Microtonal Music Composition - Revision history

Vsmercola at 01:16, 14 December 2019

2019-12-14T01:16:48Z

Vsmercola: /* Introduction */

2019-12-14T01:02:28Z

‎Introduction

Vsmercola: added name

2019-12-14T00:59:53Z

added name

Vsmercola at 18:25, 12 October 2019

2019-10-12T18:25:13Z

Vsmercola: Removed video

2019-10-12T18:14:12Z

Removed video

Vsmercola at 18:06, 12 October 2019

2019-10-12T18:06:48Z

Vsmercola at 18:03, 12 October 2019

2019-10-12T18:03:18Z

Vsmercola: Vsmercola moved page Microtonal Music Composition - Victor Mercola to Microtonal Music Composition: I don't want my name in the headline

2019-10-12T17:58:52Z

Vsmercola moved page Microtonal Music Composition - Victor Mercola to Microtonal Music Composition: I don't want my name in the headline

Vsmercola at 17:34, 12 October 2019

2019-10-12T17:34:20Z

Vsmercola at 17:29, 12 October 2019

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 == Introduction ==
-Recall that music is fundamentally based on ratios of the harmonic series (1, 1/2, 1/3, 1/4, etc.) and that an octave has the frequency ratio of 2/1, a perfect fifth has a ratio of 3/2, and a perfect fourth has a ratio of 4/3. This method of tuning an instrument based on fundamental frequencies is called just intonation, or JI. However, JI isn't used in modern music because the ratios between notes are not preserved when transposing sound. It also is mathematically impossible to tune a piano with a single rational interval such that the octave's 2/1 ratio is preserved.
+Recall that music is fundamentally based on ratios of the harmonic series (1, 1/2, 1/3, 1/4, etc.) and that an octave has the frequency ratio of 2/1, a perfect fifth has a ratio of 3/2, and a perfect fourth has a ratio of 4/3. This method of tuning an instrument based on fundamental frequencies is called just intonation, or JI. However, the JI isn't used in modern music because the ratios between notes are not preserved when transposing sound. It also is mathematically impossible to tune a piano with a single rational interval such that the octave's 2/1 ratio is preserved.
 For starters, traditional Western music breaks down the octave into 12 logarithmic equally spaced intervals. This tuning method is called 12 equal divisions of the octave, or 12edo. Two notes that are adjacent on a keyboard have the irrational frequency ratio of 2<sup>(1/12)</sup>/1. We call these twelve notes C, C♯/D♭, D, D♯/E♭, E, F, F♯/G♭, G, G♯/A♭, A, A♯/B♭, and B. The interval spanning two notes is called a whole step or a whole tone, and the interval spanning one note is called a half-step or a semitone. The sharp (♯) and flat (♭) accidentals are used to denote differences of a half step, and the natural (♮) cancels out other accidentals in a measure. Double-sharps and double-flats do exist, but are rarely used. A traditional Western diatonic scale consists of five whole steps and two half steps. For example, the standard C Major diatonic scale consists of the notes C, D, E, F, G, A, B, and C in that order. Other scales do exist (pentatonic, octatonic, etc), but the major scale is the most important.
-To better describe intervals, the semitone can be split into 100 equally spaced steps, or cents. Two notes a cent apart have a frequency ratio of 2<sup>(1/1200)</sup>/1, and there are 1200 cents equally distributed in an octave. This interval is too small for the human ear to differentiate, because human ears can only detect about a 5-10 cent difference between two notes. Using cents is useful in determining how close two notes are to each other. Solving the equation below determines how many cents the rational interval a/b spans. For example, The 3/2 interval is an interval about 701.96 cents. A fifth (C to G) in 12edo has the ratio of 2<sup>(7/12)</sup>/1; this ratio is about 2 cents flat of the ratio 3/2. The harmonic seventh (C to B♭) has a ratio of 2<sup>(5/6)</sup>/1 in 12edo, which is 31 cents sharp of its just intonation counterpart, 7/4. More divisions of the octave means higher precision for specific intervals. Higher divisions per octave (like 22edo, 31edo, and 53edo) can sometimes provide much better approximations of harmonic series ratios than 12edo. It's important to point out that microtonal music does exist historically in non-Western music; for example, some types of Indian music unequally divides the octave into 22 unequal divisions of the octave.
+To better describe intervals, the semitone can be split into 100 equally spaced steps, or cents. Two notes a cent apart have a frequency ratio of 2<sup>(1/1200)</sup>/1, and there are 1200 cents equally distributed in an octave. This interval is too small for the human ear to differentiate, because human ears can only detect about a 5-10 cent difference between two notes. Using cents is useful in determining how close two notes are to each other. Solving the equation below determines how many cents the rational interval a/b spans. For example, The 3/2 interval is an interval about 701.96 cents. A fifth (C to G) in 12edo has the ratio of 2<sup>(7/12)</sup>/1; this ratio is about 2 cents flat of the ratio 3/2. The harmonic seventh (C to B♭) has a ratio of 2<sup>(5/6)</sup>/1 in 12edo, which is 31 cents sharp of its just intonation counterpart, 7/4. More divisions of the octave means that the higher precision for specific intervals. Higher divisions per octave (like 22edo, 31edo, and 53edo) can sometimes provide much better approximations of harmonic series ratios than 12edo. Microtonal music does exist historically in non-Western music. For example, some types of Indian music unequally divides the octave into 22 unequal divisions of the octave.
 <center> (a/b) = 2<sup>(X/1200)</sup> </center>
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 [[Category:Music (popular, contemporary, non-classical)]]
-[[Category:Foundations of Music Tech (20xx)]]
+[[Category:Foundations of Music Technology (2300)]]
 [[Category: Advisor:Manzo]]

