「13.純正律」の編集履歴（バックアップ）一覧はこちら

「13.純正律」(2006/01/20 (金) 13:23:30) の最新版変更点

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align="left"><span style=
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<strong>純正律って</strong></span></p>
<p class="MsoNormal" style=
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align="left">?</p>
<p class="MsoNormal" style=
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align="left"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
&lt;解答１&gt;杉井</span></p>
<p class="MsoNormal" style=
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align="left">?</p>
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto"
align="left"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
　和音は、周波数が単純な整数比になるときに良く調和して聞こえます。ド・ミ・ソの和音が完全に調和するときの周波数比は<span lang="EN-US">4</span>：<span lang="EN-US">5</span>：<span lang="EN-US">6</span>です。長調の基本<span lang="EN-US">3</span>和音であるド・ミ・ソ、ファ・ラ・ド、ソ・シ・レの周波数比がいずれも<span lang="EN-US">4</span>：<span lang="EN-US">5</span>：<span lang="EN-US">6</span>になるように音階（長音階）を決めると、以下のようになります。</span></p>
<table class="MsoNormalTable" style="mso-cellspacing: 1.5pt" cellpadding="0"
border="1">
<tbody>
<tr style="mso-yfti-irow: 0; mso-yfti-firstrow: yes">
<td style=
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<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan" align=
"left">?</p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
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"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ド</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
レ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ミ</span></p>
</td>
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"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
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"center"><span style=
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ファ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
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"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ソ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ラ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
シ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ド</span></p>
</td>
</tr>
<tr style="mso-yfti-irow: 1">
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan" align=
"left"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
基音（ド）に対する比</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
1<br>
(1.000)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/8<br>
(1.125)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
5/4<br>
(1.250)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
4/3<br>
(1.333)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
3/2<br>
(1.500)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
5/3<br>
(1.667)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
15/8<br>
(1.875)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
2<br>
(2.000)</span></p>
</td>
</tr>
<tr style="mso-yfti-irow: 2; mso-yfti-lastrow: yes">
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan" align=
"left"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
直下の音に対する比</span></p>
</td>
<td style=
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<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
-</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/8<br>
(1.125)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
10/9<br>
(1.111)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
16/15<br>
(1.067)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/8<br>
(1.125)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
10/9<br>
(1.111)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/8<br>
(1.125)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
16/15<br>
(1.067)</span></p>
</td>
</tr>
</tbody>
</table>
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan" align=
"left"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
　さて、基音からの<span lang=
"EN-US">3</span>度音程（ド～ミ）の周波数比を<span lang=
"EN-US">4</span>：<span lang="EN-US">5</span>よりも短い<span lang=
"EN-US">5</span>：<span lang=
"EN-US">6</span>にとるのが短調です。基音をラとした短調の基本<span lang="EN-US">3</span>和音であるラ・ド・ミ、レ・ファ・ラ、ミ・ソ・シの周波数比がいずれも<span lang="EN-US">10</span>：<span lang="EN-US">12</span>：<span lang="EN-US">15</span>になるように決められた短音階は、以下のようになります。</span></p>
<table class="MsoNormalTable" style="mso-cellspacing: 1.5pt" cellpadding="0"
border="1">
<tbody>
<tr style="mso-yfti-irow: 0; mso-yfti-firstrow: yes">
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan" align=
"left">?</p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ラ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
シ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ド</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
レ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ミ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ファ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ソ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ラ</span></p>
</td>
</tr>
<tr style="mso-yfti-irow: 1">
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan" align=
"left"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
基音（ラ）に対する比</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
1<br>
(1.000)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/8<br>
(1.125)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
6/5<br>
(1.200)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
4/3<br>
(1.333)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
3/2<br>
(1.500)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
8/5<br>
(1.600)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/5<br>
(1.800)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
2<br>
(2.000)</span></p>
</td>
</tr>
<tr style="mso-yfti-irow: 2; mso-yfti-lastrow: yes">
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan" align=
