text:
Fuzzy Topology
##### 101. Applications of fuzzy $e$-open sets

Volume 07, Issue 01 , Winter 2018, , Pages 39-51

##### Abstract
The aim of this paper is to introduce and study the notions of fuzzy upper $e$-limit set, fuzzy lower $e$-limit set and fuzzy $e$-continuously convergent functions. Properties and basic relationships among fuzzy upper $e$-limit set, fuzzy lower $e$- limit set and fuzzy $e$-continuity are investigated ...  Read More

Topological groups, Lie groups
##### 102. A note on quasi irresolute topological groups

T. Oner; A. Ozek

Volume 05, Issue 01 , Winter 2016, , Pages 41-46

##### Abstract
In this study, we investigate the further properties of quasi irresolute topological groups defi ned in [20]. We show that if a group homomorphism f between quasi irresolute topological groups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semi-connected quasi ...  Read More

Functional analysis
##### 103. System of AQC functional equations in non-Archimedean normed spaces

H. Majani

Volume 08, Issue 01 , Winter 2019, , Pages 41-52

##### Abstract
In 1897, Hensel introduced a normed space which does not have the Archimedean property. During the last three decades theory of non--Archimedean spaces has gained the interest of physicists for their research in particular in problems ...  Read More

Fixed point theory
##### 104. Coupled fixed point theorems involving contractive condition of integral type in generalized metric spaces

Volume 06, Issue 01 , Winter 2017, , Pages 45-53

##### Abstract
In this manuscript, we prove some coupled fixed point theorems for two pairs of self mappings satisfying contractive conditions of integral type in generalized metric spaces. We furnish suitable illustrative examples. In this manuscript, we prove some coupled fixed point theorems for ...  Read More

Fixed point theory
##### 105. Fixed point results for Su-type contractive mappings with an application

A. Ali; H. Işık; F. Uddin; M. Arshad

Volume 09, Issue 01 , Winter 2020, , Pages 53-65

##### Abstract
In this paper, we introduce the concept of Su-type contractive mapping and establish fixed point theorems for such mappings in the setting of ordered extended partial $b$-metric space. We also develop an application for Fredholm type integral equations ...  Read More

Difference and functional equations
##### 106. On edge detour index polynomials

Sh. Safari Sabet; M. Farmani; O. Khormali; A. Mahmiani; Z. Bagheri

Volume 02, Issue 02 , Spring 2013, , Pages 83-89

##### Abstract
The edge detour index polynomials were recently introduced for computing the edge detour indices. In this paper we find relations among edge detour polynomials for the 2-dimensional graph of $TUC_4C_8(S)$ in a Euclidean plane and $TUC4C8(S)$ nanotorus.  Read More

##### 107. Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

H. R. Rezazadeh; M. Maghasedi; B. shojaee

Volume 01, Issue 02 , Spring 2012, , Pages 83-95

##### Abstract
In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.). So, we construct a stochastic linear equation system from this equation which its solution is based on ...  Read More

Functional analysis
##### 108. Compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions

Volume 03, Issue 02 , Spring 2014, , Pages 87-105

##### Abstract
We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.  Read More

General topology
##### 109. On Baer type criterion for $C$-dense, $C$-closed and quasi injectivity

H. Barzegar; H. Arianpoor

Volume 05, Issue 02 , Spring 2016, , Pages 105-109

##### Abstract
For the subclasses $\mathcal{M}_1$ and $\mathcal{M}_2$ of monomorphisms in a concrete category $\mathcal{C}$, if $\mathcal{M}_2\subseteq \mathcal{M}_1$, then $\mathcal{M}_1$-injectivity implies $\mathcal{M}_2$-injectivity. The Baer ...  Read More

Linear and multilinear algebra; matrix theory
##### 110. An accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations

Volume 08, Issue 02 , Spring 2019, , Pages 117-126

##### Abstract
In this paper, an accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations is proposed. The convergence analysis of the algorithm is investigated. We show that the proposed algorithm converges to ...  Read More

Functional analysis
##### 111. Approximation of endpoints for multi-valued mappings in metric spaces

Volume 09, Issue 02 , Spring 2020, , Pages 129-137

##### Abstract
In this paper, under some appropriate conditions, we prove some $\Delta$ and strong convergence theorems of endpoints for multi-valued nonexpansive mappings using modified Agarwal-O'Regan-Sahu iterative process in the general setting of 2-uniformly convex hyperbolic spaces. Our results extend and unify ...  Read More

Functional analysis
##### 112. New characterizations of fusion bases and Riesz fusion bases in Hilbert spaces

F. Aboutorabi Goudarzi; M. S. Asgari

Volume 04, Issue 02 , Spring 2015, , Pages 131-142

##### Abstract
In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new de nition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual ...  Read More

Combinatorics
##### 113. On the energy of non-commuting graphs

M. Ghorbani; Z. Gharavi-Alkhansari

Volume 06, Issue 02 , Spring 2017, , Pages 135-146

##### Abstract
For given non-abelian group G, the non-commuting (NC)-graph $\Gamma(G)$ is a graph with the vertex set $G$\ $Z(G)$ and two distinct vertices $x, y\in V(\Gamma)$ are adjacent whenever $xy \neq yx$. The aim of this paper is to compute the spectra of some well-known NC-graphs.  Read More

Group theory and generalizations
##### 114. A representation for some groups, a geometric approach

A. Parsian

Volume 07, Issue 02 , Spring 2018, , Pages 149-153

##### Abstract
In the present paper, we are going to use geometric and topological concepts, entities and properties of the integral curves of linear vector fields, and the theory of differential equations, to establish a representation for some groups ...  Read More

Group theory and generalizations
##### 115. On the Finite Groupoid G(n)

Volume 02, Issue 03 , Summer 2013, , Pages 153-159

##### Abstract
In this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid G(n). Also we show that G(n) contains commuting regular subsemigroup and give a necessary and sufficient condition for the groupoid G(n) ...  Read More

Ordinary differential equations
##### 116. Solution of the first order fuzzy differential equations with generalized differentiability

L. Jamshidi; T. Allahviranloo

Volume 03, Issue 03 , Summer 2014, , Pages 159-171

##### Abstract
In this paper, we study first order linear fuzzy differential equations with fuzzy coefficient and initial value. We use the generalized differentiability concept and apply the exponent matrix to present the general form of their solutions. Finally, one example is given to illustrate ...  Read More

Difference and functional equations
##### 117. Application of DJ method to Ito stochastic differential equations

H. Deilami Azodi

Volume 08, Issue 03 , Summer 2019, , Pages 183-189

##### Abstract
This paper develops iterative method described by [V. Daftardar-Gejji, H. Jafari, An iterative method for solving nonlinear functional equations, J. Math. Anal. Appl. 316 (2006) 753-763] to solve Ito stochastic ...  Read More

Difference and functional equations
##### 118. Solving systems of nonlinear equations using decomposition technique

Volume 05, Issue 03 , Summer 2016, , Pages 187-198

##### Abstract
A systematic way is presented for the construction of multi-step iterative method with frozen Jacobian. The inclusion of an auxiliary function is discussed. The presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost ...  Read More

Integral equations
##### 119. Bernoulli collocation method with residual correction for solving integral-algebraic equations

F. Mirzaee

Volume 04, Issue 03 , Summer 2015, , Pages 193-208

##### Abstract
The principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (IAE) by using the Bernoulli polynomials and the residual correction method. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its ...  Read More

Fixed point theory
##### 120. Common fixed points for a pair of mappings in $b$-Metric spaces via digraphs and altering distance functions

S. K. Mohanta; D. Biswas

Volume 07, Issue 03 , Summer 2018, , Pages 201-218

##### Abstract
In this paper, we discuss the existence and uniqueness of points of coincidence and common fixed points for a pair of self-mappings satisfying some generalized contractive type conditions in $b$-metric spaces endowed with graphs and altering distance functions. Finally, some examples are provided ...  Read More

Functional analysis
##### 121. On φ-Connes amenability of dual Banach algebras

A. Mahmoodi

Volume 03, Issue 04 , Autumn 2014, , Pages 211-217

##### Abstract
Let φ be a w-continuous homomorphism from a dual Banach algebra to C. The notion of φ-Connes amenability is studied and some characterizations is given. A type of diagonal for dual Banach algebras is de ned. It is proved that the existence of such a diagonal is equivalent to φ-Connes ...  Read More

Group theory and generalizations
##### 122. On some Frobenius groups with the same prime graph as the almost simple group ${ {\bf PGL(2,49)}}$

A. Mahmoudifar

Volume 06, Issue 03 , Summer 2017, , Pages 217-221

##### Abstract
The prime graph of a finite group $G$ is denoted by $\Gamma(G)$ whose vertex set is $\pi(G)$ and two distinct primes $p$ and $q$ are adjacent in $\Gamma(G)$, whenever $G$ contains an element with order $pq$. We say that $G$ is unrecognizable by prime graph if there is a finite group $H$ with $\Gamma(H)=\Gamma(G)$, ...  Read More

Ordinary differential equations
##### 123. Numerical solution of second-order stochastic differential equations with Gaussian random parameters

R. Farnoosh; H. Rezazadeh; A. Sobhani; D. Ebrahimibagha

Volume 02, Issue 04 , Autumn 2013, , Pages 229-241

##### Abstract
In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order ...  Read More

Integral equations
##### 124. New iteration process for approximating fixed points in Banach spaces

J. D. Bhutia; K. Tiwary

Volume 08, Issue 04 , Autumn 2019, , Pages 237-250

##### Abstract
The object of this paper is to present a new iteration process. We will show that our process is faster than the known recent iterative schemes. We discuss stability results of our iteration and prove some results in the context of uniformly convex Banach space for Suzuki generalized ...  Read More

Group theory and generalizations
##### 125. On the irreducibility of the complex specialization of the representation of the Hecke algebra of the complex reflection group $G_7$

M. Y. Chreif; M. Abdulrahim

Volume 05, Issue 04 , Autumn 2016, , Pages 263-270

##### Abstract
We consider a 2-dimensional representation of the Hecke algebra $H(G_7, u)$, where $G_7$ is the complex reflection group and $u$ is the set of indeterminates $u = (x_1,x_2,y_1,y_2,y_3,z_1,z_2,z_3)$. After specializing the indetrminates to non zero complex numbers, we then determine a necessary ...  Read More


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• ### Measurements of $\pi^\pm$, K$^\pm$, p and $\bar{\textrm{p}}$ spectra in proton-proton interactions at 20, 31, 40, 80 and 158 GeV/c with the NA61/SHINE spectrometer at the CERN SPS(1705.02467)

Sept. 27, 2017 nucl-ex
Measurements of inclusive spectra and mean multiplicities of $\pi^\pm$, K$^\pm$, p and $\bar{\textrm{p}}$ produced in inelastic p+p interactions at incident projectile momenta of 20, 31, 40, 80 and 158 GeV/c ($\sqrt{s} =$ 6.3, 7.7, 8.8, 12.3 and 17.3 GeV, respectively) were performed at the CERN Super Proton Synchrotron using the large acceptance NA61/SHINE hadron spectrometer. Spectra are presented as function of rapidity and transverse momentum and are compared to predictions of current models. The measurements serve as the baseline in the NA61/SHINE study of the properties of the onset of deconfinement and search for the critical point of strongly interacting matter.
• ### Measurement of Meson Resonance Production in $\pi^{-} +$C Interactions at SPS energies(1705.08206)

