Basic introduction to xenharmonic music - Revision history

ArrowHead294 at 13:46, 26 February 2025

2025-02-26T13:46:34Z

@@ Line 3: / Line 3: @@
 Things to cover:
-'''Unit 1''' - picking up where the AP music theory test leaves off (and getting everyone else up to speed)
+'''Unit 1:''' Picking up where the AP music theory test leaves off (and getting everyone else up to speed)
-'''Unit 2''' - frequencies, ratios, etc
+'''Unit 2:''' Frequencies, ratios, etc
-'''Unit 3''' - temperaments
+'''Unit 3:''' Temperaments
-<ol><li>Commas are enharmonic equivalences on steroids</li><li>The syntonic comma makes the world go round (probably a bad idea to write &lt;12 19 28|-4 4 -1&gt;=0 here, haha...)</li><li>Finally introduce new rank-2 temperaments, like blackwood and porcupine (epic musical examples wanted here!)</li><li>BRIEFLY introduce the concept of those rank-2 temperaments closing into other equal temperaments (e.g. as an approach to answer questions like "how do I use 15-EDO?")</li><li>List some awesome temperaments and related scales using them (equip these scales with #/b accidentals plz)</li><li>Awesome musical examples!</li><li>Temperaments are broad objects involving intonation. WTF do I do with them?</li><li>Puns! Comma pumps! Dyadic chords!</li><li>Talk about MOS series as a generalization of pentatonic/diatonic/chromatic scales!</li><li>Talk about MODMOS's!</li><li>Higher-limit JI!</li><li>EDOs support an infinite amount of rank-2 temperaments! (note: don't forget about [[Lists_of_edo-distinct_temperaments|EDO-distinct]] temperaments)</li><li>Talk about Gene's work with microtemperaments!</li><li>Ethnomusicological tunings! Mavila! Maqamic! Srutal!</li><li>Tuning accuracy for crunchy stuff!</li><li>Careful use of timbre + lower accuracy for colorful stuff!</li><li>(INVENT MORE COOL STUFF IN REAL LIFE AND WRITE IT HERE)</li></ol>
+Feel free to change
 [[Category:todo:expand]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

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Wikispaces>Sarzadoce: Imported revision 394452434 - Original comment:

2012-12-23T23:57:39Z

**Imported revision 394452434 - Original comment: **

← Older revision		Revision as of 23:57, 23 December 2012
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	: The original revision id was <tt>~~394439190~~</tt>.<br>		: The original revision id was <tt>394452434</tt>.<br>
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	# Awesome musical examples!		# Awesome musical examples!
	# Temperaments are broad objects involving intonation. WTF do I do with them?		# Temperaments are broad objects involving intonation. WTF do I do with them?
	# Puns! Comma pumps!		# Puns! Comma pumps! Dyadic chords!
	# Talk about MOS series as a generalization of pentatonic/diatonic/chromatic scales!		# Talk about MOS series as a generalization of pentatonic/diatonic/chromatic scales!
	# Talk about MODMOS's!		# Talk about MODMOS's!
	# Higher-limit JI!		# Higher-limit JI!
	# EDOs support an infinite amount of rank-2 temperaments!		# EDOs support an infinite amount of rank-2 temperaments! (note: don't forget about [[Lists of edo-distinct temperaments\|EDO-distinct]] temperaments)
	# Talk about Gene's work with microtemperaments!		# Talk about Gene's work with microtemperaments!
	# Ethnomusicological tunings! Mavila! Maqamic! Srutal!		# Ethnomusicological tunings! Mavila! Maqamic! Srutal!
Line 57:		Line 57:
	<ol><li>Talk about frequencies, ratios, cents, Hz, the harmonic series (just briefly mentioning logarithms and saying what the practical implications are - this is not for mathematicians!) (only one item but this part will actually have to be pretty long)</li><li>Approximate relationships between 12edo and JI - the fact that each interval represents many JI ratios (important because a lot of sources give exactly one JI ratio per 12edo interval which is very misleading)</li><li>Odd limit, prime limit?</li><li>JI lattices (VERY BRIEFLY) (optional: epic animation of the circle of fifths opening into a chain and then the chain itself opening into the 5-limit lattice!)</li><li>Commas as small differences between pitches you might expect to be the same (no mention of tempering them out yet)</li></ol><br />		<ol><li>Talk about frequencies, ratios, cents, Hz, the harmonic series (just briefly mentioning logarithms and saying what the practical implications are - this is not for mathematicians!) (only one item but this part will actually have to be pretty long)</li><li>Approximate relationships between 12edo and JI - the fact that each interval represents many JI ratios (important because a lot of sources give exactly one JI ratio per 12edo interval which is very misleading)</li><li>Odd limit, prime limit?</li><li>JI lattices (VERY BRIEFLY) (optional: epic animation of the circle of fifths opening into a chain and then the chain itself opening into the 5-limit lattice!)</li><li>Commas as small differences between pitches you might expect to be the same (no mention of tempering them out yet)</li></ol><br />
	<strong>Unit 3</strong> - temperaments<br />		<strong>Unit 3</strong> - temperaments<br />
	<ol><li>Commas are enharmonic equivalences on steroids</li><li>The syntonic comma makes the world go round (probably a bad idea to write &lt;12 19 28\|-4 4 -1&gt;=0 here, haha...)</li><li>Finally introduce new rank-2 temperaments, like blackwood and porcupine (epic musical examples wanted here!)</li><li>BRIEFLY introduce the concept of those rank-2 temperaments closing into other equal temperaments (e.g. as an approach to answer questions like &quot;how do I use 15-EDO?&quot;)</li><li>List some awesome temperaments and related scales using them (equip these scales with #/b accidentals plz)</li><li>Awesome musical examples!</li><li>Temperaments are broad objects involving intonation. WTF do I do with them?</li><li>Puns! Comma pumps!</li><li>Talk about MOS series as a generalization of pentatonic/diatonic/chromatic scales!</li><li>Talk about MODMOS's!</li><li>Higher-limit JI!</li><li>EDOs support an infinite amount of rank-2 temperaments!</li><li>Talk about Gene's work with microtemperaments!</li><li>Ethnomusicological tunings! Mavila! Maqamic! Srutal!</li><li>Tuning accuracy for crunchy stuff!</li><li>Careful use of timbre + lower accuracy for colorful stuff!</li><li>(INVENT MORE COOL STUFF IN REAL LIFE AND WRITE IT HERE)</li></ol><br />		<ol><li>Commas are enharmonic equivalences on steroids</li><li>The syntonic comma makes the world go round (probably a bad idea to write &lt;12 19 28\|-4 4 -1&gt;=0 here, haha...)</li><li>Finally introduce new rank-2 temperaments, like blackwood and porcupine (epic musical examples wanted here!)</li><li>BRIEFLY introduce the concept of those rank-2 temperaments closing into other equal temperaments (e.g. as an approach to answer questions like &quot;how do I use 15-EDO?&quot;)</li><li>List some awesome temperaments and related scales using them (equip these scales with #/b accidentals plz)</li><li>Awesome musical examples!</li><li>Temperaments are broad objects involving intonation. WTF do I do with them?</li><li>Puns! Comma pumps! Dyadic chords!</li><li>Talk about MOS series as a generalization of pentatonic/diatonic/chromatic scales!</li><li>Talk about MODMOS's!</li><li>Higher-limit JI!</li><li>EDOs support an infinite amount of rank-2 temperaments! (note: don't forget about <a class="wiki_link" href="/Lists%20of%20edo-distinct%20temperaments">EDO-distinct</a> temperaments)</li><li>Talk about Gene's work with microtemperaments!</li><li>Ethnomusicological tunings! Mavila! Maqamic! Srutal!</li><li>Tuning accuracy for crunchy stuff!</li><li>Careful use of timbre + lower accuracy for colorful stuff!</li><li>(INVENT MORE COOL STUFF IN REAL LIFE AND WRITE IT HERE)</li></ol><br />
	Feel free to change</body></html></pre></div>		Feel free to change</body></html></pre></div>

