Mike Sheiman's Alternative Interval Categorizations: Difference between revisions
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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:mikesheiman|mikesheiman]] and made on <tt>2014-02-22 | : This revision was by author [[User:mikesheiman|mikesheiman]] and made on <tt>2014-02-22 11:14:07 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>491212466</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">People often say xenharmonic intervals like 16/11 are "sour" and mathematically similar intervals (e.g. octave inverses like | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">People often say xenharmonic intervals like 16/11 are "sour" and mathematically similar intervals (e.g. octave inverses like | ||
1/(16/11) or 11/8) are "sweet". Doesn't that seem a bit counter intuitive? | 1/(16/11) or 11/8) are "sweet". Doesn't that seem a bit counter intuitive? | ||
We've been | We've been told via standard music theory to accept everything, **even xenharmonic/microtonal intervals, be** **pigeon-holed into some sort of diatonic category**. | ||
In 12EDO C is the tonic/"first". | In 12EDO C is the tonic/"first". | ||
C# (apx. 17/16) is a minor second | C# (apx. 17/16) is a minor second | ||
D (apx. 9/8) is a major second | D (apx. 9/8) is a major second | ||
D# (apx. 6/5) is a minor third | D# (apx. 6/5) is a minor third | ||
E (apx. 5/4) is a major third | E (apx. 5/4) is a major third | ||
| Line 23: | Line 23: | ||
B (apx 15/8) is a major seventh | B (apx 15/8) is a major seventh | ||
**Notice how...even in 12EDO, interval categories seem a bit shaky and inconsistent.** | **Notice how...even in 12EDO, interval categories seem a bit shaky and inconsistent.** | ||
So how, then, to you categorize something like an | So how, then, to you categorize something like an 11/8 or 16/11 between a fourth and a fifth? Or an interval like 14/9, between a fifth and a sixth? Furthermore, how do explain when, for example, a 16/11 feels "sour" while an 11/8 slightly below it feels upbeat/sweet? | ||
Usually we simply add additional names as necessary and further complicate the system. 16/11? That's sour because it's a **diminished** fifth. Around 14/9? That's upbeat because it's an **augmented** fifth. Why not just stick with major (**more upbeat**) and minor (**more downbeat**) and neutral (**in-between upbeat and downbeat and a bit sour**)...equally distributed among 4ths, 5ths, 6ths...? | Usually we simply add additional names as necessary and further complicate the system. 16/11? That's sour because it's a **diminished** fifth. Around 14/9? That's upbeat because it's an **augmented** fifth. Why not just stick with major (**more upbeat**) and minor (**more downbeat**) and neutral (**in-between upbeat and downbeat and a bit sour**)...equally distributed among 4ths, 5ths, 6ths...? | ||
Here's a proposal | Here's a proposal for a __**major/minor/neutral-only system**__ | ||
C is the tonic/"first". | C is the tonic/"first". | ||
(15/14 and less) is a minor second | (15/14 and less) is a minor second | ||
(13/12 to 11/10) is a neutral second | (13/12 to 11/10) is a neutral second | ||
| Line 35: | Line 34: | ||
(7/6) is a minor **second-half** | (7/6) is a minor **second-half** | ||
**(15/13) is a** neutral **second-half** | **(15/13) is a** neutral **second-half** | ||
(8/7) is a | (8/7) is a major **second-half** | ||
(19/16 to 6/5) is a minor third | |||
( | (11/9) is a neutral third | ||
(5/4-9/7) is a major third | |||
(4/3) is a **minor fourth** **(not a perfect fourth)** | |||
(15/11) is a neutral fourth | |||