May 23, 2017 nucl-ex, astro-ph.HE
We present measurements of $\rho^0$, $\omega$ and K$^{*0}$ spectra in $\pi^{-} +$C production interactions at 158 GeV/c and $\rho^0$ spectra at 350 GeV/c using the NA61/SHINE spectrometer at the CERN SPS. Spectra are presented as a function of the Feynman's variable $x_\text{F}$ in the range $0 < x_\text{F} < 1$ and $0 < x_\text{F} < 0.5$ for 158 GeV/c and 350 GeV/c respectively. Furthermore, we show comparisons with previous measurements and predictions of several hadronic interaction models. These measurements are essential for a better understanding of hadronic shower development and for improving the modeling of cosmic ray air showers.
• ### Two-particle correlations in azimuthal angle and pseudorapidity in inelastic p+p interactions at the CERN Super Proton Synchrotron(1610.00482)

Feb. 7, 2017 nucl-ex
Results on two-particle $\Delta\eta\Delta\phi$ correlations in inelastic p+p interactions at 20, 31, 40, 80, and 158~GeV/c are presented. The measurements were performed using the large acceptance NA61/SHINE hadron spectrometer at the CERN Super Proton Synchrotron. The data show structures which can be attributed mainly to effects of resonance decays, momentum conservation, and quantum statistics. The results are compared with the EPOS and UrQMD models.
• ### Measurements of $\pi^{\pm}$ differential yields from the surface of the T2K replica target for incoming 31 GeV/c protons with the NA61/SHINE spectrometer at the CERN SPS(1603.06774)

Nov. 29, 2016 hep-ex, physics.ins-det
Measurements of particle emission from a replica of the T2K 90 cm-long carbon target were performed in the NA61/SHINE experiment at CERN SPS, using data collected during a high-statistics run in 2009. An efficient use of the long-target measurements for neutrino flux predictions in T2K requires dedicated reconstruction and analysis techniques. Fully-corrected differential yields of $\pi^\pm$-mesons from the surface of the T2K replica target for incoming 31 GeV/c protons are presented. A possible strategy to implement these results into the T2K neutrino beam predictions is discussed and the propagation of the uncertainties of these results to the final neutrino flux is performed.
• ### Production of deuterium, tritium, and $^3$He in central Pb+Pb collisions at 20A, 30A, 40A, 80A, and 158A GeV at the CERN SPS(1606.04234)

June 15, 2016 nucl-ex
Production of $d$, $t$, and $^3$He nuclei in central Pb+Pb interactions was studied at five collision energies ($\sqrt{s_{NN}}=$ 6.3, 7.6, 8.8, 12.3, and 17.3 GeV) with the NA49 detector at the CERN SPS. Transverse momentum spectra, rapidity distributions, and particle ratios were measured. Yields are compared to predictions of statistical models. Phase-space distributions of light nuclei are discussed and compared to those of protons in the context of a coalescence approach. The coalescence parameters $B_2$ and $B_3$, as well as coalescence radii for $d$ and $^3$He were determined as a function of transverse mass at all energies.
• ### Production of $\Lambda$ hyperons in inelastic p+p interactions at 158 GeV/$c$(1510.03720)

April 25, 2016 hep-ex, nucl-ex
Inclusive production of $\Lambda$-hyperons was measured with the large acceptance NA61/SHINE spectrometer at the CERN SPS in inelastic p+p interactions at beam momentum of 158~\GeVc. Spectra of transverse momentum and transverse mass as well as distributions of rapidity and x$_{_F}$ are presented. The mean multiplicity was estimated to be $0.120\,\pm0.006\;(stat.)\,\pm 0.010\;(sys.)$. The results are compared with previous measurements and predictions of the EPOS, UrQMD and FRITIOF models.
• ### Measurements of $\pi^\pm$, $K^\pm$, $K^0_S$, $\Lambda$ and proton production in proton-carbon interactions at 31 GeV/$c$ with the NA61/SHINE spectrometer at the CERN SPS(1510.02703)

Feb. 24, 2016 hep-ex, nucl-ex
Measurements of hadron production in p+C interactions at 31 GeV/c are performed using the NA61/ SHINE spectrometer at the CERN SPS. The analysis is based on the full set of data collected in 2009 using a graphite target with a thickness of 4% of a nuclear interaction length. Inelastic and production cross sections as well as spectra of $\pi^\pm$, $K^\pm$, p, $K^0_S$ and $\Lambda$ are measured with high precision. These measurements are essential for improved calculations of the initial neutrino fluxes in the T2K long-baseline neutrino oscillation experiment in Japan. A comparison of the NA61/SHINE measurements with predictions of several hadroproduction models is presented.
• ### System-size and centrality dependence of charged kaon and pion production in nucleus-nucleus collisions at 40A GeV and158A GeV beam energy(1207.0348)

July 2, 2012 nucl-ex
Measurements of charged pion and kaon production are presented in centrality selected Pb+Pb collisions at 40A GeV and 158A GeV beam energy as well as in semi-central C+C and Si+Si interactions at 40A GeV. Transverse mass spectra, rapidity spectra and total yields are determined as a function of centrality. The system-size and centrality dependence of relative strangeness production in nucleus-nucleus collisions at 40A GeV and 158A GeV beam energy are derived from the data presented here and published data for C+C and Si+Si collisions at 158A GeV beam energy. At both energies a steep increase with centrality is observed for small systems followed by a weak rise or even saturation for higher centralities. This behavior is compared to calculations using transport models (UrQMD and HSD), a percolation model and the core-corona approach.
• ### Energy dependence of kaon-to-proton ratio fluctuations in central Pb+Pb collisions from $\sqrt{s_{NN}}$ = 6.3 to 17.3 GeV(1101.3250)

May 30, 2011 nucl-ex
Kaons and protons carry large parts of two conserved quantities, strangeness and baryon number. It is argued that their correlation and thus also fluctuations are sensitive to conditions prevailing at the anticipated parton-hadron phase boundary. Fluctuations of the $(\mathrm{K}^+ + \mathrm{K}^-)/(\mathrm{p}+\bar{\mathrm{p}})$ and $\mathrm{K}^+/\mathrm{p}$ ratios have been measured for the first time by NA49 in central Pb+Pb collisions at 5 SPS energies between $\sqrt{s_{NN}}$= 6.3 GeV and 17.3 GeV. Both ratios exhibit a change of sign in $\sigma_{\mathrm{dyn}}$, a measure of non-statistical fluctuations, around $\sqrt{s_{NN}}$ = 8 GeV. Below this energy, $\sigma_{\mathrm{dyn}}$ is positive, indicating higher fluctuation compared to a mixed event background sample, while for higher energies, $\sigma_{\mathrm{dyn}}$ is negative, indicating correlated emission of kaons and protons. The results are compared to UrQMD calculations which which give a good description at the higher SPS energies, but fail to reproduce the transition to positive values.
• ### Centrality dependence of proton and antiproton spectra in Pb+Pb collisions at 40A GeV and 158A GeV measured at the CERN SPS(1009.1747)

Sept. 10, 2010 nucl-ex
The yields of (anti-)protons were measured by the NA49 Collaboration in centrality selected Pb+Pb collisions at 40A GeV and 158A GeV. Particle identification was obtained in the laboratory momentum range from 5 to 63 GeV/c by the measurement of the energy loss dE/dx in the TPC detector gas. The corresponding rapidity coverage extends 1.6 units from mid-rapidity into the forward hemisphere. Transverse mass spectra, the rapidity dependences of the average transverse mass, and rapidity density distributions were studied as a function of collision centrality. The values of the average transverse mass as well as the midrapidity yields of protons when normalized to the number of wounded nucleons show only modest centrality dependences. In contrast, the shape of the rapidity distribution changes significantly with collision centrality, especially at 40A GeV. The experimental results are compared to calculations of the HSD and UrQMD transport models.
• ### Energy dependence of phi meson production in central Pb+Pb collisions at sqrt(s_nn) = 6 to 17 GeV(0806.1937)

Oct. 27, 2008 nucl-ex
Phi meson production is studied by the NA49 Collaboration in central Pb+Pb collisions at 20A, 30A, 40A, 80A and 158A GeV beam energy. The data are compared with measurements at lower and higher energies and to microscopic and thermal models. The energy dependence of yields and spectral distributions is compatible with the assumption that partonic degrees of freedom set in at low SPS energies.
• ### Event-by-event transverse momentum fluctuations in nuclear collisions at CERN SPS(0707.4608)

Feb. 28, 2008 nucl-ex
The latest NA49 results on event-by-event transverse momentum fluctuations are presented for central Pb+Pb interactions over the whole SPS energy range (20A - 158A GeV). Two different methods are applied: evaluating the $\Phi_{p_{T}}$ fluctuation measure and studying two-particle transverse momentum correlations. The obtained results are compared to predictions of the UrQMD model. The results on the energy dependence are compared to the NA49 data on the system size dependence. The NA61 (SHINE, NA49-future) strategy of searching of the QCD critical end-point is also discussed.
• ### Analysis of hadron production in nucleus-nucleus interactions up to and out of kinematical limit of free NN-collisions in the frame of FRITIOF model(hep-ph/0201074)

Jan. 10, 2002 hep-ph
In the framework of the modified FRITIOF model, the inclusive spectra of the cumulative $\pi ^0$-, $\pi ^-$-mesons and protons produced in the nucleus-nucleus interactions at 4.5 GeV/c/nucleon and 4.2 GeV/c/nucleon are calculated. It is shown that the model reproduces qualitatively, and in some cases quantitatively the main experimental regularities of $\pi$-mesons production, and "soft" part of the proton spectra. According to the model the production of the cumulative particles is connected with the mechanism of the "soft" nucleon-nucleon interaction.

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text:
Teas I have drunk, with reviews and future purchases
personal, statistics
created: 13 Apr 2011
modified: 11 Apr 2015
status:
in progress

belief:
log

Teas I have drunk, with reviews and future purchases
personal, statistics
created: 13 Apr 2011; modified: 11 Apr 2015
status:
in progress

belief:
log

Teas I have drunk, with reviews and future purchases (personal, statistics)
created: 13 Apr 2011; modified: 11 Apr 2015
status: in progress; belief: log
Teas I have drunk, with reviews and future purchases (personal, statistics)
created: 13 Apr 2011; modified: 11 Apr 2015; status: in progress; belief: log

I order a lot1 from Upton Tea Imports because they specialize in loose tea & I’m a sucker for their catalogue. Their prices seem pretty reasonable too, so I don’t bother shopping around2, even buying my tea kettle from them.3 Upton allows reviews if you’ve bought at least a certain quantity, but otherwise your notes are private. This strikes me as a little unfair (a sampler of 10g is more than enough to judge a tea!) and my reviews are a valuable guide to me in ordering, so I keep local copies of my reviews & notes.

# Tea

## Oolong

When I was young, I was a great fan of hot chocolate, but hot chocolate is troublesome to make if you are making real hot chocolate (with milk & everything). I tried coffee once or twice, but it was even more disgusting than beer. Herbal teas were drinkable, though, and I slowly graduated to green tea. Then one day a my mother bought a Bigelow box set of teas which happened to include an oolong tea.

I instantly fell in love with oolong - not quite as raw and grassy as green tea but not so bitter & disgusting as black tea. (Not that green tea is bad; I still liked it, and all my favorite oolongs tend towards the green side of the oolong spectrum. I just prefer oolongs.)

In roughly chronological order:

• Tie-Guan-Yin Oolong First Grade (★★★★☆ / ★★★☆☆)

A very nice tieguanyin (which is one of my favorite kinds of oolong). The flavor is straight oolong: in between green and black, with a tiny bit of sweetness. One of the best I’ve had. Handles re-steeping well. (It is largely the same as the second-grade, but the second had a sort of ‘woody’ taste to it that the first doesn’t.)

