Microtone: Difference between revisions

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The '''Microtone''' is an [[interval measure]] that is sufficiently precise for all thinkable musical and music-science purposes. Besides its high accuracy, it is of a high neutrality since it favors neither twelve-tonality nor even the [[octave]].

The '''Microtone''' is an [[interval measure]] that can be considered as sufficiently precise for all thinkable musical and music-science purposes. Besides its high accuracy, it is of high neutrality since it favors neither twelve-tonality nor even the [[octave]]. Nevertheless its relevance for practical application in music is low due to the incompatibility with "[[human scale]]". Humans are not good at big numbers and have only limited pitch perception (the [[Just-noticeable difference]] (JND) is around 6 cents).

One actual microtone ('''1µt''') would be defined as one millionth of the [[tone]]:

{| class="wikitable"

{| class="wikitable right-3"

|+ ~~Intervals in comparison~~

|+ Some numerical impressions (laughter permitted)

! Name

! Size in [[~~cent~~]]

! Size

! Size ([[cents|¢]], 12 decimals)

! Size (in [[cents|cents (¢)]], scientific notation)<ref>The values were produced by [https://keisan.casio.com/calculator High precision calculator].</ref>

|-

| ~~Ton~~ (=[[9/8]])

| Tone (=[[9/8]])

| ~~{{#expr: ln(9~~/8) / ~~ln(2) *1200 }}~~

| 204¢

| <tt>203.910,001,730,775</tt>

| <tt>2.03910001730774835488973465474759621023555E+2</tt>

|-

| Millitone

| ~~{{#expr: ln(9~~/~~8) / ln(~~2~~) *1200~~ /~~1000 }}~~

| 204m¢

| <tt>0.203,910,001,731</tt>

| <tt>2.03910001730774835488973465474759621023555E-1</tt>

|-

| ~~Mikcotone~~

| Microtone

| ~~{{#expr: ln(9~~/~~8) / ln(~~2~~) *1200 /1000~~ /~~1000 }}~~

| 204µ¢

| <tt>0.000,203,910,002</tt>

| <tt>2.03910001730774835488973465474759621023555E-4</tt>

|}

== The Microtone Challenge ==

~~A microtone is indeed a very small interval: 4904 microtones make one [[cent]], and 5884949 an octave.~~

Two sounds different only by 1µt produce a very slow [[beat]]; depending on the frequency one have to wait more or less to ~~recocnize~~ it. The beat frequency is

A microtone is indeed a very small interval: 4,904 microtones make one [[cent]], and 5,884,949 an octave.

Two sounds different only by 1µt produce a very slow [[beat]]; depending on the frequency one have to wait more or less to recognize it. The beat frequency is

* at the upper limit of the hearing range (20 kHz) 7 minutes

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Given this, will it be ever possible to make a ''microtone experience'' at all?

== External links ==

* [http://musictheory.zentral.zone/huntsystem2.html#2 H-Pi Instruments | Hunt System Scale] - section "The JND"

* [https://en.wikipedia.org/wiki/Pitch_(music)#Just-noticeable_difference Pitch (music) - Wikipedia] - section "Just-noticeable difference"

[[Category:Interval measure]]

@@ Line 5: / Line 5: @@
 | ja =
 }}
-The '''Microtone''' is an [[interval measure]] that is sufficiently precise for all thinkable musical and music-science purposes. Besides its high accuracy, it is of a high neutrality since it favors neither twelve-tonality nor even the [[octave]].
+The '''Microtone''' is an [[interval measure]] that can be considered as sufficiently precise for all thinkable musical and music-science purposes. Besides its high accuracy, it is of high neutrality since it favors neither twelve-tonality nor even the [[octave]]. Nevertheless its relevance for practical application in music is low due to the incompatibility with "[[human scale]]". Humans are not good at big numbers and have only limited pitch perception (the [[Just-noticeable difference]] (JND) is around 6 cents).
 One actual microtone ('''1µt''') would be defined as one millionth of the [[tone]]:
-{| class="wikitable"
+{| class="wikitable right-3"
-|+ Intervals in comparison
+|+ Some numerical impressions (laughter permitted)
 ! Name
-! Size in [[cent]]
+! Size
+! Size ([[cents|¢]], 12 decimals)
+! Size (in [[cents|cents (¢)]], scientific notation)<ref>The values were produced by [https://keisan.casio.com/calculator High precision calculator].</ref>
 |-
-| Ton (=[[9/8]])
+| Tone (=[[9/8]])
-| {{#expr: ln(9/8) / ln(2) *1200 }}
+| 204¢
+| <tt>203.910,001,730,775</tt>
+| <tt>2.03910001730774835488973465474759621023555E+2</tt>
 |-
 | Millitone
-| {{#expr: ln(9/8) / ln(2) *1200 /1000 }}
+| 204m¢
+| <tt>0.203,910,001,731</tt>
+| <tt>2.03910001730774835488973465474759621023555E-1</tt>
 |-
-| Mikcotone
+| Microtone
-| {{#expr: ln(9/8) / ln(2) *1200 /1000 /1000 }}
+| 204µ¢
+| <tt>0.000,203,910,002</tt>
+| <tt>2.03910001730774835488973465474759621023555E-4</tt>
 |}
+<references/>
 == The Microtone Challenge ==
-A microtone is indeed a very small interval: 4904 microtones make one [[cent]], and 5884949 an octave.
-Two sounds different only by 1µt produce a very slow [[beat]]; depending on the frequency one have to wait more or less to recocnize it. The beat frequency is
+A microtone is indeed a very small interval: 4,904 microtones make one [[cent]], and 5,884,949 an octave.
+Two sounds different only by 1µt produce a very slow [[beat]]; depending on the frequency one have to wait more or less to recognize it. The beat frequency is
 * at the upper limit of the hearing range (20 kHz) 7 minutes
@@ Line 34: / Line 45: @@
 Given this, will it be ever possible to make a ''microtone experience'' at all?
+== External links ==
+* [http://musictheory.zentral.zone/huntsystem2.html#2 H&#45;Pi Instruments &#124; Hunt System Scale] - section "The JND"
+* [https://en.wikipedia.org/wiki/Pitch_(music)#Just-noticeable_difference Pitch (music) &#45; Wikipedia] - section "Just-noticeable difference"
 [[Category:Interval measure]]