** | (11/8) is a **major fourth (a more upbeat fourth)** | ||
(7/5) is a **minor fourth-half (not the usual tritone)** | |||
** | **(10/7)** is a **neutral fourth-half (not the usual tritone)** | ||
(13/9) is a **major fourth-half (a "more upbeat tritone")** | |||
(16/11) is a minor fifth | |||
(22/15) is a neutral fifth | |||
(3/2) is a **major fifth (not a perfect fifth)** | |||
(17/11) is a **minor fifth-half** | |||
**---------------------** | |||
**(14/9-11/7)** is a **major fifth-half** | |||
**(8/5)** is a minor sixth | |||
(13/8-18/11) is a neutral sixth | |||
**(5/3)** is a major sixth | |||
(12/7) is a **minor sixth-half** | |||
**(26/15)** is a **neutral sixth-half** | |||
(7/4) is a **major sixth-half** | |||
(16/9-9/5) is a minor seventh | |||
(11/6) is a neutral seventh | |||
(15/8) is a major seventh | |||
**Note there is only one gap where there isn't an equal minor/neutral/major sub-type categorization for every interval number/type!** Only the fifth-half isn't perfectly even with two parts instead of 3. | |||
At a quick glance...the point is **with the latter system, you can hopefully quickly/easily tell which intervals to use to get upbeat (major), downbeat and a tad tense (minor), somewhat tense and mixed-mooded (neutral), or relatively sour (fourth-half) intervals.**</pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Mike Sheiman's Alternative Interval Categorizations</title></head><body>People often say xenharmonic intervals like 16/11 are &quot;sour&quot; and mathematically similar intervals (e.g. octave inverses like <br /> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Mike Sheiman's Alternative Interval Categorizations</title></head><body>People often say xenharmonic intervals like 16/11 are &quot;sour&quot; and mathematically similar intervals (e.g. octave inverses like<br /> | ||
1/(16/11) or 11/8) are &quot;sweet&quot;. Doesn't that seem a bit counter intuitive?<br /> | 1/(16/11) or 11/8) are &quot;sweet&quot;. Doesn't that seem a bit counter intuitive?<br /> | ||
We've been | We've been told via standard music theory to accept everything, <strong>even xenharmonic/microtonal intervals, be</strong> <strong>pigeon-holed into some sort of diatonic category</strong>.<br /> | ||
<br /> | <br /> | ||
In 12EDO C is the tonic/&quot;first&quot;. <br /> | In 12EDO C is the tonic/&quot;first&quot;.<br /> | ||
C# (apx. 17/16) is a minor second <br /> | C# (apx. 17/16) is a minor second<br /> | ||
D (apx. 9/8) is a major second <br /> | D (apx. 9/8) is a major second<br /> | ||
D# (apx. 6/5) is a minor third<br /> | D# (apx. 6/5) is a minor third<br /> | ||
E (apx. 5/4) is a major third<br /> | E (apx. 5/4) is a major third<br /> | ||
| Line 69: | Line 81: | ||
B (apx 15/8) is a major seventh<br /> | B (apx 15/8) is a major seventh<br /> | ||
<strong>Notice how...even in 12EDO, interval categories seem a bit shaky and inconsistent.</strong><br /> | <strong>Notice how...even in 12EDO, interval categories seem a bit shaky and inconsistent.</strong><br /> | ||
So how, then, to you categorize something like an | So how, then, to you categorize something like an 11/8 or 16/11 between a fourth and a fifth? Or an interval like 14/9, between a fifth and a sixth? Furthermore, how do explain when, for example, a 16/11 feels &quot;sour&quot; while an 11/8 slightly below it feels upbeat/sweet?<br /> | ||
<br /> | |||
<br /> | <br /> | ||
