Nick Vuci's Fundamentals of Xen: Difference between revisions

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=== Subharmonic Series ===

Let’s take a step back. You know about the harmonic series, sometimes called the overtone series, since harmony results from the alignment of partials. Now we have to introduce the second-to-last fundamental idea of JI, and that is the subharmonic (or undertone) series. if we go to scale workshop and choose 1 as the lowest number and 8 as the highest, we get this scale: 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1.

Let’s take a step back. You know about the harmonic series, sometimes called the overtone series, since harmony results from the alignment of partials. Now we have to introduce the second-to-last fundamental idea of JI, and that is the subharmonic (or undertone) series. if we go to scale workshop and choose 1 as the lowest number and 8 as the highest, we get this scale: 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1. Note the scale shape:

[[File:Harmonic series 2-8.png|thumb|Harmonic Series segment 2-8|none]]

~~Note the scale shape: [[harmonic_series_2-8 1.png]]~~ As we go up the scale, intervals get smaller and smaller. The subharmonic series is the Mathematical opposite of this, and the same 1/8 range gives us this undertone series segment: 8/7, 8/6, 8/5, 8/4, 8/3, 8/2, 8/1. It’s important to know that although we’re calling this the undertone series, the undertone series does not have a physical acoustic basis.

As we go up the scale, intervals get smaller and smaller. The subharmonic series is the Mathematical opposite of this, and the same 1/8 range gives us this undertone series segment: 8/7, 8/6, 8/5, 8/4, 8/3, 8/2, 8/1. It’s important to know that although we’re calling this the undertone series, the undertone series does not have a physical acoustic basis.

[[File:Subharmonic series 7-1.png|thumb|Subharmonic Series segment 7-1|none]]

Now remember how I said 4:5:6 is the major triad? Well, the subharmonic version is the minor chord: 8/6, 8/5, 8/4 or 1/(6:5:4). This means 4:5:6 and 1/(6:5:4) are Mathematical inversions for each other, or the ''otonal'' and the ''utonal'' versions (for overtone and undertone).

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 === Subharmonic Series ===
-Let’s take a step back. You know about the harmonic series, sometimes called the overtone series, since harmony results from the alignment of partials. Now we have to introduce the second-to-last fundamental idea of JI, and that is the subharmonic (or undertone) series. if we go to scale workshop and choose 1 as the lowest number and 8 as the highest, we get this scale: 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1.
+Let’s take a step back. You know about the harmonic series, sometimes called the overtone series, since harmony results from the alignment of partials. Now we have to introduce the second-to-last fundamental idea of JI, and that is the subharmonic (or undertone) series. if we go to scale workshop and choose 1 as the lowest number and 8 as the highest, we get this scale: 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1. Note the scale shape:
 [[File:Harmonic series 2-8.png|thumb|Harmonic Series segment 2-8|none]]
-Note the scale shape: [[harmonic_series_2-8 1.png]] As we go up the scale, intervals get smaller and smaller. The subharmonic series is the Mathematical opposite of this, and the same 1/8 range gives us this undertone series segment: 8/7, 8/6, 8/5, 8/4, 8/3, 8/2, 8/1. It’s important to know that although we’re calling this the undertone series, the undertone series does not have a physical acoustic basis.
+As we go up the scale, intervals get smaller and smaller. The subharmonic series is the Mathematical opposite of this, and the same 1/8 range gives us this undertone series segment: 8/7, 8/6, 8/5, 8/4, 8/3, 8/2, 8/1. It’s important to know that although we’re calling this the undertone series, the undertone series does not have a physical acoustic basis.
 [[File:Subharmonic series 7-1.png|thumb|Subharmonic Series segment 7-1|none]]
 Now remember how I said 4:5:6 is the major triad? Well, the subharmonic version is the minor chord: 8/6, 8/5, 8/4 or 1/(6:5:4). This means 4:5:6 and 1/(6:5:4) are Mathematical inversions for each other, or the ''otonal'' and the ''utonal'' versions (for overtone and undertone).