"left"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
直下の音に対する比</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
-</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/8<br>
(1.125)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
16/15<br>
(1.067)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
10/9<br>
(1.111)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/8<br>
(1.125)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
16/15<br>
(1.067)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/8<br>
(1.125)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
10/9<br>
(1.111)</span></p>
</td>
</tr>
</tbody>
</table>
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto"
align="left"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
　このように、各音の高さを和音が調和する整数比で決めた音階を<b>純正律音階</b>といいます。<span lang="EN-US"><br>
</span>　ところが、純正律音階にはやっかいな問題があります。上の表を見て、ド～レの音程の周波数比が長音階では<span lang="EN-US">8</span>：<span lang="EN-US">9</span>、短音階では<span lang="EN-US">9</span>：<span lang="EN-US">10</span>であることがおわかりでしょう。このため、ハ長調の曲の途中でイ短調のレ・ファ・ラの和音が現れると、めちゃくちゃ汚い響きになってしまうのです。したがって、ハ長調とイ短調の両方の和音を弾くには、二つのレが必要になってしまいます。ましてや、ハ短調だの変ロ長調だのに自由に転調しようとしたら、そりゃもう大騒ぎで、一オクターブあたり何十個もの鍵（けん）が必要になってしまいます。</span></p>
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto"
align="left">?</p>
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto"
align="left"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
<font face=
"Times New Roman">　そこで、一オクターブあたり12個の鍵でどのように転調しても周波数比が変わらないように決められたのが<b><a href="http://www7.atwiki.jp/05ad3/pages/42.html">平均律音階</a></b>です。平均律音階では、周波数比は指数関数で決められます。<br>
</font></span></p>
<p><a href=
"http://www7.atwiki.jp/05ad3/pages/42.html">→次のキーワードに進む</a></p>
<br>
<h3>純正律　[編集：高崎]</h3>
<pre>
<strong>純正律とは</strong>
</pre>
<blockquote dir="ltr" style="MARGIN-RIGHT: 0px">
<pre>
１５世紀、スペインのバルイトロメー・ラモスが考案した音律。<br>
ラモスはピュタゴラス音律の三度（ディトノス）の問題点を批判し、純正三度（5/4）を取り入れた。<br>
ピュタゴラス音律との決定的な違いは第三度音、第六度音、第七度音の三つ。<br>
杉井君の表を見ればわかるように、全音の比率は大全音9/8と小全音10/9の二つがあり、半音の比率は全て同じ16/15になる。
</pre></blockquote>
<pre>
<strong>純正律の問題点</strong>
</pre>
<blockquote dir="ltr" style="MARGIN-RIGHT: 0px">
<pre>

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<strong>純正律って</strong></span></p>
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align="left">?</p>
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align="left"><span style=
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&lt;解答１&gt;杉井</span></p>
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align="left">?</p>
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align="left"><span style=
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　和音は、周波数が単純な整数比になるときに良く調和して聞こえます。ド・ミ・ソの和音が完全に</span></p>
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align="left"><span style=
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調和するときの周波数比は<span lang="EN-US">4</span>：<span lang=
"EN-US">5</span>：<span lang=
"EN-US">6</span>です。長調の基本<span lang=
"EN-US">3</span>和音であるド・ミ・ソ、ファ・ラ・ド、ソ・シ・レの</span></p>
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周波数比がいずれも<span lang="EN-US">4</span>：<span lang=
"EN-US">5</span>：<span lang=
"EN-US">6</span>になるように音階（長音階）を決めると、以下のようになります。</span></p>
<table class="MsoNormalTable" style="mso-cellspacing: 1.5pt" cellpadding="0"
border="1">
<tbody>
<tr style="mso-yfti-irow: 0; mso-yfti-firstrow: yes">
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<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan" align=
"left">?</p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
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"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ド</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
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"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
レ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
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"center"><span style=
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ミ</span></p>
</td>
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"center"><span style=
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ファ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
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"center"><span style=
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ソ</span></p>
</td>
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"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
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ラ</span></p>
</td>
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シ</span></p>
</td>
<td style=
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"center"><span style=
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ド</span></p>
</td>
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<tr style="mso-yfti-irow: 1">
<td style=
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"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan" align=
"left"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
基音（ド）に対する比</span></p>
</td>
<td style=
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<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
1<br>
(1.000)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/8<br>
(1.125)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
5/4<br>
(1.250)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
4/3<br>
(1.333)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
3/2<br>
(1.500)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
5/3<br>
(1.667)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
15/8<br>
(1.875)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
2<br>
(2.000)</span></p>
</td>
</tr>
<tr style="mso-yfti-irow: 2; mso-yfti-lastrow: yes">
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan" align=
"left"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
直下の音に対する比</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