Wikispaces>keenanpepper: Imported revision 394439190 - Original comment:

2012-12-23T20:09:21Z

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Wikispaces>keenanpepper: Imported revision 337238490 - Original comment:

2012-05-19T02:26:30Z

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Wikispaces>keenanpepper: Imported revision 336851514 - Original comment: Reverted to May 17, 2012 12:42 pm: want to make changes starting from this

2012-05-17T20:56:35Z

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Wikispaces>keenanpepper: Imported revision 336780322 - Original comment:

2012-05-17T16:10:45Z

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← Older revision		Revision as of 20:09, 23 December 2012
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	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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	: The original revision id was <tt>~~337238490~~</tt>.<br>		: The original revision id was <tt>394439190</tt>.<br>
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	# Introduce the idea that instead of this leading to a "12 tone unequal temperament," it actually leads to an "infinite" tuning system that goes on forever (e.g. meantone isn't just a 12 tone unequal tuning - there exist more than 12 notes in meantone. this is the first 'aha' moment that most music students will have)		# Introduce the idea that instead of this leading to a "12 tone unequal temperament," it actually leads to an "infinite" tuning system that goes on forever (e.g. meantone isn't just a 12 tone unequal tuning - there exist more than 12 notes in meantone. this is the first 'aha' moment that most music students will have)
	# Introduce the idea of the circle of fifths "opening up" into the full neverending chain, and 12 being a particular way to "close" the chain, turning C# and Db into the same note		# Introduce the idea of the circle of fifths "opening up" into the full neverending chain, and 12 being a particular way to "close" the chain, turning C# and Db into the same note
	# Introduce the idea that 19 is another way to close the chain, and that this introduces "new enharmonic equivalences." (epic musical examples ~~needed~~)		# Introduce the idea that 19 is another way to close the chain, and that this introduces "new enharmonic equivalences." (epic musical examples desired)
	# Touch on other ways to close the chain - 17, 7, 5, 26, 31, etc. Possibly introduce the word "temperament" to explain this idea of dimensionality reduction		# Touch on other ways to close the chain - 17, 7, 5, 26, 31, etc. Possibly introduce the word "temperament" to explain this idea of dimensionality reduction
	# Introduce the idea that there's even more to music than just the circle of fifths, and that "meantone" itself is a temperament of something more fundamental (Maybe remind people about the diminished scale and augmented and so on, I dunno. BE SURE TO NOT LEAD PEOPLE INTO THE RATIOS = CATEGORIES FALLACY)		# Introduce the idea that there's even more to music than just the circle of fifths, and that "meantone" itself is a temperament of something more fundamental (Maybe remind people about the diminished scale and augmented and so on, I dunno. BE SURE TO NOT LEAD PEOPLE INTO THE RATIOS = CATEGORIES FALLACY)
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	# Commas are enharmonic equivalences on steroids		# Commas are enharmonic equivalences on steroids
	# The syntonic comma makes the world go round (probably a bad idea to write <12 19 28\|-4 4 -1>=0 here, haha...)		# The syntonic comma makes the world go round (probably a bad idea to write <12 19 28\|-4 4 -1>=0 here, haha...)
	# Finally introduce new rank-2 temperaments, like blackwood and porcupine (epic musical examples ~~needed~~ here!)		# Finally introduce new rank-2 temperaments, like blackwood and porcupine (epic musical examples wanted here!)
	# BRIEFLY introduce the concept of those rank-2 temperaments closing into other equal temperaments (e.g. as an approach to answer questions like "how do I use 15-EDO?")		# BRIEFLY introduce the concept of those rank-2 temperaments closing into other equal temperaments (e.g. as an approach to answer questions like "how do I use 15-EDO?")
	# List some awesome temperaments and related scales using them (equip these scales with #/b accidentals plz)		# List some awesome temperaments and related scales using them (equip these scales with #/b accidentals plz)
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	<br />		<br />
	<strong>Unit 1</strong> - picking up where the AP music theory test leaves off (and getting everyone else up to speed)<br />		<strong>Unit 1</strong> - picking up where the AP music theory test leaves off (and getting everyone else up to speed)<br />
	<ol><li>What 12edo really is (must drive home the point that there are 12 notes per octave, not, say, 8, as some people would say if you asked them. just very basic stuff, no acoustics)</li><li>What Western notation really is (note that there's both C# and Db for some reason, and that they both map to the same note)</li><li>Explain that historically, C# and Db were different things, and that our notation is a remnant of the historic system (most music students are up to speed at this point)</li><li>Introduce the idea that instead of this leading to a &quot;12 tone unequal temperament,&quot; it actually leads to an &quot;infinite&quot; tuning system that goes on forever (e.g. meantone isn't just a 12 tone unequal tuning - there exist more than 12 notes in meantone. this is the first 'aha' moment that most music students will have)</li><li>Introduce the idea of the circle of fifths &quot;opening up&quot; into the full neverending chain, and 12 being a particular way to &quot;close&quot; the chain, turning C# and Db into the same note</li><li>Introduce the idea that 19 is another way to close the chain, and that this introduces &quot;new enharmonic equivalences.