^Gordon Reid (2019年7月). “Arturia V Collection 7”. Sound On Sound. SOS Publications Group. 2020年12月12日閲覧。
^Julius O. Smith III (2007). “Sinusoidal Frequency Modulation (FM)”. Mathematics of the Discrete Fourier Transform (DFT): with Audio Applications (2 ed.). W3K Publishing. https://ccrma.stanford.edu/~jos/mdft/Sinusoidal_Frequency_Modulation_FM.html. "Note that, strictly speaking, it is not the frequency of the carrier that is modulated sinusoidally, but rather the instantaneous phase of the carrier. Therefore, phase modulation would be a better term (which is in fact used). ... In this book, only phase modulation will be considered, and we will call it FM, following common practice.(4.9. An important variant of FM called feedback FM, in which a single oscillator phase-modulates itself, simply does not work if true frequency modulation is implemented.)" Note: 一般論として周波数変調は、キャリアの周波数ではなくキャリアの瞬時位相がモジュレータの正弦波で変調される形になる。従って周波数変調自体も位相変調と呼ぶのが良いだろう、本文献では位相変調のみ考慮するが、それをFMと呼ぶ事にする、という説明。脚注4.9は補足として、YAMAHA独自のフィードバックFM は単一オシレータのセルフ位相変調であり、もし仮に周波数変調であれば動かないという説明をしている。
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Miller Puckette (2007). “Frequency and phase modulation”. The Theory and Technique of Electronic Music. World Scientific Press. http://msp.ucsd.edu/techniques/latest/book-html/node79.html. "Here we develop frequency modulation, usually called FM, as a special case of waveshaping the analysis given here is somewhat different. The FM technique, in its simplest form, is shown in Figure 5.8 (part a). ... It is customary to use a simpler, essentially equivalent formulation in which the phase, instead of the frequency, of the carrier sinusoid is modulated sinusoidally. (...) The phase modulation formulation is shown in part (b) of the figure." Note: この文献の該当部は、John Chowning 1973論文やYAMAHA実装の説明ではなく、Pure Data上で周波数変調および簡易版としての位相変調を実装する話である。周波数変調の代りに位相変調で簡易化した同等の式を立てるのが通例だとする指摘は有効。
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Sean Luke (2019). “9. Frequency Modulation Synthesis”. Computational Music Synthesis (zeroth ed.). https://cs.gmu.edu/~sean/book/synthesis/. "p.107: 8.1 Frequency and Phase Modulation / In fact, nearly all FM synthesizers don’t do frequency modulation at all. Rather, they apply a related method called phase modulation or PM. This isn’t bait-and-switch: phase modulation is slightly different in implementation but achieves the same exact effect.102 Both phase and frequency modulation are subsets of a general category of modulation methods called angle modulation.103 Phase modulation is easier to explain, so we’ll begin with that." "p.109: Phase and Frequency Modulation are Very Similar ..." Note: PDF版8.1節 "Frequency and Phase Modulation"で「ほとんどのFMシンセサイザは周波数変調は全くしておらず、関連方式である位相変調 (PM)を使っている」と宣言しているが、信頼のおけるソースは添えておらず検証可能性に問題がある。
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“Interview - John Chowning”. These Hopeful Machines. Radio New Zealand (2013年7月14日). 2023年3月17日閲覧。 “After the GS-1 there was the GS-2 and then in 1983 the DX-7, which was the first FM [10] synthesizer to really take off.", "[10] Strictly speaking, Yamaha’s ‘FM’ was an implementation of phase modulation, but ‘FM’ is the term universally associated with the synthesis technique, the Yamaha instruments and the sounds they typically produced.” Note: 該当ページの脚注[10]で「厳密に言えば、ヤマハの「FM」は位相変調の実装でしたが、「FM」は、合成技術、ヤマハの楽器、およびそれらが通常生成する音に普遍的に関連付けられている用語です。」と書かれているが、これはJohn Chowning本人発言ではなくインタビューア側質問文の脚注であり、記事発行元はRadio New Zealandなので専門的な検証可能性には欠ける。
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