Notes

1. Eccentric or warped record has subsonic frequencies: Off-center 0.55cycle（Lateral Wow）, Warp 1.1(one-fold) - 4.4cycles(4-fold) mainly（Vertical Wow）. According to Ladegaard (Fig 7. Velocity spectrum of phonograph records taken from Larry Happ & Frank Karlov, AES Preprint Number:926 1973 & JAES October 1976 under the title "Record Warps and System Playback Performance"), frequencies 0.5-7Hz caused by these warps have velocity 0.3-0.6cm/s max (which is larger than recorded velocity limit at 20Hz) while 10-18Hz has lower velocity around 0.2cm/s so that Ladegaard recommended to raise arm resonance frequency to 15-18Hz).  Moreover 0.55cycle as amplitude modulation is not audible for itself or not reproducible with usual set of arm and cartridge but it is not so simple. When groove or hole is 1mm eccentric, then signal of 3.15ｋHz recorded laterally at radius 6cm is fluctuating between 3.1kHz〜3.2ｋHz by 1.8sec(one turn). Thus the rate 0.55(=once per 1.8sec) does indicate modulating frequency - such frequency modulation cannot be suppressed with usual subsonic filter.

According to D.L. Taylor at JAES December 1980: Measurement of Spectral Content of Record Warps, "the horizontal variations are seen to reflect simply the center hole offset and are uncorrelated with the vertical warps. The worst case envelope for vertical warps is shown to be somewhat lower than that used by previous investigators. More importantly, the average vertical warp is seen to be an order of magnitude less than the worse case."

Our ears are said to be most sensitive to modulating frequency or wow cycle 2-4Hz so that we should avoid such wow - but what we can do for warped record ? Maybe by using stabilizer weight on record in order to flatten warped record.

2. Motor Rumble: around 25 to 30 cycles/sec with 4-pole synchronous belt-drive motor 1800rpm/60Hz or 1500rpm/50Hz (24-pole synchronous motor 5Hz? with 250-300rpm, DD motor 0.55Hz? with 100/3rpm)

3. Motor Hum: 50/60Hz and its double frequencies

4. Turntable/cabinet/plinth support resonance: around 3-10Hz? This is questionable and changing with the mass of turntable and supporting materials: Fr=(1/2pi)*SQRT(K/Mp) where K=stiffness (N/m), Mp=Mass (Kg). With conversion of above formula in SI to gravity system unit (stiffness gf/cm and Weight gram), then Fr=(1/2pi)*SQRT(980K/Mp). Being stiffness = 1/compliance, this formula is just same as that for arm-cartridge resonance. Is this vertical resonance and affecting vertical mode of arm/cart resonance only?

5. Lowest music frequency is 16Hz pipe organ. Dr. Olson said "Under very favorable conditions most individuals can obtain tonal characteristics as low as 12 cycles" (Music, Physics and Engineering: Chapter 7.4 Psychological Characteristics of Music)

These frequencies are actually differing each other - phase/vertical/lateral modes of mechanical vibrations are uncertain or unspecified usually. In USP4275888(1981) by Shure I find an interesting passage: "Although typical sources of vibrations at the resonance frequency, such as floor vibrations and record warps, have a predominantly vertical component, it has been discovered that they also have a substantial horizontal component. Some of the impact energy from a warp or a floor vibration may also be translated into lateral vibrations by passing through the tone arm suspension system".

To avoid overlapping these frequencies,  8-12Hz (resonance frequency between arm mass and cartridge compliance) is estimated as reasonable, in other words, any resonance frequency under 20Hz is possible if other factors are not affecting each other in actual product - to my regret I don't know such perfect product both on soft and hard side.

IMHO: Ladegaad in his document [Audible Effects of Mechanical Resonances in Turntables] does not refer explicitly to Psychological Characteristics of Human Ears. High or low - which is more audible? What I am inspired by Ladegaard papers is that resonance of arm/cartridge is most important factor in connection with many other resonances which affect sound.

Subsonic noise filter (HPF) or IEC suggestion about equalization (introduction of an additional time constant 7950μs/20Hz) might be made with the above consideration on arm resonance & rumble noise.  -3dB difference at 20Hz (-7db at 10Hz) between recording and reproduction results from additional time constant 7950µs（20Hz) recommended by IEC60098(clause 10.2.1) year 1987.