Usually we simply add additional names as necessary and further complicate the system. 16/11? That's sour because it's a <strong>diminished</strong> fifth. Around 14/9? That's upbeat because it's an <strong>augmented</strong> fifth. Why not just stick with major (<strong>more upbeat</strong>) and minor (<strong>more downbeat</strong>) and neutral (<strong>in-between upbeat and downbeat and a bit sour</strong>)...equally distributed among 4ths, 5ths, 6ths...?<br /> | Usually we simply add additional names as necessary and further complicate the system. 16/11? That's sour because it's a <strong>diminished</strong> fifth. Around 14/9? That's upbeat because it's an <strong>augmented</strong> fifth. Why not just stick with major (<strong>more upbeat</strong>) and minor (<strong>more downbeat</strong>) and neutral (<strong>in-between upbeat and downbeat and a bit sour</strong>)...equally distributed among 4ths, 5ths, 6ths...?<br /> | ||
<br /> | <br /> | ||
Here's a proposal<br /> | Here's a proposal for a <u><strong>major/minor/neutral-only system</strong></u><br /> | ||
C is the tonic/&quot;first&quot;. <br /> | C is the tonic/&quot;first&quot;.<br /> | ||
(15/14 and less) is a minor second<br /> | (15/14 and less) is a minor second<br /> | ||
(13/12 to 11/10) is a neutral second<br /> | (13/12 to 11/10) is a neutral second<br /> | ||
| Line 81: | Line 92: | ||
(7/6) is a minor <strong>second-half</strong><br /> | (7/6) is a minor <strong>second-half</strong><br /> | ||
<strong>(15/13) is a</strong> neutral <strong>second-half</strong><br /> | <strong>(15/13) is a</strong> neutral <strong>second-half</strong><br /> | ||
(8/7) is a | (8/7) is a major <strong>second-half</strong><br /> | ||
<br /> | (19/16 to 6/5) is a minor third<br /> | ||
( | (11/9) is a neutral third<br /> | ||
(5/4-9/7) is a major third<br /> | |||
(4/3) is a <strong>minor fourth</strong> <strong>(not a perfect fourth)</strong><br /> | |||
<strong> | (15/11) is a neutral fourth<br /> | ||
<strong> | (11/8) is a <strong>major fourth (a more upbeat fourth)</strong><br /> | ||
<br /> | (7/5) is a <strong>minor fourth-half (not the usual tritone)</strong><br /> | ||
< | <strong>(10/7)</strong> is a <strong>neutral fourth-half (not the usual tritone)</strong><br /> | ||
(13/9) is a <strong>major fourth-half (a &quot;more upbeat tritone&quot;)</strong><br /> | |||
<br /> | (16/11) is a minor fifth<br /> | ||
(22/15) is a neutral fifth<br /> | |||
(3/2) is a <strong>major fifth (not a perfect fifth)</strong><br /> | |||
(17/11) is a <strong>minor fifth-half</strong><br /> | |||
<strong>---------------------</strong><br /> | |||
<strong>(14/9-11/7)</strong> is a <strong>major fifth-half</strong><br /> | |||
<strong>(8/5)</strong> is a minor sixth<br /> | |||
(13/8-18/11) is a neutral sixth<br /> | |||
<strong>(5/3)</strong> is a major sixth<br /> | |||
(12/7) is a <strong>minor sixth-half</strong><br /> | |||
<strong>(26/15)</strong> is a <strong>neutral sixth-half</strong><br /> | |||
(7/4) is a <strong>major sixth-half</strong><br /> | |||
(16/9-9/5) is a minor seventh<br /> | |||
(11/6) is a neutral seventh<br /> | |||
(15/8) is a major seventh<br /> | |||
<br /> | <br /> | ||
<strong>Note there is only one gap where there isn't an equal minor/neutral/major sub-type categorization for every interval number/type!</strong> Only the fifth-half isn't perfectly even with two parts instead of 3.<br /> | |||
<br /> | <br /> | ||
At a quick glance...the point is <strong>with the latter system, you can hopefully quickly/easily tell which intervals to use to get upbeat (major), downbeat and a tad tense (minor), somewhat tense and mixed-mooded (neutral), or relatively sour (fourth-half) intervals.</strong></body></html></pre></div> | |||
Revision as of 11:14, 22 February 2014
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author mikesheiman and made on 2014-02-22 11:14:07 UTC.
