 7-odd-limit diamond monotone<br>9-odd-limit diamond monotone (singleton)

|-

~~16th: just~~

| || 7/4 || 968.8 ||

|-

| || 9/5 || 1017.6 ||

|}

~~[[Category:Temperaments]]~~

[[Category:Beep| ]]

[[Category:Rank-2 temperaments]]

[[Category:Exotemperaments]]

[[Category:Bug family]]

[[Category:~~Slendro~~ clan]]

[[Category:Semaphoresmic clan]]

[[Category:Septisemi temperaments]]

@@ Line 1: / Line 1: @@
-'''Beep''' is a remarkable low-complexity, though high-badness [[7-limit]] [[temperament]]. It is also called '''titanium''' by [[Mason Green]]. It [[tempering out|tempers out]] the [[21/20|septimal minor semitone (21/20)]], making it a [[septisemi temperaments|septisemi temperament]], and the [[49/48|slendro diesis (49/48)]], making it part of the [[slendro clan]]. As such, [[6/5]], [[7/6]], and [[8/7]] are all represented by the same interval (which, in fact, is the [[generator]]). Two of these generators make a very sharp [[4/3|fourth]] (which is also a very flat [[7/5]]). Since three fifths make a minor (not major) sixth, and four make a minor (not major) third, it is also similar to the [[pelogic]] temperament ([[superpelog]] in particular). It also tempers out [[27/25]] and is part of the [[bug family]]; because of this, the generator also functions as [[10/9]] (meaning this tuning has a ''negative'' syntonic comma). Finally it can be also considered a sort of messed-up variant of [[orwell]] temperament as well, since the generator falls into the same range of sizes.
+'''Beep''' is a remarkable low-complexity, though high-badness [[7-limit]] [[temperament]]. It is also called '''titanium''' by [[Mason Green]].
+It [[tempering out|tempers out]] [[27/25]] and is part of the [[bug family]]; as such, [[6/5]] and [[10/9]] are represented by the same interval which, in fact, is the [[generator]]. It also tempers out the [[21/20|septimal minor semitone (21/20)]], making it a [[septisemi temperaments|septisemi temperament]], and the [[49/48|slendro diesis (49/48)]], making it part of the [[slendro clan]]. As such, the generator also represents [[7/6]] and [[8/7]]. Two of these generators make a very sharp [[4/3|fourth]] which is also a very flat [[7/5]]. Two fifths make a second that is neutral in [[interval quality|quality]], so a good tuning typically has a ''negative'' [[syntonic comma]]. Since three fifths make a sixth that sounds minor, and four make a third that sounds minor, it is also similar to the [[pelogic]] temperament ([[superpelog]] in particular). Finally it can be also considered a sort of messed-up variant of [[orwell]] temperament as well, since the generator falls into the same range of sizes.
 The edos whose [[patent val]]s support beep are [[4edo]], [[5edo]], [[9edo]], and [[14edo]]. Many other edos can be used as non-patent vals, such as 13.
@@ Line 36: / Line 38: @@
 | 15/8
 |}
-<nowiki>*</nowiki> octave reduced, in 7-limit CTE tuning
+<nowiki />* Octave reduced, in 7-limit CTE tuning
 == Chords and harmony ==
@@ Line 54: / Line 56: @@
 |-
 | 116
-| -4
+| −4
 |-
 | 271
@@ Line 60: / Line 62: @@
 |-
 | 387
-| -3
+| −3
 |-
 | 542
@@ Line 66: / Line 68: @@
 |-
 | 658
-| -2
+| −2
 |-
 | 813 (or 774)
-| 3 (or -6)
+| 3 (or −6)
 |-
 | 929
-| -1
+| −1
 |-
 | 1045
-| -5
+| −5
 |}
@@ Line 87: / Line 89: @@
 === Suggested timbre ===
-If using brittle titanium (23cd, 14edo, etc.), one might want to consider using this as a guideline. With this spectrum, no partials are more than 25 cents above or below their perfectly harmonic values, and when using 14edo, no intervals will be more than 26 cents out of tune. This is only a guideline, and only with synthesized tones would it be possible to achieve this perfectly. With physical idiophones (celestas, gamelans, etc.) it should still be possible to get a great approximation using CAD (or trial and error).
+If using brittle beep (23cd, 14edo, etc.), one might want to consider using this as a guideline. With this spectrum, no partials are more than 25 cents above or below their perfectly harmonic values, and when using 14edo, no intervals will be more than 26 cents out of tune. This is only a guideline, and only with synthesized tones would it be possible to achieve this perfectly. With physical idiophones (celestas, gamelans, etc.) it should still be possible to get a great approximation using CAD (or trial and error).
-Fundamental (1st): just
+* Fundamental (1st): just
+* Octave (2nd): just
+* 3rd: −12.5
+* 4th: just
+* 5th: +25
+* 6th: −12.5 cents
+* 7th: −25 cents
+* 8th: just
+* 9th: −25 cents
+* 10th: +25 cents
+* 11th: −25 cents
+* 12th: −12.5 cents
+* 13th: +15 cents
+* 14th: −25 cents
+* 15th: +12.5 cents
+* 16th: just
-Octave (2nd): just
+== Tunings ==
+=== Tuning spectrum ===
-rd: -12.5
+{| class="wikitable center-all left-4"
+|-
-th: just
+! Edo<br>Generator !! Eigenmonzo<br>(Unchanged-interval) !! Generator (¢) !! Comments
+|-
-th: +25
+| || 5/3 || 884.3 ||
+|-
-th: -12.5 cents
+| 3\4 ||  || 900.0 || Lower bound of 7-odd-limit diamond monotone
+|-
-th: -25 cents
+|  || 7/5 || 908.7 ||
+|-
-th: just
+| 10\13 ||  || 923.1 ||
+|-
-th: -25 cents
+|  || 5/4 || 928.8 || 5- and 7-odd-limit minimax
+|-
-th: +25 cents
+|  || 7/6 || 933.1 ||
+|-
-th: -25 cents
+| 7\9 ||  || 933.3 ||
+|-
-th: -12.5 cents
+| 11\14 ||  || 942.9 ||
+|-
-th: +15 cents
+| || 9/7 || 945.0 || 9-odd-limit minimax
+|-
-th: -25 cents
+| || 3/2 || 951.0 ||
+|-
-th: +12.5 cents
+| 4\5 ||  || 960.0 || Upper bound of 7-odd-limit diamond monotone<br>9-odd-limit diamond monotone (singleton)
+|-
-th: just
+| || 7/4 || 968.8 ||
+|-
+| || 9/5 || 1017.6 ||
+|}
-[[Category:Temperaments]]
 [[Category:Beep| ]] <!-- main article -->
+[[Category:Rank-2 temperaments]]
+[[Category:Exotemperaments]]
 [[Category:Bug family]]
-[[Category:Slendro clan]]
+[[Category:Semaphoresmic clan]]
 [[Category:Septisemi temperaments]]