&quot; (epic musical examples ~~needed~~)</li><li>Touch on other ways to close the chain - 17, 7, 5, 26, 31, etc. Possibly introduce the word &quot;temperament&quot; to explain this idea of dimensionality reduction</li><li>Introduce the idea that there's even more to music than just the circle of fifths, and that &quot;meantone&quot; itself is a temperament of something more fundamental (Maybe remind people about the diminished scale and augmented and so on, I dunno. BE SURE TO NOT LEAD PEOPLE INTO THE RATIOS = CATEGORIES FALLACY)</li><li>Play tantalizing porcupine/blackwood/machine clips and so on</li><li>Introduce the idea that to understand what's going on, we'll dig even deeper than music and start looking at the building blocks of sound itself (except not really, lulz)</li></ol><br />		<ol><li>What 12edo really is (must drive home the point that there are 12 notes per octave, not, say, 8, as some people would say if you asked them. just very basic stuff, no acoustics)</li><li>What Western notation really is (note that there's both C# and Db for some reason, and that they both map to the same note)</li><li>Explain that historically, C# and Db were different things, and that our notation is a remnant of the historic system (most music students are up to speed at this point)</li><li>Introduce the idea that instead of this leading to a &quot;12 tone unequal temperament,&quot; it actually leads to an &quot;infinite&quot; tuning system that goes on forever (e.g. meantone isn't just a 12 tone unequal tuning - there exist more than 12 notes in meantone. this is the first 'aha' moment that most music students will have)</li><li>Introduce the idea of the circle of fifths &quot;opening up&quot; into the full neverending chain, and 12 being a particular way to &quot;close&quot; the chain, turning C# and Db into the same note</li><li>Introduce the idea that 19 is another way to close the chain, and that this introduces &quot;new enharmonic equivalences.&quot; (epic musical examples desired)</li><li>Touch on other ways to close the chain - 17, 7, 5, 26, 31, etc. Possibly introduce the word &quot;temperament&quot; to explain this idea of dimensionality reduction</li><li>Introduce the idea that there's even more to music than just the circle of fifths, and that &quot;meantone&quot; itself is a temperament of something more fundamental (Maybe remind people about the diminished scale and augmented and so on, I dunno. BE SURE TO NOT LEAD PEOPLE INTO THE RATIOS = CATEGORIES FALLACY)</li><li>Play tantalizing porcupine/blackwood/machine clips and so on</li><li>Introduce the idea that to understand what's going on, we'll dig even deeper than music and start looking at the building blocks of sound itself (except not really, lulz)</li></ol><br />
	<strong>Unit 2</strong> - frequencies, ratios, etc<br />		<strong>Unit 2</strong> - frequencies, ratios, etc<br />
	<ol><li>Talk about frequencies, ratios, cents, Hz, the harmonic series (just briefly mentioning logarithms and saying what the practical implications are - this is not for mathematicians!) (only one item but this part will actually have to be pretty long)</li><li>Approximate relationships between 12edo and JI - the fact that each interval represents many JI ratios (important because a lot of sources give exactly one JI ratio per 12edo interval which is very misleading)</li><li>Odd limit, prime limit?</li><li>JI lattices (VERY BRIEFLY) (optional: epic animation of the circle of fifths opening into a chain and then the chain itself opening into the 5-limit lattice!)</li><li>Commas as small differences between pitches you might expect to be the same (no mention of tempering them out yet)</li></ol><br />		<ol><li>Talk about frequencies, ratios, cents, Hz, the harmonic series (just briefly mentioning logarithms and saying what the practical implications are - this is not for mathematicians!) (only one item but this part will actually have to be pretty long)</li><li>Approximate relationships between 12edo and JI - the fact that each interval represents many JI ratios (important because a lot of sources give exactly one JI ratio per 12edo interval which is very misleading)</li><li>Odd limit, prime limit?</li><li>JI lattices (VERY BRIEFLY) (optional: epic animation of the circle of fifths opening into a chain and then the chain itself opening into the 5-limit lattice!)</li><li>Commas as small differences between pitches you might expect to be the same (no mention of tempering them out yet)</li></ol><br />
	<strong>Unit 3</strong> - temperaments<br />		<strong>Unit 3</strong> - temperaments<br />
	<ol><li>Commas are enharmonic equivalences on steroids</li><li>The syntonic comma makes the world go round (probably a bad idea to write &lt;12 19 28\|-4 4 -1&gt;=0 here, haha...)</li><li>Finally introduce new rank-2 temperaments, like blackwood and porcupine (epic musical examples ~~needed~~ here!)</li><li>BRIEFLY introduce the concept of those rank-2 temperaments closing into other equal temperaments (e.g. as an approach to answer questions like &quot;how do I use 15-EDO?&quot;)</li><li>List some awesome temperaments and related scales using them (equip these scales with #/b accidentals plz)</li><li>Awesome musical examples!</li><li>Temperaments are broad objects involving intonation. WTF do I do with them?</li><li>Puns! Comma pumps!</li><li>Talk about MOS series as a generalization of pentatonic/diatonic/chromatic scales!</li><li>Talk about MODMOS's!</li><li>Higher-limit JI!</li><li>EDOs support an infinite amount of rank-2 temperaments!</li><li>Talk about Gene's work with microtemperaments!</li><li>Ethnomusicological tunings! Mavila! Maqamic! Srutal!</li><li>Tuning accuracy for crunchy stuff!</li><li>Careful use of timbre + lower accuracy for colorful stuff!</li><li>(INVENT MORE COOL STUFF IN REAL LIFE AND WRITE IT HERE)</li></ol><br />		<ol><li>Commas are enharmonic equivalences on steroids</li><li>The syntonic comma makes the world go round (probably a bad idea to write &lt;12 19 28\|-4 4 -1&gt;=0 here, haha...)</li><li>Finally introduce new rank-2 temperaments, like blackwood and porcupine (epic musical examples wanted here!)</li><li>BRIEFLY introduce the concept of those rank-2 temperaments closing into other equal temperaments (e.g. as an approach to answer questions like &quot;how do I use 15-EDO?&quot;)</li><li>List some awesome temperaments and related scales using them (equip these scales with #/b accidentals plz)</li><li>Awesome musical examples!</li><li>Temperaments are broad objects involving intonation. WTF do I do with them?</li><li>Puns! Comma pumps!</li><li>Talk about MOS series as a generalization of pentatonic/diatonic/chromatic scales!</li><li>Talk about MODMOS's!</li><li>Higher-limit JI!</li><li>EDOs support an infinite amount of rank-2 temperaments!</li><li>Talk about Gene's work with microtemperaments!</li><li>Ethnomusicological tunings! Mavila! Maqamic! Srutal!</li><li>Tuning accuracy for crunchy stuff!</li><li>Careful use of timbre + lower accuracy for colorful stuff!</li><li>(INVENT MORE COOL STUFF IN REAL LIFE AND WRITE IT HERE)</li></ol><br />
	Feel free to change</body></html></pre></div>		Feel free to change</body></html></pre></div>