On the strength of this tasting from 2009, I ordered 400g of it in 2012 to be my standard tea when I ran out of samplers; to my great disappointment, it does not taste as good as I remember it. I don’t know whether my palate has become more demanding or whether the quality has fallen. An online acquaintance happened to order some at the same time, and was very satisfied with it, suggesting the former.
• Tindharia Estate Oolong (★★★☆☆)

Nothing memorable.
• Bao Jun (★★☆☆☆)

Like the Tindharia, nothing memorable. In fact, this was pretty weak in flavor.
• Far too bitter and dark and ‘burnt’ tasting!
• Formosa Jade Oolong Imperial (★★★★★)

Extremely good! One of the, if not the best, oolongs I’ve ever had. But also tremendously expensive. But still so good I’m tempted to splurge on 100g anyway.
• Just slightly woody. Otherwise, a solid good oolong.
• China Oolong Buddha’s Palm (★★☆☆☆)

Too smoky.
• Osmanthus Oolong Se Chung (★★★★☆)

It’s a solid oolong, but the floral taste (I don’t know how to describe the osmanthus flavor) really makes this for me. I like to mix a little of it into some of my other oolongs, though it’s not the best re-steeper I’ve ever had.

This was my default oolong for a long time because 500g was just $18. One of the downsides of buying in such bulk is that the osmanthus fragments exhibited a Brazil nut effect and the last hundred cups were more osmanthus than tea. • Fen Huan Dan Cong (★★☆☆☆) The description promises a strong flavor, but perhaps I prepared it poorly because the flavor struck me as weak, nor did I particularly notice any peach. I was disappointed; I’d’ve been better off buying some more of the Osmanthus or 1st-grade Imperial. • A solid oolong somewhere between the Second and First Grade oolongs • Fancy Oolong Imperial (★★★★☆) Very good; similar to the First Grade Imperial oolong. • Benshan (★★★★☆) I bought this and the roasted barley tea (see later) from the Rainbow Grocery Cooperative when I was visiting my sister in San Francisco. Benshan is a fairly green oolong and right up my alley, although it struck me as lacking the slight sweetness and floral overtones I expect from the best oolongs. But regardless, it was pretty tasty, and adding a little bit of the barley made the benshan oolong even better. • Iron Buddha from Teavana (★★★☆☆) Standard oolong; nothing memorable. • Oolong Fine Grade (★★★☆☆); standard oolong • Formosa Amber Oolong (★★☆☆☆); too black-tea-like • Formosa Jade Oolong (★★★☆☆ / ★★★★☆); quite tasty, in the same vein as the First and Second Grade oolongs (although not as good) • China Oolong Se Chung (★★☆☆☆); just as described - too woody for me • Ruan Zhi Thai (★★★☆☆) I didn’t expect much of a Thai tea, since I’ve never heard of oolongs from Thailand before. To a little surprise, I found it to be a completely normal oolong. Nothing floral to the taste, just a plain ordinary oolong. I would not have suspected you of lying if you had told me it was a Formosan oolong. • Very good oolong. Comparable to the First and Second grade Imperial oolongs, without doubt. • A disappointment; nothing special - the subtle notes are too subtle for me. • Tie-Guan-Yin Special Tribute (★★★☆☆) Rolled leaf-balls. Similar to the Oolong Fine Grade; but has a somewhat mysterious floral taste I can’t really compare to anything. Doesn’t seem to re-steep very well. • Wuyi Golden Guan Yin (★★☆☆☆) Loosely rolled long leaves; weak flavor with nothing of interest about it. (I’ll agree with the Upton’s description that it’s not bitter, but calling it ‘sweet’ or having a ‘raisin-like’ flavor is just hyperbole.) Disappointing. • Floral Jinxuan (★★★☆☆) At first, I thought this was ordinary, but upon resteeping I noticed the promised floral notes - they reminded me strongly of the osmanthus oolong. • Formosa Oolong Spring Dragon (★★★☆☆) Like the Special Tribute, but weaker in flavor, I think. • “Tea at the Empress” (★★☆☆☆); I picked up this dark blue cylindrical tin of teabags somewhere or other. It doesn’t even specify what kind of tea it is, but apparently it has something to do with a hotel, and claims to be from “The Fairmont Store” (although no item is listed similar to the tin). It’s not very good oolong. It starts off fairly bitter and doesn’t improve, but at least it doesn’t get too horrible as it resteeps. Regardless, I don’t know where I would get more and I would not get more if I knew. • Empress Guei-Fei Oolong (★★★☆☆) At 5 minutes of steeping, a pretty ordinary oolong; by 10 minutes, a strong floral taste had developed. Continued steeping made the flavor weaker and bitterer (as one would expect), but no other changes. It reminded me of the osmanthus oolong. During the second tasting, the floral flavor was not as overpowering; I was careful to use the same tsp amount of tea for each of the 9 teas, which suggests that perhaps last time I used too much of the Empress. Not bad at all, I may order it again. • Oolong Choice Grade (★★★★☆) At 5 minutes, another ordinary oolong, but by 10 minutes, the flavor has not become bitter but rather continued to develop into a very oolong flavor. Little change with re-steepings. In the second tasting, I noted that it was ‘a sharper blacker flavor than Anxi and Empress’. A good oolong, might be a candidate for my ‘standard’ tea (but would need to check prices of the others). • Formosa Oolong Choicest (★★☆☆☆) The 5 minute steeping tasted both woody and floral, an odd combination which bothered me (I had expected more - it cost twice what the Oolong Choice Grade did). The 10 minute steeping wasn’t much better: it was sweeter tasting, but the stem/wood flavor was even stronger, and it didn’t improve or change very much at any subsequent steeping. It’s possible I prepared it wrong or picked a pinch of stems, but it seems unlikely I will pay the premium for this tea when I am not sure I can even describe it as ‘good’. (In the second tasting, I noted only that it was ‘slightly sour’.) • “Anxi tikwanyin” (★★★☆☆) Another gift from my sister. This is a mild medium oolong with relatively little floral taste compared to everything else I’ve been testing. As expected from the Anxi county tea region, their Tie-Guan-Yin is perfectly acceptable. • “Momo Oolong Super Grade”, Lupicia Fresh Tea (★★★☆☆ / ★★★★☆) As the name indicates, this is a peach-flavored oolong. I bought a bag of 10 teabags during Sakura Matsuri 2012. I wondered if$12 was too much to pay, but the bag seemed oddly heavy and the back said each bag had 2g of tea in them! 2 grams is a lot, and 20g is more reasonable for $12 - similar to Upton’s samples when S&H is included. (When I checked online, I saw the loose tea was$13 for 50g. Oh well.)

The bags were the first I’ve seen made with a plastic mesh, and when I brewed the first one, the taste was far too strong. It was without doubt peach-flavored. For the next batches, I cut open the bag and used a fourth of the contents. This made a much more reasonable flavor, which holds up well under resteeping, and the peach-flavor is not as artificial-tasting as the other peach tea I have now. One thing I’ve learned after drinking many mugs is that this tea quickly becomes flavorless - it doesn’t hold up under resteeping; this may be because it was designed for quick release as tea bags - but hopefully the loose tea is unshredded leaves and this would be less of a problem. When I run out of tea, I may order a batch of Lupicia since besides the Momo Oolong, they have some oolongs I haven’t tried before.
• Floral, but oddly it also tasted sour. Not recommended, to say the least, but perhaps the first tasting was simply an aberrant cup. On later tastings, I didn’t notice further sourness, and it seemed more acceptable. Dosing is difficult because the large whole leaves are very tightly wrapped but sometimes are just stems, so it is easy to add too few or too many.
• Neither left a strong enough impression to review although the Floral Superior lived up to at least the first part of the name; they were both similar to the Special Grade. At times during this tasting, I wondered if Upton had screwed up & they were the same teas (but they couldn’t’ve been because the tea leaves were visibly different). The Floral Superior does not handle resteeping well, quickly losing flavor.
• Super Fancy Oolong (★☆☆☆☆)

Indescribable taste, but whatever it is, makes it bad.
• Roasted Oolong (★★★☆☆)

Pretty much as expected: a standard oolong taste with a smoky aftertaste. Smoky oolongs are not my cup of tea, but I had to try. The upside is that it turns out to resteep very well, and the smoky aftertaste slowly changes to a sweeter honey-like aftertaste.
• Magnolia Blossom Oolong (★★★☆☆)

The magnolia flavor is strong with this one. I was surprised to instantly recognize the flavor, because as far as I knew I had never had anything magnolia-flavored before. The flavor itself leaves me mixed - I sort of like but also sort of don’t. This may be one of the teas best consumed only at intervals or mixed in with another. It doesn’t resteep well, almost immediately losing any flavor.
• Pre-Chingming Da Hong Pao (★★☆☆☆)

Floral and weak. More green-white than oolong.
• Organic Da Hong Pao Oolong (★★☆☆☆)

A stronger Pre-Chingming Da Hong Pao, which then undercuts the improvement by tacking on an aftertaste which is not smoky but burnt. In general, this batch of oolongs was a disappointment: either boring or bad. I may finally have exhausted Upton’s oolong catalog.
• A Christmas gift, this flavored oolong comes in the nice little plastic mesh bags that non-loose-tea products seem to be moving towards these days. The Se Chung and Shui Xian blend is heavily flavored with safflower, peach, and apricot for a somewhat overwhelmingly floral taste which makes it hard to judge the underlying oolong (it seems OK, but not great). Seems to handle a few resteeps well.
• Discover Tea’s “Ti Kuan Yin” (★★★☆☆)

A perfectly ordinary and satisfactory oolong; it handles steeping well and delivers a cup medium between green and black. While I was at their Williamsburg shop, I had a cup of their “Glenburn Moonshine Oolong”; it’s hard to judge from one cup you didn’t make, but while the leaves have a lovely silver fuzz and the brew was pretty good, I didn’t like it sufficiently to justify the 2-3x premium over the tie kuan yin.
• Bao Zhong oolong with coconut extract. I am not a fan of coconut flavor and bought it out of curiosity when I wandered into their Williamsburg shop before Christmas 2013 (I also bought an ounce of their genmai-cha). It was better than I expected: the coconut is a light overlay and not overpowering, and the base Bao Zhong seems to be fine.
• Solid oolong, much like a tieguanyin with the floral after-taste I love so much in oolongs. Resteeps normally without becoming too bitter.
• Tao of Tea, “Black Dragon Oolong Tea” (★★★☆☆)

A black tea in all but name; very similar to the Amali African Queen. Steeps perhaps twice. Didn’t much enjoy, but not as bitter & unpleasant as most black teas.
• Tea’s Etc, “Ginseng Loose Leaf Oolong Tea” (★★★☆☆/★★★★☆)

I hadn’t tried a ginseng tea before, and when this one popped up on Amazon, I thought I’d give it a try. While I strongly suspect the health benefits of ginseng have been overblown4, the flavor might still be nice. The tea comes in coated pellets, with some wisps of straw-colored plant matter which I assume are ginseng itself. The ginseng flavor is sweet, mild, fruity & difficult for me to compare to anything (I guess I should just describe it as ginseng-like!). I think I like it, although like the coconut oolong I wouldn’t want to drink too many cups in a row of it.
• Daniel Clough, Golden Lily Wulong (★★★☆☆)

1 of 4 oolongs gifted me by Clough after his travels in China. Interesting and not what I expected, since the tea looked more like a tieguanyin. The Golden Lily almost doesn’t taste like an oolong at all: it tastes sweet, perhaps like honey?, and something harder to describe - googling, it seems the usual description is milky, which on further reflection seems like it’s a good analogy.
• Clough, Lan Gui Ren ginseng (★★☆☆☆)