-</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/8<br>
(1.125)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
10/9<br>
(1.111)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
16/15<br>
(1.067)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/8<br>
(1.125)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
10/9<br>
(1.111)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/8<br>
(1.125)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
16/15<br>
(1.067)</span></p>
</td>
</tr>
</tbody>
</table>
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan" align=
"left"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
　さて、基音からの<span lang=
"EN-US">3</span>度音程（ド～ミ）の周波数比を<span lang=
"EN-US">4</span>：<span lang="EN-US">5</span>よりも短い<span lang=
"EN-US">5</span>：<span lang=
"EN-US">6</span>にとるのが短調です。</span></p>
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan" align=
"left"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
基音をラとした短調の基本<span lang=
"EN-US">3</span>和音であるラ・ド・ミ、レ・ファ・ラ、ミ・ソ・シの周波数比がいずれも</span></p>
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan" align=
"left"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
<span lang="EN-US">10</span>：<span lang="EN-US">12</span>：<span lang=
"EN-US">15</span>になるように決められた短音階は、以下のようになります。</span></p>
<table class="MsoNormalTable" style="mso-cellspacing: 1.5pt" cellpadding="0"
border="1">
<tbody>
<tr style="mso-yfti-irow: 0; mso-yfti-firstrow: yes">
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan" align=
"left">?</p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ラ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
シ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ド</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
レ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ミ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ファ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ソ</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
ラ</span></p>
</td>
</tr>
<tr style="mso-yfti-irow: 1">
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan" align=
"left"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
基音（ラ）に対する比</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
1<br>
(1.000)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/8<br>
(1.125)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
6/5<br>
(1.200)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
4/3<br>
(1.333)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
3/2<br>
(1.500)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
8/5<br>
(1.600)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/5<br>
(1.800)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
2<br>
(2.000)</span></p>
</td>
</tr>
<tr style="mso-yfti-irow: 2; mso-yfti-lastrow: yes">
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan" align=
"left"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
直下の音に対する比</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
-</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/8<br>
(1.125)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
16/15<br>
(1.067)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
10/9<br>
(1.111)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/8<br>
(1.125)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
16/15<br>
(1.067)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
9/8<br>
(1.125)</span></p>
</td>
<td style=
"BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0.75pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 0.75pt; PADDING-BOTTOM: 0.75pt; BORDER-LEFT: #ece9d8; PADDING-TOP: 0.75pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: center; mso-pagination: widow-orphan" align=
"center"><span lang="EN-US" style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
10/9<br>
(1.111)</span></p>
</td>
</tr>
</tbody>
</table>
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto"
align="left"><span style=
"FONT-FAMILY: 'ＭＳ Ｐゴシック'; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: 'ＭＳ Ｐゴシック'; mso-font-kerning: 0pt">
　このように、各音の高さを和音が調和する整数比で決めた音階を<b>純正律音階</b>といいます。<span lang="EN-US"><br>
</span>　ところが、純正律音階にはやっかいな問題があります。上の表を見て、ド～レの音程の周波数比が</span></p>
<p class="MsoNormal" style=
"MARGIN: 0mm 0mm 0pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto"
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長音階では<span lang="EN-US">8</span>：<span lang=
"EN-US">9</span>、短音階では<span lang="EN-US">9</span>：<span lang=
"EN-US">10</span>であることがおわかりでしょう。このため、ハ長調の曲の途中で</span></p>
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イ短調のレ・ファ・ラの和音が現れると、めちゃくちゃ汚い響きになってしまうのです。</span></p>
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したがって、ハ長調とイ短調の両方の和音を弾くには、二つのレが必要になってしまいます。</span></p>
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ましてや、ハ短調だの変ロ長調だのに自由に転調しようとしたら、そりゃもう大騒ぎで、</span></p>
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一オクターブあたり何十個もの鍵（けん）が必要になってしまいます。</span></p>
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align="left">?</p>
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<font face=
"Times New Roman">　そこで、一オクターブあたり12個の鍵でどのように転調しても周波数比が変わらないように</font></span></p>
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<font face="Times New Roman">決められたのが<b><a href=
"http://www7.atwiki.jp/05ad3/pages/42.html">平均律音階</a></b>です。平均律音階では、周波数比は指数関数で決められます。<br>
</font></span></p>
<p><a href=
"http://www7.atwiki.jp/05ad3/pages/42.html">→次のキーワードに進む</a></p>
<br>
<h3>純正律　[編集：高崎]</h3>
<pre>
<strong>純正律とは</strong>
</pre>
<blockquote dir="ltr" style="MARGIN-RIGHT: 0px">
<pre>
１５世紀、スペインのバルイトロメー・ラモスが考案した音律。<br>
ラモスはピュタゴラス音律の三度（ディトノス）の問題点を批判し、
</pre>
<pre>
純正三度（5/4）を取り入れた。<br>
ピュタゴラス音律との決定的な違いは第三度音、第六度音、第七度音の三つ。<br>
杉井君の表を見ればわかるように、全音の比率は大全音9/8と小全音10/9の
</pre>
<pre>
二つがあり、半音の比率は全て同じ16/15になる。
</pre></blockquote>
<pre>
<strong>純正律の問題点</strong>
</pre>
<blockquote dir="ltr" style="MARGIN-RIGHT: 0px">
<pre>