← Older revision		Revision as of 02:26, 19 May 2012
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	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:keenanpepper\|keenanpepper]] and made on <tt>2012-05-19 02:00:09 UTC</tt>.<br>		: This revision was by author [[User:keenanpepper\|keenanpepper]] and made on <tt>2012-05-19 02:26:30 UTC</tt>.<br>
	: The original revision id was <tt>~~337235896~~</tt>.<br>		: The original revision id was <tt>337238490</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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	# EDOs support an infinite amount of rank-2 temperaments!		# EDOs support an infinite amount of rank-2 temperaments!
	# Talk about Gene's work with microtemperaments!		# Talk about Gene's work with microtemperaments!
	# Ethnomusicological tunings! Mavila! Maqamic! ~~Slendric! (maybe)~~ Srutal!		# Ethnomusicological tunings! Mavila! Maqamic! Srutal!
	# Tuning accuracy for crunchy stuff!		# Tuning accuracy for crunchy stuff!
	# Careful use of timbre + lower accuracy for colorful stuff!		# Careful use of timbre + lower accuracy for colorful stuff!
Line 57:		Line 57:
	<ol><li>Talk about frequencies, ratios, cents, Hz, the harmonic series (just briefly mentioning logarithms and saying what the practical implications are - this is not for mathematicians!) (only one item but this part will actually have to be pretty long)</li><li>Approximate relationships between 12edo and JI - the fact that each interval represents many JI ratios (important because a lot of sources give exactly one JI ratio per 12edo interval which is very misleading)</li><li>Odd limit, prime limit?</li><li>JI lattices (VERY BRIEFLY) (optional: epic animation of the circle of fifths opening into a chain and then the chain itself opening into the 5-limit lattice!)</li><li>Commas as small differences between pitches you might expect to be the same (no mention of tempering them out yet)</li></ol><br />		<ol><li>Talk about frequencies, ratios, cents, Hz, the harmonic series (just briefly mentioning logarithms and saying what the practical implications are - this is not for mathematicians!) (only one item but this part will actually have to be pretty long)</li><li>Approximate relationships between 12edo and JI - the fact that each interval represents many JI ratios (important because a lot of sources give exactly one JI ratio per 12edo interval which is very misleading)</li><li>Odd limit, prime limit?</li><li>JI lattices (VERY BRIEFLY) (optional: epic animation of the circle of fifths opening into a chain and then the chain itself opening into the 5-limit lattice!)</li><li>Commas as small differences between pitches you might expect to be the same (no mention of tempering them out yet)</li></ol><br />
	<strong>Unit 3</strong> - temperaments<br />		<strong>Unit 3</strong> - temperaments<br />
	<ol><li>Commas are enharmonic equivalences on steroids</li><li>The syntonic comma makes the world go round (probably a bad idea to write &lt;12 19 28\|-4 4 -1&gt;=0 here, haha...)</li><li>Finally introduce new rank-2 temperaments, like blackwood and porcupine (epic musical examples needed here!)</li><li>BRIEFLY introduce the concept of those rank-2 temperaments closing into other equal temperaments (e.g. as an approach to answer questions like &quot;how do I use 15-EDO?&quot;)</li><li>List some awesome temperaments and related scales using them (equip these scales with #/b accidentals plz)</li><li>Awesome musical examples!</li><li>Temperaments are broad objects involving intonation. WTF do I do with them?</li><li>Puns! Comma pumps!</li><li>Talk about MOS series as a generalization of pentatonic/diatonic/chromatic scales!</li><li>Talk about MODMOS's!</li><li>Higher-limit JI!</li><li>EDOs support an infinite amount of rank-2 temperaments!</li><li>Talk about Gene's work with microtemperaments!</li><li>Ethnomusicological tunings! Mavila! Maqamic! ~~Slendric! (maybe)~~ Srutal!</li><li>Tuning accuracy for crunchy stuff!</li><li>Careful use of timbre + lower accuracy for colorful stuff!</li><li>(INVENT MORE COOL STUFF IN REAL LIFE AND WRITE IT HERE)</li></ol><br />		<ol><li>Commas are enharmonic equivalences on steroids</li><li>The syntonic comma makes the world go round (probably a bad idea to write &lt;12 19 28\|-4 4 -1&gt;=0 here, haha...)</li><li>Finally introduce new rank-2 temperaments, like blackwood and porcupine (epic musical examples needed here!)</li><li>BRIEFLY introduce the concept of those rank-2 temperaments closing into other equal temperaments (e.g. as an approach to answer questions like &quot;how do I use 15-EDO?&quot;)</li><li>List some awesome temperaments and related scales using them (equip these scales with #/b accidentals plz)</li><li>Awesome musical examples!</li><li>Temperaments are broad objects involving intonation. WTF do I do with them?</li><li>Puns! Comma pumps!</li><li>Talk about MOS series as a generalization of pentatonic/diatonic/chromatic scales!</li><li>Talk about MODMOS's!</li><li>Higher-limit JI!</li><li>EDOs support an infinite amount of rank-2 temperaments!</li><li>Talk about Gene's work with microtemperaments!</li><li>Ethnomusicological tunings! Mavila! Maqamic! Srutal!</li><li>Tuning accuracy for crunchy stuff!</li><li>Careful use of timbre + lower accuracy for colorful stuff!</li><li>(INVENT MORE COOL STUFF IN REAL LIFE AND WRITE IT HERE)</li></ol><br />
	Feel free to change</body></html></pre></div>		Feel free to change</body></html></pre></div>

