Dreyblatt tuning system
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from Arnold Dreyblatt: //Tuning Systems Explanation//, [[http://www.dreyblatt.net/html/music.php?id=67|www.dreyblatt.net/html/music.php?id=67]] The //Dreyblatt Tuning System// is calculated from the third, fifth, seventh, ninth and eleventh overtones and their multiples in the following pattern: || 1 || 3 || 5 || 7 || 9 || 11 || || 3 || 9 || 15 || 21 || 27 || 33 || || 5 || 15 || 25 || 35 || 45 || 55 || || 7 || 21 || 35 || 49 || 63 || 77 || || 9 || 27 || 45 || 63 || 81 || 99 || || 11 || 33 || 55 || 77 || 99 || 121 || These mathematically related overtones are heard as tonal relationships when they are transposed and sounded above a fundamental tone. In this process of transposition from their position in the natural overtone series, these tones fall (unequally) in the span of one octave in the following order: 1, 33, 35, 9, 77, 5, 81, 21, [11,] 45, 3, 49, 99, 25, 27, 55, 7, 15, 121, 63, (2) These tones are performed in "just intonation' based on a fundamental tone of "F". || Note || Freq. || Partial || Cents || || F || 349.2 || 1 || 0 || || F# || 360.11 || 33 || -47 || || G || 381.93 || 35 || -45 || || G# || 392.85 || 9 || +4 || || G# || 420.13 || 77 || +20 || || A || 436.5 || 5 || -14 || || A || 441.95 || 81 || +8 || || A# || 458.32 || 21 || -29 || || B || 480.15 || 11 || -49 || || B || 491.06 || 45 || -10 || || C || 523.8 || 3 || +2 || || C || 534.71 || 49 || +38 || || C# || 540.16 || 99 || -45 || || C# || 545.62 || 25 || -28 || || D || 589.27 || 27 || +6 || || D || 600.18 || 55 || +37 || || D# || 611.1 || 7 || -31 || || E || 654.75 || 15 || -12 || || E || 660.20 || 121 || +2 || || F || 687.48 || 63 || -27 ||
Original HTML content:
<html><head><title>Arnold Dreyblatt</title></head><body>from Arnold Dreyblatt: <em>Tuning Systems Explanation</em>, <a class="wiki_link_ext" href="http://www.dreyblatt.net/html/music.php?id=67" rel="nofollow">www.dreyblatt.net/html/music.php?id=67</a><br />
<br />
The <em>Dreyblatt Tuning System</em> is calculated from the third, fifth, seventh, ninth and eleventh overtones and their multiples in the following pattern:<br />
<table class="wiki_table">
<tr>
<td>1<br />
</td>
<td>3<br />
</td>
<td>5<br />
</td>
<td>7<br />
</td>
<td>9<br />
</td>
<td>11<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>9<br />
</td>
<td>15<br />
</td>
<td>21<br />
</td>
<td>27<br />
</td>
<td>33<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>15<br />
</td>
<td>25<br />
</td>
<td>35<br />
</td>
<td>45<br />
</td>
<td>55<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>21<br />
</td>
<td>35<br />
</td>
<td>49<br />
</td>
<td>63<br />
</td>
<td>77<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>27<br />
</td>
<td>45<br />
</td>
<td>63<br />
</td>
<td>81<br />
</td>
<td>99<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>33<br />
</td>
<td>55<br />
</td>
<td>77<br />
</td>
<td>99<br />
</td>
<td>121<br />
</td>
</tr>
</table>
<br />
These mathematically related overtones are heard as tonal relationships when they are transposed and sounded above a fundamental tone. In this process of transposition from their position in the natural overtone series, these tones fall (unequally) in the span of one octave in the following order:<br />
<br />
1, 33, 35, 9, 77, 5, 81, 21, [11,] 45, 3, 49, 99, 25, 27, 55, 7, 15, 121, 63, (2)<br />
<br />
These tones are performed in "just intonation' based on a fundamental tone of "F". <br />
<table class="wiki_table">
<tr>
<td>Note<br />
</td>
<td>Freq.<br />
</td>
<td>Partial<br />
</td>
<td>Cents<br />
</td>
</tr>
<tr>
<td>F<br />
</td>
<td>349.2<br />
</td>
<td>1<br />
</td>
<td>0<br />
</td>
</tr>
<tr>
<td>F#<br />
</td>
<td>360.11<br />
</td>
<td>33<br />
</td>
<td>-47<br />
</td>
</tr>
<tr>
<td>G<br />
</td>
<td>381.93<br />
</td>
<td>35<br />
</td>
<td>-45<br />
</td>
</tr>
<tr>
<td>G#<br />
</td>
<td>392.85<br />
</td>
<td>9<br />
</td>
<td>+4<br />
</td>
</tr>
<tr>
<td>G#<br />
</td>
<td>420.13<br />
</td>
<td>77<br />
</td>
<td>+20<br />
</td>
</tr>
<tr>
<td>A<br />
</td>
<td>436.5<br />
</td>
<td>5<br />
</td>
<td>-14<br />
</td>
</tr>
<tr>
<td>A<br />
</td>
<td>441.95<br />
</td>
<td>81<br />
</td>
<td>+8<br />
</td>
</tr>
<tr>
<td>A#<br />
</td>
<td>458.32<br />
</td>
<td>21<br />
</td>
<td>-29<br />
</td>
</tr>
<tr>
<td>B<br />
</td>
<td>480.15<br />
</td>
<td>11<br />
</td>
<td>-49<br />
</td>
</tr>
<tr>
<td>B<br />
</td>
<td>491.06<br />
</td>
<td>45<br />
</td>
<td>-10<br />
</td>
</tr>
<tr>
<td>C<br />
</td>
<td>523.8<br />
</td>
<td>3<br />
</td>
<td>+2<br />
</td>
</tr>
<tr>
<td>C<br />
</td>
<td>534.71<br />
</td>
<td>49<br />
</td>
<td>+38<br />
</td>
</tr>
<tr>
<td>C#<br />
</td>
<td>540.16<br />
</td>
<td>99<br />
</td>
<td>-45<br />
</td>
</tr>
<tr>
<td>C#<br />
</td>
<td>545.62<br />
</td>
<td>25<br />
</td>
<td>-28<br />
</td>
</tr>
<tr>
<td>D<br />
</td>
<td>589.27<br />
</td>
<td>27<br />
</td>
<td>+6<br />
</td>
</tr>
<tr>
<td>D<br />
</td>
<td>600.18<br />
</td>
<td>55<br />
</td>
<td>+37<br />
</td>
</tr>
<tr>
<td>D#<br />
</td>
<td>611.1<br />
</td>
<td>7<br />
</td>
<td>-31<br />
</td>
</tr>
<tr>
<td>E<br />
</td>
<td>654.75<br />
</td>
<td>15<br />
</td>
<td>-12<br />
</td>
</tr>
<tr>
<td>E<br />
</td>
<td>660.20<br />
</td>
<td>121<br />
</td>
<td>+2<br />
</td>
</tr>
<tr>
<td>F<br />
</td>
<td>687.48<br />
</td>
<td>63<br />
</td>
<td>-27<br />
</td>
</tr>
</table>
</body></html>