A ginseng oolong like the previous Tea’s Etc; there’s no ‘straw’ in it, and the coated pellets are much smaller, although unlike the other, the pellets do open up into tea leaves. Weakly ginseng, sweeter, and almost completely tasteless after the first steep. This one was a disappointment; I hope the other ginseng turns out to be better.
• Clough, unknown ginseng (★★★☆☆)

A normal foil baggy of little ginseng pellets; no straw, small more irregular pellets, green color. Similar the Tea’s Etc one.
• Clough, unknown oolong (★★★☆☆/★★★★☆)

A vacuum-sealed small sample (10g?) of Chinese tea; I didn’t recognize any of the names or characters on it (I took a photo just in case it turned out to matter). The first steep is a fairly tasty quasi-tieguanyin, but subsequent steeps are absolutely tasteless, which meant I used it up quickly.
• Tao of Tea, “Wu Yi Oolong Tea” (★★★☆☆)

Very similar to Tao of Tea’s “Black Dragon Oolong Tea”, which I didn’t much like either, but is better than the usual black.
• Summit Tea Company, “Tie Guan Yin Oolong Tea” (★★★☆☆)

Medium oolong, somewhat floral, survives only one steep, not terrible but fairly weak flavor. Tie Guan Yin on a budget: I’m not sure if one can do better for cheaper, but one could easily do better.
• Art of Tea, “Iron Goddess of Mercy Oolong Tea” (★★★★☆)

Reasonable Tie Guan Yin, very green, nice floral aftertaste; sensitive to temperature, though, and easily prepared too hot. Probably can do better quality vs price-wise. Container is a bit flimsy and if it falls to the ground, will spill contents all over (as I found out the hard way).
• Tao of Tea’s “Royal Phoenix Oolong Tea” (★★★☆☆/★★★★☆)

Toasty texture, fragrant aroma and sweet, high-bounce taste similar to nectarines and peaches. Origin is Guangdong Province, China

No reviews, but I thought the description sounded promising and Tao of Tea has earned a little bit of trust, so I took a gamble with it. The leaves are long stringy black leaves. It resteeps well. My initial impression was that the flavor is indeed somewhat sweet and, grandiose name notwithstanding, it tastes like a middle of the road oolong with no particular additional flavors or aftertaste - just sort of oolongy. I was disappointed: OK, not good I think I must have prepared it badly the first few times (perhaps too hot or steeped too long) because as I drink the rest of it, I’m enjoying it more and the flavor seems closer to the floral sort of Tie Guan Yin flavor I like most.
• Huang Jin Gui Oolong (★★★★☆)

This premium Oolong is produced in Anxi county of Fujian province, with a light oxidation level of less than 20%. The name Huang Jin Gui translates to “golden osmanthus,” referring to the cup’s light gold hue and the osmanthus-like aroma and flavor.

(This and the next 3 are all Chinese teas.) Description is entirely accurate for once. I liked it.
• China Tie-Guan-Yin Organic (★★★☆☆/★★★★☆)

This organic selection has a sweet aroma with hints of tropical flowers and a suggestion of toasted coconut. The cup has interesting notes of stone fruit, golden raisins, and walnuts. The finish has a fruity/floral quality, which is balanced by a light mineral note.

Regular TGY. I don’t find the complexities that Upton’s described, but it’s fine.
• While not a true Wu Yi Mountain tea, this Fujian province Oolong is a flavorful and affordable alternative. The dark, chocolate-brown leaves produce a dusky ecru liquor with a harmonious flavor profile, accented with a sweet, lingering finish. Some who have enjoyed this selection have commented about nuances of honeysuckle, citrus and peach.

On the black end of the spectrum; it’s not as bitter as the previous Wu Yi I tried, which I am grateful for and makes it reasonably drinkable, but this one settles it: Wu Yis just aren’t for me. Time to give up on them, and probably time to start avoiding any oolong which is sufficiently oxidized to be described as black or chocolate-colored.
• Zhang Ping Shui Hsian Oolong (★☆☆☆☆)

This loosely-rolled Fujian province tea is tightly packed into paper-wrapped “bricks”. Infusing reveals bold, skillfully crafted leaves with a fresh aroma and a hearty cup with a lilac/hyacinth fragrance. The sweet finish has a delicate suggestion of cardamom.

I thought this sounded cute - paper-wrapped bricks of tea, a throwback to the traditional methods of packaging and storing tea in China. And it sounded quite good too, a greener oolong right up my alley. But this one was a serious disappointment! The bricks turn out to be a lot of small bricks, and they are a pain to work with; you cannot simply reach in and get some tea, you have to break off compacted chunks of tea, which are hard to measure right and scatter debris (if you do it outside the bag, it’s a mess to clean up, and if you do it inside, the dust will fall to the bottom). I could put up with this format except to my perplexity, the tea seems almost tasteless, not “hearty”; I tried steeping at a variety of water temperatures (though Upton’s calls for 190 degrees, which is not exotic or unusual), convinced I was simply preparing it wrong, but none of them did the trick. (To avoid death by a thousand cleanups, I wound up crushing all the bricks by hand in a big bowl and then pouring them back in.) Expensive, messy, and tasteless.
• Tranquil Tuesday: Phoenix Honey Orchid Oolong (★★★☆☆)
• Golden Dragon (?): Tie Guan Yin Oolong Tea - Iron Goddess of Mercy (WuLong) ()
• The Tao of Tea, Osmanthus Oolong Tea ()

## Green

• Pinhead Gunpowder is a green Chinese tea. Pale straw colored, the brew is light and refreshing in flavor. Each leaf is hand-rolled into a pellet-shaped ball. Because the tightly rolled shape helps the tea retain its freshness, it was one of the first teas to be exported from China. 1/4 lb. Loose Tea, No.42316

I originally bought a packet on a trip to Colonial Williamsburg around 2005 or so. It struck me as rather grassy and the tightly-rolled leaves seemed to easily oversteep and become bitter. Having received another batch in Christmas 2013 and preparing it with more respect for being a green tea (sub-boiling water, much shorter steep time), I find it more palatable and so I think my early impressions may have been more my fault than the tea’s fault.
• Xian Shan Pouchong (★★★☆☆)

Rolled green tea; strongly reminiscent of oolongs and definitely on the border. Fairly good considered as a green/oolong cross, but nothing memorable about the flavor - similar to Oolong Fine Grade.
• “Green Tea Pomegranate”, English Tea Shop (★☆☆☆☆)
• Satori Tea Company’s Sencha Klaus (★★☆☆☆)

Gift from sister; a tin of variegated green (long thin leaves, stems, broken leaves) mixed with flakes of thin orange peel or skin. As the name indicates, it’s a Christmas-style tea which makes it taste like potpourri. The flavor is interesting; after the first few minutes, it struck me as a sweeter kind of green but I can’t figure out the flavor - minty? Floral? Some sort of citrus orange? After another 5 minutes, it’s much stronger and I feel confident identifying it as an orange flavor. It’s strong enough that I don’t think I want to drink it on its own, but perhaps I could mix in the Dae-Jak. (Satori’s description identifies the contents: “almond bits, cinnamon bits, natural flavor and orange blossoms”. Makes sense.) I ultimately wound up picking out all the orange peel to make it more palatable.
• TeaAndAbsinthe’s “sun dew apricot mango” mix (★★★☆☆)

Purchased at ICON 2012; after losing the bidding war for the tea item, I resolved to go find the original vendor in the dealers’ room, which I succeeded in doing. To my surprise, they were primarily a steampunk clothing vendor who happened to have one shelf-unit of tea mixes. Mostly blacks and rooibos, but there was one green that smelled nice and I was piqued that I had lost the bidding war Saturday for the awesome original ICON artwork and then the bidding war Sunday for the 3 teas, and it was just $3 an ounce. I had a nice chat with the guy, and bought an ounce of the mango green tea. It has a pleasant green flavor with no real negatives, and the mango/apricot is not overwhelming. It degrades gracefully under resteeping. Overall, it’s quite good: better than most floral flavorings, above the peach tea (but below osmanthus oolong) in my estimation. Unfortunately, when I checked their website, they seem to offer no online shopping or long-distance ordering capability. I guess I will have to wait for ICON 2013 to buy some more. • Choice Organic Tea’s Twig Ku-ki cha (★★★☆☆ / ★★★★☆) This was a random try of a tea bag, and I was a little dubious - “twig kukicha” doesn’t sound very promising, and “twiggy” is usually a bad adjective coming from me. But the first steep turned out to be fairly good, as did the second steep. The Wikipedia description of it as “mildly nutty” and slightly “sweet” turns out to be on the money; it also reminded me of genmai-cha. There was only one tea bag, so my first impression will remain limited, but I think I will try some kukichas in the future. (Upton’s stocks 3 Japanese kukichas and 1 Chinese.) • Stash Premium, Mangosteen Green Tea (★☆☆☆☆) A disappointment. Not a good green, and the mangosteen just tasted too sweet. I didn’t bother with a second steep. • Davids Tea, “Daydreamer” (★★★☆☆) Small sample packet - a sencha green with mango & mangosteen. Much better than the Stash Premium. It started off well, and handled resteeping admirably. Competitive with TeaAndAbsinthe’s “sun dew apricot mango” mix, although a simpler overall flavor. • Korean greens: • Dae-Jak (★★☆☆☆) After 5 minutes, struck me as rather grassy, akin to gyokuro, but with a weaker flavor. By 10 minutes, it was still grassy but a certain unpleasant edge had crept in, which was still there after the resteep. Not impressed. During the second-tasting, the unpleasant edge was weaker than I remembered, but otherwise both the Dae-Jak and Jung-Jak tasted the same. • Jung-Jak (★★☆☆☆) Very similar to the Dae-Jak, but less sweet (when tasting them side by side); the sweetness passed Dae-Jak at 10 minutes, and at 15 minutes, I wasn’t noticing the unpleasant edge. Better than the Dae-Jak, but I still doubt I’ll be ordering it again. • Gyokuro Kenjyo (★★★☆☆) At 1 minute, it’s a sharp tasting green which reminds me of a previous green tea I’ve had, but maddeningly, I can’t seem to place the specific aftertaste. At 5 minutes, the taste is stronger (but not more bitter or worse). • Pre-Chingming Snow Dragon (★☆☆☆☆) At 1 and 5 minutes, this is almost tasteless. I’d liken it to a white tea, which it may well be better classified as. I’d call it bad, but that implied there was any real flavor to dislike. • Kagoshima Kabuse Sencha (★★★☆☆) A ordinary sencha, the only thing I’d note is the slight floral note. Handles resteeping well. • Organic China Ku-ki Cha (★★★★☆) To my sorrow, this was the only ku-ki tea Upton’s had in stock when I ordered this batch, and not the one I was most interested in (the roasted ku-ki cha). This may be a continuing effect from the Fukushima incident which cut off many rarer Japanese teas. Regardless, I like it. It has a sort of hybrid green-oolong taste, but with a nutty or roasted-barley overtone. (The only downside was that I drink my teas without a strainer or tea ball, and the stems & twigs all float!) This suggests that the one packet I tried before was not an aberration; if Upton’s doesn’t have any more when next I order, I’ll probably look for another retailer which does have some. • Yamamotoyama’s “Genmai-cha Green Tea with Roasted Brown Rice” 16-pack (★★★☆☆) Picked up at my grocery store for$2 out of curiosity. As the instructions warn you, this green doesn’t handle resteeping very well and turns bitter after a few minutes. The roasted brown rice flavor is very strong and one can smell it upon opening a teabag packet. The green tea itself is acceptable. The combination is not bad, but I think the rice is over-toasted and comes off as a bit too burnt. The lesson here may be to find my own source of more lightly toasted brown rice.
• Spice & Tea Exchange, Genmaicha (★★★☆☆)

This improves on the Yamamotoyama. The rice is toasted much more lightly. I liked it, especially for drinking in the morning, although it doesn’t handle resteeps well and tastes a bit burned. I think genmai-cha can probably be even better, though.
• Tao of Tea, “Genmaicha Green Tea And Toasted Rice” (★★☆☆☆)

Devoid of the toasted-rice flavor - there’s grains of rice, yes, but it’s hard to believe they were ever toasted. It doesn’t taste nearly as good as the other two genmai-chas, and was a waste of money since it’s not that good a green tea on its own.
• A traditional combination of organic green tea with toasted brown rice produces a mild and smooth cup with nutty nuance and sweet, lingering aftertaste.