← Older revision		Revision as of 16:10, 17 May 2012
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	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:keenanpepper\|keenanpepper]] and made on <tt>2012-05-17 16:04:30 UTC</tt>.<br>		: This revision was by author [[User:keenanpepper\|keenanpepper]] and made on <tt>2012-05-17 16:10:45 UTC</tt>.<br>
	: The original revision id was <tt>~~336778378~~</tt>.<br>		: The original revision id was <tt>336780322</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
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	# Odd limit, prime limit?		# Odd limit, prime limit?
	# JI lattices (VERY BRIEFLY) (optional: epic animation of the circle of fifths opening into a chain and then the chain itself opening into the 5-limit lattice!)		# JI lattices (VERY BRIEFLY) (optional: epic animation of the circle of fifths opening into a chain and then the chain itself opening into the 5-limit lattice!)
	# ~~The~~ diatonic scale in JI, and the wolf intervals ~~in it~~		# Trying to make the diatonic scale in JI (Pythagorean, Zarlino/Ptolemy...), and the unavoidable appearance of wolf intervals

	Unit 3 - temperaments		Unit 3 - temperaments
Line 56:		Line 56:
	<ol><li>What 12edo really is (must drive home the point that there are 12 notes per octave, not, say, 8, as some people would say if you asked them. just very basic stuff, no acoustics)</li><li>What Western notation really is (note that there's both C# and Db for some reason, and that they both map to the same note)</li><li>Explain that historically, C# and Db were different things, and that our notation is a remnant of the historic system (most music students are up to speed at this point)</li><li>Introduce the idea that instead of this leading to a &quot;12 tone unequal temperament,&quot; it actually leads to an &quot;infinite&quot; tuning system that goes on forever (e.g. meantone isn't just a 12 tone unequal tuning - there exist more than 12 notes in meantone. this is the first 'aha' moment that most music students will have)</li><li>Introduce the idea of the circle of fifths &quot;opening up&quot; into the full neverending chain, and 12 being a particular way to &quot;close&quot; the chain, turning C# and Db into the same note</li><li>Introduce the idea that 19 is another way to close the chain, and that this introduces &quot;new enharmonic equivalences.&quot; (epic musical examples needed)</li><li>Touch on other ways to close the chain - 17, 7, 5, 26, 31, etc. Possibly introduce the word &quot;temperament&quot; to explain this idea of dimensionality reduction</li><li>Introduce the idea that there's even more to music than just the circle of fifths, and that &quot;meantone&quot; itself is a temperament of something more fundamental (Maybe remind people about the diminished scale and augmented and so on, I dunno. BE SURE TO NOT LEAD PEOPLE INTO THE RATIOS = CATEGORIES FALLACY)</li><li>Play tantalizing porcupine/blackwood/machine clips and so on</li><li>Introduce the idea that to understand what's going on, we'll dig even deeper than music and start looking at the building blocks of sound itself (except not really, lulz)</li></ol><br />		<ol><li>What 12edo really is (must drive home the point that there are 12 notes per octave, not, say, 8, as some people would say if you asked them. just very basic stuff, no acoustics)</li><li>What Western notation really is (note that there's both C# and Db for some reason, and that they both map to the same note)</li><li>Explain that historically, C# and Db were different things, and that our notation is a remnant of the historic system (most music students are up to speed at this point)</li><li>Introduce the idea that instead of this leading to a &quot;12 tone unequal temperament,&quot; it actually leads to an &quot;infinite&quot; tuning system that goes on forever (e.g. meantone isn't just a 12 tone unequal tuning - there exist more than 12 notes in meantone. this is the first 'aha' moment that most music students will have)</li><li>Introduce the idea of the circle of fifths &quot;opening up&quot; into the full neverending chain, and 12 being a particular way to &quot;close&quot; the chain, turning C# and Db into the same note</li><li>Introduce the idea that 19 is another way to close the chain, and that this introduces &quot;new enharmonic equivalences.&quot; (epic musical examples needed)</li><li>Touch on other ways to close the chain - 17, 7, 5, 26, 31, etc. Possibly introduce the word &quot;temperament&quot; to explain this idea of dimensionality reduction</li><li>Introduce the idea that there's even more to music than just the circle of fifths, and that &quot;meantone&quot; itself is a temperament of something more fundamental (Maybe remind people about the diminished scale and augmented and so on, I dunno. BE SURE TO NOT LEAD PEOPLE INTO THE RATIOS = CATEGORIES FALLACY)</li><li>Play tantalizing porcupine/blackwood/machine clips and so on</li><li>Introduce the idea that to understand what's going on, we'll dig even deeper than music and start looking at the building blocks of sound itself (except not really, lulz)</li></ol><br />