The following equation is taken from a pamphlet attached to MJ test record:
Resonance Q=2pi*ft*mt/(rb+rp)=(1/(rb+rp))*mt/SQRT(mt*C)=(1/(rb+rp))*SQRT(mt)/SQRT(C)
where rb is armature resistance at cartridge, rp is resistance at arm pivot. 

The following table is based on the above equation. Note that ft x Q becomes a constant irrespective of additional weight if combination of arm+cartridge is unchanged. This is natural result from equation ft x Q=(1/(2pi*SQRT(mt*C)))x(1/(rb+rp))*SQRT(mt)/SQRT(C)=(1/(rb+rp))*(1/2pi)/C.　Note on damping factors (rb&rp): what is the relation between rb (armature resistance) and rp (resistance around arm pivot)? Yamamoto in his book (1971) explained as follows: "There are two ways of controlling the arm resonance at low frequency, that is, by equivalent resistances shown in Fig 3-13: one is armature resistance (rb) and another is resistance at arm pivot (rp). Fig 6-4, 6-5, 6-6, 6-7 shows the cases by controlling arm resonance by each factor independently. In case (Fig 6-4&6-6) of control by rb, the mechanical impedance for mid frequency increases.  In case (Fig.6-5&6-7) of control by rp, the mechanical impedance for lowest frequency increases. In order to trace the record with light VTF, the mechanical impedance must be low enough for full range. Hence rb is set so as to make the high frequency flat and mechanical impedance matching. Arm resonance shall be controlled mainly by rp. But if rp is made too large, then the impedance at lowest frequency will be increased so that heavier VTF is required to trace on the warped or off-centered record."

非直線・非対称なコンプライアンスの問題：Grado氏は晩年にリニアトラッキング・アームの特許を日本に申請していました（特許公開S55-42399)ーその発明内容(針先を溝以外の余計な力から開放する工夫＊下注参照）は疑問ですが針先に掛かる力を分析しているところに興味を惹かれました。針圧により縦方向にダンパーが圧縮するので、実際のカートリッジのコンプライアンスは縦方向で少なく、横方向で大きくなることが多い。それを補正するために、以下のように異形(デベソ）のダンパー（Denon DL-7)が用いられることがあります。ダンパーについては他にもいろいろな工夫が試みられています：armaureの前後に配置するdouble dampers(Denon/Ortofonの製品の一部で実現）、ハイコンプライアンスを維持するためダンパーの硬さを中心が硬く外周で軟らかくする工夫(2重ドーナツJP57018006やドーム状ダンパーJP57008903)、周辺温度変化により高域特性が変わるのを防ぐためダンパーの材質を従来のブチルゴムにシリコンゴムを混入する工夫（テクニクスのTTDD=US4232869や日本コロムビアのJP56094503）等等。
＊注：針先を溝以外の余計な力から開放することは興味深い問題を提示しています。ダンパーのコンプライアンス（＝１/Stiffness)は小さすぎるとそれ自体が運動ロスになるので或る程度大きいことが望まれます。従ってコンプライアンスは5cu〜50cuの範囲に限定されてきた背景があります。LP時代カートリッジを含めたアームの実効質量も最低でリニアトラックの場合9g前後、最高で50g前後になります。アームとカートリッジの組み合わせは低域共振周波数が通常８〜１６Hzの範囲に成るように選択されます。針先とレコード盤との間の摩擦によるstylus dragは針先・アーム支点間のテンションとなりカートリッジの実効コンプライアンスに影響を与えます。実際の製品ではコンプライアンスだけでなくアームの回転感度もしくは摩擦抵抗も縦横方向で違うものが多いのでいくら理論を展開しても実効がないことが多いと感じています。光学を用いたLaser Turntableはstylus dragの厄介な諸問題から逃れた例だと思います。 

ピックアップシステム（arm+cartridge)と針圧と針形状についての参考文献（JVC/Yamamoto/Stevenson/Bastiaans/Hunt etc.)についての記述は2021年4月削除しました。自分のお勉強用の資料でここに公開すべきものではないと判断しました。

Recently (April 2021) I omitted some referenes to Stevenson/Bastiaans/Hunt/Yamamoto/JVC and others since these references are for my reading only and nobody cares now.