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 == Introduction ==
-Recall that music is fundamentally based on ratios of the harmonic series (1, 1/2, 1/3, 1/4, etc.) and that an octave has the frequency ratio of 2/1, a perfect fifth has a ratio of 3/2, and a perfect fourth has a ratio of 4/3. This method of tuning an instrument based on fundamental frequencies is called just intonation, or JI. However, the JI isn't used in modern music because the ratios between notes are not preserved when transposing sound. It also is mathematically impossible to tune a piano with a single rational interval such that the octave's 2/1 ratio is preserved.
+Recall that music is fundamentally based on ratios of the harmonic series (1, 1/2, 1/3, 1/4, etc.) and that an octave has the frequency ratio of 2/1, a perfect fifth has a ratio of 3/2, and a perfect fourth has a ratio of 4/3. This method of tuning an instrument based on fundamental frequencies is called just intonation, or JI. However, JI isn't used in modern music because the ratios between notes are not preserved when transposing sound. It also is mathematically impossible to tune a piano with a single rational interval such that the octave's 2/1 ratio is preserved.
 For starters, traditional Western music breaks down the octave into 12 logarithmic equally spaced intervals. This tuning method is called 12 equal divisions of the octave, or 12edo. Two notes that are adjacent on a keyboard have the irrational frequency ratio of 2<sup>(1/12)</sup>/1. We call these twelve notes C, C♯/D♭, D, D♯/E♭, E, F, F♯/G♭, G, G♯/A♭, A, A♯/B♭, and B. The interval spanning two notes is called a whole step or a whole tone, and the interval spanning one note is called a half-step or a semitone. The sharp (♯) and flat (♭) accidentals are used to denote differences of a half step, and the natural (♮) cancels out other accidentals in a measure. Double-sharps and double-flats do exist, but are rarely used. A traditional Western diatonic scale consists of five whole steps and two half steps. For example, the standard C Major diatonic scale consists of the notes C, D, E, F, G, A, B, and C in that order. Other scales do exist (pentatonic, octatonic, etc), but the major scale is the most important.
-To better describe intervals, the semitone can be split into 100 equally spaced steps, or cents. Two notes a cent apart have a frequency ratio of 2<sup>(1/1200)</sup>/1, and there are 1200 cents equally distributed in an octave. This interval is too small for the human ear to differentiate, because human ears can only detect about a 5-10 cent difference between two notes. Using cents is useful in determining how close two notes are to each other. Solving the equation below determines how many cents the rational interval a/b spans. For example, The 3/2 interval is an interval about 701.96 cents. A fifth (C to G) in 12edo has the ratio of 2<sup>(7/12)</sup>/1; this ratio is about 2 cents flat of the ratio 3/2. The harmonic seventh (C to B♭) has a ratio of 2<sup>(5/6)</sup>/1 in 12edo, which is 31 cents sharp of its just intonation counterpart, 7/4. More divisions of the octave means that the higher precision for specific intervals. Higher divisions per octave (like 22edo, 31edo, and 53edo) can sometimes provide much better approximations of harmonic series ratios than 12edo. Microtonal music does exist historically in non-Western music. For example, some types of Indian music unequally divides the octave into 22 unequal divisions of the octave.
+To better describe intervals, the semitone can be split into 100 equally spaced steps, or cents. Two notes a cent apart have a frequency ratio of 2<sup>(1/1200)</sup>/1, and there are 1200 cents equally distributed in an octave. This interval is too small for the human ear to differentiate, because human ears can only detect about a 5-10 cent difference between two notes. Using cents is useful in determining how close two notes are to each other. Solving the equation below determines how many cents the rational interval a/b spans. For example, The 3/2 interval is an interval about 701.96 cents. A fifth (C to G) in 12edo has the ratio of 2<sup>(7/12)</sup>/1; this ratio is about 2 cents flat of the ratio 3/2. The harmonic seventh (C to B♭) has a ratio of 2<sup>(5/6)</sup>/1 in 12edo, which is 31 cents sharp of its just intonation counterpart, 7/4. More divisions of the octave means higher precision for specific intervals. Higher divisions per octave (like 22edo, 31edo, and 53edo) can sometimes provide much better approximations of harmonic series ratios than 12edo. It's important to point out that microtonal music does exist historically in non-Western music; for example, some types of Indian music unequally divides the octave into 22 unequal divisions of the octave.
 <center> (a/b) = 2<sup>(X/1200)</sup> </center>