	<strong>Unit 2</strong> - frequencies, ratios, etc<br />		<strong>Unit 2</strong> - frequencies, ratios, etc<br />
	<ol><li>Talk about frequencies, ratios, cents, Hz, the harmonic series (just briefly mentioning logarithms and saying what the practical implications are - this is not for mathematicians!) (only one item but this part will actually have to be pretty long)</li><li>Approximate relationships between 12edo and JI - the fact that each interval represents many JI ratios (important because a lot of sources give exactly one JI ratio per 12edo interval which is very misleading)</li><li>Odd limit, prime limit?</li><li>JI lattices (VERY BRIEFLY) (optional: epic animation of the circle of fifths opening into a chain and then the chain itself opening into the 5-limit lattice!)</li><li>~~The~~ diatonic scale in JI, and the wolf intervals ~~in it~~</li></ol><br />		<ol><li>Talk about frequencies, ratios, cents, Hz, the harmonic series (just briefly mentioning logarithms and saying what the practical implications are - this is not for mathematicians!) (only one item but this part will actually have to be pretty long)</li><li>Approximate relationships between 12edo and JI - the fact that each interval represents many JI ratios (important because a lot of sources give exactly one JI ratio per 12edo interval which is very misleading)</li><li>Odd limit, prime limit?</li><li>JI lattices (VERY BRIEFLY) (optional: epic animation of the circle of fifths opening into a chain and then the chain itself opening into the 5-limit lattice!)</li><li>Trying to make the diatonic scale in JI (Pythagorean, Zarlino/Ptolemy...), and the unavoidable appearance of wolf intervals</li></ol><br />
	<strong>Unit 3</strong> - temperaments<br />		<strong>Unit 3</strong> - temperaments<br />
	<ol><li>The diatonic scale in 12edo has patterns of intervals that can't possibly exist in JI (wolves)</li><li>Commas are enharmonic equivalences on steroids</li><li>The syntonic comma makes the world go round (probably a bad idea to write &lt;12 19 28\|-4 4 -1&gt;=0 here, haha...)</li><li>Meantone temperament (tie it back to the chain of fifths in unit 1) - the diatonic scale always &quot;works&quot; in it</li></ol>Other points in no particular order yet:<br />		<ol><li>The diatonic scale in 12edo has patterns of intervals that can't possibly exist in JI (wolves)</li><li>Commas are enharmonic equivalences on steroids</li><li>The syntonic comma makes the world go round (probably a bad idea to write &lt;12 19 28\|-4 4 -1&gt;=0 here, haha...)</li><li>Meantone temperament (tie it back to the chain of fifths in unit 1) - the diatonic scale always &quot;works&quot; in it</li></ol>Other points in no particular order yet:<br />
	<ul><li>Finally introduce new rank-2 temperaments, like blackwood and porcupine (epic musical examples needed here!)</li><li>BRIEFLY introduce the concept of those rank-2 temperaments closing into other equal temperaments (e.g. as an approach to answer questions like &quot;how do I use 15-EDO?&quot;)</li><li>List some awesome temperaments and related scales using them (equip these scales with #/b accidentals plz)</li><li>Awesome musical examples!</li><li>Temperaments are broad objects involving intonation. WTF do I do with them?</li><li>Puns! Comma pumps!</li><li>Talk about MOS series as a generalization of pentatonic/diatonic/chromatic scales!</li><li>Talk about MODMOS's!</li><li>Higher-limit JI!</li><li>EDOs support an infinite amount of rank-2 temperaments!</li><li>Talk about Gene's work with microtemperaments!</li><li>Ethnomusicological tunings! Mavila! Maqamic! Slendric! (maybe) Srutal!</li><li>Tuning accuracy for crunchy stuff!</li><li>Careful use of timbre + lower accuracy for colorful stuff!</li><li>(INVENT MORE COOL STUFF IN REAL LIFE AND WRITE IT HERE)</li></ul><br />		<ul><li>Finally introduce new rank-2 temperaments, like blackwood and porcupine (epic musical examples needed here!)</li><li>BRIEFLY introduce the concept of those rank-2 temperaments closing into other equal temperaments (e.g. as an approach to answer questions like &quot;how do I use 15-EDO?&quot;)</li><li>List some awesome temperaments and related scales using them (equip these scales with #/b accidentals plz)</li><li>Awesome musical examples!</li><li>Temperaments are broad objects involving intonation. WTF do I do with them?</li><li>Puns! Comma pumps!</li><li>Talk about MOS series as a generalization of pentatonic/diatonic/chromatic scales!</li><li>Talk about MODMOS's!</li><li>Higher-limit JI!</li><li>EDOs support an infinite amount of rank-2 temperaments!</li><li>Talk about Gene's work with microtemperaments!</li><li>Ethnomusicological tunings! Mavila! Maqamic! Slendric! (maybe) Srutal!</li><li>Tuning accuracy for crunchy stuff!</li><li>Careful use of timbre + lower accuracy for colorful stuff!</li><li>(INVENT MORE COOL STUFF IN REAL LIFE AND WRITE IT HERE)</li></ul><br />
	Feel free to change</body></html></pre></div>		Feel free to change</body></html></pre></div>