A sweet and mild green, with an equally mild toasted-rice flavor. Definitely a good gen-mai cha.
• Gen-mai Cha (Japan) (★★★☆☆)

Literally, Gen-mai Cha means brown rice tea. Toasted and partially puffed rice is blended with large-leaf Sencha.

Not as mild as the China gen-mai, with more of a green edge. The toasted-rice taste isn’t there, though.
• Gyokuro (★★★★☆/★★★★★)

The finest Japanese green tea, only shade-grown tips are used for Gyokuro. Prized for its delicate flavor and natural sweetness.

Delicious. It’s described as sweet, and it really is! The taste is entirely different from your more usual green teas. It’s a pity it’s so much more expensive (3x $/g). • The Tao of Tea, Handrolled Jasmine Pearls Green Tea () • The Tao of Tea, Pearl Green Tea () ## White My general take on white tea is that they seem to be rather fragile and I generally prefer stronger flavors from green/oolongs. (Subtle flavors can be good, but for white teas, it seems that their subtlety usually comes across as weak or tasteless.) It’s possible I’ve either not had really good white tea or I’ve ruined the ones I had. • Special Grade Shou Mei (★★☆☆☆) Fairly twiggy (little in the way of leaves proper). Very white - tasted like a weak green with a certain floral overtone. In its favor, it handled re-steeping very well, not becoming bitter even slightly & tasting the same over multiple cups. • Organic Pai Mu Tan (★★★☆☆) The Pai Mu Tan tasted like the Shou Mei or Yin Zhen Bai Hao, but much more so, and so gets more approval from me; probably won’t buy it again, though. (I don’t actually dislike the general white tea flavor, it’s just usually far too weak to be worth drinking.) • As promised, the pekoe is indeed ‘downy’ - the leaves & branches are downright fuzzy. However, it tastes almost identical to the Shou Mei. • Peach Momotaro (★★☆☆☆) A gift from the littler sister. I was amused at the clever title - an allusion to the Japanese folktale Momotarō (literally “Peach Tarō” or “Peach Boy”). I didn’t have much hope for this flowering tea, but it improved on my expectations: the bloomed tea ball was a lovely white stalk on a grassy green base, and the peach flavor was respectable and comparable to the other peach tea I have. Flavor-wise, the tea was pretty weak (I was under the impression it was either a green or oolong tea) and overpowered by the peach, but at least it had a flavor and so was better than the previous flowering teas. It improved a little bit by the 10 minute mark, having sweetened a little. The weak tea flavor was explained when I learned it was a white tea; such a flavor is pretty par for the course for whites. • Tranquil Tuesday: White Peony White Tea (★★★☆☆) ## Black I am not a fan of black teas, but I still try them out occasionally: • “Ginger Peach Tea”, bag-tea by English Tea Shop (★★☆☆☆) It is a black tea mixed with ‘ginger pieces and peach flavor’. To my surprise, it was fairly good. The black tea is a pretty weak black and as far as I can tell, towards the oolong end of the spectrum. The peach flavor is entirely dominant over the ginger, which is as I would prefer, peach being an old favorite of mine. The first steep is good, but it falls off very quickly and needs replacing by the fourth steep or so. • Satori Tea Company’s Amali African Queen (★★★☆☆) Another gift; this one confused me because it was clearly labeled oolong, but when I tried it out, it tasted very much like a black tea and the leaves were pretty oxidized and produced a black-tea-looking liquor (extremely dark as opposed to amber), and quickly began thinking of Earl Grey. My confusion was resolved when I began to look up the teas and found that the African Queen was in fact a black tea (as opposed to a peculiarly black oolong). • Upton’s “Traditional Masala Chai” (★★☆☆☆) “A traditional Indian spiced tea recipe with a warm and robust character. The full flavor notes of cinnamon, cardamom, ginger and clove hold up to milk and honey, the traditional way to take this tea.” Christmas gift. Tastes like the description, and does indeed taste better with some milk & honey added. ## Pu’erh I have tried pu’erh tea from time to time, Without exception of brand or preparation method, I have not liked them. # Tisane Tisanes are any ‘tea’ which does not incorporate Camellia sinensis - so this category includes barley tea or mint tea or ‘red tea’ (rooibos) or honeybush. (I once ordered rooibos & honeybush from Upton’s for my mother; I found them so unmemorable I can’t even review them here.) • Roasted barley tea (★★☆☆☆) Like the Benshan oolong, bought from Rainbow Grocery Cooperative. I was initially going to only buy some genmaicha but then I saw their oolongs, so I went with plain roasted barley instead and combined it. The barley was very… nutty and barley-ish on its own. Not entirely drinkable, I thought, although it added some strength and robustness to the Benshan oolong in small amounts. • Ginger herbal tea (★☆☆☆☆/★★☆☆☆) This Royal King product was, as it promised, gingery. I’d have to say I don’t actually like the flavor of ginger that much, and couldn’t drink it very often. • Rote Grütze (★☆☆☆☆): disgustingly sweet and fruity (“accented with dried blackcurrants, blueberries, strawberries and wild cherries” is an understatement). The best I can liken it to is drinking one of those potpourri or stuffed pomegranates old women buy. It initially seemed to re-steep well but I realized it was somehow ineffably becoming more and more offputting with each steep. I can’t see it really motivates me to try any more kinds of rooibos. • Superior Organic (★★☆☆☆): much better than the Rote Grütze, with just the right amount of sweetness. • Honeybush: honeybush vanilla (★★☆☆☆) reminded me a little of rooibos (though different species entirely), but much toned down, sweet like its name suggests, and the vanilla combined nicely. I actually liked it a little. Good for occasional breaks or when I want something hot to drink but caffeine would be a bad idea (eg. past 7 PM). • Maracuja/Orange Fruit Tea (★★★☆☆) Contains fruit pieces, rose hips, hibiscus flowers, citrus peel and flavoring. Ingredients: apple bits, hibiscus, rose hip peels, beetroot bits, orange bits, citrus peels, artificial flavor A strongly-flavored, tangerine-like herbal tea. • Cape Cod Cranberry Fruit Tea (★★★☆☆) A special blend of dried cranberries, hibiscus and apple bits. Caffeine free and delicious. Ingredients: apple bits, hibiscus, cranberries (cranberries, sugar, sunflower oil), artificial flavor Despite the differing ingredient list, tastes very similar to the Maracuja. The cranberries add their own kick to the orange-like flavor. I noticed I could eat it straight out of the bag like it were trail-mix. • Lemon Myrtle (★★☆☆☆) Grown in the sub-tropical rainforests of Queensland, Australia, Lemon Myrtle (Backhousia citriodora) is a relatively new caffeine-free tisane. It is a natural source of citral essential oils, antioxidants which imparts a stout lemony aroma and flavor. Overwhelmingly sweet and lemon-tasting; lemon, lemon, and more lemon. A little goes a long way. I ultimately found it too much of a muchness, and couldn’t finish it. • Mulberry tea / Kuwa-cha: apparently mulberry tree leaves make a decent sencha-like powdered tea; an acquaintance described it as being like a good green tea. As it happens, I have a longstanding fondness for mulberries. Unfortunately, though mulberry trees are not rare trees (there were several growing wild within blocks of where I grew up), the prices are not as cheap as one would hope; apparently there’s a fad diet cluttering listings & driving up prices. Anyway, out of curiosity I ordered 45g of$12 mulberry tea (★★☆☆☆/★★★☆☆) from Kesennuma (grown in Miyagi Prefecture).

It is a nice slightly-dark green, shredded finely like confetti, and reminds me a bit of how sencha green tea looks; the smell is faint and the best my impoverished scent vocabulary can come up with is “a bit musty”. Steeped, the water is also a nice green; my first impression of the taste is that it’s slightly sweet. Beyond that… it tastes perhaps like a white or green would if one removed all hint of bitterness and grass ie. there’s not much of a flavor beyond the slight sweetness. The directions suggest preparing with hot water, but the mulberry tea tastes much the same prepared with cold or cool water and the flavor is easier to taste without heat in the way. (You can make iced tea with it, but I don’t advise brewing for more than a week - it seems to gain an offputting aftertaste after that.)

Do I like it? Well, I don’t dislike it but a very inoffensive green tea isn’t something I have a pressing need for. I think it would make a decent summer tea since you could prepare & serve it cold, but I like barley tea and genmai-cha better, so I don’t need a mulberry tea. Still, interesting to try out - who knew mulberry leaves could be used to make an OK tea?

# Tea kettles

Besides the teas themselves, kettles are key equipment. An occasional drinker may use a stove-top kettle, which have some advantages:

• cheap / free
• nearly-indestructible
• even simpler to operate

(In the sense that everyone knows how to turn on & turn off a stove burner already, not that electric kettles require a PhD to operate - typically, it’s a single button to push to boil some water.)
• somewhat more compact
• often picturesque
• always ceramic or metal, so no possibility of the water tasting like plastic

But for regular tea-drinkers, stove-top kettles come with serious disadvantages compared to electric kettles, and some of the advantages are negated:

• they are much slower to heat compared to electric kettles

Even in the USA, an electric kettle will be faster than stove-top. I haven’t tested it with a timer, but I think the difference between the T-fal and the metal kettle I was was ~2-3x. The delay is irritating
• they are energy-inefficient: much of the heat of the stove-top is not transferred into the water but the air, which is a waste of electricity or gas, and during summer will unpleasantly warm the house
• picturesque means that they are not always designed with safety or ergonomics in mind; I’ve seen more than a few which bade fair to burn users somewhile
• temperature control is difficult without a thermometer, so one must either compromise the simplicity & convenience of a stove-top kettle or risk destroying white/green/oolong teas by overheating the water
• it’s often easy to not notice when the water has reached a boil, or to not be present when the kettle does begin to whistle

This results in a waste of time, of water (increasing humidity, incidentally), overheating & de-oxygenating the water, and poses a safety hazard if the kettle boils dry

On the downside, the electric kettles lose most of the stove-top kettle advantages (they cost real money, can break, take up counter space, and the pretty ones are more expensive). But on net, I prefer an expensive electric tea kettle which will heat fast, not dump excess heat into the room, has boil-dry protection, and different heat settings.

I bought my first electric tea kettle on 7 January 2008 from Upton’s. It was their (since-discontinued) AK16 model (“Upton Tea Imports® Variable Temp. Electric Kettle”), and cost $43.80. Besides my daily tea, I used it for heating water for ramen, speeding up cooking of soups & stews, humidifying rooms, and unclogging drains. It worked well for years until the handle snapped off somewhere in winter 2013 or so. (It was my fault: I had been using it to humidify the room and had placed a book on the handle to keep the kettle boiling past the temperature shut-off.) This wasn’t a fatal problem because it was easy to take a small screwdriver and wiggle the switch inside the base. The kettle finally broke fully on 19 January 2014, having given me ~2203 days of loyal service at 2¢ a day (ignoring the electricity consumption). I would have bought it again except Upton’s no longer sold it or a replacement electric tea kettle; their website noes “New kettle sources are being evaluated.” I made do with a stove-top kettle laying around, but eventually the hassle of waiting twice or thrice as long, occasionally burning a green/oolong, and the upcoming hot summer spurred me to buy another. I had an unused Target gift card, so on 15 April 2014, I spent$36.04 to buy an “Oster Digital Electric Tea Kettle model BVST-EK5967” from Target; it was the only electric tea kettle they had in stock with temperature control. I liked the digital temperature control (the Upton’s was an analogue knob with tea ranges), and it worked well. My main complaint was that the digital control would forget the previous temperature setting after use, and would reset to 212° so one had to set the temperature every use. By 20 May 2014, after 35 days, it had broken: it would turn on, but the water would never get hot. I thought perhaps it was a loose connection but a great deal of wiggling & experimenting failed to help matters, and I noticed the inside of the base seemed partially melted - so perhaps it couldn’t withstand its own heat? Target’s return policy didn’t seem to allow a return, so I had to give up. Much too late, I checked the Amazon page for the Oster BVST-EK5967 and saw that I was far from alone in having a bad experience with BVST-EK5967s dying unreasonably early. Oh well!

