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“神秘的” なハーモニーの作り方
Satoru Tagawa
講師の紹介
• 田川 慧 (Satoru Tagawa)
• 父親がバークリー音楽大学に行くために渡米
• コロラドの大学で 2 年間音楽を専攻して中退
– Double Bass Performance
• ケンタッキー大学で電気工学で卒業
– Microphone array を用いての音声信号処理
• Broadway Musical “The Producers” でベーシスト
として全米ツアー参加
• 現在 Software Engineer
フレットの無い世界
• 弦楽四重奏、コーラス、など
– ハーモニーがとにかく綺麗
– 1つのコードが奏でられてるだけで心が洗われる
• 実際何が違うの?
3 Qualities of Sound
• Pitch
• Sound Envelop
• Overtone Series
Overtone Series とは
fn = nf1
• 例えば 55Hz だと:
Overtone の音達は鳴っている
Overtone #
Magnitude
Ratio
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Series1
フーリエ変換
• どの周波数の音がどれだけあるかを教えてく
れる数式
• これを使えば Overtone の比率が分かる!
実際の楽器の Overtone
Overtone の比率 (1/2)
• この特性によって音色が変わる
– 同じ高さの人の声でも違う人と認識
– 楽器の音色の違いは、ほぼ Overtone の比率の
違い
Overtone の比率 (2/2)
• 声が大きければ説得力がある訳ではない
– オペラ歌手、パブリックスピーカーなど
• 基本周波数がしっかりしている
• 高い Overtone がしっかりしている
• その間の Overtone は比較的小さい
• どうすればいい?
– 弦楽器の場合
• 弓をブリッジに近づけて弾くと高い Overtone が出る
チューニング手法
• 平均律
– 各半音の周波数の比率が一定 @ 2^(1/12)
• 純正律
– 各音階音の周波数を Overtone Series の比率に
基づいて計算
• 要するに既に鳴っている音に合わせる
重要な音階
• 短三度 (Minor 3rd)
– やや高めに (15.6セント)
• 長三度 (Major 3rd)
– やや低めに (13.7セント)
• 完全五度 (Perfect 5th)
– 大体合ってるが、気持ち高めに (2セント)
まとめ
• Pitch,Envelop,Overtone で音の性質が決まる
• 純正音程でコードを奏でると神秘的で素敵
Shameless plug
• 明日 (6/27) Rokko でジャズの演奏します
– Chie Sugiyama (ウッドベース)
• 7/4 夏祭りで弾きます (3 バンド)
– Kazu Gorai (エレキベース、チェロ)
– Miki Takano (エレキベース)
– Ken Matsuda (チェロ)
• 8/1 Rokko でポップスの演奏します
– Miki Takano (エレキベース)
Resources
• https://musicnotes101.wordpress.com/2010/04/20/the-musical-alphabet-clefs-the-musical-
staff-and-the-keyboard/
• http://filmsound.org/articles/ninecomponents/9components.htm
• http://www.phy.mtu.edu/~suits/overtone.html
• http://in.music.sc.edu/fs/bain/atmi02/hs/index-noaudio.html
https://en.wikipedia.org/?title=Fourier_transform
• https://ja.m.wikipedia.org/wiki/%E5%B9%B3%E5%9D%87%E5%BE%8B
• http://newt.phys.unsw.edu.au/jw/sound.spectrum.html

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神秘的なハーモニーの作り方