← Older revision		Revision as of 00:59, 14 December 2019
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		+	By Victor Mercola
		+
	Microtonal music, by definition, is a type of music that uses intervals between notes smaller than a traditional semitone or half-step. However, it has become an umbrella term for music that doesn't use the standard 12-note tuning system. For my MU2300 final project, I created one original song and made a cover of another song, both of which did not use the standard tuning style.		Microtonal music, by definition, is a type of music that uses intervals between notes smaller than a traditional semitone or half-step. However, it has become an umbrella term for music that doesn't use the standard 12-note tuning system. For my MU2300 final project, I created one original song and made a cover of another song, both of which did not use the standard tuning style.

← Older revision		Revision as of 18:25, 12 October 2019
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	== 22edo, in MuseScore ==		== 22edo, in MuseScore ==
		+
		+	<mediaplayer>File:22edo test.mp4</mediaplayer>
		+
	Instead of breaking the octave into twelve equally spaced notes per octave, let’s break it into 22 equally spaced notes per octave. The ratio of two adjacent notes on this keyboard would be 2<sup>(1/22)</sup>/1, or about 54.55 cents. Since 22edo has almost twice the amount of notes as 12edo, new accidentals have to be introduced to denote the interval changes. One way to do this is to introduce "up" (↑) and "down" (↓) to denote shifting the base note up or down by one step, respectively. Sharps and flats can be repurposed to denote increments of three steps. We can combine these two types of accidentals together to get a range of accidents from -4 steps to +4 steps. Just like double-sharps and double-flats in 12edo, sharp-ups and flat-downs might not be used as much as the other accidentals.		Instead of breaking the octave into twelve equally spaced notes per octave, let’s break it into 22 equally spaced notes per octave. The ratio of two adjacent notes on this keyboard would be 2<sup>(1/22)</sup>/1, or about 54.55 cents. Since 22edo has almost twice the amount of notes as 12edo, new accidentals have to be introduced to denote the interval changes. One way to do this is to introduce "up" (↑) and "down" (↓) to denote shifting the base note up or down by one step, respectively. Sharps and flats can be repurposed to denote increments of three steps. We can combine these two types of accidentals together to get a range of accidents from -4 steps to +4 steps. Just like double-sharps and double-flats in 12edo, sharp-ups and flat-downs might not be used as much as the other accidentals.

← Older revision		Revision as of 18:14, 12 October 2019
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	== 22edo, in MuseScore ==		== 22edo, in MuseScore ==
−
−	~~<mediaplayer>File:22edo test.mp4</mediaplayer>~~
−
	Instead of breaking the octave into twelve equally spaced notes per octave, let’s break it into 22 equally spaced notes per octave. The ratio of two adjacent notes on this keyboard would be 2<sup>(1/22)</sup>/1, or about 54.55 cents. Since 22edo has almost twice the amount of notes as 12edo, new accidentals have to be introduced to denote the interval changes. One way to do this is to introduce "up" (↑) and "down" (↓) to denote shifting the base note up or down by one step, respectively. Sharps and flats can be repurposed to denote increments of three steps. We can combine these two types of accidentals together to get a range of accidents from -4 steps to +4 steps. Just like double-sharps and double-flats in 12edo, sharp-ups and flat-downs might not be used as much as the other accidentals.		Instead of breaking the octave into twelve equally spaced notes per octave, let’s break it into 22 equally spaced notes per octave. The ratio of two adjacent notes on this keyboard would be 2<sup>(1/22)</sup>/1, or about 54.55 cents. Since 22edo has almost twice the amount of notes as 12edo, new accidentals have to be introduced to denote the interval changes. One way to do this is to introduce "up" (↑) and "down" (↓) to denote shifting the base note up or down by one step, respectively. Sharps and flats can be repurposed to denote increments of three steps. We can combine these two types of accidentals together to get a range of accidents from -4 steps to +4 steps. Just like double-sharps and double-flats in 12edo, sharp-ups and flat-downs might not be used as much as the other accidentals.

