Comparison of mode notation systems: Difference between revisions

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

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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>

|| old scale name || new scale name || Ls pattern || example on white keys || genchain ||

|| Lydian || 1st Meantone[7] || LLLs LLs || F G A B C D E F || __**F**__ C G D A E B ||

F G A C E F, with genchain __**F**__ C G * A E. No amount of altering will make an unbroken genchain, so the name is F 1st Meantone[6] no 6.

==__Why not just use UDP notation?__==  

One problem with UDP is that avoiding chroma-negative generators causes the genchain to reverse direction frequently as you lengthen or shorten it. If exploring the various MOS's of a temperament, one has to constantly check the genchain direction.

|| Meantone [2] || 3/2 || C G || 3/2 || C G ||

|| Meantone [3] || 4/3 || D G C || 3/2 || C G D ||

|| Meantone [7] || 3/2 || C G D A E B F# || 3/2 || C G D A E B F# ||

|| Meantone [2] || C G || C G ||

|| Meantone [3] || D G C || C G D ||

An even larger problem is that Meantone[12] generated by 701¢ has a different genchain than Meantone[12] generated by 699¢, so slight differences in tempering result in different mode names. In other words the notation is overly tuning-dependent. One might address this problem by reasonably constraining meantone's fifth to be less than 700¢. Likewise one could constrain Superpyth[12]'s fifth to be more than 700¢. But this approach fails with Dominant meantone, which tempers out both 81/80 and 64/63, and in which the fifth can reasonably be either more or less than 700¢. This makes every single UDP mode of Dominant[12] ambiguous. For example "Dominant 8|3" could mean either "4th Dominant[12]" or "9th Dominant[12]". Something similar happens with Meantone[19]. If the fifth is greater than 694¢ = 11\19, the generator is 3/2, but if less than 694¢, it's 4/3. This makes every UDP mode of Meantone[19] ambiguous. Another example is Dicot[7] when the neutral 3rd generator is greater or less than 2\7 = 343¢. Another example is Semaphore[5]'s generator of ~8/7 or ~7/6 if near 1\5 = 240¢. In general, this ambiguity arises whenever the generator of an N-note MOS ranges from slightly flat of any N-edo interval to slightly sharp of it.

Admins: Please delete the blank page at http://xenharmonic.wikispaces.com/Modal+Notation+by+Genchain+Position</pre></div>

<h4>Original HTML content:</h4>

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  As in modal UDP notation, these are written as MOS scales with chromatic alterations. To find the scale's name, start with the genchain for the scale, which will always have gaps. Compact it into a chain without gaps by altering one or more notes. If there is more than one way to do this, the way that alters as few notes as possible is generally preferable. Determine the mode number from the compacted genchain, then add the appropriate alterations.&lt;br /&gt;

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  Fractional-period rank-2 temperaments have multiple genchains running in parallel. For example, shrutal[10] might look like this:&lt;br /&gt;

Eb -- Bb -- F --- C --- G&lt;br /&gt;

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  Compact the genchain to remove any gaps via chromatic alterations. The mode number is derived from the compacted genchain. Examples:&lt;br /&gt;

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  One problem with UDP is that avoiding chroma-negative generators causes the genchain to reverse direction frequently as you lengthen or shorten it. If exploring the various MOS's of a temperament, one has to constantly check the genchain direction.&lt;br /&gt;

         &lt;td&gt;UDP genchain&lt;br /&gt;

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         &lt;td&gt;UDP genchain&lt;br /&gt;

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An even larger problem is that Meantone[12] generated by 701¢ has a different genchain than Meantone[12] generated by 699¢, so slight differences in tempering result in different mode names. In other words the notation is overly tuning-dependent. One might address this problem by reasonably constraining meantone's fifth to be less than 700¢. Likewise one could constrain Superpyth[12]'s fifth to be more than 700¢. But this approach fails with Dominant meantone, which tempers out both 81/80 and 64/63, and in which the fifth can reasonably be either more or less than 700¢. This makes every single UDP mode of Dominant[12] ambiguous. For example &amp;quot;Dominant 8|3&amp;quot; could mean either &amp;quot;4th Dominant[12]&amp;quot; or &amp;quot;9th Dominant[12]&amp;quot;. Something similar happens with Meantone[19]. If the fifth is greater than 694¢ = 11\19, the generator is 3/2, but if less than 694¢, it's 4/3. This makes every UDP mode of Meantone[19] ambiguous. Another example is Dicot[7] when the neutral 3rd generator is greater or less than 2\7 = 343¢. Another example is Semaphore[5]'s generator of ~8/7 or ~7/6 if near 1\5 = 240¢. In general, this ambiguity arises whenever the generator of an N-note MOS ranges from slightly flat of any N-edo interval to slightly sharp of it.&lt;br /&gt;

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