Having learned my lessons about ignoring user reviews, this third time I’m going with one of the top-reviewed electric tea kettles with temperature control on Amazon: the “T-fal BF6138US Balanced Living 1-Liter 1750-Watt Electric Mini Kettle” ($23.62). Unfortunately for me, my first order arrived broken. Reasoning that since it’s one of the top-reviewed models, it’s more likely that I got a bad item than it’s a rubbish model like the Oster, I decided to return it for a replacement (which Amazon makes reasonably easy: you print out an address and a bar code, slap it on the shipping box, and mail it at your local post office). The second order arrived working, and aside from the garish green-black coloring, seems to do its job well (although I miss the built-in thermometer of the Oster, which made it easier to find optimal temperatures for particular teas). # TODO # Appendix ## Electric vs stove kettle: fight! Electric kettles are faster, but I was curious how much faster my electric kettle heated water to high or boiling temperatures than does my stove-top kettle. So I collected some data and compared them directly, trying out a number of statistical methods (principally: nonparametric & parametric tests of difference, linear & beta regression models, and a Bayesian measurement error model). My electric kettle is faster than the stove-top kettle (the difference is both statistically-significant p≪0.01 & the posterior probability of difference is P≈1), and the modeling suggests time to boil is largely predictable from a combination of volume, end-temperature, and kettle type. ### Experiment My electric kettle is a “T-fal BF6138US Balanced Living 1-Liter 1750-Watt Electric Mini Kettle”, plugged into a normal electrical socket. The stove-top is a generic old metal kettle with a copper-clad bottom (it may have been intended to be a coffee percolator, given the shape, but it works well as a kettle) on a small resistance-heating coil stove burner (why not one of the 2 large coils? because the kettle bottom doesn’t cover the full surface area of the large burners); the stove is some very old small Gaffers-Sattler 4-burner stove/oven (no model name or number I could find in an accessible spot, but I’d guess it’s >30 years old). I began comparing them on the afternoon of 16 February 2015; the sea-level kitchen was at a warm 77.1° Fahrenheit & 49% relative humidity (as measured by my Kongin temperature/humidity datalogger). For measuring water volume, I used an ordinary 1-cup kitchen measuring cup (~235ml). And for measuring water temperature, I used a Taylor 9847N Antimicrobial Instant Read Digital Thermometer (Amazon), which claims to measure in units of .1°F up to 450° and so can handle boiling water; I can’t seem to find accuracy numbers for this particular model, but I did find a listing saying that a similarly-priced model (the “Taylor 9877FDA Waterproof Pocket Digital Thermometer”) is accurate ±2°, which should be enough. The relevant quantity of water for me is at least one of my fox tea mugs, which turns out to be almost exactly 2 cups of water ( or ~0.5l marking on electric kettle). My testing procedure was as follows: 1. rinse out each kettle with fresh cold water from the tap (43°), fill with some, let sit for a few minutes 2. dump out all water from kettles 3. pour in with measuring cup 2-4 cups of cold water, put onto respective spots 4. adjust temperature setting on electric kettle if necessary I divide the T-Fal temperature control into min/medium-low/medium/max. 5. start timer software, then turn on kettles as quickly as possible (I’d guess this was a delay of ~3s; 3s has been subtracted from the times, but there’s still imprecision or measurement error in how fast I looked at the stopwatch or how long it took me to react or whether I jumped the gun.) 6. wait until electric kettle ‘clicks’, record time in seconds; turn electric kettle off, insert thermometer, and read final temperature of electrical kettle; then insert thermometer into stove-top kettle to measure stove-top kettle’s intermediate temperature 7. record time and 2 temperatures 8. place thermometer back into stove-top kettle, and watch the temperature reading until the stove-top’s temperature has reached the electric kettle’s final temperature; record the time 9. turn off stove heat, dump out hot water, return to step #1 This ensures that both kettles start equal, and the stove-top kettle is run only as long as it takes to reach the same temperature that the electric kettle reached; the intermediate temperature could also be useful for estimating temperature vs time curves. I ran 12 tests at various combinations of water-volume and temperature setting. I wound up not testing temperature settings thoroughly because once I began measuring final temperatures, I was dismayed to see that the T-fal temperature control was almost non-existent: 3/4s of the dial equated essentially to ‘boil’, and even the minimum heat setting still resulted in temperatures as high as 180°! - which makes the temperature control almost useless, since I think one needs colder water than that to prepare white teas and the more delicate greens… I am not happy with T-fal, but at least now I know what temperatures the dial settings correspond to. ### Data The data from each kettle (time in seconds, temperatures in Fahrenheit): boiling <- read.csv(stdin(),header=TRUE) Test,Setting,Type,Volume.cups,Time,Temp.final,Temp.intermediate.stove 1,max,electric,2,144,210,120 1,max,stove,2,344,210,120 2,max,electric,3,199,211,108 2,max,stove,3,665,211,108 3,max,electric,3,210,211,120 3,max,stove,3,701,211,120 4,max,electric,2,141,211,107 4,max,stove,2,524,211,107 5,medium,electric,2,142,209,130 5,medium,stove,2,399,209,130 6,medium-low,electric,2,145,207,131 6,medium-low,stove,2,408,207,131 7,min,electric,2,110,190,101 7,min,stove,2,423,190,101 8,min,electric,3,146,180,108 8,min,stove,3,435,180,108 9,min,electric,4,178,172,99 9,min,stove,4,567,172,99 10,min,electric,2,105,186,106 10,min,stove,2,362,186,106 11,min,electric,2,109,187,108 11,min,stove,2,331,187,108 12,min,electric,2,113,187,114 12,min,stove,2,341,187,114 ### Analysis There many ways to analyze this data: are we interested in the mean difference in seconds over all combinations of volume/final-temperature, as a two-sample or paired-sample? In modeling the time it takes? In the ratio or relative speed of electric and stove-top? In correcting for the measurement error (±2° for each temperature measurement, and perhaps also how much water was in each)? We could look at all of them. #### Hypothesis testing Means, ratios, and tests of difference: abs(mean(boiling[boiling$Type=="electric",]$Time) - mean(boiling[boiling$Type=="stove",]$Time)) # [1] 313.1666667 boiling[boiling$Type=="electric",]$Time / boiling[boiling$Type=="stove",]$Time # [1] 0.4186046512 0.2992481203 0.2995720399 0.2690839695 0.3558897243 0.3553921569 0.2600472813 # [8] 0.3356321839 0.3139329806 0.2900552486 0.3293051360 0.3313782991 summary(boiling[boiling$Type=="electric",]$Time / boiling[boiling$Type=="stove",]$Time) # Min. 1st Qu. Median Mean 3rd Qu. Max. # 0.2600473 0.2969499 0.3216191 0.3215118 0.3405722 0.4186047 wilcox.test(Time ~ Type, paired=TRUE, data=boiling) # # Wilcoxon signed rank test with continuity correction # # data: Time by Type # V = 0, p-value = 0.002516 # alternative hypothesis: true location shift is not equal to 0 wilcox.test(Time ~ Type, paired=FALSE, data=boiling) # # Wilcoxon rank sum test # # data: Time by Type # W = 0, p-value = 7.396e-07 # alternative hypothesis: true location shift is not equal to 0 t.test(Time ~ Type, data=boiling) # # Welch Two Sample t-test # # data: Time by Type # t = -8.2263, df = 12.648, p-value = 1.983e-06 # alternative hypothesis: true difference in means is not equal to 0 # 95% confidence interval: # -395.6429254 -230.6904079 # sample estimates: # mean in group electric mean in group stove # 145.1666667 458.3333333 t.test(Time ~ Type, paired=TRUE, data=boiling) # # Paired t-test # # data: Time by Type # t = -11.1897, df = 11, p-value = 2.378e-07 # alternative hypothesis: true difference in means is not equal to 0 # 95% confidence interval: # -374.7655610 -251.5677723 # sample estimates: # mean of the differences # -313.1666667 So the electric kettle is, as expected, faster - by 5 minutes on average, ranging from 4x faster to 2x faster, and the advantage is statistically-significant. (Nothing surprising so far.) #### Linear regression How much variance do the listed variables capture? summary(lm(Time ~ Test + Temp.final + as.ordered(Setting) + Type + Volume.cups, data=boiling)) # ... # Residuals: # Min 1Q Median 3Q Max # -89.37786 -28.86586 12.18942 29.12054 93.64656 # # Coefficients: # Estimate Std. Error t value Pr(>|t|) # (Intercept) -2619.607015 1179.160067 -2.22159 0.04108708 # Test 5.808909 9.295290 0.62493 0.54082745 # Temp.final 11.696298 5.422822 2.15687 0.04657229 # as.ordered(Setting).L 124.978494 109.450857 1.14187 0.27031014 # as.ordered(Setting).Q 88.043187 54.791923 1.60686 0.12763657 # as.ordered(Setting).C 24.081255 48.488960 0.49663 0.62620135 # Typestove 313.166667 24.560050 12.75106 8.4966e-10 # Volume.cups 157.883148 38.444409 4.10679 0.00082473 # # Residual standard error: 60.15959 on 16 degrees of freedom # Multiple R-squared: 0.9257358, Adjusted R-squared: 0.8932452 # F-statistic: 28.49242 on 7 and 16 DF, p-value: 6.927389e-08 summary(step(lm(Time ~ Test + Temp.final + as.ordered(Setting) + Type + Volume.cups, data=boiling))) # ...Residuals: # Min 1Q Median 3Q Max # -115.480920 -41.874831 -3.183459 38.182981 125.963323 # # Coefficients: # Estimate Std. Error t value Pr(>|t|) # (Intercept) -835.055578 206.880137 -4.03642 0.00064609 # Temp.final 3.607011 0.934039 3.86174 0.00097187 # Typestove 313.166667 24.083037 13.00362 3.247e-11 # Volume.cups 111.948746 20.132673 5.56055 1.922e-05 # # Residual standard error: 58.99115 on 20 degrees of freedom # Multiple R-squared: 0.9107407, Adjusted R-squared: 0.8973518 # F-statistic: 68.02206 on 3 and 20 DF, p-value: 1.138609e-10 Because I controlled water volume and volume and final-temperature, the mean difference should be identical, and it is, 313s. The signs are also appropriate and coefficients sensible: each additional degree is +3.6s, a cup is +111s, and the setting variable drops out as useless (as it should since it should be redundant with the final-temperature measurement) as does the test number (suggesting no major change over time as a result of testing). We can plot the electric and stove-top data separately as 3D plots with residuals to see if any big issues jump out: library(scatterplot3d) plot3D <- function(k) { with(boiling[boiling$Type==k,], {
b3d <- scatterplot3d(x=Temp.final, y=Volume.cups, Time, main=k);
b3d$plane3d(my.lm <- lm(Time ~ Temp.final + Volume.cups), lty = "dotted"); orig <- b3d$xyz.convert(Temp.final, Volume.cups, Time);