@@ Line 12: / Line 12: @@
 == 22edo, in MuseScore ==
-[[File:22edo test.mp4]]
+<mediaplayer>File:22edo test.mp4</mediaplayer>
 Instead of breaking the octave into twelve equally spaced notes per octave, let’s break it into 22 equally spaced notes per octave. The ratio of two adjacent notes on this keyboard would be 2<sup>(1/22)</sup>/1, or about 54.55 cents. Since 22edo has almost twice the amount of notes as 12edo, new accidentals have to be introduced to denote the interval changes. One way to do this is to introduce "up" (↑) and "down" (↓) to denote shifting the base note up or down by one step, respectively. Sharps and flats can be repurposed to denote increments of three steps. We can combine these two types of accidentals together to get a range of accidents from -4 steps to +4 steps. Just like double-sharps and double-flats in 12edo, sharp-ups and flat-downs might not be used as much as the other accidentals.

← Older revision		Revision as of 18:03, 12 October 2019
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	== 22edo, in MuseScore ==		== 22edo, in MuseScore ==
		+
		+	[[File:22edo test.mp4]]
	Instead of breaking the octave into twelve equally spaced notes per octave, let’s break it into 22 equally spaced notes per octave. The ratio of two adjacent notes on this keyboard would be 2<sup>(1/22)</sup>/1, or about 54.55 cents. Since 22edo has almost twice the amount of notes as 12edo, new accidentals have to be introduced to denote the interval changes. One way to do this is to introduce "up" (↑) and "down" (↓) to denote shifting the base note up or down by one step, respectively. Sharps and flats can be repurposed to denote increments of three steps. We can combine these two types of accidentals together to get a range of accidents from -4 steps to +4 steps. Just like double-sharps and double-flats in 12edo, sharp-ups and flat-downs might not be used as much as the other accidentals.		Instead of breaking the octave into twelve equally spaced notes per octave, let’s break it into 22 equally spaced notes per octave. The ratio of two adjacent notes on this keyboard would be 2<sup>(1/22)</sup>/1, or about 54.55 cents. Since 22edo has almost twice the amount of notes as 12edo, new accidentals have to be introduced to denote the interval changes. One way to do this is to introduce "up" (↑) and "down" (↓) to denote shifting the base note up or down by one step, respectively. Sharps and flats can be repurposed to denote increments of three steps. We can combine these two types of accidentals together to get a range of accidents from -4 steps to +4 steps. Just like double-sharps and double-flats in 12edo, sharp-ups and flat-downs might not be used as much as the other accidentals.

← Older revision	Revision as of 17:58, 12 October 2019
(No difference)

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 The 72edo octave is grouped into 6 sets of 12 scales, each 1/6 of a semitone apart (~16.67 cents) in ascending order: red, orange, yellow, green, blue, violet. The scale starts from C-red, goes across the C's of the other scales, then returns to D-red, and so on.
-Using the Simpler tool in Live, I converted an excerpt of me playing piano into a single instrument, used the tuner in Live to tune it to A-432 Hz (as instructed on the sheet music), then adjusted it as closely as possible to the cent difference required for 72edos scales.
+Using the Simpler tool in Live, I converted an excerpt of me playing piano into a single instrument, used the tuner in Live to tune it to A-432 Hz (as instructed on the sheet music), then adjusted it as closely as possible to the cent difference required for 72edo's six separate scales.
 <mp3player>File:Toward-The-Continuum-72edo.mp3</mp3player>

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 The 22edo diatonic scale isn't the only scale that can be made with these 22 notes, though. Similar to 12edo, the starting point of the scale can be changed to make the Major, Dorian, Lydian, Mixolydian, Minor, and Locrian modes.  The 22edo Porcupine[7] scale has one long step and six short steps in the pattern "long-short-short-short-short-short-short", where the long step spans four notes and the short step spans three notes. Porcupine is denoted as "1L6s" - its modes are named "Chinchillian", "Badgerian", "Zebrian", "Dingoian", "Gazellian", "Lemurian", and "Pandian" <sup>[citation/fact-check needed]</sup>.
-One major notation difference when composing with these note names is that accidental notes that are equivalent in 12edo are not equal in 22edo. For example, A♯ and B♭ are equivalent in 12edo, but are two steps different in 22edo.
+One major notation difference when composing with these note names is that accidental notes that are equivalent in 12edo are not equal in 22edo. For example, A♯ and B♭ are equivalent in 12edo, but are two steps apart in 22edo.
 This is an etude I made in A↓ (A-down) minor in MuseScore using the [https://github.com/euwbah/musescore-n-tet-plugins 22edo plugin made by GitHub user eubwah]. The PDF file for the score can be downloaded here: [[File:Etude-in-a-down-minor-score.pdf]].