← Older revision		Revision as of 16:04, 17 May 2012
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:keenanpepper\|keenanpepper]] and made on <tt>2012-05-17 16:00:11 UTC</tt>.<br>		: This revision was by author [[User:keenanpepper\|keenanpepper]] and made on <tt>2012-05-17 16:04:30 UTC</tt>.<br>
	: The original revision id was <tt>~~336777026~~</tt>.<br>		: The original revision id was <tt>336778378</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Line 23:		Line 23:
	# Talk about frequencies, ratios, cents, Hz, the harmonic series (just briefly mentioning logarithms and saying what the practical implications are - this is not for mathematicians!) (only one item but this part will actually have to be pretty long)		# Talk about frequencies, ratios, cents, Hz, the harmonic series (just briefly mentioning logarithms and saying what the practical implications are - this is not for mathematicians!) (only one item but this part will actually have to be pretty long)
	# Approximate relationships between 12edo and JI - the fact that each interval represents many JI ratios (important because a lot of sources give exactly one JI ratio per 12edo interval which is very misleading)		# Approximate relationships between 12edo and JI - the fact that each interval represents many JI ratios (important because a lot of sources give exactly one JI ratio per 12edo interval which is very misleading)
			# Odd limit, prime limit?
	# JI lattices (VERY BRIEFLY) (optional: epic animation of the circle of fifths opening into a chain and then the chain itself opening into the 5-limit lattice!)		# JI lattices (VERY BRIEFLY) (optional: epic animation of the circle of fifths opening into a chain and then the chain itself opening into the 5-limit lattice!)
	# The diatonic scale in JI, and the wolf intervals in it		# The diatonic scale in JI, and the wolf intervals in it
Line 55:		Line 56:
	<ol><li>What 12edo really is (must drive home the point that there are 12 notes per octave, not, say, 8, as some people would say if you asked them. just very basic stuff, no acoustics)</li><li>What Western notation really is (note that there's both C# and Db for some reason, and that they both map to the same note)</li><li>Explain that historically, C# and Db were different things, and that our notation is a remnant of the historic system (most music students are up to speed at this point)</li><li>Introduce the idea that instead of this leading to a &quot;12 tone unequal temperament,&quot; it actually leads to an &quot;infinite&quot; tuning system that goes on forever (e.g. meantone isn't just a 12 tone unequal tuning - there exist more than 12 notes in meantone. this is the first 'aha' moment that most music students will have)</li><li>Introduce the idea of the circle of fifths &quot;opening up&quot; into the full neverending chain, and 12 being a particular way to &quot;close&quot; the chain, turning C# and Db into the same note</li><li>Introduce the idea that 19 is another way to close the chain, and that this introduces &quot;new enharmonic equivalences.&quot; (epic musical examples needed)</li><li>Touch on other ways to close the chain - 17, 7, 5, 26, 31, etc. Possibly introduce the word &quot;temperament&quot; to explain this idea of dimensionality reduction</li><li>Introduce the idea that there's even more to music than just the circle of fifths, and that &quot;meantone&quot; itself is a temperament of something more fundamental (Maybe remind people about the diminished scale and augmented and so on, I dunno. BE SURE TO NOT LEAD PEOPLE INTO THE RATIOS = CATEGORIES FALLACY)</li><li>Play tantalizing porcupine/blackwood/machine clips and so on</li><li>Introduce the idea that to understand what's going on, we'll dig even deeper than music and start looking at the building blocks of sound itself (except not really, lulz)</li></ol><br />		<ol><li>What 12edo really is (must drive home the point that there are 12 notes per octave, not, say, 8, as some people would say if you asked them. just very basic stuff, no acoustics)</li><li>What Western notation really is (note that there's both C# and Db for some reason, and that they both map to the same note)</li><li>Explain that historically, C# and Db were different things, and that our notation is a remnant of the historic system (most music students are up to speed at this point)</li><li>Introduce the idea that instead of this leading to a &quot;12 tone unequal temperament,&quot; it actually leads to an &quot;infinite&quot; tuning system that goes on forever (e.g. meantone isn't just a 12 tone unequal tuning - there exist more than 12 notes in meantone. this is the first 'aha' moment that most music students will have)</li><li>Introduce the idea of the circle of fifths &quot;opening up&quot; into the full neverending chain, and 12 being a particular way to &quot;close&quot; the chain, turning C# and Db into the same note</li><li>Introduce the idea that 19 is another way to close the chain, and that this introduces &quot;new enharmonic equivalences.&quot; (epic musical examples needed)</li><li>Touch on other ways to close the chain - 17, 7, 5, 26, 31, etc. Possibly introduce the word &quot;temperament&quot; to explain this idea of dimensionality reduction</li><li>Introduce the idea that there's even more to music than just the circle of fifths, and that &quot;meantone&quot; itself is a temperament of something more fundamental (Maybe remind people about the diminished scale and augmented and so on, I dunno. BE SURE TO NOT LEAD PEOPLE INTO THE RATIOS = CATEGORIES FALLACY)</li><li>Play tantalizing porcupine/blackwood/machine clips and so on</li><li>Introduce the idea that to understand what's going on, we'll dig even deeper than music and start looking at the building blocks of sound itself (except not really, lulz)</li></ol><br />