plane <- b3d$xyz.convert(Temp.final, Volume.cups, fitted(my.lm)); i.negpos <- 1 + (resid(my.lm) > 0); segments(orig$x, orig$y, plane$x, plane$y, col = c("blue", "red")[i.negpos], lty = (2:1)[i.negpos]); }) } png(file="~/wiki/images/tea-kettle-electricvstove.png", width = 680, height = 800) par(mfrow = c(2, 1)) plot3D("electric") plot3D("stove") invisible(dev.off()) It looks pretty good. But in general towards the edges the points seem systematically high or low, suggesting there might be a bit of nonlinearity, and the fit seems to be worse for the stove-top results, suggesting that’s noisier than electric (this could be due either to slight differences in setting the analogue temperature dial on the stove or perhaps differences in positioning on the burner coil). #### Beta regression Regressing on the relative times / ratios, using the unusual beta regression, might be interesting; if electric was always 1:3, say, then one would expect the ratio to be constant and independent of the covariates, whereas if the ratio increases or decreases based on the covariates then that suggests some bending or flexing of the plane: boilingW <- read.csv(stdin(),header=TRUE) Test,Setting,Volume.cups,Time.electric,Time.stove,Time.ratio,Temp.final,Temp.intermediate.stove 1,max,2,144,344,0.4186046512,210,120 2,max,3,199,665,0.2992481203,211,108 3,max,3,210,701,0.2995720399,211,120 4,max,2,141,524,0.2690839695,211,107 5,medium,2,142,399,0.3558897243,209,130 6,medium-low,2,145,408,0.3553921569,207,131 7,min,2,110,423,0.2600472813,190,101 8,min,3,146,435,0.3356321839,180,108 9,min,4,178,567,0.3139329806,172,99 10,min,2,105,362,0.2900552486,186,106 11,min,2,109,331,0.329305136,187,108 12,min,2,113,341,0.3313782991,187,114 library(betareg) summary(betareg(Time.ratio ~ Temp.final + as.ordered(Setting) + Volume.cups, data=boilingW)) # Standardized weighted residuals 2: # Min 1Q Median 3Q Max # -3.0750244 -0.9096389 0.1394863 0.7292433 2.8146091 # # Coefficients (mean model with logit link): # Estimate Std. Error z value Pr(>|z|) # (Intercept) 7.49624231 4.15031174 1.80619 0.070889 # Temp.final -0.03782627 0.01921650 -1.96843 0.049019 # as.ordered(Setting).L -0.73487186 0.36540077 -2.01114 0.044311 # as.ordered(Setting).Q -0.47817927 0.19405990 -2.46408 0.013737 # as.ordered(Setting).C -0.18696030 0.16717555 -1.11835 0.263419 # Volume.cups -0.22934320 0.13345514 -1.71850 0.085705 # # Phi coefficients (precision model with identity link): # Estimate Std. Error z value Pr(>|z|) # (phi) 201.71768 82.16848 2.45493 0.014091 # # Type of estimator: ML (maximum likelihood) # Log-likelihood: 24.01264 on 7 Df # Pseudo R-squared: 0.3653261 # Number of iterations: 751 (BFGS) + 3 (Fisher scoring) Excluding the Setting variable, it looks like the temperature and volume may affect the timing, but not much. #### SEM Moving on to measurement error, one favored way of handling measurement error is through latent variables and a structural equation model, which in this case we might model in lavaan this way: library(lavaan) Kettle.model <- ' Temp.final.true =~ Temp.final Time.true =~ Time Volume.cups.true =~ Volume.cups Time.true ~ Test + Temp.final.true + as.ordered(Setting) + Type + Volume.cups.true ' Kettle.fit <- sem(model = Kettle.model, data = boiling) summary(Kettle.fit) # lavaan (0.5-16) converged normally after 120 iterations # # Number of observations 24 # # Estimator ML # Minimum Function Test Statistic 65.575 # Degrees of freedom 6 # P-value (Chi-square) 0.000 # # Parameter estimates: # # Information Expected # Standard Errors Standard # # Estimate Std.err Z-value P(>|z|) # Latent variables: # Temp.final.true =~ # Temp.final 1.000 # Time.true =~ # Time 1.000 # Volume.cups.true =~ # Volume.cups 1.000 # # Regressions: # Time.true ~ # Test 6.572 6.394 1.028 0.304 # Temp.final.tr 5.237 0.547 9.568 0.000 # Setting 0.385 16.210 0.024 0.981 # Type 313.163 18.009 17.390 0.000 # Volume.cps.tr 126.450 15.055 8.399 0.000 But the latent variable step turns out to be a waste of time (eg Temp.final.true =~ Temp.final 1.000), presumably because I don’t have multiple measurements of the same data which might allow an estimate of an underlying factor/latent variable, and so it’s the same as the linear model, more or less. #### Bayesian models What I need is some way of expressing my prior information, like my guess that the temperature numbers are ±2° or the times ±3s… in a Bayesian measurement error model. JAGS comes to mind. (Stan is currently too new and hard to install.) library(rjags) model1<-" model { for (i in 1:n) { Time[i] ~ dnorm(Time.hat[i], tau) Time.hat[i] <- a + b1*Test[i] + b2*Temp.final[i] + b3*Setting[i] + b4*Type[i] + b5*Volume.cups[i] } # intercept a ~ dnorm(0, .00001) # coefficients b1 ~ dnorm(0, .00001) b2 ~ dnorm(0, .00001) b3 ~ dnorm(0, .00001) b4 ~ dnorm(0, .00001) b5 ~ dnorm(0, .00001) # convert SD to 'precision' unit that JAGS's distributions use instead sigma ~ dunif(0, 100) tau <- pow(sigma, -2) } " j1 <- with(boiling, jags(data=list(n=nrow(boiling), Time=Time, Temp.final=Temp.final, Volume.cups=Volume.cups, Type=Type, Setting=Setting, Test=Test), parameters.to.save=c("b1", "b2", "b3", "b4", "b5"), model.file=textConnection(model1), n.chains=4, n.iter=100000)) j1 # Inference for Bugs model at "5", fit using jags, # 4 chains, each with 1e+05 iterations (first 50000 discarded), n.thin = 50 # n.sims = 4000 iterations saved # mu.vect sd.vect 2.5% 25% 50% 75% 97.5% Rhat n.eff # b1 2.156 10.191 -18.143 -4.569 2.085 9.022 22.003 1.001 4000 # b2 -0.406 1.266 -2.906 -1.265 -0.373 0.419 2.061 1.001 4000 # b3 -40.428 26.908 -96.024 -58.060 -40.351 -22.395 11.220 1.001 2700 # b4 308.501 28.348 253.075 289.747 308.563 327.221 363.598 1.001 4000 # b5 80.985 23.082 33.622 66.062 81.784 96.441 125.030 1.001 4000 # deviance 269.384 4.058 263.056 266.473 268.887 271.673 279.300 1.001 4000 # # For each parameter, n.eff is a crude measure of effective sample size, # and Rhat is the potential scale reduction factor (at convergence, Rhat=1). # # DIC info (using the rule, pD = var(deviance)/2) # pD = 8.2 and DIC = 277.6 # DIC is an estimate of expected predictive error (lower deviance is better). ## Stepwise-reduced variables: model2<-" model { for (i in 1:n) { Time[i] ~ dnorm(Time.hat[i], tau) Time.hat[i] <- a + b2 * Temp.final[i] + b4 * Type[i] + b5 * Volume.cups[i] } a ~ dnorm(0, .00001) b2 ~ dnorm(0, .00001) b4 ~ dnorm(0, .00001) b5 ~ dnorm(0, .00001) tau <- pow(sigma, -2) sigma ~ dunif(0, 100) } " j2 <- with(boiling, jags(data=list(n=nrow(boiling),Time=Time, Temp.final=Temp.final, Type=Type, Volume.cups=Volume.cups), parameters.to.save=c("b2", "b4", "b5"), model.file=textConnection(model2), n.chains=4, n.iter=100000)) j2 # mu.vect sd.vect 2.5% 25% 50% 75% 97.5% Rhat n.eff # b2 1.830 0.941 -0.140 1.235 1.875 2.474 3.594 1.001 4000 # b4 302.778 27.696 246.532 285.082 303.193 321.338 355.959 1.001 4000 # b5 90.526 22.306 46.052 75.869 90.848 105.883 133.368 1.001 4000 # deviance 268.859 4.767 261.564 265.238 268.276 271.854 279.749 1.001 4000 # ... # DIC info (using the rule, pD = var(deviance)/2) # pD = 11.4 and DIC = 280.2 # DIC is an estimate of expected predictive error (lower deviance is better). The point-estimates are similar but pulled towards zero, as expected of noninformative priors. With a Bayesian analysis, we can ask directly, “what is the probability that the difference stove-top vs electric (b4) is >0?” A plot of the posterior samples shows that no sample is ≤0, so the probability that electric and stove-top differs is ~100%, which is comforting to know. Measurement-error for Temp.final; we need to define a latent variable (true.Temp.final) which has our usual noninformative prior, but then we define how precise our measurement is (tau.Temp.final) by taking our two-degree estimate, converting it into units of standard deviations of the Temp.final data (2/14.093631), and then converting to the ‘precision’ unit (exponentiation followed by division): model3<-" model { for (i in 1:n) { true.Temp.final[i] ~ dnorm(0, .00001) Temp.final[i] ~ dnorm(true.Temp.final[i], tau.Temp.final) Time[i] ~ dnorm(Time.hat[i], tau) Time.hat[i] <- a + b2 * Temp.final[i] + b4 * Type[i] + b5 * Volume.cups[i] } a ~ dnorm(0, .00001) b2 ~ dnorm(0, .00001) b4 ~ dnorm(0, .00001) b5 ~ dnorm(0, .00001) sigma ~ dunif(0, 100) tau <- pow(sigma, -2) tau.Temp.final <- 1 / pow((2/14.093631), 2) } " j3 <- with(boiling, jags(data=list(n=nrow(boiling), Time=Time, Temp.final=Temp.final, Type=Type, Volume.cups=Volume.cups), parameters.to.save=c("b2", "b4", "b5"), model.file=textConnection(model3), n.chains=4, n.iter=100000)) j3 # mu.vect sd.vect 2.5% 25% 50% 75% 97.5% Rhat n.eff # b2 1.843 0.936 -0.106 1.238 1.889 2.497 3.570 1.001 4000 # b4 303.132 27.966 248.699 285.056 302.651 321.256 359.027 1.001 2900 # b5 89.503 21.985 43.631 75.713 90.076 104.306 130.206 1.001 4000 # deviance 242.944 8.204 228.833 237.013 242.222 248.095 260.670 1.001 2500 # ... # DIC info (using the rule, pD = var(deviance)/2) # pD = 33.6 and DIC = 276.6 # DIC is an estimate of expected predictive error (lower deviance is better). In this case, ±2° degrees is precise enough, and the Temp.final variable just one of 3 variables used, that it seems to not make a big difference. Another variable is how much water was in kettle. While I tried to measure cups as evenly as possible and shake out each kettle after rinsing, I couldn’t say it was hugely exact. There could easily have been a 5% difference between the kettles (and the standard deviation of the cups is not that small, it’s 0.653). So we’ll add that as a measurement error too: model4<-" model { for (i in 1:n) { true.Temp.final[i] ~ dnorm(0, .00001) Temp.final[i] ~ dnorm(true.Temp.final[i], tau.Temp.final) true.Volume.cups[i] ~ dnorm(0, .00001) Volume.cups[i] ~ dnorm(true.Volume.cups[i], tau.Volume.cups) Time[i] ~ dnorm(Time.hat[i], tau) Time.hat[i] <- a + b2 * Temp.final[i] + b4 * Type[i] + b5 * Volume.cups[i] } a ~ dnorm(0, .00001) b2 ~ dnorm(0, .00001) b4 ~ dnorm(0, .00001) b5 ~ dnorm(0, .00001) sigma ~ dunif(0, 100) tau <- pow(sigma, -2) tau.Temp.final <- 1 / pow((2/14.093631), 2) tau.Volume.cups <- 1 / pow((0.05/0.6538625482), 2) } " j4 <- with(boiling, jags(data=list(n=nrow(boiling), Time=Time, Temp.final=Temp.final, Type=Type, Volume.cups=Volume.cups), parameters.to.save=c("b2", "b4", "b5"), model.file=textConnection(model4), n.chains=4, n.iter=600000)) j4 # mu.vect sd.vect 2.5% 25% 50% 75% 97.5% Rhat n.eff # b2 1.832 0.962 -0.213 1.210 1.885 2.488 3.603 1.001 4000 # b4 302.310 27.773 245.668 284.605 302.509 320.646 355.748 1.001 4000 # b5 89.655 21.768 44.154 75.561 90.428 104.743 129.892 1.002 2100 # deviance 188.133 10.943 169.013 180.519 187.413 195.102 211.908 1.001 4000 # ... # DIC info (using the rule, pD = var(deviance)/2) # pD = 59.9 and DIC = 248.0 While the DIC seems to have improved, the estimates look mostly the same. In this case, it seems that the variables are precise enough (measurement-errors small enough) that adjusting for them doesn’t change the results too much 1. Looking through my history 2006-2012, I order tea on a roughly annual or semi-annual basis: 1. 10/16/2006 ($19.30)
2. 12/17/2007 ($19.70) 3. 1/8/2008 ($43.80)
4. 2/15/2010 ($34.92) Thinking back, that 2 year gap between orders #3 and #4 was probably due to a Christmas where I received more than 2 pounds of tea, which took me a very long time to drink. 5. 7/5/2010 ($32.30)
6. 5/14/2011 ($51.20) 7. 12/4/2011 ($39.20)
8. 7/15/2012 ($75.10) 9. 2013, overall ($87.37)

