Just Hammond: Difference between revisions
1st example added |
Table 2 edited |
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<u>Table 2:</u> Mapping a single interval | <u>Table 2:</u> Mapping a single interval | ||
{| class="wikitable" | |||
! rowspan="3" style="text-align: center;" | Pitch<br> | |||
Class | |||
! colspan="2" style="text-align: center;" | | |||
Gear Ratio<br> | |||
(canceled) | |||
! colspan="5" style="text-align: center; font-weight:bold;" | | |||
! style="text-align: center;" | | |||
Ascending<br> | |||
Partial Numbers of<br> | |||
an Overtone Scale | |||
! rowspan="3" style="text-align: center;" | | |||
Partial found<br> | |||
in Octave #<br> | |||
<br><br> | |||
(counted<br> | |||
from 1/1) | |||
|- | |||
| style="text-align: center;" | (C) | |||
| style="text-align: center; font-weight:bold;" | (D) | |||
| rowspan="2" colspan="5" style="text-align: center; font-weight:bold; background-color:#ffffff;" | | |||
Prime<br> | |||
Factorization<br> | |||
of Column (D) | |||
| rowspan="2" style="text-align: center;" | | |||
Recalculated<br> | |||
Numerator<br> | |||
=<br> | |||
Partial # | |||
|- | |||
| colspan="2" style="text-align: center;" | Fraction | |||
(C)/(D) | |||
|- | |||
| style="text-align: center;" | E | |||
| style="text-align: right; background-color:#ffffff;" | 103 | |||
| style="font-weight:bold; background-color:#ffffff;" | 100 | |||
| style="background-color:#cbcefb;" | 2 | |||
| style="background-color:#cbcefb;" | 2 | |||
| style="background-color:#cbcefb;" | | |||
| style="background-color:#cbcefb;" | 5 | |||
| style="background-color:#cbcefb;" | 5 | |||
| style="text-align: center;" | 206 | |||
| style="text-align: center;" | 8.7 | |||
|- | |||
| style="text-align: center;" | A | |||
| style="text-align: right; background-color:#ffffff;" | 11 | |||
| style="font-weight:bold; background-color:#ffffff;" | 8 | |||
| style="background-color:#cbcefb;" | 2 | |||
| style="background-color:#cbcefb;" | 2 | |||
| style="background-color:#cbcefb;" | 2 | |||
| style="background-color:#cbcefb;" | | |||
| style="background-color:#cbcefb;" | | |||
| style="text-align: center;" | 275 | |||
| style="text-align: center;" | 9.6 | |||
|- | |||
| colspan="3" style="font-weight:bold;" | | |||
Multiply ------------><br> | |||
to find (D)'s least<br> | |||
common multiple (LCM) | |||
| style="font-weight:bold; background-color:#cbcefb;" | 2<br><br><br> | |||
| style="font-weight:bold; background-color:#cbcefb;" | 2<br><br><br> | |||
| style="font-weight:bold; background-color:#cbcefb;" | 2<br><br><br> | |||
| style="font-weight:bold; background-color:#cbcefb;" | 5<br><br><br> | |||
| style="font-weight:bold; background-color:#cbcefb;" | 5<br><br><br> | |||
| style="text-align: center; font-weight:bold;" | 200<br> | |||
<br>(LCM) | |||
| style="text-align: center;" | 8.6 | |||
Decimal printed<br> | |||
for orientation only | |||
|} | |||
The resulting interval appears between partial # 206 and partial # 275. The frequency ratio is (275:206), which equals 500.14 cents. | The resulting interval appears between partial # 206 and partial # 275. The frequency ratio is (275:206), which equals 500.14 cents. | ||