	<strong>Unit 2</strong> - frequencies, ratios, etc<br />		<strong>Unit 2</strong> - frequencies, ratios, etc<br />
	<ol><li>Talk about frequencies, ratios, cents, Hz, the harmonic series (just briefly mentioning logarithms and saying what the practical implications are - this is not for mathematicians!) (only one item but this part will actually have to be pretty long)</li><li>Approximate relationships between 12edo and JI - the fact that each interval represents many JI ratios (important because a lot of sources give exactly one JI ratio per 12edo interval which is very misleading)</li><li>JI lattices (VERY BRIEFLY) (optional: epic animation of the circle of fifths opening into a chain and then the chain itself opening into the 5-limit lattice!)</li><li>The diatonic scale in JI, and the wolf intervals in it</li></ol><br />		<ol><li>Talk about frequencies, ratios, cents, Hz, the harmonic series (just briefly mentioning logarithms and saying what the practical implications are - this is not for mathematicians!) (only one item but this part will actually have to be pretty long)</li><li>Approximate relationships between 12edo and JI - the fact that each interval represents many JI ratios (important because a lot of sources give exactly one JI ratio per 12edo interval which is very misleading)</li><li>Odd limit, prime limit?</li><li>JI lattices (VERY BRIEFLY) (optional: epic animation of the circle of fifths opening into a chain and then the chain itself opening into the 5-limit lattice!)</li><li>The diatonic scale in JI, and the wolf intervals in it</li></ol><br />
	<strong>Unit 3</strong> - temperaments<br />		<strong>Unit 3</strong> - temperaments<br />
	<ol><li>The diatonic scale in 12edo has patterns of intervals that can't possibly exist in JI (wolves)</li><li>Commas are enharmonic equivalences on steroids</li><li>The syntonic comma makes the world go round (probably a bad idea to write &lt;12 19 28\|-4 4 -1&gt;=0 here, haha...)</li><li>Meantone temperament (tie it back to the chain of fifths in unit 1) - the diatonic scale always &quot;works&quot; in it</li></ol>Other points in no particular order yet:<br />		<ol><li>The diatonic scale in 12edo has patterns of intervals that can't possibly exist in JI (wolves)</li><li>Commas are enharmonic equivalences on steroids</li><li>The syntonic comma makes the world go round (probably a bad idea to write &lt;12 19 28\|-4 4 -1&gt;=0 here, haha...)</li><li>Meantone temperament (tie it back to the chain of fifths in unit 1) - the diatonic scale always &quot;works&quot; in it</li></ol>Other points in no particular order yet:<br />
	<ul><li>Finally introduce new rank-2 temperaments, like blackwood and porcupine (epic musical examples needed here!)</li><li>BRIEFLY introduce the concept of those rank-2 temperaments closing into other equal temperaments (e.g. as an approach to answer questions like &quot;how do I use 15-EDO?&quot;)</li><li>List some awesome temperaments and related scales using them (equip these scales with #/b accidentals plz)</li><li>Awesome musical examples!</li><li>Temperaments are broad objects involving intonation. WTF do I do with them?</li><li>Puns! Comma pumps!</li><li>Talk about MOS series as a generalization of pentatonic/diatonic/chromatic scales!</li><li>Talk about MODMOS's!</li><li>Higher-limit JI!</li><li>EDOs support an infinite amount of rank-2 temperaments!</li><li>Talk about Gene's work with microtemperaments!</li><li>Ethnomusicological tunings! Mavila! Maqamic! Slendric! (maybe) Srutal!</li><li>Tuning accuracy for crunchy stuff!</li><li>Careful use of timbre + lower accuracy for colorful stuff!</li><li>(INVENT MORE COOL STUFF IN REAL LIFE AND WRITE IT HERE)</li></ul><br />		<ul><li>Finally introduce new rank-2 temperaments, like blackwood and porcupine (epic musical examples needed here!)</li><li>BRIEFLY introduce the concept of those rank-2 temperaments closing into other equal temperaments (e.g. as an approach to answer questions like &quot;how do I use 15-EDO?&quot;)</li><li>List some awesome temperaments and related scales using them (equip these scales with #/b accidentals plz)</li><li>Awesome musical examples!</li><li>Temperaments are broad objects involving intonation. WTF do I do with them?</li><li>Puns! Comma pumps!</li><li>Talk about MOS series as a generalization of pentatonic/diatonic/chromatic scales!</li><li>Talk about MODMOS's!</li><li>Higher-limit JI!</li><li>EDOs support an infinite amount of rank-2 temperaments!</li><li>Talk about Gene's work with microtemperaments!</li><li>Ethnomusicological tunings! Mavila! Maqamic! Slendric! (maybe) Srutal!</li><li>Tuning accuracy for crunchy stuff!</li><li>Careful use of timbre + lower accuracy for colorful stuff!</li><li>(INVENT MORE COOL STUFF IN REAL LIFE AND WRITE IT HERE)</li></ul><br />
	Feel free to change</body></html></pre></div>		Feel free to change</body></html></pre></div>

Basic introduction to xenharmonic music - Revision history

ArrowHead294 at 13:46, 26 February 2025

Wikispaces>FREEZE at 00:00, 17 July 2018

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