I tried broadening my horizons and ordered 9 teas from a number of retailers through Amazon.com (principally Tao of Tea, Pure Herbal, & Summit Tea), and while some of Tao of Tea was good, overall I was not impressed.

2. Which is pretty unusual for me. On the other hand, in ages past, back when I was on the rec.food.drink.tea Usenet group, a fair number of other people also ordered from Upton.

3. How does an electric tea kettle differ from ordinary electric kettles? Principally they have temperature settings - a little knob to choose between temperatures for black, oolong, green, and white tea. The less oxidized the tea, the cooler the water should be - white tea water should be dozens of degrees cooler than black tea water.

4. Much of the research is of poor quality and from East Asia & China in particular, which is always a red flag for anything to do with traditional Asian treatments; reviews/meta-analyses, like the Cochrane reviews on Shengmai (a traditional Chinese herbal medicine) for heart failure” & “Ginseng for cognition” typically find few high-quality studies & small inconsistent benefits.


text:
III. Form

# Expansion and Contraction at the Phrase Level

John Peterson

Key Takeaways

• make a phrase last longer than expected. They can be internal (between the beginning and ending of the phrase) or external (before the beginning or after the end).
• Internal expansion techniques include , , , and .
• External expansions fall into two categories:
• occur before the beginning, such as an introduction.
• occur after the cadence, such as , , and .
• make a phrase shorter than expected.

The terms and refer to ways composers play with the expected length of a phrase.

What does “expected length” mean?

• When a  invokes one of the  without following it exactly, we can often identify how long a closer representation of that archetype would have been.
• Sometimes the cadential motion of the phrase allows us to anticipate where a cadence might occur, but the phrase the expected cadence.
• Sometimes a piece states two versions of a phrase—one unexpanded and the other expanded—giving us a model to which we can compare the expanded version.

Expansion refers to the process of making a phrase longer than we expect. This lengthening might occur within the phrase (““) or outside of the phrase (““). Contraction refers to the process of making a phrase shorter than we expect, and it always occurs within a phrase.

In this chapter, we offer an overview of several techniques for phrase expansion and contraction. This isn’t an exhaustive list, but it covers several of the more common techniques. The terminology concerning expansion and contraction techniques can quickly become overwhelming. What’s most important is to be able to recognize when a phrase is longer or shorter than expected and to be able to describe what’s creating the difference in length.

# Internal Expansions

The four techniques we discuss below—, , , and —all occur within a phrase: after the phrase’s beginning, but before its cadence. Often, composers use these techniques in combination; in fact, it’s relatively rare to find a phrase that’s expanded using only one technique.

## Repetition

Sometimes when a composer repeats material, the  creates extra length.

Example 1 shows an exact repetition of a motive within a unit that creates extra length: a four-measure is followed by an expanded five-measure . The extra length results from a repeated within a unit.

Example 2 shows a varied repetition in which a whole unit is repeated to add extra length: a four-measure is followed by a five-measure . The continuation begins with a that expands it from the expected four measures to five.

Not all repetitions create expansion! Be careful to differentiate expansion-creating repetitions, which are unexpected, from more predictable repetitions, such as when the basic idea is repeated in a presentation.

## Stretching

Sometimes composers will lengthen a harmony or melody by increasing its duration so that it lasts longer than expected. When that happens, we say that the unit that contains the harmony or melody has been . In Example 3, a four-measure is followed by a five-measure . The continuation’s is stretched when a $\mathrm{I}^6$ chord and the cadential dominant (embellished by a $\mathrm{Ger}^6$ and a cadential $^6_4$) each last for a full measure as opposed to both occurring within a single measure.

## One-More-Time Technique (o.m.t.)

Coined by Janet Schmalfeldt (1989), the one-more-time technique involves three steps: 1) the music tries to cadence, 2) the attempted cadence is evaded, and 3) the music retries the cadence. The re-tried cadence often uses the same material, such that it feels like the music is “backing up,” but it may also retry the cadence with different cadential material.

In Example 4, a cadence is proposed in m. 10, but it’s evaded ($\mathrm{cad^6_4 – V^4_2 – I^6}$). A one-more-time repetition of the ensues. The one-more-time unit is : notice that it takes two measures (compared to one originally) for the melody to descend C–B♭–A–G, and it takes a full measure (compared to a half measure originally) for the cadential $\mathrm{^6_4}$ to resolve to $\mathrm{V}^7$.

## Alternative Paths

An occurs when unexpected new material either temporarily or permanently causes a phrase to deviate from its expected trajectory toward a cadence. A temporary deviation is called a . Detours return to previous material from within the phrase before the phrase achieves a cadence. A permanent deviation is called a . Reroutes achieve cadences without returning to previous material from within the phrase.

Example 5 shows a detour: the sentence’s continuation is repeated. We realize the repetition is getting “off track” when the motive in the cadential idea (m. 19) is repeated (m. 20), which did not happen in the analogous place before (m. 15). A highly contrasting two-measure passage emerges (mm. 21–22) that leads to a return of material (mm. 23–26) similar to the cadential idea in mm. 19–20, now stretched.

Example 6 shows a reroute: a four-measure is followed by a six-measure expanded . The consequent begins with the same as the antecedent, but its moves in a markedly different direction, one that doesn’t lead to a cadence. A new cadential idea is needed to bring the phrase to a .

Although and alternative paths both involve cadences, they are very different techniques, as explained below:

 One-more-time technique Alternative path Passage has tried and failed to achieve a cadence Feels as though the phrase backs up to try the failed cadence again Passage has not yet tried to cadence Feels as though the phrase has gone off course

# External Expansions

When composers add length outside of a phrase, they may add measures before the beginning () or after the cadence (). In diagrams, we indicate external expansions using dashed arcs or brackets.

## The Prefix

A occurs before the beginning of a phrase, usually taking the form of an introduction. A prefix can be small, but it may also be large, such as when a composer begins a symphony with a slow introduction. Example 7 shows a small prefix. As is very common with songs, this opens with an instrumental introduction before the singer enters—that is, before the phrase beginningg. Note also that this phrase includes a variant on the typical . Instead of mi-fa-sol-do ($\hat{3}-\hat{4}-\hat{5}-\hat{1}$), Chaminade writes di-re-sol-do ($\uparrow\hat{1}-\hat{2}-\hat{5}-\hat{1}$) (mm. 8–11).

## The Suffix

A suffix occurs after a phrase has cadenced. The terms in Example 8 are flexibly used to describe different types of suffix. While Example 8 provides guidelines for their use, what one person calls a , another might choose to call a . It’s more important to recognize that a given suffix adds length outside the bounds of a phrase than to worry about which term is most appropriate.

Term Avg. Length Characteristics Typical Location Example
(1-2 mm.)
• Insubstantial: little or no melodic material
• Often repeats the chords of the cadence (e.g. V–I) or the final tonic
• Atypical to state an entire phrase
After the end of a phrase within a section Example 9
Codetta Medium
(4-8 mm.)
• Often features short motivic material that gets repeated
• May cycle through an entire cadential progression
• May or may not state an entire phrase
After the end of a section within a piece or movement Example 10
Coda Long
(8+ mm.)
• Substantial: may feature a new theme or reprise of a previous theme
• Often contains multiple phrases
After the end of a piece or movement Example 11

Example 8. Characteristics that differentiate common suffix types.

Example 9 shows the end of a lengthy . After the perfect authentic cadence that ends the , a two-measure post-cadential extension prolongs the final tonic via arpeggiation.[1]

In Example 10, a lengthy phrase ends the exposition of the piano sonata with a PAC in A♭ major at m. 41. The cadence is followed by a codetta: notice that it features a repeated two-measure unit harmonized with the cadential bass line fi-sol-do ($\uparrow\hat{4}-\hat{5}-\hat{1}$).

Example 11 features the longest kind of suffix: a coda. After the introduction returns (4:52) and then is varied (5:03), an elided PAC ends the piece proper (5:32). The coda (also at 5:32) presents an energetic celebration of the piece’s closure, featuring a fast version of a previously-heard theme with several phrases.

Timestamp Event
4:52 Introduction returns in varied form
5:03 A second variation on the introduction begins
5:32 Coda begins; its material is drawn from the second theme (from 2:00)

Example 11. External expansion via suffix () in Shostakovich, Festive Overture

# Contraction

Contractions occur less frequently than expansions. A occurs when a phrase is shorter than we might expect it to be.

In Example 12, a four-measure is followed by a three-measure continuation. Given the length of the compound basic idea, we might have expected the continuation to be four measures long to create proportional balance. As you listen, notice how the cadence feels abrupt, a feeling that usually accompanies contraction.

• Jarvis, Brian, and John Peterson. 2019. “Alternative Paths, Phrase Expansion, and the Music of Felix Mendelssohn.” Music Theory Spectrum 41, no. 2 (Fall): 187–217.
• Schmalfeldt, Janet. 1992. “Cadential Processes: The Evaded Cadence and the ‘One More Time’ Technique.” Journal of Musicological Research 12 (1–2): 1–52.
Assignments
1. Analyzing expansion techniques (.pdf, .docx). Asks students to name, segment, and label the form of excerpts and identify the location of any expansion technique(s). Optional harmonic analysis included.
2. Analyzing multiple expansion techniques (.pdf, .docx). More complicated examples than in worksheet 1. Each excerpt is significantly expanded.
3. Recomposing to remove expansions (.pdf, .docx). Asks students to recompose excerpts from worksheet 1 to remove the expanded portion of the archetypal form.