- The original revision id was 491212466.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
People often say xenharmonic intervals like 16/11 are "sour" and mathematically similar intervals (e.g. octave inverses like 1/(16/11) or 11/8) are "sweet". Doesn't that seem a bit counter intuitive? We've been told via standard music theory to accept everything, **even xenharmonic/microtonal intervals, be** **pigeon-holed into some sort of diatonic category**. In 12EDO C is the tonic/"first". C# (apx. 17/16) is a minor second D (apx. 9/8) is a major second D# (apx. 6/5) is a minor third E (apx. 5/4) is a major third **F (apx 4/3) is a perfect fourth** (Why not a major or minor? Inconsistency...) **F# (apx. 7/5) is on the borderline between a fourth and fifth** **G (apx. 3/2) is a perfect fifth** (Again, no major or minor. Inconsistency...) G# (apx. 8/5)is a minor sixth A (apx. 5/3) is a major sixth A# (apx. 9/5) is a minor seventh B (apx 15/8) is a major seventh **Notice how...even in 12EDO, interval categories seem a bit shaky and inconsistent.** So how, then, to you categorize something like an 11/8 or 16/11 between a fourth and a fifth? Or an interval like 14/9, between a fifth and a sixth? Furthermore, how do explain when, for example, a 16/11 feels "sour" while an 11/8 slightly below it feels upbeat/sweet? Usually we simply add additional names as necessary and further complicate the system. 16/11? That's sour because it's a **diminished** fifth. Around 14/9? That's upbeat because it's an **augmented** fifth. Why not just stick with major (**more upbeat**) and minor (**more downbeat**) and neutral (**in-between upbeat and downbeat and a bit sour**)...equally distributed among 4ths, 5ths, 6ths...? Here's a proposal for a __**major/minor/neutral-only system**__ C is the tonic/"first". (15/14 and less) is a minor second (13/12 to 11/10) is a neutral second (10/9 to 9/8) is a major second (7/6) is a minor **second-half** **(15/13) is a** neutral **second-half** (8/7) is a major **second-half** (19/16 to 6/5) is a minor third (11/9) is a neutral third (5/4-9/7) is a major third (4/3) is a **minor fourth** **(not a perfect fourth)** (15/11) is a neutral fourth (11/8) is a **major fourth (a more upbeat fourth)** (7/5) is a **minor fourth-half (not the usual tritone)** **(10/7)** is a **neutral fourth-half (not the usual tritone)** (13/9) is a **major fourth-half (a "more upbeat tritone")** (16/11) is a minor fifth (22/15) is a neutral fifth (3/2) is a **major fifth (not a perfect fifth)** (17/11) is a **minor fifth-half** **---------------------** **(14/9-11/7)** is a **major fifth-half** **(8/5)** is a minor sixth (13/8-18/11) is a neutral sixth **(5/3)** is a major sixth (12/7) is a **minor sixth-half** **(26/15)** is a **neutral sixth-half** (7/4) is a **major sixth-half** (16/9-9/5) is a minor seventh (11/6) is a neutral seventh (15/8) is a major seventh **Note there is only one gap where there isn't an equal minor/neutral/major sub-type categorization for every interval number/type!** Only the fifth-half isn't perfectly even with two parts instead of 3. At a quick glance...the point is **with the latter system, you can hopefully quickly/easily tell which intervals to use to get upbeat (major), downbeat and a tad tense (minor), somewhat tense and mixed-mooded (neutral), or relatively sour (fourth-half) intervals.**
Original HTML content:
<html><head><title>Mike Sheiman's Alternative Interval Categorizations</title></head><body>People often say xenharmonic intervals like 16/11 are "sour" and mathematically similar intervals (e.g. octave inverses like<br /> 1/(16/11) or 11/8) are "sweet". Doesn't that seem a bit counter intuitive?<br /> We've been told via standard music theory to accept everything, <strong>even xenharmonic/microtonal intervals, be</strong> <strong>pigeon-holed into some sort of diatonic category</strong>.<br /> <br /> In 12EDO C is the tonic/"first".<br /> C# (apx. 17/16) is a minor second<br /> D (apx. 9/8) is a major second<br /> D# (apx. 6/5) is a minor third<br /> E (apx. 5/4) is a major third<br /> <strong>F (apx 4/3) is a perfect fourth</strong> (Why not a major or minor? Inconsistency...)<br /> <strong>F# (apx. 7/5) is on the borderline between a fourth and fifth</strong><br /> <strong>G (apx. 3/2) is a perfect fifth</strong> (Again, no major or minor. Inconsistency...)<br /> G# (apx. 8/5)is a minor sixth<br /> A (apx. 5/3) is a major sixth<br /> A# (apx. 9/5) is a minor seventh<br /> B (apx 15/8) is a major seventh<br /> <strong>Notice how...even in 12EDO, interval categories seem a bit shaky and inconsistent.</strong><br /> So how, then, to you categorize something like an 11/8 or 16/11 between a fourth and a fifth? Or an interval like 14/9, between a fifth and a sixth? Furthermore, how do explain when, for example, a 16/11 feels "sour" while an 11/8 slightly below it feels upbeat/sweet?<br /> <br /> Usually we simply add additional names as necessary and further complicate the system. 16/11? That's sour because it's a <strong>diminished</strong> fifth. Around 14/9? That's upbeat because it's an <strong>augmented</strong> fifth. Why not just stick with major (<strong>more upbeat</strong>) and minor (<strong>more downbeat</strong>) and neutral (<strong>in-between upbeat and downbeat and a bit sour</strong>)...equally distributed among 4ths, 5ths, 6ths...?<br /> <br /> Here's a proposal for a <u><strong>major/minor/neutral-only system</strong></u><br /> C is the tonic/"first".<br /> (15/14 and less) is a minor second<br /> (13/12 to 11/10) is a neutral second<br /> (10/9 to 9/8) is a major second<br /> (7/6) is a minor <strong>second-half</strong><br /> <strong>(15/13) is a</strong> neutral <strong>second-half</strong><br /> (8/7) is a major <strong>second-half</strong><br /> (19/16 to 6/5) is a minor third<br /> (11/9) is a neutral third<br /> (5/4-9/7) is a major third<br /> (4/3) is a <strong>minor fourth</strong> <strong>(not a perfect fourth)</strong><br /> (15/11) is a neutral fourth<br /> (11/8) is a <strong>major fourth (a more upbeat fourth)</strong><br /> (7/5) is a <strong>minor fourth-half (not the usual tritone)</strong><br /> <strong>(10/7)</strong> is a <strong>neutral fourth-half (not the usual tritone)</strong><br /> (13/9) is a <strong>major fourth-half (a "more upbeat tritone")</strong><br /> (16/11) is a minor fifth<br /> (22/15) is a neutral fifth<br /> (3/2) is a <strong>major fifth (not a perfect fifth)</strong><br /> (17/11) is a <strong>minor fifth-half</strong><br /> <strong>---------------------</strong><br /> <strong>(14/9-11/7)</strong> is a <strong>major fifth-half</strong><br /> <strong>(8/5)</strong> is a minor sixth<br /> (13/8-18/11) is a neutral sixth<br /> <strong>(5/3)</strong> is a major sixth<br /> (12/7) is a <strong>minor sixth-half</strong><br /> <strong>(26/15)</strong> is a <strong>neutral sixth-half</strong><br /> (7/4) is a <strong>major sixth-half</strong><br /> (16/9-9/5) is a minor seventh<br /> (11/6) is a neutral seventh<br /> (15/8) is a major seventh<br /> <br /> <strong>Note there is only one gap where there isn't an equal minor/neutral/major sub-type categorization for every interval number/type!</strong> Only the fifth-half isn't perfectly even with two parts instead of 3.<br /> <br /> At a quick glance...the point is <strong>with the latter system, you can hopefully quickly/easily tell which intervals to use to get upbeat (major), downbeat and a tad tense (minor), somewhat tense and mixed-mooded (neutral), or relatively sour (fourth-half) intervals.</strong></body></html>